Uncertainty in BMP evaluation and optimization for watershed management

NASA Astrophysics Data System (ADS)

Chaubey, I.; Cibin, R.; Sudheer, K.; Her, Y.

2012-12-01

Use of computer simulation models have increased substantially to make watershed management decisions and to develop strategies for water quality improvements. These models are often used to evaluate potential benefits of various best management practices (BMPs) for reducing losses of pollutants from sources areas into receiving waterbodies. Similarly, use of simulation models in optimizing selection and placement of best management practices under single (maximization of crop production or minimization of pollutant transport) and multiple objective functions has increased recently. One of the limitations of the currently available assessment and optimization approaches is that the BMP strategies are considered deterministic. Uncertainties in input data (e.g. precipitation, streamflow, sediment, nutrient and pesticide losses measured, land use) and model parameters may result in considerable uncertainty in watershed response under various BMP options. We have developed and evaluated options to include uncertainty in BMP evaluation and optimization for watershed management. We have also applied these methods to evaluate uncertainty in ecosystem services from mixed land use watersheds. In this presentation, we will discuss methods to to quantify uncertainties in BMP assessment and optimization solutions due to uncertainties in model inputs and parameters. We have used a watershed model (Soil and Water Assessment Tool or SWAT) to simulate the hydrology and water quality in mixed land use watershed located in Midwest USA. The SWAT model was also used to represent various BMPs in the watershed needed to improve water quality. SWAT model parameters, land use change parameters, and climate change parameters were considered uncertain. It was observed that model parameters, land use and climate changes resulted in considerable uncertainties in BMP performance in reducing P, N, and sediment loads. In addition, climate change scenarios also affected uncertainties in SWAT simulated crop yields. Considerable uncertainties in the net cost and the water quality improvements resulted due to uncertainties in land use, climate change, and model parameter values.

Uncertainty analysis in geospatial merit matrix–based hydropower resource assessment

DOE PAGES

Pasha, M. Fayzul K.; Yeasmin, Dilruba; Saetern, Sen; ...

2016-03-30

Hydraulic head and mean annual streamflow, two main input parameters in hydropower resource assessment, are not measured at every point along the stream. Translation and interpolation are used to derive these parameters, resulting in uncertainties. This study estimates the uncertainties and their effects on model output parameters: the total potential power and the number of potential locations (stream-reach). These parameters are quantified through Monte Carlo Simulation (MCS) linking with a geospatial merit matrix based hydropower resource assessment (GMM-HRA) Model. The methodology is applied to flat, mild, and steep terrains. Results show that the uncertainty associated with the hydraulic head ismore » within 20% for mild and steep terrains, and the uncertainty associated with streamflow is around 16% for all three terrains. Output uncertainty increases as input uncertainty increases. However, output uncertainty is around 10% to 20% of the input uncertainty, demonstrating the robustness of the GMM-HRA model. Hydraulic head is more sensitive to output parameters in steep terrain than in flat and mild terrains. Furthermore, mean annual streamflow is more sensitive to output parameters in flat terrain.« less

Rational selection of experimental readout and intervention sites for reducing uncertainties in computational model predictions.

PubMed

Flassig, Robert J; Migal, Iryna; der Zalm, Esther van; Rihko-Struckmann, Liisa; Sundmacher, Kai

2015-01-16

Understanding the dynamics of biological processes can substantially be supported by computational models in the form of nonlinear ordinary differential equations (ODE). Typically, this model class contains many unknown parameters, which are estimated from inadequate and noisy data. Depending on the ODE structure, predictions based on unmeasured states and associated parameters are highly uncertain, even undetermined. For given data, profile likelihood analysis has been proven to be one of the most practically relevant approaches for analyzing the identifiability of an ODE structure, and thus model predictions. In case of highly uncertain or non-identifiable parameters, rational experimental design based on various approaches has shown to significantly reduce parameter uncertainties with minimal amount of effort. In this work we illustrate how to use profile likelihood samples for quantifying the individual contribution of parameter uncertainty to prediction uncertainty. For the uncertainty quantification we introduce the profile likelihood sensitivity (PLS) index. Additionally, for the case of several uncertain parameters, we introduce the PLS entropy to quantify individual contributions to the overall prediction uncertainty. We show how to use these two criteria as an experimental design objective for selecting new, informative readouts in combination with intervention site identification. The characteristics of the proposed multi-criterion objective are illustrated with an in silico example. We further illustrate how an existing practically non-identifiable model for the chlorophyll fluorescence induction in a photosynthetic organism, D. salina, can be rendered identifiable by additional experiments with new readouts. Having data and profile likelihood samples at hand, the here proposed uncertainty quantification based on prediction samples from the profile likelihood provides a simple way for determining individual contributions of parameter uncertainties to uncertainties in model predictions. The uncertainty quantification of specific model predictions allows identifying regions, where model predictions have to be considered with care. Such uncertain regions can be used for a rational experimental design to render initially highly uncertain model predictions into certainty. Finally, our uncertainty quantification directly accounts for parameter interdependencies and parameter sensitivities of the specific prediction.

Parameter optimization, sensitivity, and uncertainty analysis of an ecosystem model at a forest flux tower site in the United States

USGS Publications Warehouse

Wu, Yiping; Liu, Shuguang; Huang, Zhihong; Yan, Wende

2014-01-01

Ecosystem models are useful tools for understanding ecological processes and for sustainable management of resources. In biogeochemical field, numerical models have been widely used for investigating carbon dynamics under global changes from site to regional and global scales. However, it is still challenging to optimize parameters and estimate parameterization uncertainty for complex process-based models such as the Erosion Deposition Carbon Model (EDCM), a modified version of CENTURY, that consider carbon, water, and nutrient cycles of ecosystems. This study was designed to conduct the parameter identifiability, optimization, sensitivity, and uncertainty analysis of EDCM using our developed EDCM-Auto, which incorporated a comprehensive R package—Flexible Modeling Framework (FME) and the Shuffled Complex Evolution (SCE) algorithm. Using a forest flux tower site as a case study, we implemented a comprehensive modeling analysis involving nine parameters and four target variables (carbon and water fluxes) with their corresponding measurements based on the eddy covariance technique. The local sensitivity analysis shows that the plant production-related parameters (e.g., PPDF1 and PRDX) are most sensitive to the model cost function. Both SCE and FME are comparable and performed well in deriving the optimal parameter set with satisfactory simulations of target variables. Global sensitivity and uncertainty analysis indicate that the parameter uncertainty and the resulting output uncertainty can be quantified, and that the magnitude of parameter-uncertainty effects depends on variables and seasons. This study also demonstrates that using the cutting-edge R functions such as FME can be feasible and attractive for conducting comprehensive parameter analysis for ecosystem modeling.

A general model for attitude determination error analysis

NASA Technical Reports Server (NTRS)

Markley, F. Landis; Seidewitz, ED; Nicholson, Mark

1988-01-01

An overview is given of a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The models presented include both batch least-squares and sequential attitude estimation processes for both spin-stabilized and three-axis stabilized spacecraft. The discussion includes a brief description of a dynamics model of strapdown gyros, but it does not cover other sensor models. Model parameters can be chosen to be solve-for parameters, which are assumed to be estimated as part of the determination process, or consider parameters, which are assumed to have errors but not to be estimated. The only restriction on this choice is that the time evolution of the consider parameters must not depend on any of the solve-for parameters. The result of an error analysis is an indication of the contributions of the various error sources to the uncertainties in the determination of the spacecraft solve-for parameters. The model presented gives the uncertainty due to errors in the a priori estimates of the solve-for parameters, the uncertainty due to measurement noise, the uncertainty due to dynamic noise (also known as process noise or measurement noise), the uncertainty due to the consider parameters, and the overall uncertainty due to all these sources of error.

Assessing the importance of rainfall uncertainty on hydrological models with different spatial and temporal scale

NASA Astrophysics Data System (ADS)

Nossent, Jiri; Pereira, Fernando; Bauwens, Willy

2015-04-01

Precipitation is one of the key inputs for hydrological models. As long as the values of the hydrological model parameters are fixed, a variation of the rainfall input is expected to induce a change in the model output. Given the increased awareness of uncertainty on rainfall records, it becomes more important to understand the impact of this input - output dynamic. Yet, modellers often still have the intention to mimic the observed flow, whatever the deviation of the employed records from the actual rainfall might be, by recklessly adapting the model parameter values. But is it actually possible to vary the model parameter values in such a way that a certain (observed) model output can be generated based on inaccurate rainfall inputs? Thus, how important is the rainfall uncertainty for the model output with respect to the model parameter importance? To address this question, we apply the Sobol' sensitivity analysis method to assess and compare the importance of the rainfall uncertainty and the model parameters on the output of the hydrological model. In order to be able to treat the regular model parameters and input uncertainty in the same way, and to allow a comparison of their influence, a possible approach is to represent the rainfall uncertainty by a parameter. To tackle the latter issue, we apply so called rainfall multipliers on hydrological independent storm events, as a probabilistic parameter representation of the possible rainfall variation. As available rainfall records are very often point measurements at a discrete time step (hourly, daily, monthly,…), they contain uncertainty due to a latent lack of spatial and temporal variability. The influence of the latter variability can also be different for hydrological models with different spatial and temporal scale. Therefore, we perform the sensitivity analyses on a semi-distributed model (SWAT) and a lumped model (NAM). The assessment and comparison of the importance of the rainfall uncertainty and the model parameters is achieved by considering different scenarios for the included parameters and the state of the models.

Application of identified sensitive physical parameters in reducing the uncertainty of numerical simulation

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2016-04-01

An important source of uncertainty, which then causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. There are many physical parameters in numerical models in the atmospheric and oceanic sciences, and it would cost a great deal to reduce uncertainties in all physical parameters. Therefore, finding a subset of these parameters, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach. The results imply that nonlinear interactions among parameters play a key role in the uncertainty of numerical simulations in arid and semi-arid regions of China compared to those in northern, northeastern and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization

NASA Astrophysics Data System (ADS)

Christensen, H. M.; Moroz, I.; Palmer, T.

2015-12-01

It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic ensemble forecasts, and a number of different techniques have been proposed for this purpose. Stochastic convection parameterization schemes use random numbers to represent the difference between a deterministic parameterization scheme and the true atmosphere, accounting for the unresolved sub grid-scale variability associated with convective clouds. An alternative approach varies the values of poorly constrained physical parameters in the model to represent the uncertainty in these parameters. This study presents new perturbed parameter schemes for use in the European Centre for Medium Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parametrisation scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are changed between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, Stochastically Perturbed Parametrisation Tendencies (SPPT), and to a model which does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parametrisation in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skilful representations of model uncertainty due to convection parametrisation. Reference: H. M. Christensen, I. M. Moroz, and T. N. Palmer, 2015: Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization. J. Atmos. Sci., 72, 2525-2544.

Incorporating rainfall uncertainty in a SWAT model: the river Zenne basin (Belgium) case study

NASA Astrophysics Data System (ADS)

Tolessa Leta, Olkeba; Nossent, Jiri; van Griensven, Ann; Bauwens, Willy

2013-04-01

The European Union Water Framework Directive (EU-WFD) called its member countries to achieve a good ecological status for all inland and coastal water bodies by 2015. According to recent studies, the river Zenne (Belgium) is far from this objective. Therefore, an interuniversity and multidisciplinary project "Towards a Good Ecological Status in the river Zenne (GESZ)" was launched to evaluate the effects of wastewater management plans on the river. In this project, different models have been developed and integrated using the Open Modelling Interface (OpenMI). The hydrologic, semi-distributed Soil and Water Assessment Tool (SWAT) is hereby used as one of the model components in the integrated modelling chain in order to model the upland catchment processes. The assessment of the uncertainty of SWAT is an essential aspect of the decision making process, in order to design robust management strategies that take the predicted uncertainties into account. Model uncertainty stems from the uncertainties on the model parameters, the input data (e.g, rainfall), the calibration data (e.g., stream flows) and on the model structure itself. The objective of this paper is to assess the first three sources of uncertainty in a SWAT model of the river Zenne basin. For the assessment of rainfall measurement uncertainty, first, we identified independent rainfall periods, based on the daily precipitation and stream flow observations and using the Water Engineering Time Series PROcessing tool (WETSPRO). Secondly, we assigned a rainfall multiplier parameter for each of the independent rainfall periods, which serves as a multiplicative input error corruption. Finally, we treated these multipliers as latent parameters in the model optimization and uncertainty analysis (UA). For parameter uncertainty assessment, due to the high number of parameters of the SWAT model, first, we screened out its most sensitive parameters using the Latin Hypercube One-factor-At-a-Time (LH-OAT) technique. Subsequently, we only considered the most sensitive parameters for parameter optimization and UA. To explicitly account for the stream flow uncertainty, we assumed that the stream flow measurement error increases linearly with the stream flow value. To assess the uncertainty and infer posterior distributions of the parameters, we used a Markov Chain Monte Carlo (MCMC) sampler - differential evolution adaptive metropolis (DREAM) that uses sampling from an archive of past states to generate candidate points in each individual chain. It is shown that the marginal posterior distributions of the rainfall multipliers vary widely between individual events, as a consequence of rainfall measurement errors and the spatial variability of the rain. Only few of the rainfall events are well defined. The marginal posterior distributions of the SWAT model parameter values are well defined and identified by DREAM, within their prior ranges. The posterior distributions of output uncertainty parameter values also show that the stream flow data is highly uncertain. The approach of using rainfall multipliers to treat rainfall uncertainty for a complex model has an impact on the model parameter marginal posterior distributions and on the model results Corresponding author: Tel.: +32 (0)2629 3027; fax: +32(0)2629 3022. E-mail: otolessa@vub.ac.be

Quantifying the impact of the longitudinal dispersion coefficient parameter uncertainty on the physical transport processes in rivers

NASA Astrophysics Data System (ADS)

Camacho Suarez, V. V.; Shucksmith, J.; Schellart, A.

2016-12-01

Analytical and numerical models can be used to represent the advection-dispersion processes governing the transport of pollutants in rivers (Fan et al., 2015; Van Genuchten et al., 2013). Simplifications, assumptions and parameter estimations in these models result in various uncertainties within the modelling process and estimations of pollutant concentrations. In this study, we explore both: 1) the structural uncertainty due to the one dimensional simplification of the Advection Dispersion Equation (ADE) and 2) the parameter uncertainty due to the semi empirical estimation of the longitudinal dispersion coefficient. The relative significance of these uncertainties has not previously been examined. By analysing both the relative structural uncertainty of analytical solutions of the ADE, and the parameter uncertainty due to the longitudinal dispersion coefficient via a Monte Carlo analysis, an evaluation of the dominant uncertainties for a case study in the river Chillan, Chile is presented over a range of spatial scales.

Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment.

PubMed

Sweetapple, Christine; Fu, Guangtao; Butler, David

2013-09-01

This study investigates sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment, through the use of local and global sensitivity analysis tools, and contributes to an in-depth understanding of wastewater treatment modelling by revealing critical parameters and parameter interactions. One-factor-at-a-time sensitivity analysis is used to screen model parameters and identify those with significant individual effects on three performance indicators: total greenhouse gas emissions, effluent quality and operational cost. Sobol's method enables identification of parameters with significant higher order effects and of particular parameter pairs to which model outputs are sensitive. Use of a variance-based global sensitivity analysis tool to investigate parameter interactions enables identification of important parameters not revealed in one-factor-at-a-time sensitivity analysis. These interaction effects have not been considered in previous studies and thus provide a better understanding wastewater treatment plant model characterisation. It was found that uncertainty in modelled nitrous oxide emissions is the primary contributor to uncertainty in total greenhouse gas emissions, due largely to the interaction effects of three nitrogen conversion modelling parameters. The higher order effects of these parameters are also shown to be a key source of uncertainty in effluent quality. Copyright © 2013 Elsevier Ltd. All rights reserved.

Shock Layer Radiation Modeling and Uncertainty for Mars Entry

NASA Technical Reports Server (NTRS)

Johnston, Christopher O.; Brandis, Aaron M.; Sutton, Kenneth

2012-01-01

A model for simulating nonequilibrium radiation from Mars entry shock layers is presented. A new chemical kinetic rate model is developed that provides good agreement with recent EAST and X2 shock tube radiation measurements. This model includes a CO dissociation rate that is a factor of 13 larger than the rate used widely in previous models. Uncertainties in the proposed rates are assessed along with uncertainties in translational-vibrational relaxation modeling parameters. The stagnation point radiative flux uncertainty due to these flowfield modeling parameter uncertainties is computed to vary from 50 to 200% for a range of free-stream conditions, with densities ranging from 5e-5 to 5e-4 kg/m3 and velocities ranging from of 6.3 to 7.7 km/s. These conditions cover the range of anticipated peak radiative heating conditions for proposed hypersonic inflatable aerodynamic decelerators (HIADs). Modeling parameters for the radiative spectrum are compiled along with a non-Boltzmann rate model for the dominant radiating molecules, CO, CN, and C2. A method for treating non-local absorption in the non-Boltzmann model is developed, which is shown to result in up to a 50% increase in the radiative flux through absorption by the CO 4th Positive band. The sensitivity of the radiative flux to the radiation modeling parameters is presented and the uncertainty for each parameter is assessed. The stagnation point radiative flux uncertainty due to these radiation modeling parameter uncertainties is computed to vary from 18 to 167% for the considered range of free-stream conditions. The total radiative flux uncertainty is computed as the root sum square of the flowfield and radiation parametric uncertainties, which results in total uncertainties ranging from 50 to 260%. The main contributors to these significant uncertainties are the CO dissociation rate and the CO heavy-particle excitation rates. Applying the baseline flowfield and radiation models developed in this work, the radiative heating for the Mars Pathfinder probe is predicted to be nearly 20 W/cm2. In contrast to previous studies, this value is shown to be significant relative to the convective heating.

The critical role of uncertainty in projections of hydrological extremes

NASA Astrophysics Data System (ADS)

Meresa, Hadush K.; Romanowicz, Renata J.

2017-08-01

This paper aims to quantify the uncertainty in projections of future hydrological extremes in the Biala Tarnowska River at Koszyce gauging station, south Poland. The approach followed is based on several climate projections obtained from the EURO-CORDEX initiative, raw and bias-corrected realizations of catchment precipitation, and flow simulations derived using multiple hydrological model parameter sets. The projections cover the 21st century. Three sources of uncertainty are considered: one related to climate projection ensemble spread, the second related to the uncertainty in hydrological model parameters and the third related to the error in fitting theoretical distribution models to annual extreme flow series. The uncertainty of projected extreme indices related to hydrological model parameters was conditioned on flow observations from the reference period using the generalized likelihood uncertainty estimation (GLUE) approach, with separate criteria for high- and low-flow extremes. Extreme (low and high) flow quantiles were estimated using the generalized extreme value (GEV) distribution at different return periods and were based on two different lengths of the flow time series. A sensitivity analysis based on the analysis of variance (ANOVA) shows that the uncertainty introduced by the hydrological model parameters can be larger than the climate model variability and the distribution fit uncertainty for the low-flow extremes whilst for the high-flow extremes higher uncertainty is observed from climate models than from hydrological parameter and distribution fit uncertainties. This implies that ignoring one of the three uncertainty sources may cause great risk to future hydrological extreme adaptations and water resource planning and management.

DRAINMOD-GIS: a lumped parameter watershed scale drainage and water quality model

Treesearch

G.P. Fernandez; G.M. Chescheir; R.W. Skaggs; D.M. Amatya

2006-01-01

A watershed scale lumped parameter hydrology and water quality model that includes an uncertainty analysis component was developed and tested on a lower coastal plain watershed in North Carolina. Uncertainty analysis was used to determine the impacts of uncertainty in field and network parameters of the model on the predicted outflows and nitrate-nitrogen loads at the...

Parameter sensitivity analysis of a 1-D cold region lake model for land-surface schemes

NASA Astrophysics Data System (ADS)

Guerrero, José-Luis; Pernica, Patricia; Wheater, Howard; Mackay, Murray; Spence, Chris

2017-12-01

Lakes might be sentinels of climate change, but the uncertainty in their main feedback to the atmosphere - heat-exchange fluxes - is often not considered within climate models. Additionally, these fluxes are seldom measured, hindering critical evaluation of model output. Analysis of the Canadian Small Lake Model (CSLM), a one-dimensional integral lake model, was performed to assess its ability to reproduce diurnal and seasonal variations in heat fluxes and the sensitivity of simulated fluxes to changes in model parameters, i.e., turbulent transport parameters and the light extinction coefficient (Kd). A C++ open-source software package, Problem Solving environment for Uncertainty Analysis and Design Exploration (PSUADE), was used to perform sensitivity analysis (SA) and identify the parameters that dominate model behavior. The generalized likelihood uncertainty estimation (GLUE) was applied to quantify the fluxes' uncertainty, comparing daily-averaged eddy-covariance observations to the output of CSLM. Seven qualitative and two quantitative SA methods were tested, and the posterior likelihoods of the modeled parameters, obtained from the GLUE analysis, were used to determine the dominant parameters and the uncertainty in the modeled fluxes. Despite the ubiquity of the equifinality issue - different parameter-value combinations yielding equivalent results - the answer to the question was unequivocal: Kd, a measure of how much light penetrates the lake, dominates sensible and latent heat fluxes, and the uncertainty in their estimates is strongly related to the accuracy with which Kd is determined. This is important since accurate and continuous measurements of Kd could reduce modeling uncertainty.

The Effect of Nondeterministic Parameters on Shock-Associated Noise Prediction Modeling

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Khavaran, Abbas

2010-01-01

Engineering applications for aircraft noise prediction contain models for physical phenomenon that enable solutions to be computed quickly. These models contain parameters that have an uncertainty not accounted for in the solution. To include uncertainty in the solution, nondeterministic computational methods are applied. Using prediction models for supersonic jet broadband shock-associated noise, fixed model parameters are replaced by probability distributions to illustrate one of these methods. The results show the impact of using nondeterministic parameters both on estimating the model output uncertainty and on the model spectral level prediction. In addition, a global sensitivity analysis is used to determine the influence of the model parameters on the output, and to identify the parameters with the least influence on model output.

Rainfall or parameter uncertainty? The power of sensitivity analysis on grouped factors

NASA Astrophysics Data System (ADS)

Nossent, Jiri; Pereira, Fernando; Bauwens, Willy

2017-04-01

Hydrological models are typically used to study and represent (a part of) the hydrological cycle. In general, the output of these models mostly depends on their input rainfall and parameter values. Both model parameters and input precipitation however, are characterized by uncertainties and, therefore, lead to uncertainty on the model output. Sensitivity analysis (SA) allows to assess and compare the importance of the different factors for this output uncertainty. Hereto, the rainfall uncertainty can be incorporated in the SA by representing it as a probabilistic multiplier. Such multiplier can be defined for the entire time series, or several of these factors can be determined for every recorded rainfall pulse or for hydrological independent storm events. As a consequence, the number of parameters included in the SA related to the rainfall uncertainty can be (much) lower or (much) higher than the number of model parameters. Although such analyses can yield interesting results, it remains challenging to determine which type of uncertainty will affect the model output most due to the different weight both types will have within the SA. In this study, we apply the variance based Sobol' sensitivity analysis method to two different hydrological simulators (NAM and HyMod) for four diverse watersheds. Besides the different number of model parameters (NAM: 11 parameters; HyMod: 5 parameters), the setup of our sensitivity and uncertainty analysis-combination is also varied by defining a variety of scenarios including diverse numbers of rainfall multipliers. To overcome the issue of the different number of factors and, thus, the different weights of the two types of uncertainty, we build on one of the advantageous properties of the Sobol' SA, i.e. treating grouped parameters as a single parameter. The latter results in a setup with a single factor for each uncertainty type and allows for a straightforward comparison of their importance. In general, the results show a clear influence of the weights in the different SA scenarios. However, working with grouped factors resolves this issue and leads to clear importance results.

Uncertainty for calculating transport on Titan: A probabilistic description of bimolecular diffusion parameters

NASA Astrophysics Data System (ADS)

Plessis, S.; McDougall, D.; Mandt, K.; Greathouse, T.; Luspay-Kuti, A.

2015-11-01

Bimolecular diffusion coefficients are important parameters used by atmospheric models to calculate altitude profiles of minor constituents in an atmosphere. Unfortunately, laboratory measurements of these coefficients were never conducted at temperature conditions relevant to the atmosphere of Titan. Here we conduct a detailed uncertainty analysis of the bimolecular diffusion coefficient parameters as applied to Titan's upper atmosphere to provide a better understanding of the impact of uncertainty for this parameter on models. Because temperature and pressure conditions are much lower than the laboratory conditions in which bimolecular diffusion parameters were measured, we apply a Bayesian framework, a problem-agnostic framework, to determine parameter estimates and associated uncertainties. We solve the Bayesian calibration problem using the open-source QUESO library which also performs a propagation of uncertainties in the calibrated parameters to temperature and pressure conditions observed in Titan's upper atmosphere. Our results show that, after propagating uncertainty through the Massman model, the uncertainty in molecular diffusion is highly correlated to temperature and we observe no noticeable correlation with pressure. We propagate the calibrated molecular diffusion estimate and associated uncertainty to obtain an estimate with uncertainty due to bimolecular diffusion for the methane molar fraction as a function of altitude. Results show that the uncertainty in methane abundance due to molecular diffusion is in general small compared to eddy diffusion and the chemical kinetics description. However, methane abundance is most sensitive to uncertainty in molecular diffusion above 1200 km where the errors are nontrivial and could have important implications for scientific research based on diffusion models in this altitude range.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Post, Wilfred M; King, Anthony Wayne; Dragoni, Danilo

Many parameters in terrestrial biogeochemical models are inherently uncertain, leading to uncertainty in predictions of key carbon cycle variables. At observation sites, this uncertainty can be quantified by applying model-data fusion techniques to estimate model parameters using eddy covariance observations and associated biometric data sets as constraints. Uncertainty is reduced as data records become longer and different types of observations are added. We estimate parametric and associated predictive uncertainty at the Morgan Monroe State Forest in Indiana, USA. Parameters in the Local Terrestrial Ecosystem Carbon (LoTEC) are estimated using both synthetic and actual constraints. These model parameters and uncertainties aremore » then used to make predictions of carbon flux for up to 20 years. We find a strong dependence of both parametric and prediction uncertainty on the length of the data record used in the model-data fusion. In this model framework, this dependence is strongly reduced as the data record length increases beyond 5 years. If synthetic initial biomass pool constraints with realistic uncertainties are included in the model-data fusion, prediction uncertainty is reduced by more than 25% when constraining flux records are less than 3 years. If synthetic annual aboveground woody biomass increment constraints are also included, uncertainty is similarly reduced by an additional 25%. When actual observed eddy covariance data are used as constraints, there is still a strong dependence of parameter and prediction uncertainty on data record length, but the results are harder to interpret because of the inability of LoTEC to reproduce observed interannual variations and the confounding effects of model structural error.« less

Contribution of crop model structure, parameters and climate projections to uncertainty in climate change impact assessments.

PubMed

Tao, Fulu; Rötter, Reimund P; Palosuo, Taru; Gregorio Hernández Díaz-Ambrona, Carlos; Mínguez, M Inés; Semenov, Mikhail A; Kersebaum, Kurt Christian; Nendel, Claas; Specka, Xenia; Hoffmann, Holger; Ewert, Frank; Dambreville, Anaelle; Martre, Pierre; Rodríguez, Lucía; Ruiz-Ramos, Margarita; Gaiser, Thomas; Höhn, Jukka G; Salo, Tapio; Ferrise, Roberto; Bindi, Marco; Cammarano, Davide; Schulman, Alan H

2018-03-01

Climate change impact assessments are plagued with uncertainties from many sources, such as climate projections or the inadequacies in structure and parameters of the impact model. Previous studies tried to account for the uncertainty from one or two of these. Here, we developed a triple-ensemble probabilistic assessment using seven crop models, multiple sets of model parameters and eight contrasting climate projections together to comprehensively account for uncertainties from these three important sources. We demonstrated the approach in assessing climate change impact on barley growth and yield at Jokioinen, Finland in the Boreal climatic zone and Lleida, Spain in the Mediterranean climatic zone, for the 2050s. We further quantified and compared the contribution of crop model structure, crop model parameters and climate projections to the total variance of ensemble output using Analysis of Variance (ANOVA). Based on the triple-ensemble probabilistic assessment, the median of simulated yield change was -4% and +16%, and the probability of decreasing yield was 63% and 31% in the 2050s, at Jokioinen and Lleida, respectively, relative to 1981-2010. The contribution of crop model structure to the total variance of ensemble output was larger than that from downscaled climate projections and model parameters. The relative contribution of crop model parameters and downscaled climate projections to the total variance of ensemble output varied greatly among the seven crop models and between the two sites. The contribution of downscaled climate projections was on average larger than that of crop model parameters. This information on the uncertainty from different sources can be quite useful for model users to decide where to put the most effort when preparing or choosing models or parameters for impact analyses. We concluded that the triple-ensemble probabilistic approach that accounts for the uncertainties from multiple important sources provide more comprehensive information for quantifying uncertainties in climate change impact assessments as compared to the conventional approaches that are deterministic or only account for the uncertainties from one or two of the uncertainty sources. © 2017 John Wiley & Sons Ltd.

Full uncertainty quantification of N2O and NO emissions using the biogeochemical model LandscapeDNDC on site and regional scale

NASA Astrophysics Data System (ADS)

Haas, Edwin; Santabarbara, Ignacio; Kiese, Ralf; Butterbach-Bahl, Klaus

2017-04-01

Numerical simulation models are increasingly used to estimate greenhouse gas emissions at site to regional / national scale and are outlined as the most advanced methodology (Tier 3) in the framework of UNFCCC reporting. Process-based models incorporate the major processes of the carbon and nitrogen cycle of terrestrial ecosystems and are thus thought to be widely applicable at various conditions and spatial scales. Process based modelling requires high spatial resolution input data on soil properties, climate drivers and management information. The acceptance of model based inventory calculations depends on the assessment of the inventory's uncertainty (model, input data and parameter induced uncertainties). In this study we fully quantify the uncertainty in modelling soil N2O and NO emissions from arable, grassland and forest soils using the biogeochemical model LandscapeDNDC. We address model induced uncertainty (MU) by contrasting two different soil biogeochemistry modules within LandscapeDNDC. The parameter induced uncertainty (PU) was assessed by using joint parameter distributions for key parameters describing microbial C and N turnover processes as obtained by different Bayesian calibration studies for each model configuration. Input data induced uncertainty (DU) was addressed by Bayesian calibration of soil properties, climate drivers and agricultural management practices data. For the MU, DU and PU we performed several hundred simulations each to contribute to the individual uncertainty assessment. For the overall uncertainty quantification we assessed the model prediction probability, followed by sampled sets of input datasets and parameter distributions. Statistical analysis of the simulation results have been used to quantify the overall full uncertainty of the modelling approach. With this study we can contrast the variation in model results to the different sources of uncertainties for each ecosystem. Further we have been able to perform a fully uncertainty analysis for modelling N2O and NO emissions from arable, grassland and forest soils necessary for the comprehensibility of modelling results. We have applied the methodology to a regional inventory to assess the overall modelling uncertainty for a regional N2O and NO emissions inventory for the state of Saxony, Germany.

Uncertainty Quantification and Regional Sensitivity Analysis of Snow-related Parameters in the Canadian LAnd Surface Scheme (CLASS)

NASA Astrophysics Data System (ADS)

Badawy, B.; Fletcher, C. G.

2017-12-01

The parameterization of snow processes in land surface models is an important source of uncertainty in climate simulations. Quantifying the importance of snow-related parameters, and their uncertainties, may therefore lead to better understanding and quantification of uncertainty within integrated earth system models. However, quantifying the uncertainty arising from parameterized snow processes is challenging due to the high-dimensional parameter space, poor observational constraints, and parameter interaction. In this study, we investigate the sensitivity of the land simulation to uncertainty in snow microphysical parameters in the Canadian LAnd Surface Scheme (CLASS) using an uncertainty quantification (UQ) approach. A set of training cases (n=400) from CLASS is used to sample each parameter across its full range of empirical uncertainty, as determined from available observations and expert elicitation. A statistical learning model using support vector regression (SVR) is then constructed from the training data (CLASS output variables) to efficiently emulate the dynamical CLASS simulations over a much larger (n=220) set of cases. This approach is used to constrain the plausible range for each parameter using a skill score, and to identify the parameters with largest influence on the land simulation in CLASS at global and regional scales, using a random forest (RF) permutation importance algorithm. Preliminary sensitivity tests indicate that snow albedo refreshment threshold and the limiting snow depth, below which bare patches begin to appear, have the highest impact on snow output variables. The results also show a considerable reduction of the plausible ranges of the parameters values and hence reducing their uncertainty ranges, which can lead to a significant reduction of the model uncertainty. The implementation and results of this study will be presented and discussed in details.

Parameter uncertainty analysis of a biokinetic model of caesium

DOE PAGES

Li, W. B.; Klein, W.; Blanchardon, Eric; ...

2014-04-17

Parameter uncertainties for the biokinetic model of caesium (Cs) developed by Leggett et al. were inventoried and evaluated. The methods of parameter uncertainty analysis were used to assess the uncertainties of model predictions with the assumptions of model parameter uncertainties and distributions. Furthermore, the importance of individual model parameters was assessed by means of sensitivity analysis. The calculated uncertainties of model predictions were compared with human data of Cs measured in blood and in the whole body. It was found that propagating the derived uncertainties in model parameter values reproduced the range of bioassay data observed in human subjects atmore » different times after intake. The maximum ranges, expressed as uncertainty factors (UFs) (defined as a square root of ratio between 97.5th and 2.5th percentiles) of blood clearance, whole-body retention and urinary excretion of Cs predicted at earlier time after intake were, respectively: 1.5, 1.0 and 2.5 at the first day; 1.8, 1.1 and 2.4 at Day 10 and 1.8, 2.0 and 1.8 at Day 100; for the late times (1000 d) after intake, the UFs were increased to 43, 24 and 31, respectively. The model parameters of transfer rates between kidneys and blood, muscle and blood and the rate of transfer from kidneys to urinary bladder content are most influential to the blood clearance and to the whole-body retention of Cs. For the urinary excretion, the parameters of transfer rates from urinary bladder content to urine and from kidneys to urinary bladder content impact mostly. The implication and effect on the estimated equivalent and effective doses of the larger uncertainty of 43 in whole-body retention in the later time, say, after Day 500 will be explored in a successive work in the framework of EURADOS.« less

Reliability of a new biokinetic model of zirconium in internal dosimetry: part I, parameter uncertainty analysis.

PubMed

Li, Wei Bo; Greiter, Matthias; Oeh, Uwe; Hoeschen, Christoph

2011-12-01

The reliability of biokinetic models is essential in internal dose assessments and radiation risk analysis for the public, occupational workers, and patients exposed to radionuclides. In this paper, a method for assessing the reliability of biokinetic models by means of uncertainty and sensitivity analysis was developed. The paper is divided into two parts. In the first part of the study published here, the uncertainty sources of the model parameters for zirconium (Zr), developed by the International Commission on Radiological Protection (ICRP), were identified and analyzed. Furthermore, the uncertainty of the biokinetic experimental measurement performed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU) for developing a new biokinetic model of Zr was analyzed according to the Guide to the Expression of Uncertainty in Measurement, published by the International Organization for Standardization. The confidence interval and distribution of model parameters of the ICRP and HMGU Zr biokinetic models were evaluated. As a result of computer biokinetic modelings, the mean, standard uncertainty, and confidence interval of model prediction calculated based on the model parameter uncertainty were presented and compared to the plasma clearance and urinary excretion measured after intravenous administration. It was shown that for the most important compartment, the plasma, the uncertainty evaluated for the HMGU model was much smaller than that for the ICRP model; that phenomenon was observed for other organs and tissues as well. The uncertainty of the integral of the radioactivity of Zr up to 50 y calculated by the HMGU model after ingestion by adult members of the public was shown to be smaller by a factor of two than that of the ICRP model. It was also shown that the distribution type of the model parameter strongly influences the model prediction, and the correlation of the model input parameters affects the model prediction to a certain extent depending on the strength of the correlation. In the case of model prediction, the qualitative comparison of the model predictions with the measured plasma and urinary data showed the HMGU model to be more reliable than the ICRP model; quantitatively, the uncertainty model prediction by the HMGU systemic biokinetic model is smaller than that of the ICRP model. The uncertainty information on the model parameters analyzed in this study was used in the second part of the paper regarding a sensitivity analysis of the Zr biokinetic models.

Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty

NASA Astrophysics Data System (ADS)

Kuczera, George

1983-10-01

A Bayesian methodology is developed to evaluate parameter uncertainty in catchment models fitted to a hydrologic response such as runoff, the goal being to improve the chance of successful regionalization. The catchment model is posed as a nonlinear regression model with stochastic errors possibly being both autocorrelated and heteroscedastic. The end result of this methodology, which may use Box-Cox power transformations and ARMA error models, is the posterior distribution, which summarizes what is known about the catchment model parameters. This can be simplified to a multivariate normal provided a linearization in parameter space is acceptable; means of checking and improving this assumption are discussed. The posterior standard deviations give a direct measure of parameter uncertainty, and study of the posterior correlation matrix can indicate what kinds of data are required to improve the precision of poorly determined parameters. Finally, a case study involving a nine-parameter catchment model fitted to monthly runoff and soil moisture data is presented. It is shown that use of ordinary least squares when its underlying error assumptions are violated gives an erroneous description of parameter uncertainty.

Verification Techniques for Parameter Selection and Bayesian Model Calibration Presented for an HIV Model

NASA Astrophysics Data System (ADS)

Wentworth, Mami Tonoe

Uncertainty quantification plays an important role when making predictive estimates of model responses. In this context, uncertainty quantification is defined as quantifying and reducing uncertainties, and the objective is to quantify uncertainties in parameter, model and measurements, and propagate the uncertainties through the model, so that one can make a predictive estimate with quantified uncertainties. Two of the aspects of uncertainty quantification that must be performed prior to propagating uncertainties are model calibration and parameter selection. There are several efficient techniques for these processes; however, the accuracy of these methods are often not verified. This is the motivation for our work, and in this dissertation, we present and illustrate verification frameworks for model calibration and parameter selection in the context of biological and physical models. First, HIV models, developed and improved by [2, 3, 8], describe the viral infection dynamics of an HIV disease. These are also used to make predictive estimates of viral loads and T-cell counts and to construct an optimal control for drug therapy. Estimating input parameters is an essential step prior to uncertainty quantification. However, not all the parameters are identifiable, implying that they cannot be uniquely determined by the observations. These unidentifiable parameters can be partially removed by performing parameter selection, a process in which parameters that have minimal impacts on the model response are determined. We provide verification techniques for Bayesian model calibration and parameter selection for an HIV model. As an example of a physical model, we employ a heat model with experimental measurements presented in [10]. A steady-state heat model represents a prototypical behavior for heat conduction and diffusion process involved in a thermal-hydraulic model, which is a part of nuclear reactor models. We employ this simple heat model to illustrate verification techniques for model calibration. For Bayesian model calibration, we employ adaptive Metropolis algorithms to construct densities for input parameters in the heat model and the HIV model. To quantify the uncertainty in the parameters, we employ two MCMC algorithms: Delayed Rejection Adaptive Metropolis (DRAM) [33] and Differential Evolution Adaptive Metropolis (DREAM) [66, 68]. The densities obtained using these methods are compared to those obtained through the direct numerical evaluation of the Bayes' formula. We also combine uncertainties in input parameters and measurement errors to construct predictive estimates for a model response. A significant emphasis is on the development and illustration of techniques to verify the accuracy of sampling-based Metropolis algorithms. We verify the accuracy of DRAM and DREAM by comparing chains, densities and correlations obtained using DRAM, DREAM and the direct evaluation of Bayes formula. We also perform similar analysis for credible and prediction intervals for responses. Once the parameters are estimated, we employ energy statistics test [63, 64] to compare the densities obtained by different methods for the HIV model. The energy statistics are used to test the equality of distributions. We also consider parameter selection and verification techniques for models having one or more parameters that are noninfluential in the sense that they minimally impact model outputs. We illustrate these techniques for a dynamic HIV model but note that the parameter selection and verification framework is applicable to a wide range of biological and physical models. To accommodate the nonlinear input to output relations, which are typical for such models, we focus on global sensitivity analysis techniques, including those based on partial correlations, Sobol indices based on second-order model representations, and Morris indices, as well as a parameter selection technique based on standard errors. A significant objective is to provide verification strategies to assess the accuracy of those techniques, which we illustrate in the context of the HIV model. Finally, we examine active subspace methods as an alternative to parameter subset selection techniques. The objective of active subspace methods is to determine the subspace of inputs that most strongly affect the model response, and to reduce the dimension of the input space. The major difference between active subspace methods and parameter selection techniques is that parameter selection identifies influential parameters whereas subspace selection identifies a linear combination of parameters that impacts the model responses significantly. We employ active subspace methods discussed in [22] for the HIV model and present a verification that the active subspace successfully reduces the input dimensions.

Effects of temporal and spatial resolution of calibration data on integrated hydrologic water quality model identification

NASA Astrophysics Data System (ADS)

Jiang, Sanyuan; Jomaa, Seifeddine; Büttner, Olaf; Rode, Michael

2014-05-01

Hydrological water quality modeling is increasingly used for investigating runoff and nutrient transport processes as well as watershed management but it is mostly unclear how data availablity determins model identification. In this study, the HYPE (HYdrological Predictions for the Environment) model, which is a process-based, semi-distributed hydrological water quality model, was applied in two different mesoscale catchments (Selke (463 km2) and Weida (99 km2)) located in central Germany to simulate discharge and inorganic nitrogen (IN) transport. PEST and DREAM(ZS) were combined with the HYPE model to conduct parameter calibration and uncertainty analysis. Split-sample test was used for model calibration (1994-1999) and validation (1999-2004). IN concentration and daily IN load were found to be highly correlated with discharge, indicating that IN leaching is mainly controlled by runoff. Both dynamics and balances of water and IN load were well captured with NSE greater than 0.83 during validation period. Multi-objective calibration (calibrating hydrological and water quality parameters simultaneously) was found to outperform step-wise calibration in terms of model robustness. Multi-site calibration was able to improve model performance at internal sites, decrease parameter posterior uncertainty and prediction uncertainty. Nitrogen-process parameters calibrated using continuous daily averages of nitrate-N concentration observations produced better and more robust simulations of IN concentration and load, lower posterior parameter uncertainty and IN concentration prediction uncertainty compared to the calibration against uncontinuous biweekly nitrate-N concentration measurements. Both PEST and DREAM(ZS) are efficient in parameter calibration. However, DREAM(ZS) is more sound in terms of parameter identification and uncertainty analysis than PEST because of its capability to evolve parameter posterior distributions and estimate prediction uncertainty based on global search and Bayesian inference schemes.

Using Predictive Uncertainty Analysis to Assess Hydrologic Model Performance for a Watershed in Oregon

NASA Astrophysics Data System (ADS)

Brannan, K. M.; Somor, A.

2016-12-01

A variety of statistics are used to assess watershed model performance but these statistics do not directly answer the question: what is the uncertainty of my prediction. Understanding predictive uncertainty is important when using a watershed model to develop a Total Maximum Daily Load (TMDL). TMDLs are a key component of the US Clean Water Act and specify the amount of a pollutant that can enter a waterbody when the waterbody meets water quality criteria. TMDL developers use watershed models to estimate pollutant loads from nonpoint sources of pollution. We are developing a TMDL for bacteria impairments in a watershed in the Coastal Range of Oregon. We setup an HSPF model of the watershed and used the calibration software PEST to estimate HSPF hydrologic parameters and then perform predictive uncertainty analysis of stream flow. We used Monte-Carlo simulation to run the model with 1,000 different parameter sets and assess predictive uncertainty. In order to reduce the chance of specious parameter sets, we accounted for the relationships among parameter values by using mathematically-based regularization techniques and an estimate of the parameter covariance when generating random parameter sets. We used a novel approach to select flow data for predictive uncertainty analysis. We set aside flow data that occurred on days that bacteria samples were collected. We did not use these flows in the estimation of the model parameters. We calculated a percent uncertainty for each flow observation based 1,000 model runs. We also used several methods to visualize results with an emphasis on making the data accessible to both technical and general audiences. We will use the predictive uncertainty estimates in the next phase of our work, simulating bacteria fate and transport in the watershed.

Active subspace uncertainty quantification for a polydomain ferroelectric phase-field model

NASA Astrophysics Data System (ADS)

Leon, Lider S.; Smith, Ralph C.; Miles, Paul; Oates, William S.

2018-03-01

Quantum-informed ferroelectric phase field models capable of predicting material behavior, are necessary for facilitating the development and production of many adaptive structures and intelligent systems. Uncertainty is present in these models, given the quantum scale at which calculations take place. A necessary analysis is to determine how the uncertainty in the response can be attributed to the uncertainty in the model inputs or parameters. A second analysis is to identify active subspaces within the original parameter space, which quantify directions in which the model response varies most dominantly, thus reducing sampling effort and computational cost. In this investigation, we identify an active subspace for a poly-domain ferroelectric phase-field model. Using the active variables as our independent variables, we then construct a surrogate model and perform Bayesian inference. Once we quantify the uncertainties in the active variables, we obtain uncertainties for the original parameters via an inverse mapping. The analysis provides insight into how active subspace methodologies can be used to reduce computational power needed to perform Bayesian inference on model parameters informed by experimental or simulated data.

Uncertainty in a monthly water balance model using the generalized likelihood uncertainty estimation methodology

NASA Astrophysics Data System (ADS)

Rivera, Diego; Rivas, Yessica; Godoy, Alex

2015-02-01

Hydrological models are simplified representations of natural processes and subject to errors. Uncertainty bounds are a commonly used way to assess the impact of an input or model architecture uncertainty in model outputs. Different sets of parameters could have equally robust goodness-of-fit indicators, which is known as Equifinality. We assessed the outputs from a lumped conceptual hydrological model to an agricultural watershed in central Chile under strong interannual variability (coefficient of variability of 25%) by using the Equifinality concept and uncertainty bounds. The simulation period ran from January 1999 to December 2006. Equifinality and uncertainty bounds from GLUE methodology (Generalized Likelihood Uncertainty Estimation) were used to identify parameter sets as potential representations of the system. The aim of this paper is to exploit the use of uncertainty bounds to differentiate behavioural parameter sets in a simple hydrological model. Then, we analyze the presence of equifinality in order to improve the identification of relevant hydrological processes. The water balance model for Chillan River exhibits, at a first stage, equifinality. However, it was possible to narrow the range for the parameters and eventually identify a set of parameters representing the behaviour of the watershed (a behavioural model) in agreement with observational and soft data (calculation of areal precipitation over the watershed using an isohyetal map). The mean width of the uncertainty bound around the predicted runoff for the simulation period decreased from 50 to 20 m3s-1 after fixing the parameter controlling the areal precipitation over the watershed. This decrement is equivalent to decreasing the ratio between simulated and observed discharge from 5.2 to 2.5. Despite the criticisms against the GLUE methodology, such as the lack of statistical formality, it is identified as a useful tool assisting the modeller with the identification of critical parameters.

Ensemble urban flood simulation in comparison with laboratory-scale experiments: Impact of interaction models for manhole, sewer pipe, and surface flow

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Lee, Seungsoo; An, Hyunuk; Kawaike, Kenji; Nakagawa, Hajime

2016-11-01

An urban flood is an integrated phenomenon that is affected by various uncertainty sources such as input forcing, model parameters, complex geometry, and exchanges of flow among different domains in surfaces and subsurfaces. Despite considerable advances in urban flood modeling techniques, limited knowledge is currently available with regard to the impact of dynamic interaction among different flow domains on urban floods. In this paper, an ensemble method for urban flood modeling is presented to consider the parameter uncertainty of interaction models among a manhole, a sewer pipe, and surface flow. Laboratory-scale experiments on urban flood and inundation are performed under various flow conditions to investigate the parameter uncertainty of interaction models. The results show that ensemble simulation using interaction models based on weir and orifice formulas reproduces experimental data with high accuracy and detects the identifiability of model parameters. Among interaction-related parameters, the parameters of the sewer-manhole interaction show lower uncertainty than those of the sewer-surface interaction. Experimental data obtained under unsteady-state conditions are more informative than those obtained under steady-state conditions to assess the parameter uncertainty of interaction models. Although the optimal parameters vary according to the flow conditions, the difference is marginal. Simulation results also confirm the capability of the interaction models and the potential of the ensemble-based approaches to facilitate urban flood simulation.

Using statistical model to simulate the impact of climate change on maize yield with climate and crop uncertainties

NASA Astrophysics Data System (ADS)

Zhang, Yi; Zhao, Yanxia; Wang, Chunyi; Chen, Sining

2017-11-01

Assessment of the impact of climate change on crop productions with considering uncertainties is essential for properly identifying and decision-making agricultural practices that are sustainable. In this study, we employed 24 climate projections consisting of the combinations of eight GCMs and three emission scenarios representing the climate projections uncertainty, and two crop statistical models with 100 sets of parameters in each model representing parameter uncertainty within the crop models. The goal of this study was to evaluate the impact of climate change on maize ( Zea mays L.) yield at three locations (Benxi, Changling, and Hailun) across Northeast China (NEC) in periods 2010-2039 and 2040-2069, taking 1976-2005 as the baseline period. The multi-models ensembles method is an effective way to deal with the uncertainties. The results of ensemble simulations showed that maize yield reductions were less than 5 % in both future periods relative to the baseline. To further understand the contributions of individual sources of uncertainty, such as climate projections and crop model parameters, in ensemble yield simulations, variance decomposition was performed. The results indicated that the uncertainty from climate projections was much larger than that contributed by crop model parameters. Increased ensemble yield variance revealed the increasing uncertainty in the yield simulation in the future periods.

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiu; Lei, Huan; Gao, Peiyuan

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many moremore » types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.« less

Importance analysis for Hudson River PCB transport and fate model parameters using robust sensitivity studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, S.; Toll, J.; Cothern, K.

1995-12-31

The authors have performed robust sensitivity studies of the physico-chemical Hudson River PCB model PCHEPM to identify the parameters and process uncertainties contributing the most to uncertainty in predictions of water column and sediment PCB concentrations, over the time period 1977--1991 in one segment of the lower Hudson River. The term ``robust sensitivity studies`` refers to the use of several sensitivity analysis techniques to obtain a more accurate depiction of the relative importance of different sources of uncertainty. Local sensitivity analysis provided data on the sensitivity of PCB concentration estimates to small perturbations in nominal parameter values. Range sensitivity analysismore » provided information about the magnitude of prediction uncertainty associated with each input uncertainty. Rank correlation analysis indicated which parameters had the most dominant influence on model predictions. Factorial analysis identified important interactions among model parameters. Finally, term analysis looked at the aggregate influence of combinations of parameters representing physico-chemical processes. The authors scored the results of the local and range sensitivity and rank correlation analyses. The authors considered parameters that scored high on two of the three analyses to be important contributors to PCB concentration prediction uncertainty, and treated them probabilistically in simulations. They also treated probabilistically parameters identified in the factorial analysis as interacting with important parameters. The authors used the term analysis to better understand how uncertain parameters were influencing the PCB concentration predictions. The importance analysis allowed us to reduce the number of parameters to be modeled probabilistically from 16 to 5. This reduced the computational complexity of Monte Carlo simulations, and more importantly, provided a more lucid depiction of prediction uncertainty and its causes.« less

A new approach to identify the sensitivity and importance of physical parameters combination within numerical models using the Lund-Potsdam-Jena (LPJ) model as an example

NASA Astrophysics Data System (ADS)

Sun, Guodong; Mu, Mu

2017-05-01

An important source of uncertainty, which causes further uncertainty in numerical simulations, is that residing in the parameters describing physical processes in numerical models. Therefore, finding a subset among numerous physical parameters in numerical models in the atmospheric and oceanic sciences, which are relatively more sensitive and important parameters, and reducing the errors in the physical parameters in this subset would be a far more efficient way to reduce the uncertainties involved in simulations. In this context, we present a new approach based on the conditional nonlinear optimal perturbation related to parameter (CNOP-P) method. The approach provides a framework to ascertain the subset of those relatively more sensitive and important parameters among the physical parameters. The Lund-Potsdam-Jena (LPJ) dynamical global vegetation model was utilized to test the validity of the new approach in China. The results imply that nonlinear interactions among parameters play a key role in the identification of sensitive parameters in arid and semi-arid regions of China compared to those in northern, northeastern, and southern China. The uncertainties in the numerical simulations were reduced considerably by reducing the errors of the subset of relatively more sensitive and important parameters. The results demonstrate that our approach not only offers a new route to identify relatively more sensitive and important physical parameters but also that it is viable to then apply "target observations" to reduce the uncertainties in model parameters.

Probabilistic biosphere modeling for the long-term safety assessment of geological disposal facilities for radioactive waste using first- and second-order Monte Carlo simulation.

PubMed

Ciecior, Willy; Röhlig, Klaus-Jürgen; Kirchner, Gerald

2018-10-01

In the present paper, deterministic as well as first- and second-order probabilistic biosphere modeling approaches are compared. Furthermore, the sensitivity of the influence of the probability distribution function shape (empirical distribution functions and fitted lognormal probability functions) representing the aleatory uncertainty (also called variability) of a radioecological model parameter as well as the role of interacting parameters are studied. Differences in the shape of the output distributions for the biosphere dose conversion factor from first-order Monte Carlo uncertainty analysis using empirical and fitted lognormal distribution functions for input parameters suggest that a lognormal approximation is possibly not always an adequate representation of the aleatory uncertainty of a radioecological parameter. Concerning the comparison of the impact of aleatory and epistemic parameter uncertainty on the biosphere dose conversion factor, the latter here is described using uncertain moments (mean, variance) while the distribution itself represents the aleatory uncertainty of the parameter. From the results obtained, the solution space of second-order Monte Carlo simulation is much larger than that from first-order Monte Carlo simulation. Therefore, the influence of epistemic uncertainty of a radioecological parameter on the output result is much larger than that one caused by its aleatory uncertainty. Parameter interactions are only of significant influence in the upper percentiles of the distribution of results as well as only in the region of the upper percentiles of the model parameters. Copyright © 2018 Elsevier Ltd. All rights reserved.

Modeling sugar cane yield with a process-based model from site to continental scale: uncertainties arising from model structure and parameter values

NASA Astrophysics Data System (ADS)

Valade, A.; Ciais, P.; Vuichard, N.; Viovy, N.; Huth, N.; Marin, F.; Martiné, J.-F.

2014-01-01

Agro-Land Surface Models (agro-LSM) have been developed from the integration of specific crop processes into large-scale generic land surface models that allow calculating the spatial distribution and variability of energy, water and carbon fluxes within the soil-vegetation-atmosphere continuum. When developing agro-LSM models, a particular attention must be given to the effects of crop phenology and management on the turbulent fluxes exchanged with the atmosphere, and the underlying water and carbon pools. A part of the uncertainty of Agro-LSM models is related to their usually large number of parameters. In this study, we quantify the parameter-values uncertainty in the simulation of sugar cane biomass production with the agro-LSM ORCHIDEE-STICS, using a multi-regional approach with data from sites in Australia, La Réunion and Brazil. In ORCHIDEE-STICS, two models are chained: STICS, an agronomy model that calculates phenology and management, and ORCHIDEE, a land surface model that calculates biomass and other ecosystem variables forced by STICS' phenology. First, the parameters that dominate the uncertainty of simulated biomass at harvest date are determined through a screening of 67 different parameters of both STICS and ORCHIDEE on a multi-site basis. Secondly, the uncertainty of harvested biomass attributable to those most sensitive parameters is quantified and specifically attributed to either STICS (phenology, management) or to ORCHIDEE (other ecosystem variables including biomass) through distinct Monte-Carlo runs. The uncertainty on parameter values is constrained using observations by calibrating the model independently at seven sites. In a third step, a sensitivity analysis is carried out by varying the most sensitive parameters to investigate their effects at continental scale. A Monte-Carlo sampling method associated with the calculation of Partial Ranked Correlation Coefficients is used to quantify the sensitivity of harvested biomass to input parameters on a continental scale across the large regions of intensive sugar cane cultivation in Australia and Brazil. Ten parameters driving most of the uncertainty in the ORCHIDEE-STICS modeled biomass at the 7 sites are identified by the screening procedure. We found that the 10 most sensitive parameters control phenology (maximum rate of increase of LAI) and root uptake of water and nitrogen (root profile and root growth rate, nitrogen stress threshold) in STICS, and photosynthesis (optimal temperature of photosynthesis, optimal carboxylation rate), radiation interception (extinction coefficient), and transpiration and respiration (stomatal conductance, growth and maintenance respiration coefficients) in ORCHIDEE. We find that the optimal carboxylation rate and photosynthesis temperature parameters contribute most to the uncertainty in harvested biomass simulations at site scale. The spatial variation of the ranked correlation between input parameters and modeled biomass at harvest is well explained by rain and temperature drivers, suggesting climate-mediated different sensitivities of modeled sugar cane yield to the model parameters, for Australia and Brazil. This study reveals the spatial and temporal patterns of uncertainty variability for a highly parameterized agro-LSM and calls for more systematic uncertainty analyses of such models.

Modeling sugarcane yield with a process-based model from site to continental scale: uncertainties arising from model structure and parameter values

NASA Astrophysics Data System (ADS)

Valade, A.; Ciais, P.; Vuichard, N.; Viovy, N.; Caubel, A.; Huth, N.; Marin, F.; Martiné, J.-F.

2014-06-01

Agro-land surface models (agro-LSM) have been developed from the integration of specific crop processes into large-scale generic land surface models that allow calculating the spatial distribution and variability of energy, water and carbon fluxes within the soil-vegetation-atmosphere continuum. When developing agro-LSM models, particular attention must be given to the effects of crop phenology and management on the turbulent fluxes exchanged with the atmosphere, and the underlying water and carbon pools. A part of the uncertainty of agro-LSM models is related to their usually large number of parameters. In this study, we quantify the parameter-values uncertainty in the simulation of sugarcane biomass production with the agro-LSM ORCHIDEE-STICS, using a multi-regional approach with data from sites in Australia, La Réunion and Brazil. In ORCHIDEE-STICS, two models are chained: STICS, an agronomy model that calculates phenology and management, and ORCHIDEE, a land surface model that calculates biomass and other ecosystem variables forced by STICS phenology. First, the parameters that dominate the uncertainty of simulated biomass at harvest date are determined through a screening of 67 different parameters of both STICS and ORCHIDEE on a multi-site basis. Secondly, the uncertainty of harvested biomass attributable to those most sensitive parameters is quantified and specifically attributed to either STICS (phenology, management) or to ORCHIDEE (other ecosystem variables including biomass) through distinct Monte Carlo runs. The uncertainty on parameter values is constrained using observations by calibrating the model independently at seven sites. In a third step, a sensitivity analysis is carried out by varying the most sensitive parameters to investigate their effects at continental scale. A Monte Carlo sampling method associated with the calculation of partial ranked correlation coefficients is used to quantify the sensitivity of harvested biomass to input parameters on a continental scale across the large regions of intensive sugarcane cultivation in Australia and Brazil. The ten parameters driving most of the uncertainty in the ORCHIDEE-STICS modeled biomass at the 7 sites are identified by the screening procedure. We found that the 10 most sensitive parameters control phenology (maximum rate of increase of LAI) and root uptake of water and nitrogen (root profile and root growth rate, nitrogen stress threshold) in STICS, and photosynthesis (optimal temperature of photosynthesis, optimal carboxylation rate), radiation interception (extinction coefficient), and transpiration and respiration (stomatal conductance, growth and maintenance respiration coefficients) in ORCHIDEE. We find that the optimal carboxylation rate and photosynthesis temperature parameters contribute most to the uncertainty in harvested biomass simulations at site scale. The spatial variation of the ranked correlation between input parameters and modeled biomass at harvest is well explained by rain and temperature drivers, suggesting different climate-mediated sensitivities of modeled sugarcane yield to the model parameters, for Australia and Brazil. This study reveals the spatial and temporal patterns of uncertainty variability for a highly parameterized agro-LSM and calls for more systematic uncertainty analyses of such models.

Management of groundwater in-situ bioremediation system using reactive transport modelling under parametric uncertainty: field scale application

NASA Astrophysics Data System (ADS)

Verardo, E.; Atteia, O.; Rouvreau, L.

2015-12-01

In-situ bioremediation is a commonly used remediation technology to clean up the subsurface of petroleum-contaminated sites. Forecasting remedial performance (in terms of flux and mass reduction) is a challenge due to uncertainties associated with source properties and the uncertainties associated with contribution and efficiency of concentration reducing mechanisms. In this study, predictive uncertainty analysis of bio-remediation system efficiency is carried out with the null-space Monte Carlo (NSMC) method which combines the calibration solution-space parameters with the ensemble of null-space parameters, creating sets of calibration-constrained parameters for input to follow-on remedial efficiency. The first step in the NSMC methodology for uncertainty analysis is model calibration. The model calibration was conducted by matching simulated BTEX concentration to a total of 48 observations from historical data before implementation of treatment. Two different bio-remediation designs were then implemented in the calibrated model. The first consists in pumping/injection wells and the second in permeable barrier coupled with infiltration across slotted piping. The NSMC method was used to calculate 1000 calibration-constrained parameter sets for the two different models. Several variants of the method were implemented to investigate their effect on the efficiency of the NSMC method. The first variant implementation of the NSMC is based on a single calibrated model. In the second variant, models were calibrated from different initial parameter sets. NSMC calibration-constrained parameter sets were sampled from these different calibrated models. We demonstrate that in context of nonlinear model, second variant avoids to underestimate parameter uncertainty which may lead to a poor quantification of predictive uncertainty. Application of the proposed approach to manage bioremediation of groundwater in a real site shows that it is effective to provide support in management of the in-situ bioremediation systems. Moreover, this study demonstrates that the NSMC method provides a computationally efficient and practical methodology of utilizing model predictive uncertainty methods in environmental management.

A multi-model assessment of terrestrial biosphere model data needs

NASA Astrophysics Data System (ADS)

Gardella, A.; Cowdery, E.; De Kauwe, M. G.; Desai, A. R.; Duveneck, M.; Fer, I.; Fisher, R.; Knox, R. G.; Kooper, R.; LeBauer, D.; McCabe, T.; Minunno, F.; Raiho, A.; Serbin, S.; Shiklomanov, A. N.; Thomas, A.; Walker, A.; Dietze, M.

2017-12-01

Terrestrial biosphere models provide us with the means to simulate the impacts of climate change and their uncertainties. Going beyond direct observation and experimentation, models synthesize our current understanding of ecosystem processes and can give us insight on data needed to constrain model parameters. In previous work, we leveraged the Predictive Ecosystem Analyzer (PEcAn) to assess the contribution of different parameters to the uncertainty of the Ecosystem Demography model v2 (ED) model outputs across various North American biomes (Dietze et al., JGR-G, 2014). While this analysis identified key research priorities, the extent to which these priorities were model- and/or biome-specific was unclear. Furthermore, because the analysis only studied one model, we were unable to comment on the effect of variability in model structure to overall predictive uncertainty. Here, we expand this analysis to all biomes globally and a wide sample of models that vary in complexity: BioCro, CABLE, CLM, DALEC, ED2, FATES, G'DAY, JULES, LANDIS, LINKAGES, LPJ-GUESS, MAESPA, PRELES, SDGVM, SIPNET, and TEM. Prior to performing uncertainty analyses, model parameter uncertainties were assessed by assimilating all available trait data from the combination of the BETYdb and TRY trait databases, using an updated multivariate version of PEcAn's Hierarchical Bayesian meta-analysis. Next, sensitivity analyses were performed for all models across a range of sites globally to assess sensitivities for a range of different outputs (GPP, ET, SH, Ra, NPP, Rh, NEE, LAI) at multiple time scales from the sub-annual to the decadal. Finally, parameter uncertainties and model sensitivities were combined to evaluate the fractional contribution of each parameter to the predictive uncertainty for a specific variable at a specific site and timescale. Facilitated by PEcAn's automated workflows, this analysis represents the broadest assessment of the sensitivities and uncertainties in terrestrial models to date, and provides a comprehensive roadmap for constraining model uncertainties through model development and data collection.

Multi-objective calibration and uncertainty analysis of hydrologic models; A comparative study between formal and informal methods

NASA Astrophysics Data System (ADS)

Shafii, M.; Tolson, B.; Matott, L. S.

2012-04-01

Hydrologic modeling has benefited from significant developments over the past two decades. This has resulted in building of higher levels of complexity into hydrologic models, which eventually makes the model evaluation process (parameter estimation via calibration and uncertainty analysis) more challenging. In order to avoid unreasonable parameter estimates, many researchers have suggested implementation of multi-criteria calibration schemes. Furthermore, for predictive hydrologic models to be useful, proper consideration of uncertainty is essential. Consequently, recent research has emphasized comprehensive model assessment procedures in which multi-criteria parameter estimation is combined with statistically-based uncertainty analysis routines such as Bayesian inference using Markov Chain Monte Carlo (MCMC) sampling. Such a procedure relies on the use of formal likelihood functions based on statistical assumptions, and moreover, the Bayesian inference structured on MCMC samplers requires a considerably large number of simulations. Due to these issues, especially in complex non-linear hydrological models, a variety of alternative informal approaches have been proposed for uncertainty analysis in the multi-criteria context. This study aims at exploring a number of such informal uncertainty analysis techniques in multi-criteria calibration of hydrological models. The informal methods addressed in this study are (i) Pareto optimality which quantifies the parameter uncertainty using the Pareto solutions, (ii) DDS-AU which uses the weighted sum of objective functions to derive the prediction limits, and (iii) GLUE which describes the total uncertainty through identification of behavioral solutions. The main objective is to compare such methods with MCMC-based Bayesian inference with respect to factors such as computational burden, and predictive capacity, which are evaluated based on multiple comparative measures. The measures for comparison are calculated both for calibration and evaluation periods. The uncertainty analysis methodologies are applied to a simple 5-parameter rainfall-runoff model, called HYMOD.

Improving the precision of lake ecosystem metabolism estimates by identifying predictors of model uncertainty

USGS Publications Warehouse

Rose, Kevin C.; Winslow, Luke A.; Read, Jordan S.; Read, Emily K.; Solomon, Christopher T.; Adrian, Rita; Hanson, Paul C.

2014-01-01

Diel changes in dissolved oxygen are often used to estimate gross primary production (GPP) and ecosystem respiration (ER) in aquatic ecosystems. Despite the widespread use of this approach to understand ecosystem metabolism, we are only beginning to understand the degree and underlying causes of uncertainty for metabolism model parameter estimates. Here, we present a novel approach to improve the precision and accuracy of ecosystem metabolism estimates by identifying physical metrics that indicate when metabolism estimates are highly uncertain. Using datasets from seventeen instrumented GLEON (Global Lake Ecological Observatory Network) lakes, we discovered that many physical characteristics correlated with uncertainty, including PAR (photosynthetically active radiation, 400-700 nm), daily variance in Schmidt stability, and wind speed. Low PAR was a consistent predictor of high variance in GPP model parameters, but also corresponded with low ER model parameter variance. We identified a threshold (30% of clear sky PAR) below which GPP parameter variance increased rapidly and was significantly greater in nearly all lakes compared with variance on days with PAR levels above this threshold. The relationship between daily variance in Schmidt stability and GPP model parameter variance depended on trophic status, whereas daily variance in Schmidt stability was consistently positively related to ER model parameter variance. Wind speeds in the range of ~0.8-3 m s–1 were consistent predictors of high variance for both GPP and ER model parameters, with greater uncertainty in eutrophic lakes. Our findings can be used to reduce ecosystem metabolism model parameter uncertainty and identify potential sources of that uncertainty.

Predictive Uncertainty And Parameter Sensitivity Of A Sediment-Flux Model: Nitrogen Flux and Sediment Oxygen Demand

EPA Science Inventory

Estimating model predictive uncertainty is imperative to informed environmental decision making and management of water resources. This paper applies the Generalized Sensitivity Analysis (GSA) to examine parameter sensitivity and the Generalized Likelihood Uncertainty Estimation...

Model parameter uncertainty analysis for an annual field-scale P loss model

NASA Astrophysics Data System (ADS)

Bolster, Carl H.; Vadas, Peter A.; Boykin, Debbie

2016-08-01

Phosphorous (P) fate and transport models are important tools for developing and evaluating conservation practices aimed at reducing P losses from agricultural fields. Because all models are simplifications of complex systems, there will exist an inherent amount of uncertainty associated with their predictions. It is therefore important that efforts be directed at identifying, quantifying, and communicating the different sources of model uncertainties. In this study, we conducted an uncertainty analysis with the Annual P Loss Estimator (APLE) model. Our analysis included calculating parameter uncertainties and confidence and prediction intervals for five internal regression equations in APLE. We also estimated uncertainties of the model input variables based on values reported in the literature. We then predicted P loss for a suite of fields under different management and climatic conditions while accounting for uncertainties in the model parameters and inputs and compared the relative contributions of these two sources of uncertainty to the overall uncertainty associated with predictions of P loss. Both the overall magnitude of the prediction uncertainties and the relative contributions of the two sources of uncertainty varied depending on management practices and field characteristics. This was due to differences in the number of model input variables and the uncertainties in the regression equations associated with each P loss pathway. Inspection of the uncertainties in the five regression equations brought attention to a previously unrecognized limitation with the equation used to partition surface-applied fertilizer P between leaching and runoff losses. As a result, an alternate equation was identified that provided similar predictions with much less uncertainty. Our results demonstrate how a thorough uncertainty and model residual analysis can be used to identify limitations with a model. Such insight can then be used to guide future data collection and model development and evaluation efforts.

Generalized Likelihood Uncertainty Estimation (GLUE) Using Multi-Optimization Algorithm as Sampling Method

NASA Astrophysics Data System (ADS)

Wang, Z.

2015-12-01

For decades, distributed and lumped hydrological models have furthered our understanding of hydrological system. The development of hydrological simulation in large scale and high precision elaborated the spatial descriptions and hydrological behaviors. Meanwhile, the new trend is also followed by the increment of model complexity and number of parameters, which brings new challenges of uncertainty quantification. Generalized Likelihood Uncertainty Estimation (GLUE) has been widely used in uncertainty analysis for hydrological models referring to Monte Carlo method coupled with Bayesian estimation. However, the stochastic sampling method of prior parameters adopted by GLUE appears inefficient, especially in high dimensional parameter space. The heuristic optimization algorithms utilizing iterative evolution show better convergence speed and optimality-searching performance. In light of the features of heuristic optimization algorithms, this study adopted genetic algorithm, differential evolution, shuffled complex evolving algorithm to search the parameter space and obtain the parameter sets of large likelihoods. Based on the multi-algorithm sampling, hydrological model uncertainty analysis is conducted by the typical GLUE framework. To demonstrate the superiority of the new method, two hydrological models of different complexity are examined. The results shows the adaptive method tends to be efficient in sampling and effective in uncertainty analysis, providing an alternative path for uncertainty quantilization.

Streamflow hindcasting in European river basins via multi-parametric ensemble of the mesoscale hydrologic model (mHM)

NASA Astrophysics Data System (ADS)

Noh, Seong Jin; Rakovec, Oldrich; Kumar, Rohini; Samaniego, Luis

2016-04-01

There have been tremendous improvements in distributed hydrologic modeling (DHM) which made a process-based simulation with a high spatiotemporal resolution applicable on a large spatial scale. Despite of increasing information on heterogeneous property of a catchment, DHM is still subject to uncertainties inherently coming from model structure, parameters and input forcing. Sequential data assimilation (DA) may facilitate improved streamflow prediction via DHM using real-time observations to correct internal model states. In conventional DA methods such as state updating, parametric uncertainty is, however, often ignored mainly due to practical limitations of methodology to specify modeling uncertainty with limited ensemble members. If parametric uncertainty related with routing and runoff components is not incorporated properly, predictive uncertainty by DHM may be insufficient to capture dynamics of observations, which may deteriorate predictability. Recently, a multi-scale parameter regionalization (MPR) method was proposed to make hydrologic predictions at different scales using a same set of model parameters without losing much of the model performance. The MPR method incorporated within the mesoscale hydrologic model (mHM, http://www.ufz.de/mhm) could effectively represent and control uncertainty of high-dimensional parameters in a distributed model using global parameters. In this study, we present a global multi-parametric ensemble approach to incorporate parametric uncertainty of DHM in DA to improve streamflow predictions. To effectively represent and control uncertainty of high-dimensional parameters with limited number of ensemble, MPR method is incorporated with DA. Lagged particle filtering is utilized to consider the response times and non-Gaussian characteristics of internal hydrologic processes. The hindcasting experiments are implemented to evaluate impacts of the proposed DA method on streamflow predictions in multiple European river basins having different climate and catchment characteristics. Because augmentation of parameters is not required within an assimilation window, the approach could be stable with limited ensemble members and viable for practical uses.

Uncertainty quantification and propagation in dynamic models using ambient vibration measurements, application to a 10-story building

NASA Astrophysics Data System (ADS)

Behmanesh, Iman; Yousefianmoghadam, Seyedsina; Nozari, Amin; Moaveni, Babak; Stavridis, Andreas

2018-07-01

This paper investigates the application of Hierarchical Bayesian model updating for uncertainty quantification and response prediction of civil structures. In this updating framework, structural parameters of an initial finite element (FE) model (e.g., stiffness or mass) are calibrated by minimizing error functions between the identified modal parameters and the corresponding parameters of the model. These error functions are assumed to have Gaussian probability distributions with unknown parameters to be determined. The estimated parameters of error functions represent the uncertainty of the calibrated model in predicting building's response (modal parameters here). The focus of this paper is to answer whether the quantified model uncertainties using dynamic measurement at building's reference/calibration state can be used to improve the model prediction accuracies at a different structural state, e.g., damaged structure. Also, the effects of prediction error bias on the uncertainty of the predicted values is studied. The test structure considered here is a ten-story concrete building located in Utica, NY. The modal parameters of the building at its reference state are identified from ambient vibration data and used to calibrate parameters of the initial FE model as well as the error functions. Before demolishing the building, six of its exterior walls were removed and ambient vibration measurements were also collected from the structure after the wall removal. These data are not used to calibrate the model; they are only used to assess the predicted results. The model updating framework proposed in this paper is applied to estimate the modal parameters of the building at its reference state as well as two damaged states: moderate damage (removal of four walls) and severe damage (removal of six walls). Good agreement is observed between the model-predicted modal parameters and those identified from vibration tests. Moreover, it is shown that including prediction error bias in the updating process instead of commonly-used zero-mean error function can significantly reduce the prediction uncertainties.

Bayesian inference of uncertainties in precipitation-streamflow modeling in a snow affected catchment

NASA Astrophysics Data System (ADS)

Koskela, J. J.; Croke, B. W. F.; Koivusalo, H.; Jakeman, A. J.; Kokkonen, T.

2012-11-01

Bayesian inference is used to study the effect of precipitation and model structural uncertainty on estimates of model parameters and confidence limits of predictive variables in a conceptual rainfall-runoff model in the snow-fed Rudbäck catchment (142 ha) in southern Finland. The IHACRES model is coupled with a simple degree day model to account for snow accumulation and melt. The posterior probability distribution of the model parameters is sampled by using the Differential Evolution Adaptive Metropolis (DREAM(ZS)) algorithm and the generalized likelihood function. Precipitation uncertainty is taken into account by introducing additional latent variables that were used as multipliers for individual storm events. Results suggest that occasional snow water equivalent (SWE) observations together with daily streamflow observations do not contain enough information to simultaneously identify model parameters, precipitation uncertainty and model structural uncertainty in the Rudbäck catchment. The addition of an autoregressive component to account for model structure error and latent variables having uniform priors to account for input uncertainty lead to dubious posterior distributions of model parameters. Thus our hypothesis that informative priors for latent variables could be replaced by additional SWE data could not be confirmed. The model was found to work adequately in 1-day-ahead simulation mode, but the results were poor in the simulation batch mode. This was caused by the interaction of parameters that were used to describe different sources of uncertainty. The findings may have lessons for other cases where parameterizations are similarly high in relation to available prior information.

MOESHA: A genetic algorithm for automatic calibration and estimation of parameter uncertainty and sensitivity of hydrologic models

EPA Science Inventory

Characterization of uncertainty and sensitivity of model parameters is an essential and often overlooked facet of hydrological modeling. This paper introduces an algorithm called MOESHA that combines input parameter sensitivity analyses with a genetic algorithm calibration routin...

Sensitivity analysis of respiratory parameter uncertainties: impact of criterion function form and constraints.

PubMed

Lutchen, K R

1990-08-01

A sensitivity analysis based on weighted least-squares regression is presented to evaluate alternative methods for fitting lumped-parameter models to respiratory impedance data. The goal is to maintain parameter accuracy simultaneously with practical experiment design. The analysis focuses on predicting parameter uncertainties using a linearized approximation for joint confidence regions. Applications are with four-element parallel and viscoelastic models for 0.125- to 4-Hz data and a six-element model with separate tissue and airway properties for input and transfer impedance data from 2-64 Hz. The criterion function form was evaluated by comparing parameter uncertainties when data are fit as magnitude and phase, dynamic resistance and compliance, or real and imaginary parts of input impedance. The proper choice of weighting can make all three criterion variables comparable. For the six-element model, parameter uncertainties were predicted when both input impedance and transfer impedance are acquired and fit simultaneously. A fit to both data sets from 4 to 64 Hz could reduce parameter estimate uncertainties considerably from those achievable by fitting either alone. For the four-element models, use of an independent, but noisy, measure of static compliance was assessed as a constraint on model parameters. This may allow acceptable parameter uncertainties for a minimum frequency of 0.275-0.375 Hz rather than 0.125 Hz. This reduces data acquisition requirements from a 16- to a 5.33- to 8-s breath holding period. These results are approximations, and the impact of using the linearized approximation for the confidence regions is discussed.

Uncertainty Modeling of Pollutant Transport in Atmosphere and Aquatic Route Using Soft Computing

NASA Astrophysics Data System (ADS)

Datta, D.

2010-10-01

Hazardous radionuclides are released as pollutants in the atmospheric and aquatic environment (ATAQE) during the normal operation of nuclear power plants. Atmospheric and aquatic dispersion models are routinely used to assess the impact of release of radionuclide from any nuclear facility or hazardous chemicals from any chemical plant on the ATAQE. Effect of the exposure from the hazardous nuclides or chemicals is measured in terms of risk. Uncertainty modeling is an integral part of the risk assessment. The paper focuses the uncertainty modeling of the pollutant transport in atmospheric and aquatic environment using soft computing. Soft computing is addressed due to the lack of information on the parameters that represent the corresponding models. Soft-computing in this domain basically addresses the usage of fuzzy set theory to explore the uncertainty of the model parameters and such type of uncertainty is called as epistemic uncertainty. Each uncertain input parameters of the model is described by a triangular membership function.

Equifinality and process-based modelling

NASA Astrophysics Data System (ADS)

Khatami, S.; Peel, M. C.; Peterson, T. J.; Western, A. W.

2017-12-01

Equifinality is understood as one of the fundamental difficulties in the study of open complex systems, including catchment hydrology. A review of the hydrologic literature reveals that the term equifinality has been widely used, but in many cases inconsistently and without coherent recognition of the various facets of equifinality, which can lead to ambiguity but also methodological fallacies. Therefore, in this study we first characterise the term equifinality within the context of hydrological modelling by reviewing the genesis of the concept of equifinality and then presenting a theoretical framework. During past decades, equifinality has mainly been studied as a subset of aleatory (arising due to randomness) uncertainty and for the assessment of model parameter uncertainty. Although the connection between parameter uncertainty and equifinality is undeniable, we argue there is more to equifinality than just aleatory parameter uncertainty. That is, the importance of equifinality and epistemic uncertainty (arising due to lack of knowledge) and their implications is overlooked in our current practice of model evaluation. Equifinality and epistemic uncertainty in studying, modelling, and evaluating hydrologic processes are treated as if they can be simply discussed in (or often reduced to) probabilistic terms (as for aleatory uncertainty). The deficiencies of this approach to conceptual rainfall-runoff modelling are demonstrated for selected Australian catchments by examination of parameter and internal flux distributions and interactions within SIMHYD. On this basis, we present a new approach that expands equifinality concept beyond model parameters to inform epistemic uncertainty. The new approach potentially facilitates the identification and development of more physically plausible models and model evaluation schemes particularly within the multiple working hypotheses framework, and is generalisable to other fields of environmental modelling as well.

Uncertainty Modeling for Structural Control Analysis and Synthesis

NASA Technical Reports Server (NTRS)

Campbell, Mark E.; Crawley, Edward F.

1996-01-01

The development of an accurate model of uncertainties for the control of structures that undergo a change in operational environment, based solely on modeling and experimentation in the original environment is studied. The application used throughout this work is the development of an on-orbit uncertainty model based on ground modeling and experimentation. A ground based uncertainty model consisting of mean errors and bounds on critical structural parameters is developed. The uncertainty model is created using multiple data sets to observe all relevant uncertainties in the system. The Discrete Extended Kalman Filter is used as an identification/parameter estimation method for each data set, in addition to providing a covariance matrix which aids in the development of the uncertainty model. Once ground based modal uncertainties have been developed, they are localized to specific degrees of freedom in the form of mass and stiffness uncertainties. Two techniques are presented: a matrix method which develops the mass and stiffness uncertainties in a mathematical manner; and a sensitivity method which assumes a form for the mass and stiffness uncertainties in macroelements and scaling factors. This form allows the derivation of mass and stiffness uncertainties in a more physical manner. The mass and stiffness uncertainties of the ground based system are then mapped onto the on-orbit system, and projected to create an analogous on-orbit uncertainty model in the form of mean errors and bounds on critical parameters. The Middeck Active Control Experiment is introduced as experimental verification for the localization and projection methods developed. In addition, closed loop results from on-orbit operations of the experiment verify the use of the uncertainty model for control analysis and synthesis in space.

Toward Scientific Numerical Modeling

NASA Technical Reports Server (NTRS)

Kleb, Bil

2007-01-01

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and verifying that numerical models are translated into code correctly, however, are necessary first steps toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. To address these two shortcomings, two proposals are offered: (1) an unobtrusive mechanism to document input parameter uncertainties in situ and (2) an adaptation of the Scientific Method to numerical model development and deployment. Because these two steps require changes in the computational simulation community to bear fruit, they are presented in terms of the Beckhard-Harris-Gleicher change model.

Parameter estimation for groundwater models under uncertain irrigation data

USGS Publications Warehouse

Demissie, Yonas; Valocchi, Albert J.; Cai, Ximing; Brozovic, Nicholas; Senay, Gabriel; Gebremichael, Mekonnen

2015-01-01

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression-based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least-squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least-squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least-squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.

Uncertainty quantification of Antarctic contribution to sea-level rise using the fast Elementary Thermomechanical Ice Sheet (f.ETISh) model

NASA Astrophysics Data System (ADS)

Bulthuis, Kevin; Arnst, Maarten; Pattyn, Frank; Favier, Lionel

2017-04-01

Uncertainties in sea-level rise projections are mostly due to uncertainties in Antarctic ice-sheet predictions (IPCC AR5 report, 2013), because key parameters related to the current state of the Antarctic ice sheet (e.g. sub-ice-shelf melting) and future climate forcing are poorly constrained. Here, we propose to improve the predictions of Antarctic ice-sheet behaviour using new uncertainty quantification methods. As opposed to ensemble modelling (Bindschadler et al., 2013) which provides a rather limited view on input and output dispersion, new stochastic methods (Le Maître and Knio, 2010) can provide deeper insight into the impact of uncertainties on complex system behaviour. Such stochastic methods usually begin with deducing a probabilistic description of input parameter uncertainties from the available data. Then, the impact of these input parameter uncertainties on output quantities is assessed by estimating the probability distribution of the outputs by means of uncertainty propagation methods such as Monte Carlo methods or stochastic expansion methods. The use of such uncertainty propagation methods in glaciology may be computationally costly because of the high computational complexity of ice-sheet models. This challenge emphasises the importance of developing reliable and computationally efficient ice-sheet models such as the f.ETISh ice-sheet model (Pattyn, 2015), a new fast thermomechanical coupled ice sheet/ice shelf model capable of handling complex and critical processes such as the marine ice-sheet instability mechanism. Here, we apply these methods to investigate the role of uncertainties in sub-ice-shelf melting, calving rates and climate projections in assessing Antarctic contribution to sea-level rise for the next centuries using the f.ETISh model. We detail the methods and show results that provide nominal values and uncertainty bounds for future sea-level rise as a reflection of the impact of the input parameter uncertainties under consideration, as well as a ranking of the input parameter uncertainties in the order of the significance of their contribution to uncertainty in future sea-level rise. In addition, we discuss how limitations posed by the available information (poorly constrained data) pose challenges that motivate our current research.

Using global sensitivity analysis of demographic models for ecological impact assessment.

PubMed

Aiello-Lammens, Matthew E; Akçakaya, H Resit

2017-02-01

Population viability analysis (PVA) is widely used to assess population-level impacts of environmental changes on species. When combined with sensitivity analysis, PVA yields insights into the effects of parameter and model structure uncertainty. This helps researchers prioritize efforts for further data collection so that model improvements are efficient and helps managers prioritize conservation and management actions. Usually, sensitivity is analyzed by varying one input parameter at a time and observing the influence that variation has over model outcomes. This approach does not account for interactions among parameters. Global sensitivity analysis (GSA) overcomes this limitation by varying several model inputs simultaneously. Then, regression techniques allow measuring the importance of input-parameter uncertainties. In many conservation applications, the goal of demographic modeling is to assess how different scenarios of impact or management cause changes in a population. This is challenging because the uncertainty of input-parameter values can be confounded with the effect of impacts and management actions. We developed a GSA method that separates model outcome uncertainty resulting from parameter uncertainty from that resulting from projected ecological impacts or simulated management actions, effectively separating the 2 main questions that sensitivity analysis asks. We applied this method to assess the effects of predicted sea-level rise on Snowy Plover (Charadrius nivosus). A relatively small number of replicate models (approximately 100) resulted in consistent measures of variable importance when not trying to separate the effects of ecological impacts from parameter uncertainty. However, many more replicate models (approximately 500) were required to separate these effects. These differences are important to consider when using demographic models to estimate ecological impacts of management actions. © 2016 Society for Conservation Biology.

Predicting uncertainty in future marine ice sheet volume using Bayesian statistical methods

NASA Astrophysics Data System (ADS)

Davis, A. D.

2015-12-01

The marine ice instability can trigger rapid retreat of marine ice streams. Recent observations suggest that marine ice systems in West Antarctica have begun retreating. However, unknown ice dynamics, computationally intensive mathematical models, and uncertain parameters in these models make predicting retreat rate and ice volume difficult. In this work, we fuse current observational data with ice stream/shelf models to develop probabilistic predictions of future grounded ice sheet volume. Given observational data (e.g., thickness, surface elevation, and velocity) and a forward model that relates uncertain parameters (e.g., basal friction and basal topography) to these observations, we use a Bayesian framework to define a posterior distribution over the parameters. A stochastic predictive model then propagates uncertainties in these parameters to uncertainty in a particular quantity of interest (QoI)---here, the volume of grounded ice at a specified future time. While the Bayesian approach can in principle characterize the posterior predictive distribution of the QoI, the computational cost of both the forward and predictive models makes this effort prohibitively expensive. To tackle this challenge, we introduce a new Markov chain Monte Carlo method that constructs convergent approximations of the QoI target density in an online fashion, yielding accurate characterizations of future ice sheet volume at significantly reduced computational cost.Our second goal is to attribute uncertainty in these Bayesian predictions to uncertainties in particular parameters. Doing so can help target data collection, for the purpose of constraining the parameters that contribute most strongly to uncertainty in the future volume of grounded ice. For instance, smaller uncertainties in parameters to which the QoI is highly sensitive may account for more variability in the prediction than larger uncertainties in parameters to which the QoI is less sensitive. We use global sensitivity analysis to help answer this question, and make the computation of sensitivity indices computationally tractable using a combination of polynomial chaos and Monte Carlo techniques.

Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality

NASA Astrophysics Data System (ADS)

Keating, Elizabeth H.; Doherty, John; Vrugt, Jasper A.; Kang, Qinjun

2010-10-01

Highly parameterized and CPU-intensive groundwater models are increasingly being used to understand and predict flow and transport through aquifers. Despite their frequent use, these models pose significant challenges for parameter estimation and predictive uncertainty analysis algorithms, particularly global methods which usually require very large numbers of forward runs. Here we present a general methodology for parameter estimation and uncertainty analysis that can be utilized in these situations. Our proposed method includes extraction of a surrogate model that mimics key characteristics of a full process model, followed by testing and implementation of a pragmatic uncertainty analysis technique, called null-space Monte Carlo (NSMC), that merges the strengths of gradient-based search and parameter dimensionality reduction. As part of the surrogate model analysis, the results of NSMC are compared with a formal Bayesian approach using the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm. Such a comparison has never been accomplished before, especially in the context of high parameter dimensionality. Despite the highly nonlinear nature of the inverse problem, the existence of multiple local minima, and the relatively large parameter dimensionality, both methods performed well and results compare favorably with each other. Experiences gained from the surrogate model analysis are then transferred to calibrate the full highly parameterized and CPU intensive groundwater model and to explore predictive uncertainty of predictions made by that model. The methodology presented here is generally applicable to any highly parameterized and CPU-intensive environmental model, where efficient methods such as NSMC provide the only practical means for conducting predictive uncertainty analysis.

Convergence in parameters and predictions using computational experimental design.

PubMed

Hagen, David R; White, Jacob K; Tidor, Bruce

2013-08-06

Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design techniques can select sets of experiments whose members probe complementary aspects of a biochemical network that together can account for its full behaviour. Here, we implemented an experimental design approach for selecting sets of experiments that constrain parameter uncertainty. We demonstrated with a model of the epidermal growth factor-nerve growth factor pathway that, after synthetically performing a handful of optimal experiments, the uncertainty in all 48 parameters converged below 10 per cent. Furthermore, the fitted parameters converged to their true values with a small error consistent with the residual uncertainty. When untested experimental conditions were simulated with the fitted models, the predicted species concentrations converged to their true values with errors that were consistent with the residual uncertainty. This paper suggests that accurate parameter estimation is achievable with complementary experiments specifically designed for the task, and that the resulting parametrized models are capable of accurate predictions.

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions

NASA Technical Reports Server (NTRS)

Nearing, Grey S.; Mocko, David M.; Peters-Lidard, Christa D.; Kumar, Sujay V.; Xia, Youlong

2016-01-01

Model benchmarking allows us to separate uncertainty in model predictions caused 1 by model inputs from uncertainty due to model structural error. We extend this method with a large-sample approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances.

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions

PubMed Central

Nearing, Grey S.; Mocko, David M.; Peters-Lidard, Christa D.; Kumar, Sujay V.; Xia, Youlong

2018-01-01

Model benchmarking allows us to separate uncertainty in model predictions caused by model inputs from uncertainty due to model structural error. We extend this method with a “large-sample” approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances. PMID:29697706

Benchmarking NLDAS-2 Soil Moisture and Evapotranspiration to Separate Uncertainty Contributions.

PubMed

Nearing, Grey S; Mocko, David M; Peters-Lidard, Christa D; Kumar, Sujay V; Xia, Youlong

2016-03-01

Model benchmarking allows us to separate uncertainty in model predictions caused by model inputs from uncertainty due to model structural error. We extend this method with a "large-sample" approach (using data from multiple field sites) to measure prediction uncertainty caused by errors in (i) forcing data, (ii) model parameters, and (iii) model structure, and use it to compare the efficiency of soil moisture state and evapotranspiration flux predictions made by the four land surface models in the North American Land Data Assimilation System Phase 2 (NLDAS-2). Parameters dominated uncertainty in soil moisture estimates and forcing data dominated uncertainty in evapotranspiration estimates; however, the models themselves used only a fraction of the information available to them. This means that there is significant potential to improve all three components of the NLDAS-2 system. In particular, continued work toward refining the parameter maps and look-up tables, the forcing data measurement and processing, and also the land surface models themselves, has potential to result in improved estimates of surface mass and energy balances.

Dynamic Modelling under Uncertainty: The Case of Trypanosoma brucei Energy Metabolism

PubMed Central

Achcar, Fiona; Kerkhoven, Eduard J.; Bakker, Barbara M.; Barrett, Michael P.; Breitling, Rainer

2012-01-01

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies. PMID:22379410

Influences of system uncertainties on the numerical transfer path analysis of engine systems

NASA Astrophysics Data System (ADS)

Acri, A.; Nijman, E.; Acri, A.; Offner, G.

2017-10-01

Practical mechanical systems operate with some degree of uncertainty. In numerical models uncertainties can result from poorly known or variable parameters, from geometrical approximation, from discretization or numerical errors, from uncertain inputs or from rapidly changing forcing that can be best described in a stochastic framework. Recently, random matrix theory was introduced to take parameter uncertainties into account in numerical modeling problems. In particular in this paper, Wishart random matrix theory is applied on a multi-body dynamic system to generate random variations of the properties of system components. Multi-body dynamics is a powerful numerical tool largely implemented during the design of new engines. In this paper the influence of model parameter variability on the results obtained from the multi-body simulation of engine dynamics is investigated. The aim is to define a methodology to properly assess and rank system sources when dealing with uncertainties. Particular attention is paid to the influence of these uncertainties on the analysis and the assessment of the different engine vibration sources. Examples of the effects of different levels of uncertainties are illustrated by means of examples using a representative numerical powertrain model. A numerical transfer path analysis, based on system dynamic substructuring, is used to derive and assess the internal engine vibration sources. The results obtained from this analysis are used to derive correlations between parameter uncertainties and statistical distribution of results. The derived statistical information can be used to advance the knowledge of the multi-body analysis and the assessment of system sources when uncertainties in model parameters are considered.

How to Make Data a Blessing to Parametric Uncertainty Quantification and Reduction?

NASA Astrophysics Data System (ADS)

Ye, M.; Shi, X.; Curtis, G. P.; Kohler, M.; Wu, J.

2013-12-01

In a Bayesian point of view, probability of model parameters and predictions are conditioned on data used for parameter inference and prediction analysis. It is critical to use appropriate data for quantifying parametric uncertainty and its propagation to model predictions. However, data are always limited and imperfect. When a dataset cannot properly constrain model parameters, it may lead to inaccurate uncertainty quantification. While in this case data appears to be a curse to uncertainty quantification, a comprehensive modeling analysis may help understand the cause and characteristics of parametric uncertainty and thus turns data into a blessing. In this study, we illustrate impacts of data on uncertainty quantification and reduction using an example of surface complexation model (SCM) developed to simulate uranyl (U(VI)) adsorption. The model includes two adsorption sites, referred to as strong and weak sites. The amount of uranium adsorption on these sites determines both the mean arrival time and the long tail of the breakthrough curves. There is one reaction on the weak site but two reactions on the strong site. The unknown parameters include fractions of the total surface site density of the two sites and surface complex formation constants of the three reactions. A total of seven experiments were conducted with different geochemical conditions to estimate these parameters. The experiments with low initial concentration of U(VI) result in a large amount of parametric uncertainty. A modeling analysis shows that it is because the experiments cannot distinguish the relative adsorption affinity of the strong and weak sites on uranium adsorption. Therefore, the experiments with high initial concentration of U(VI) are needed, because in the experiments the strong site is nearly saturated and the weak site can be determined. The experiments with high initial concentration of U(VI) are a blessing to uncertainty quantification, and the experiments with low initial concentration help modelers turn a curse into a blessing. The data impacts on uncertainty quantification and reduction are quantified using probability density functions of model parameters obtained from Markov Chain Monte Carlo simulation using the DREAM algorithm. This study provides insights to model calibration, uncertainty quantification, experiment design, and data collection in groundwater reactive transport modeling and other environmental modeling.

Estimating winter wheat phenological parameters: Implications for crop modeling

USDA-ARS?s Scientific Manuscript database

Crop parameters, such as the timing of developmental events, are critical for accurate simulation results in crop simulation models, yet uncertainty often exists in determining the parameters. Factors contributing to the uncertainty include: a) sources of variation within a plant (i.e., within diffe...

Application of Bayesian model averaging to measurements of the primordial power spectrum

NASA Astrophysics Data System (ADS)

Parkinson, David; Liddle, Andrew R.

2010-11-01

Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for assessing parameter uncertainties in situations where there is also uncertainty in the underlying model. We apply model averaging to the estimation of the parameters associated with the primordial power spectra of curvature and tensor perturbations. We use CosmoNest and MultiNest to compute the model evidences and posteriors, using cosmic microwave data from WMAP, ACBAR, BOOMERanG, and CBI, plus large-scale structure data from the SDSS DR7. We find that the model-averaged 95% credible interval for the spectral index using all of the data is 0.940

Uncertainty Analysis and Parameter Estimation For Nearshore Hydrodynamic Models

NASA Astrophysics Data System (ADS)

Ardani, S.; Kaihatu, J. M.

2012-12-01

Numerical models represent deterministic approaches used for the relevant physical processes in the nearshore. Complexity of the physics of the model and uncertainty involved in the model inputs compel us to apply a stochastic approach to analyze the robustness of the model. The Bayesian inverse problem is one powerful way to estimate the important input model parameters (determined by apriori sensitivity analysis) and can be used for uncertainty analysis of the outputs. Bayesian techniques can be used to find the range of most probable parameters based on the probability of the observed data and the residual errors. In this study, the effect of input data involving lateral (Neumann) boundary conditions, bathymetry and off-shore wave conditions on nearshore numerical models are considered. Monte Carlo simulation is applied to a deterministic numerical model (the Delft3D modeling suite for coupled waves and flow) for the resulting uncertainty analysis of the outputs (wave height, flow velocity, mean sea level and etc.). Uncertainty analysis of outputs is performed by random sampling from the input probability distribution functions and running the model as required until convergence to the consistent results is achieved. The case study used in this analysis is the Duck94 experiment, which was conducted at the U.S. Army Field Research Facility at Duck, North Carolina, USA in the fall of 1994. The joint probability of model parameters relevant for the Duck94 experiments will be found using the Bayesian approach. We will further show that, by using Bayesian techniques to estimate the optimized model parameters as inputs and applying them for uncertainty analysis, we can obtain more consistent results than using the prior information for input data which means that the variation of the uncertain parameter will be decreased and the probability of the observed data will improve as well. Keywords: Monte Carlo Simulation, Delft3D, uncertainty analysis, Bayesian techniques, MCMC

Quantum-memory-assisted entropic uncertainty in spin models with Dzyaloshinskii-Moriya interaction

NASA Astrophysics Data System (ADS)

Huang, Zhiming

2018-02-01

In this article, we investigate the dynamics and correlations of quantum-memory-assisted entropic uncertainty, the tightness of the uncertainty, entanglement, quantum correlation and mixedness for various spin chain models with Dzyaloshinskii-Moriya (DM) interaction, including the XXZ model with DM interaction, the XY model with DM interaction and the Ising model with DM interaction. We find that the uncertainty grows to a stable value with growing temperature but reduces as the coupling coefficient, anisotropy parameter and DM values increase. It is found that the entropic uncertainty is closely correlated with the mixedness of the system. The increasing quantum correlation can result in a decrease in the uncertainty, and the robustness of quantum correlation is better than entanglement since entanglement means sudden birth and death. The tightness of the uncertainty drops to zero, apart from slight volatility as various parameters increase. Furthermore, we propose an effective approach to steering the uncertainty by weak measurement reversal.

Global sensitivity analysis for identifying important parameters of nitrogen nitrification and denitrification under model uncertainty and scenario uncertainty

NASA Astrophysics Data System (ADS)

Chen, Zhuowei; Shi, Liangsheng; Ye, Ming; Zhu, Yan; Yang, Jinzhong

2018-06-01

Nitrogen reactive transport modeling is subject to uncertainty in model parameters, structures, and scenarios. By using a new variance-based global sensitivity analysis method, this paper identifies important parameters for nitrogen reactive transport with simultaneous consideration of these three uncertainties. A combination of three scenarios of soil temperature and two scenarios of soil moisture creates a total of six scenarios. Four alternative models describing the effect of soil temperature and moisture content are used to evaluate the reduction functions used for calculating actual reaction rates. The results show that for nitrogen reactive transport problem, parameter importance varies substantially among different models and scenarios. Denitrification and nitrification process is sensitive to soil moisture content status rather than to the moisture function parameter. Nitrification process becomes more important at low moisture content and low temperature. However, the changing importance of nitrification activity with respect to temperature change highly relies on the selected model. Model-averaging is suggested to assess the nitrification (or denitrification) contribution by reducing the possible model error. Despite the introduction of biochemical heterogeneity or not, fairly consistent parameter importance rank is obtained in this study: optimal denitrification rate (Kden) is the most important parameter; reference temperature (Tr) is more important than temperature coefficient (Q10); empirical constant in moisture response function (m) is the least important one. Vertical distribution of soil moisture but not temperature plays predominant role controlling nitrogen reaction. This study provides insight into the nitrogen reactive transport modeling and demonstrates an effective strategy of selecting the important parameters when future temperature and soil moisture carry uncertainties or when modelers face with multiple ways of establishing nitrogen models.

Uncertainty quantification and global sensitivity analysis of the Los Alamos sea ice model

NASA Astrophysics Data System (ADS)

Urrego-Blanco, Jorge R.; Urban, Nathan M.; Hunke, Elizabeth C.; Turner, Adrian K.; Jeffery, Nicole

2016-04-01

Changes in the high-latitude climate system have the potential to affect global climate through feedbacks with the atmosphere and connections with midlatitudes. Sea ice and climate models used to understand these changes have uncertainties that need to be characterized and quantified. We present a quantitative way to assess uncertainty in complex computer models, which is a new approach in the analysis of sea ice models. We characterize parametric uncertainty in the Los Alamos sea ice model (CICE) in a standalone configuration and quantify the sensitivity of sea ice area, extent, and volume with respect to uncertainty in 39 individual model parameters. Unlike common sensitivity analyses conducted in previous studies where parameters are varied one at a time, this study uses a global variance-based approach in which Sobol' sequences are used to efficiently sample the full 39-dimensional parameter space. We implement a fast emulator of the sea ice model whose predictions of sea ice extent, area, and volume are used to compute the Sobol' sensitivity indices of the 39 parameters. Main effects and interactions among the most influential parameters are also estimated by a nonparametric regression technique based on generalized additive models. A ranking based on the sensitivity indices indicates that model predictions are most sensitive to snow parameters such as snow conductivity and grain size, and the drainage of melt ponds. It is recommended that research be prioritized toward more accurately determining these most influential parameter values by observational studies or by improving parameterizations in the sea ice model.

Assessment of uncertainties of the models used in thermal-hydraulic computer codes

NASA Astrophysics Data System (ADS)

Gricay, A. S.; Migrov, Yu. A.

2015-09-01

The article deals with matters concerned with the problem of determining the statistical characteristics of variable parameters (the variation range and distribution law) in analyzing the uncertainty and sensitivity of calculation results to uncertainty in input data. A comparative analysis of modern approaches to uncertainty in input data is presented. The need to develop an alternative method for estimating the uncertainty of model parameters used in thermal-hydraulic computer codes, in particular, in the closing correlations of the loop thermal hydraulics block, is shown. Such a method shall feature the minimal degree of subjectivism and must be based on objective quantitative assessment criteria. The method includes three sequential stages: selecting experimental data satisfying the specified criteria, identifying the key closing correlation using a sensitivity analysis, and carrying out case calculations followed by statistical processing of the results. By using the method, one can estimate the uncertainty range of a variable parameter and establish its distribution law in the above-mentioned range provided that the experimental information is sufficiently representative. Practical application of the method is demonstrated taking as an example the problem of estimating the uncertainty of a parameter appearing in the model describing transition to post-burnout heat transfer that is used in the thermal-hydraulic computer code KORSAR. The performed study revealed the need to narrow the previously established uncertainty range of this parameter and to replace the uniform distribution law in the above-mentioned range by the Gaussian distribution law. The proposed method can be applied to different thermal-hydraulic computer codes. In some cases, application of the method can make it possible to achieve a smaller degree of conservatism in the expert estimates of uncertainties pertinent to the model parameters used in computer codes.

Parametric uncertainties in global model simulations of black carbon column mass concentration

NASA Astrophysics Data System (ADS)

Pearce, Hana; Lee, Lindsay; Reddington, Carly; Carslaw, Ken; Mann, Graham

2016-04-01

Previous studies have deduced that the annual mean direct radiative forcing from black carbon (BC) aerosol may regionally be up to 5 W m-2 larger than expected due to underestimation of global atmospheric BC absorption in models. We have identified the magnitude and important sources of parametric uncertainty in simulations of BC column mass concentration from a global aerosol microphysics model (GLOMAP-Mode). A variance-based uncertainty analysis of 28 parameters has been performed, based on statistical emulators trained on model output from GLOMAP-Mode. This is the largest number of uncertain model parameters to be considered in a BC uncertainty analysis to date and covers primary aerosol emissions, microphysical processes and structural parameters related to the aerosol size distribution. We will present several recommendations for further research to improve the fidelity of simulated BC. In brief, we find that the standard deviation around the simulated mean annual BC column mass concentration varies globally between 2.5 x 10-9 g cm-2 in remote marine regions and 1.25 x 10-6 g cm-2 near emission sources due to parameter uncertainty Between 60 and 90% of the variance over source regions is due to uncertainty associated with primary BC emission fluxes, including biomass burning, fossil fuel and biofuel emissions. While the contributions to BC column uncertainty from microphysical processes, for example those related to dry and wet deposition, are increased over remote regions, we find that emissions still make an important contribution in these areas. It is likely, however, that the importance of structural model error, i.e. differences between models, is greater than parametric uncertainty. We have extended our analysis to emulate vertical BC profiles at several locations in the mid-Pacific Ocean and identify the parameters contributing to uncertainty in the vertical distribution of black carbon at these locations. We will present preliminary comparisons of emulated BC vertical profiles from the AeroCom multi-model ensemble and Hiaper Pole-to-Pole (HIPPO) observations.

Assessment of parametric uncertainty for groundwater reactive transport modeling,

USGS Publications Warehouse

Shi, Xiaoqing; Ye, Ming; Curtis, Gary P.; Miller, Geoffery L.; Meyer, Philip D.; Kohler, Matthias; Yabusaki, Steve; Wu, Jichun

2014-01-01

The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM(zs)) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris- and DREAM(ZS)-based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

Uncertainties of flood frequency estimation approaches based on continuous simulation using data resampling

NASA Astrophysics Data System (ADS)

Arnaud, Patrick; Cantet, Philippe; Odry, Jean

2017-11-01

Flood frequency analyses (FFAs) are needed for flood risk management. Many methods exist ranging from classical purely statistical approaches to more complex approaches based on process simulation. The results of these methods are associated with uncertainties that are sometimes difficult to estimate due to the complexity of the approaches or the number of parameters, especially for process simulation. This is the case of the simulation-based FFA approach called SHYREG presented in this paper, in which a rainfall generator is coupled with a simple rainfall-runoff model in an attempt to estimate the uncertainties due to the estimation of the seven parameters needed to estimate flood frequencies. The six parameters of the rainfall generator are mean values, so their theoretical distribution is known and can be used to estimate the generator uncertainties. In contrast, the theoretical distribution of the single hydrological model parameter is unknown; consequently, a bootstrap method is applied to estimate the calibration uncertainties. The propagation of uncertainty from the rainfall generator to the hydrological model is also taken into account. This method is applied to 1112 basins throughout France. Uncertainties coming from the SHYREG method and from purely statistical approaches are compared, and the results are discussed according to the length of the recorded observations, basin size and basin location. Uncertainties of the SHYREG method decrease as the basin size increases or as the length of the recorded flow increases. Moreover, the results show that the confidence intervals of the SHYREG method are relatively small despite the complexity of the method and the number of parameters (seven). This is due to the stability of the parameters and takes into account the dependence of uncertainties due to the rainfall model and the hydrological calibration. Indeed, the uncertainties on the flow quantiles are on the same order of magnitude as those associated with the use of a statistical law with two parameters (here generalised extreme value Type I distribution) and clearly lower than those associated with the use of a three-parameter law (here generalised extreme value Type II distribution). For extreme flood quantiles, the uncertainties are mostly due to the rainfall generator because of the progressive saturation of the hydrological model.

Uncertainty quantification and global sensitivity analysis of the Los Alamos sea ice model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urrego-Blanco, Jorge Rolando; Urban, Nathan Mark; Hunke, Elizabeth Clare

Changes in the high-latitude climate system have the potential to affect global climate through feedbacks with the atmosphere and connections with midlatitudes. Sea ice and climate models used to understand these changes have uncertainties that need to be characterized and quantified. We present a quantitative way to assess uncertainty in complex computer models, which is a new approach in the analysis of sea ice models. We characterize parametric uncertainty in the Los Alamos sea ice model (CICE) in a standalone configuration and quantify the sensitivity of sea ice area, extent, and volume with respect to uncertainty in 39 individual modelmore » parameters. Unlike common sensitivity analyses conducted in previous studies where parameters are varied one at a time, this study uses a global variance-based approach in which Sobol' sequences are used to efficiently sample the full 39-dimensional parameter space. We implement a fast emulator of the sea ice model whose predictions of sea ice extent, area, and volume are used to compute the Sobol' sensitivity indices of the 39 parameters. Main effects and interactions among the most influential parameters are also estimated by a nonparametric regression technique based on generalized additive models. A ranking based on the sensitivity indices indicates that model predictions are most sensitive to snow parameters such as snow conductivity and grain size, and the drainage of melt ponds. Lastly, it is recommended that research be prioritized toward more accurately determining these most influential parameter values by observational studies or by improving parameterizations in the sea ice model.« less

Uncertainty quantification and global sensitivity analysis of the Los Alamos sea ice model

DOE PAGES

Urrego-Blanco, Jorge Rolando; Urban, Nathan Mark; Hunke, Elizabeth Clare; ...

2016-04-01

Changes in the high-latitude climate system have the potential to affect global climate through feedbacks with the atmosphere and connections with midlatitudes. Sea ice and climate models used to understand these changes have uncertainties that need to be characterized and quantified. We present a quantitative way to assess uncertainty in complex computer models, which is a new approach in the analysis of sea ice models. We characterize parametric uncertainty in the Los Alamos sea ice model (CICE) in a standalone configuration and quantify the sensitivity of sea ice area, extent, and volume with respect to uncertainty in 39 individual modelmore » parameters. Unlike common sensitivity analyses conducted in previous studies where parameters are varied one at a time, this study uses a global variance-based approach in which Sobol' sequences are used to efficiently sample the full 39-dimensional parameter space. We implement a fast emulator of the sea ice model whose predictions of sea ice extent, area, and volume are used to compute the Sobol' sensitivity indices of the 39 parameters. Main effects and interactions among the most influential parameters are also estimated by a nonparametric regression technique based on generalized additive models. A ranking based on the sensitivity indices indicates that model predictions are most sensitive to snow parameters such as snow conductivity and grain size, and the drainage of melt ponds. Lastly, it is recommended that research be prioritized toward more accurately determining these most influential parameter values by observational studies or by improving parameterizations in the sea ice model.« less

Large-Scale Transport Model Uncertainty and Sensitivity Analysis: Distributed Sources in Complex Hydrogeologic Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sig Drellack, Lance Prothro

2007-12-01

The Underground Test Area (UGTA) Project of the U.S. Department of Energy, National Nuclear Security Administration Nevada Site Office is in the process of assessing and developing regulatory decision options based on modeling predictions of contaminant transport from underground testing of nuclear weapons at the Nevada Test Site (NTS). The UGTA Project is attempting to develop an effective modeling strategy that addresses and quantifies multiple components of uncertainty including natural variability, parameter uncertainty, conceptual/model uncertainty, and decision uncertainty in translating model results into regulatory requirements. The modeling task presents multiple unique challenges to the hydrological sciences as a result ofmore » the complex fractured and faulted hydrostratigraphy, the distributed locations of sources, the suite of reactive and non-reactive radionuclides, and uncertainty in conceptual models. Characterization of the hydrogeologic system is difficult and expensive because of deep groundwater in the arid desert setting and the large spatial setting of the NTS. Therefore, conceptual model uncertainty is partially addressed through the development of multiple alternative conceptual models of the hydrostratigraphic framework and multiple alternative models of recharge and discharge. Uncertainty in boundary conditions is assessed through development of alternative groundwater fluxes through multiple simulations using the regional groundwater flow model. Calibration of alternative models to heads and measured or inferred fluxes has not proven to provide clear measures of model quality. Therefore, model screening by comparison to independently-derived natural geochemical mixing targets through cluster analysis has also been invoked to evaluate differences between alternative conceptual models. Advancing multiple alternative flow models, sensitivity of transport predictions to parameter uncertainty is assessed through Monte Carlo simulations. The simulations are challenged by the distributed sources in each of the Corrective Action Units, by complex mass transfer processes, and by the size and complexity of the field-scale flow models. An efficient methodology utilizing particle tracking results and convolution integrals provides in situ concentrations appropriate for Monte Carlo analysis. Uncertainty in source releases and transport parameters including effective porosity, fracture apertures and spacing, matrix diffusion coefficients, sorption coefficients, and colloid load and mobility are considered. With the distributions of input uncertainties and output plume volumes, global analysis methods including stepwise regression, contingency table analysis, and classification tree analysis are used to develop sensitivity rankings of parameter uncertainties for each model considered, thus assisting a variety of decisions.« less

Model Update of a Micro Air Vehicle (MAV) Flexible Wing Frame with Uncertainty Quantification

NASA Technical Reports Server (NTRS)

Reaves, Mercedes C.; Horta, Lucas G.; Waszak, Martin R.; Morgan, Benjamin G.

2004-01-01

This paper describes a procedure to update parameters in the finite element model of a Micro Air Vehicle (MAV) to improve displacement predictions under aerodynamics loads. Because of fabrication, materials, and geometric uncertainties, a statistical approach combined with Multidisciplinary Design Optimization (MDO) is used to modify key model parameters. Static test data collected using photogrammetry are used to correlate with model predictions. Results show significant improvements in model predictions after parameters are updated; however, computed probabilities values indicate low confidence in updated values and/or model structure errors. Lessons learned in the areas of wing design, test procedures, modeling approaches with geometric nonlinearities, and uncertainties quantification are all documented.

Computer-Based Model Calibration and Uncertainty Analysis: Terms and Concepts

DTIC Science & Technology

2015-07-01

uncertainty analyses throughout the lifecycle of planning, designing, and operating of Civil Works flood risk management projects as described in...value 95% of the time. In the frequentist approach to PE, model parameters area regarded as having true values, and their estimate is based on the...in catchment models. 1. Evaluating parameter uncertainty. Water Resources Research 19(5):1151–1172. Lee, P. M. 2012. Bayesian statistics: An

Parameter-induced uncertainty quantification of a regional N2O and NO3 inventory using the biogeochemical model LandscapeDNDC

NASA Astrophysics Data System (ADS)

Haas, Edwin; Klatt, Steffen; Kraus, David; Werner, Christian; Ruiz, Ignacio Santa Barbara; Kiese, Ralf; Butterbach-Bahl, Klaus

2014-05-01

Numerical simulation models are increasingly used to estimate greenhouse gas emissions at site to regional and national scales and are outlined as the most advanced methodology (Tier 3) for national emission inventory in the framework of UNFCCC reporting. Process-based models incorporate the major processes of the carbon and nitrogen cycle of terrestrial ecosystems like arable land and grasslands and are thus thought to be widely applicable at various spatial and temporal scales. The high complexity of ecosystem processes mirrored by such models requires a large number of model parameters. Many of those parameters are lumped parameters describing simultaneously the effect of environmental drivers on e.g. microbial community activity and individual processes. Thus, the precise quantification of true parameter states is often difficult or even impossible. As a result model uncertainty is not solely originating from input uncertainty but also subject to parameter-induced uncertainty. In this study we quantify regional parameter-induced model uncertainty on nitrous oxide (N2O) emissions and nitrate (NO3) leaching from arable soils of Saxony (Germany) using the biogeochemical model LandscapeDNDC. For this we calculate a regional inventory using a joint parameter distribution for key parameters describing microbial C and N turnover processes as obtained by a Bayesian calibration study. We representatively sampled 400 different parameter vectors from the discrete joint parameter distribution comprising approximately 400,000 parameter combinations and used these to calculate 400 individual realizations of the regional inventory. The spatial domain (represented by 4042 polygons) is set up with spatially explicit soil and climate information and a region-typical 3-year crop rotation consisting of winter wheat, rape- seed, and winter barley. Average N2O emission from arable soils in the state of Saxony across all 400 realizations was 1.43 ± 1.25 [kg N / ha] with a median value of 1.05 [kg N / ha]. Using the default IPCC emission factor approach (Tier 1) for direct emissions reveal a higher average N2O emission of 1.51 [kg N / ha] due to fertilizer use. In the regional uncertainty quantification the 20% likelihood range for N2O emissions is 0.79 - 1.37 [kg N / ha] (50% likelihood: 0.46 - 2.05 [kg N / ha]; 90% likelihood: 0.11 - 4.03 [kg N / ha]). Respective quantities were calculated for nitrate leaching. The method has proven its applicability to quantify parameter-induced uncertainty of simulated regional greenhouse gas emission and nitrate leaching inventories using process based biogeochemical models.

Relating Data and Models to Characterize Parameter and Prediction Uncertainty

EPA Science Inventory

Applying PBPK models in risk analysis requires that we realistically assess the uncertainty of relevant model predictions in as quantitative a way as possible. The reality of human variability may add a confusing feature to the overall uncertainty assessment, as uncertainty and v...

Forward and backward uncertainty propagation: an oxidation ditch modelling example.

PubMed

Abusam, A; Keesman, K J; van Straten, G

2003-01-01

In the field of water technology, forward uncertainty propagation is frequently used, whereas backward uncertainty propagation is rarely used. In forward uncertainty analysis, one moves from a given (or assumed) parameter subspace towards the corresponding distribution of the output or objective function. However, in the backward uncertainty propagation, one moves in the reverse direction, from the distribution function towards the parameter subspace. Backward uncertainty propagation, which is a generalisation of parameter estimation error analysis, gives information essential for designing experimental or monitoring programmes, and for tighter bounding of parameter uncertainty intervals. The procedure of carrying out backward uncertainty propagation is illustrated in this technical note by working example for an oxidation ditch wastewater treatment plant. Results obtained have demonstrated that essential information can be achieved by carrying out backward uncertainty propagation analysis.

Sensitivity and Uncertainty Analysis for Streamflow Prediction Using Different Objective Functions and Optimization Algorithms: San Joaquin California

NASA Astrophysics Data System (ADS)

Paul, M.; Negahban-Azar, M.

2017-12-01

The hydrologic models usually need to be calibrated against observed streamflow at the outlet of a particular drainage area through a careful model calibration. However, a large number of parameters are required to fit in the model due to their unavailability of the field measurement. Therefore, it is difficult to calibrate the model for a large number of potential uncertain model parameters. This even becomes more challenging if the model is for a large watershed with multiple land uses and various geophysical characteristics. Sensitivity analysis (SA) can be used as a tool to identify most sensitive model parameters which affect the calibrated model performance. There are many different calibration and uncertainty analysis algorithms which can be performed with different objective functions. By incorporating sensitive parameters in streamflow simulation, effects of the suitable algorithm in improving model performance can be demonstrated by the Soil and Water Assessment Tool (SWAT) modeling. In this study, the SWAT was applied in the San Joaquin Watershed in California covering 19704 km2 to calibrate the daily streamflow. Recently, sever water stress escalating due to intensified climate variability, prolonged drought and depleting groundwater for agricultural irrigation in this watershed. Therefore it is important to perform a proper uncertainty analysis given the uncertainties inherent in hydrologic modeling to predict the spatial and temporal variation of the hydrologic process to evaluate the impacts of different hydrologic variables. The purpose of this study was to evaluate the sensitivity and uncertainty of the calibrated parameters for predicting streamflow. To evaluate the sensitivity of the calibrated parameters three different optimization algorithms (Sequential Uncertainty Fitting- SUFI-2, Generalized Likelihood Uncertainty Estimation- GLUE and Parameter Solution- ParaSol) were used with four different objective functions (coefficient of determination- r2, Nash-Sutcliffe efficiency- NSE, percent bias- PBIAS, and Kling-Gupta efficiency- KGE). The preliminary results showed that using the SUFI-2 algorithm with the objective function NSE and KGE has improved significantly the calibration (e.g. R2 and NSE is found 0.52 and 0.47 respectively for daily streamflow calibration).

Assessment and Reduction of Model Parametric Uncertainties: A Case Study with A Distributed Hydrological Model

NASA Astrophysics Data System (ADS)

Gan, Y.; Liang, X. Z.; Duan, Q.; Xu, J.; Zhao, P.; Hong, Y.

2017-12-01

The uncertainties associated with the parameters of a hydrological model need to be quantified and reduced for it to be useful for operational hydrological forecasting and decision support. An uncertainty quantification framework is presented to facilitate practical assessment and reduction of model parametric uncertainties. A case study, using the distributed hydrological model CREST for daily streamflow simulation during the period 2008-2010 over ten watershed, was used to demonstrate the performance of this new framework. Model behaviors across watersheds were analyzed by a two-stage stepwise sensitivity analysis procedure, using LH-OAT method for screening out insensitive parameters, followed by MARS-based Sobol' sensitivity indices for quantifying each parameter's contribution to the response variance due to its first-order and higher-order effects. Pareto optimal sets of the influential parameters were then found by the adaptive surrogate-based multi-objective optimization procedure, using MARS model for approximating the parameter-response relationship and SCE-UA algorithm for searching the optimal parameter sets of the adaptively updated surrogate model. The final optimal parameter sets were validated against the daily streamflow simulation of the same watersheds during the period 2011-2012. The stepwise sensitivity analysis procedure efficiently reduced the number of parameters that need to be calibrated from twelve to seven, which helps to limit the dimensionality of calibration problem and serves to enhance the efficiency of parameter calibration. The adaptive MARS-based multi-objective calibration exercise provided satisfactory solutions to the reproduction of the observed streamflow for all watersheds. The final optimal solutions showed significant improvement when compared to the default solutions, with about 65-90% reduction in 1-NSE and 60-95% reduction in |RB|. The validation exercise indicated a large improvement in model performance with about 40-85% reduction in 1-NSE, and 35-90% reduction in |RB|. Overall, this uncertainty quantification framework is robust, effective and efficient for parametric uncertainty analysis, the results of which provide useful information that helps to understand the model behaviors and improve the model simulations.

Classifying the Sizes of Explosive Eruptions using Tephra Deposits: The Advantages of a Numerical Inversion Approach

NASA Astrophysics Data System (ADS)

Connor, C.; Connor, L.; White, J.

2015-12-01

Explosive volcanic eruptions are often classified by deposit mass and eruption column height. How well are these eruption parameters determined in older deposits, and how well can we reduce uncertainty using robust numerical and statistical methods? We describe an efficient and effective inversion and uncertainty quantification approach for estimating eruption parameters given a dataset of tephra deposit thickness and granulometry. The inversion and uncertainty quantification is implemented using the open-source PEST++ code. Inversion with PEST++ can be used with a variety of forward models and here is applied using Tephra2, a code that simulates advective and dispersive tephra transport and deposition. The Levenburg-Marquardt algorithm is combined with formal Tikhonov and subspace regularization to invert eruption parameters; a linear equation for conditional uncertainty propagation is used to estimate posterior parameter uncertainty. Both the inversion and uncertainty analysis support simultaneous analysis of the full eruption and wind-field parameterization. The combined inversion/uncertainty-quantification approach is applied to the 1992 eruption of Cerro Negro (Nicaragua), the 2011 Kirishima-Shinmoedake (Japan), and the 1913 Colima (Mexico) eruptions. These examples show that although eruption mass uncertainty is reduced by inversion against tephra isomass data, considerable uncertainty remains for many eruption and wind-field parameters, such as eruption column height. Supplementing the inversion dataset with tephra granulometry data is shown to further reduce the uncertainty of most eruption and wind-field parameters. We think the use of such robust models provides a better understanding of uncertainty in eruption parameters, and hence eruption classification, than is possible with more qualitative methods that are widely used.

Global Sensitivity of Simulated Water Balance Indicators Under Future Climate Change in the Colorado Basin

NASA Astrophysics Data System (ADS)

Bennett, Katrina E.; Urrego Blanco, Jorge R.; Jonko, Alexandra; Bohn, Theodore J.; Atchley, Adam L.; Urban, Nathan M.; Middleton, Richard S.

2018-01-01

The Colorado River Basin is a fundamentally important river for society, ecology, and energy in the United States. Streamflow estimates are often provided using modeling tools which rely on uncertain parameters; sensitivity analysis can help determine which parameters impact model results. Despite the fact that simulated flows respond to changing climate and vegetation in the basin, parameter sensitivity of the simulations under climate change has rarely been considered. In this study, we conduct a global sensitivity analysis to relate changes in runoff, evapotranspiration, snow water equivalent, and soil moisture to model parameters in the Variable Infiltration Capacity (VIC) hydrologic model. We combine global sensitivity analysis with a space-filling Latin Hypercube Sampling of the model parameter space and statistical emulation of the VIC model to examine sensitivities to uncertainties in 46 model parameters following a variance-based approach. We find that snow-dominated regions are much more sensitive to uncertainties in VIC parameters. Although baseflow and runoff changes respond to parameters used in previous sensitivity studies, we discover new key parameter sensitivities. For instance, changes in runoff and evapotranspiration are sensitive to albedo, while changes in snow water equivalent are sensitive to canopy fraction and Leaf Area Index (LAI) in the VIC model. It is critical for improved modeling to narrow uncertainty in these parameters through improved observations and field studies. This is important because LAI and albedo are anticipated to change under future climate and narrowing uncertainty is paramount to advance our application of models such as VIC for water resource management.

Understanding Climate Uncertainty with an Ocean Focus

NASA Astrophysics Data System (ADS)

Tokmakian, R. T.

2009-12-01

Uncertainty in climate simulations arises from various aspects of the end-to-end process of modeling the Earth’s climate. First, there is uncertainty from the structure of the climate model components (e.g. ocean/ice/atmosphere). Even the most complex models are deficient, not only in the complexity of the processes they represent, but in which processes are included in a particular model. Next, uncertainties arise from the inherent error in the initial and boundary conditions of a simulation. Initial conditions are the state of the weather or climate at the beginning of the simulation and other such things, and typically come from observations. Finally, there is the uncertainty associated with the values of parameters in the model. These parameters may represent physical constants or effects, such as ocean mixing, or non-physical aspects of modeling and computation. The uncertainty in these input parameters propagates through the non-linear model to give uncertainty in the outputs. The models in 2020 will no doubt be better than today’s models, but they will still be imperfect, and development of uncertainty analysis technology is a critical aspect of understanding model realism and prediction capability. Smith [2002] and Cox and Stephenson [2007] discuss the need for methods to quantify the uncertainties within complicated systems so that limitations or weaknesses of the climate model can be understood. In making climate predictions, we need to have available both the most reliable model or simulation and a methods to quantify the reliability of a simulation. If quantitative uncertainty questions of the internal model dynamics are to be answered with complex simulations such as AOGCMs, then the only known path forward is based on model ensembles that characterize behavior with alternative parameter settings [e.g. Rougier, 2007]. The relevance and feasibility of using "Statistical Analysis of Computer Code Output" (SACCO) methods for examining uncertainty in ocean circulation due to parameter specification will be described and early results using the ocean/ice components of the CCSM climate model in a designed experiment framework will be shown. Cox, P. and D. Stephenson, Climate Change: A Changing Climate for Prediction, 2007, Science 317 (5835), 207, DOI: 10.1126/science.1145956. Rougier, J. C., 2007: Probabilistic Inference for Future Climate Using an Ensemble of Climate Model Evaluations, Climatic Change, 81, 247-264. Smith L., 2002, What might we learn from climate forecasts? Proc. Nat’l Academy of Sciences, Vol. 99, suppl. 1, 2487-2492 doi:10.1073/pnas.012580599.

Uncertainty in predictions of oil spill trajectories in a coastal zone

NASA Astrophysics Data System (ADS)

Sebastião, P.; Guedes Soares, C.

2006-12-01

A method is introduced to determine the uncertainties in the predictions of oil spill trajectories using a classic oil spill model. The method considers the output of the oil spill model as a function of random variables, which are the input parameters, and calculates the standard deviation of the output results which provides a measure of the uncertainty of the model as a result of the uncertainties of the input parameters. In addition to a single trajectory that is calculated by the oil spill model using the mean values of the parameters, a band of trajectories can be defined when various simulations are done taking into account the uncertainties of the input parameters. This band of trajectories defines envelopes of the trajectories that are likely to be followed by the spill given the uncertainties of the input. The method was applied to an oil spill that occurred in 1989 near Sines in the southwestern coast of Portugal. This model represented well the distinction between a wind driven part that remained offshore, and a tide driven part that went ashore. For both parts, the method defined two trajectory envelopes, one calculated exclusively with the wind fields, and the other using wind and tidal currents. In both cases reasonable approximation to the observed results was obtained. The envelope of likely trajectories that is obtained with the uncertainty modelling proved to give a better interpretation of the trajectories that were simulated by the oil spill model.

Assessing uncertainty and sensitivity of model parameterizations and parameters in WRF affecting simulated surface fluxes and land-atmosphere coupling over the Amazon region

NASA Astrophysics Data System (ADS)

Qian, Y.; Wang, C.; Huang, M.; Berg, L. K.; Duan, Q.; Feng, Z.; Shrivastava, M. B.; Shin, H. H.; Hong, S. Y.

2016-12-01

This study aims to quantify the relative importance and uncertainties of different physical processes and parameters in affecting simulated surface fluxes and land-atmosphere coupling strength over the Amazon region. We used two-legged coupling metrics, which include both terrestrial (soil moisture to surface fluxes) and atmospheric (surface fluxes to atmospheric state or precipitation) legs, to diagnose the land-atmosphere interaction and coupling strength. Observations made using the Department of Energy's Atmospheric Radiation Measurement (ARM) Mobile Facility during the GoAmazon field campaign together with satellite and reanalysis data are used to evaluate model performance. To quantify the uncertainty in physical parameterizations, we performed a 120 member ensemble of simulations with the WRF model using a stratified experimental design including 6 cloud microphysics, 3 convection, 6 PBL and surface layer, and 3 land surface schemes. A multiple-way analysis of variance approach is used to quantitatively analyze the inter- and intra-group (scheme) means and variances. To quantify parameter sensitivity, we conducted an additional 256 WRF simulations in which an efficient sampling algorithm is used to explore the multiple-dimensional parameter space. Three uncertainty quantification approaches are applied for sensitivity analysis (SA) of multiple variables of interest to 20 selected parameters in YSU PBL and MM5 surface layer schemes. Results show consistent parameter sensitivity across different SA methods. We found that 5 out of 20 parameters contribute more than 90% total variance, and first-order effects dominate comparing to the interaction effects. Results of this uncertainty quantification study serve as guidance for better understanding the roles of different physical processes in land-atmosphere interactions, quantifying model uncertainties from various sources such as physical processes, parameters and structural errors, and providing insights for improving the model physics parameterizations.

Automated parameter tuning applied to sea ice in a global climate model

NASA Astrophysics Data System (ADS)

Roach, Lettie A.; Tett, Simon F. B.; Mineter, Michael J.; Yamazaki, Kuniko; Rae, Cameron D.

2018-01-01

This study investigates the hypothesis that a significant portion of spread in climate model projections of sea ice is due to poorly-constrained model parameters. New automated methods for optimization are applied to historical sea ice in a global coupled climate model (HadCM3) in order to calculate the combination of parameters required to reduce the difference between simulation and observations to within the range of model noise. The optimized parameters result in a simulated sea-ice time series which is more consistent with Arctic observations throughout the satellite record (1980-present), particularly in the September minimum, than the standard configuration of HadCM3. Divergence from observed Antarctic trends and mean regional sea ice distribution reflects broader structural uncertainty in the climate model. We also find that the optimized parameters do not cause adverse effects on the model climatology. This simple approach provides evidence for the contribution of parameter uncertainty to spread in sea ice extent trends and could be customized to investigate uncertainties in other climate variables.

WE-D-BRE-07: Variance-Based Sensitivity Analysis to Quantify the Impact of Biological Uncertainties in Particle Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamp, F.; Brueningk, S.C.; Wilkens, J.J.

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g.more » RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data, providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.« less

Uncertainty and the Social Cost of Methane Using Bayesian Constrained Climate Models

NASA Astrophysics Data System (ADS)

Errickson, F. C.; Anthoff, D.; Keller, K.

2016-12-01

Social cost estimates of greenhouse gases are important for the design of sound climate policies and are also plagued by uncertainty. One major source of uncertainty stems from the simplified representation of the climate system used in the integrated assessment models that provide these social cost estimates. We explore how uncertainty over the social cost of methane varies with the way physical processes and feedbacks in the methane cycle are modeled by (i) coupling three different methane models to a simple climate model, (ii) using MCMC to perform a Bayesian calibration of the three coupled climate models that simulates direct sampling from the joint posterior probability density function (pdf) of model parameters, and (iii) producing probabilistic climate projections that are then used to calculate the Social Cost of Methane (SCM) with the DICE and FUND integrated assessment models. We find that including a temperature feedback in the methane cycle acts as an additional constraint during the calibration process and results in a correlation between the tropospheric lifetime of methane and several climate model parameters. This correlation is not seen in the models lacking this feedback. Several of the estimated marginal pdfs of the model parameters also exhibit different distributional shapes and expected values depending on the methane model used. As a result, probabilistic projections of the climate system out to the year 2300 exhibit different levels of uncertainty and magnitudes of warming for each of the three models under an RCP8.5 scenario. We find these differences in climate projections result in differences in the distributions and expected values for our estimates of the SCM. We also examine uncertainty about the SCM by performing a Monte Carlo analysis using a distribution for the climate sensitivity while holding all other climate model parameters constant. Our SCM estimates using the Bayesian calibration are lower and exhibit less uncertainty about extremely high values in the right tail of the distribution compared to the Monte Carlo approach. This finding has important climate policy implications and suggests previous work that accounts for climate model uncertainty by only varying the climate sensitivity parameter may overestimate the SCM.

An NTCP Analysis of Urethral Complications from Low Doserate Mono- and Bi-Radionuclide Brachytherapy.

PubMed

Nuttens, V E; Nahum, A E; Lucas, S

2011-01-01

Urethral NTCP has been determined for three prostates implanted with seeds based on (125)I (145 Gy), (103)Pd (125 Gy), (131)Cs (115 Gy), (103)Pd-(125)I (145 Gy), or (103)Pd-(131)Cs (115 Gy or 130 Gy). First, DU(20), meaning that 20% of the urhral volume receive a dose of at least DU(20), is converted into an I-125 LDR equivalent DU(20) in order to use the urethral NTCP model. Second, the propagation of uncertainties through the steps in the NTCP calculation was assessed in order to identify the parameters responsible for large data uncertainties. Two sets of radiobiological parameters were studied. The NTCP results all fall in the 19%-23% range and are associated with large uncertainties, making the comparison difficult. Depending on the dataset chosen, the ranking of NTCP values among the six seed implants studied changes. Moreover, the large uncertainties on the fitting parameters of the urethral NTCP model result in large uncertainty on the NTCP value. In conclusion, the use of NTCP model for permanent brachytherapy is feasible but it is essential that the uncertainties on the parameters in the model be reduced.

Evaluation of habitat suitability index models by global sensitivity and uncertainty analyses: a case study for submerged aquatic vegetation

USGS Publications Warehouse

Zajac, Zuzanna; Stith, Bradley M.; Bowling, Andrea C.; Langtimm, Catherine A.; Swain, Eric D.

2015-01-01

Habitat suitability index (HSI) models are commonly used to predict habitat quality and species distributions and are used to develop biological surveys, assess reserve and management priorities, and anticipate possible change under different management or climate change scenarios. Important management decisions may be based on model results, often without a clear understanding of the level of uncertainty associated with model outputs. We present an integrated methodology to assess the propagation of uncertainty from both inputs and structure of the HSI models on model outputs (uncertainty analysis: UA) and relative importance of uncertain model inputs and their interactions on the model output uncertainty (global sensitivity analysis: GSA). We illustrate the GSA/UA framework using simulated hydrology input data from a hydrodynamic model representing sea level changes and HSI models for two species of submerged aquatic vegetation (SAV) in southwest Everglades National Park: Vallisneria americana (tape grass) and Halodule wrightii (shoal grass). We found considerable spatial variation in uncertainty for both species, but distributions of HSI scores still allowed discrimination of sites with good versus poor conditions. Ranking of input parameter sensitivities also varied spatially for both species, with high habitat quality sites showing higher sensitivity to different parameters than low-quality sites. HSI models may be especially useful when species distribution data are unavailable, providing means of exploiting widely available environmental datasets to model past, current, and future habitat conditions. The GSA/UA approach provides a general method for better understanding HSI model dynamics, the spatial and temporal variation in uncertainties, and the parameters that contribute most to model uncertainty. Including an uncertainty and sensitivity analysis in modeling efforts as part of the decision-making framework will result in better-informed, more robust decisions.

Accounting for methodological, structural, and parameter uncertainty in decision-analytic models: a practical guide.

PubMed

Bilcke, Joke; Beutels, Philippe; Brisson, Marc; Jit, Mark

2011-01-01

Accounting for uncertainty is now a standard part of decision-analytic modeling and is recommended by many health technology agencies and published guidelines. However, the scope of such analyses is often limited, even though techniques have been developed for presenting the effects of methodological, structural, and parameter uncertainty on model results. To help bring these techniques into mainstream use, the authors present a step-by-step guide that offers an integrated approach to account for different kinds of uncertainty in the same model, along with a checklist for assessing the way in which uncertainty has been incorporated. The guide also addresses special situations such as when a source of uncertainty is difficult to parameterize, resources are limited for an ideal exploration of uncertainty, or evidence to inform the model is not available or not reliable. for identifying the sources of uncertainty that influence results most are also described. Besides guiding analysts, the guide and checklist may be useful to decision makers who need to assess how well uncertainty has been accounted for in a decision-analytic model before using the results to make a decision.

Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation

NASA Astrophysics Data System (ADS)

Debusschere, Bert J.; Najm, Habib N.; Matta, Alain; Knio, Omar M.; Ghanem, Roger G.; Le Maître, Olivier P.

2003-08-01

This paper presents a model for two-dimensional electrochemical microchannel flow including the propagation of uncertainty from model parameters to the simulation results. For a detailed representation of electroosmotic and pressure-driven microchannel flow, the model considers the coupled momentum, species transport, and electrostatic field equations, including variable zeta potential. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. Uncertainty from the model parameters and boundary conditions is propagated to the model predictions using a pseudo-spectral stochastic formulation with polynomial chaos (PC) representations for parameters and field quantities. Using a Galerkin approach, the governing equations are reformulated into equations for the coefficients in the PC expansion. The implementation of the physical model with the stochastic uncertainty propagation is applied to protein-labeling in a homogeneous buffer, as well as in two-dimensional electrochemical microchannel flow. The results for the two-dimensional channel show strong distortion of sample profiles due to ion movement and consequent buffer disturbances. The uncertainty in these results is dominated by the uncertainty in the applied voltage across the channel.

Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters

PubMed Central

Liu, Fei; Heiner, Monika; Yang, Ming

2016-01-01

Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information. PMID:26910830

Dealing with uncertainty in landscape genetic resistance models: a case of three co-occurring marsupials.

PubMed

Dudaniec, Rachael Y; Worthington Wilmer, Jessica; Hanson, Jeffrey O; Warren, Matthew; Bell, Sarah; Rhodes, Jonathan R

2016-01-01

Landscape genetics lacks explicit methods for dealing with the uncertainty in landscape resistance estimation, which is particularly problematic when sample sizes of individuals are small. Unless uncertainty can be quantified, valuable but small data sets may be rendered unusable for conservation purposes. We offer a method to quantify uncertainty in landscape resistance estimates using multimodel inference as an improvement over single model-based inference. We illustrate the approach empirically using co-occurring, woodland-preferring Australian marsupials within a common study area: two arboreal gliders (Petaurus breviceps, and Petaurus norfolcensis) and one ground-dwelling antechinus (Antechinus flavipes). First, we use maximum-likelihood and a bootstrap procedure to identify the best-supported isolation-by-resistance model out of 56 models defined by linear and non-linear resistance functions. We then quantify uncertainty in resistance estimates by examining parameter selection probabilities from the bootstrapped data. The selection probabilities provide estimates of uncertainty in the parameters that drive the relationships between landscape features and resistance. We then validate our method for quantifying uncertainty using simulated genetic and landscape data showing that for most parameter combinations it provides sensible estimates of uncertainty. We conclude that small data sets can be informative in landscape genetic analyses provided uncertainty can be explicitly quantified. Being explicit about uncertainty in landscape genetic models will make results more interpretable and useful for conservation decision-making, where dealing with uncertainty is critical. © 2015 John Wiley & Sons Ltd.

Uncertainty based modeling of rainfall-runoff: Combined differential evolution adaptive Metropolis (DREAM) and K-means clustering

NASA Astrophysics Data System (ADS)

Zahmatkesh, Zahra; Karamouz, Mohammad; Nazif, Sara

2015-09-01

Simulation of rainfall-runoff process in urban areas is of great importance considering the consequences and damages of extreme runoff events and floods. The first issue in flood hazard analysis is rainfall simulation. Large scale climate signals have been proved to be effective in rainfall simulation and prediction. In this study, an integrated scheme is developed for rainfall-runoff modeling considering different sources of uncertainty. This scheme includes three main steps of rainfall forecasting, rainfall-runoff simulation and future runoff prediction. In the first step, data driven models are developed and used to forecast rainfall using large scale climate signals as rainfall predictors. Due to high effect of different sources of uncertainty on the output of hydrologic models, in the second step uncertainty associated with input data, model parameters and model structure is incorporated in rainfall-runoff modeling and simulation. Three rainfall-runoff simulation models are developed for consideration of model conceptual (structural) uncertainty in real time runoff forecasting. To analyze the uncertainty of the model structure, streamflows generated by alternative rainfall-runoff models are combined, through developing a weighting method based on K-means clustering. Model parameters and input uncertainty are investigated using an adaptive Markov Chain Monte Carlo method. Finally, calibrated rainfall-runoff models are driven using the forecasted rainfall to predict future runoff for the watershed. The proposed scheme is employed in the case study of the Bronx River watershed, New York City. Results of uncertainty analysis of rainfall-runoff modeling reveal that simultaneous estimation of model parameters and input uncertainty significantly changes the probability distribution of the model parameters. It is also observed that by combining the outputs of the hydrological models using the proposed clustering scheme, the accuracy of runoff simulation in the watershed is remarkably improved up to 50% in comparison to the simulations by the individual models. Results indicate that the developed methodology not only provides reliable tools for rainfall and runoff modeling, but also adequate time for incorporating required mitigation measures in dealing with potentially extreme runoff events and flood hazard. Results of this study can be used in identification of the main factors affecting flood hazard analysis.

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions.

PubMed

Vernon, Ian; Liu, Junli; Goldstein, Michael; Rowe, James; Topping, Jen; Lindsey, Keith

2018-01-02

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology. Bayesian statistical methodology for the uncertainty analysis of complex models is introduced, which is designed to address the high dimensional global parameter search problem. Bayesian emulators that mimic the systems biology model but which are extremely fast to evaluate are embeded within an iterative history match: an efficient method to search high dimensional spaces within a more formal statistical setting, while incorporating major sources of uncertainty. The approach is demonstrated via application to a model of hormonal crosstalk in Arabidopsis root development, which has 32 rate parameters, for which we identify the sets of rate parameter values that lead to acceptable matches between model output and observed trend data. The multiple insights into the model's structure that this analysis provides are discussed. The methodology is applied to a second related model, and the biological consequences of the resulting comparison, including the evaluation of gene functions, are described. Bayesian uncertainty analysis for complex models using both emulators and history matching is shown to be a powerful technique that can greatly aid the study of a large class of systems biology models. It both provides insight into model behaviour and identifies the sets of rate parameters of interest.

A model-averaging method for assessing groundwater conceptual model uncertainty.

PubMed

Ye, Ming; Pohlmann, Karl F; Chapman, Jenny B; Pohll, Greg M; Reeves, Donald M

2010-01-01

This study evaluates alternative groundwater models with different recharge and geologic components at the northern Yucca Flat area of the Death Valley Regional Flow System (DVRFS), USA. Recharge over the DVRFS has been estimated using five methods, and five geological interpretations are available at the northern Yucca Flat area. Combining the recharge and geological components together with additional modeling components that represent other hydrogeological conditions yields a total of 25 groundwater flow models. As all the models are plausible given available data and information, evaluating model uncertainty becomes inevitable. On the other hand, hydraulic parameters (e.g., hydraulic conductivity) are uncertain in each model, giving rise to parametric uncertainty. Propagation of the uncertainty in the models and model parameters through groundwater modeling causes predictive uncertainty in model predictions (e.g., hydraulic head and flow). Parametric uncertainty within each model is assessed using Monte Carlo simulation, and model uncertainty is evaluated using the model averaging method. Two model-averaging techniques (on the basis of information criteria and GLUE) are discussed. This study shows that contribution of model uncertainty to predictive uncertainty is significantly larger than that of parametric uncertainty. For the recharge and geological components, uncertainty in the geological interpretations has more significant effect on model predictions than uncertainty in the recharge estimates. In addition, weighted residuals vary more for the different geological models than for different recharge models. Most of the calibrated observations are not important for discriminating between the alternative models, because their weighted residuals vary only slightly from one model to another.

Chasing Perfection: Should We Reduce Model Uncertainty in Carbon Cycle-Climate Feedbacks

NASA Astrophysics Data System (ADS)

Bonan, G. B.; Lombardozzi, D.; Wieder, W. R.; Lindsay, K. T.; Thomas, R. Q.

2015-12-01

Earth system model simulations of the terrestrial carbon (C) cycle show large multi-model spread in the carbon-concentration and carbon-climate feedback parameters. Large differences among models are also seen in their simulation of global vegetation and soil C stocks and other aspects of the C cycle, prompting concern about model uncertainty and our ability to faithfully represent fundamental aspects of the terrestrial C cycle in Earth system models. Benchmarking analyses that compare model simulations with common datasets have been proposed as a means to assess model fidelity with observations, and various model-data fusion techniques have been used to reduce model biases. While such efforts will reduce multi-model spread, they may not help reduce uncertainty (and increase confidence) in projections of the C cycle over the twenty-first century. Many ecological and biogeochemical processes represented in Earth system models are poorly understood at both the site scale and across large regions, where biotic and edaphic heterogeneity are important. Our experience with the Community Land Model (CLM) suggests that large uncertainty in the terrestrial C cycle and its feedback with climate change is an inherent property of biological systems. The challenge of representing life in Earth system models, with the rich diversity of lifeforms and complexity of biological systems, may necessitate a multitude of modeling approaches to capture the range of possible outcomes. Such models should encompass a range of plausible model structures. We distinguish between model parameter uncertainty and model structural uncertainty. Focusing on improved parameter estimates may, in fact, limit progress in assessing model structural uncertainty associated with realistically representing biological processes. Moreover, higher confidence may be achieved through better process representation, but this does not necessarily reduce uncertainty.

Use of Bayesian Inference in Crystallographic Structure Refinement via Full Diffraction Profile Analysis

PubMed Central

Fancher, Chris M.; Han, Zhen; Levin, Igor; Page, Katharine; Reich, Brian J.; Smith, Ralph C.; Wilson, Alyson G.; Jones, Jacob L.

2016-01-01

A Bayesian inference method for refining crystallographic structures is presented. The distribution of model parameters is stochastically sampled using Markov chain Monte Carlo. Posterior probability distributions are constructed for all model parameters to properly quantify uncertainty by appropriately modeling the heteroskedasticity and correlation of the error structure. The proposed method is demonstrated by analyzing a National Institute of Standards and Technology silicon standard reference material. The results obtained by Bayesian inference are compared with those determined by Rietveld refinement. Posterior probability distributions of model parameters provide both estimates and uncertainties. The new method better estimates the true uncertainties in the model as compared to the Rietveld method. PMID:27550221

Application of Bayesian Maximum Entropy Filter in parameter calibration of groundwater flow model in PingTung Plain

NASA Astrophysics Data System (ADS)

Cheung, Shao-Yong; Lee, Chieh-Han; Yu, Hwa-Lung

2017-04-01

Due to the limited hydrogeological observation data and high levels of uncertainty within, parameter estimation of the groundwater model has been an important issue. There are many methods of parameter estimation, for example, Kalman filter provides a real-time calibration of parameters through measurement of groundwater monitoring wells, related methods such as Extended Kalman Filter and Ensemble Kalman Filter are widely applied in groundwater research. However, Kalman Filter method is limited to linearity. This study propose a novel method, Bayesian Maximum Entropy Filtering, which provides a method that can considers the uncertainty of data in parameter estimation. With this two methods, we can estimate parameter by given hard data (certain) and soft data (uncertain) in the same time. In this study, we use Python and QGIS in groundwater model (MODFLOW) and development of Extended Kalman Filter and Bayesian Maximum Entropy Filtering in Python in parameter estimation. This method may provide a conventional filtering method and also consider the uncertainty of data. This study was conducted through numerical model experiment to explore, combine Bayesian maximum entropy filter and a hypothesis for the architecture of MODFLOW groundwater model numerical estimation. Through the virtual observation wells to simulate and observe the groundwater model periodically. The result showed that considering the uncertainty of data, the Bayesian maximum entropy filter will provide an ideal result of real-time parameters estimation.

A Monte Carlo Uncertainty Analysis of Ozone Trend Predictions in a Two Dimensional Model. Revision

NASA Technical Reports Server (NTRS)

Considine, D. B.; Stolarski, R. S.; Hollandsworth, S. M.; Jackman, C. H.; Fleming, E. L.

1998-01-01

We use Monte Carlo analysis to estimate the uncertainty in predictions of total O3 trends between 1979 and 1995 made by the Goddard Space Flight Center (GSFC) two-dimensional (2D) model of stratospheric photochemistry and dynamics. The uncertainty is caused by gas-phase chemical reaction rates, photolysis coefficients, and heterogeneous reaction parameters which are model inputs. The uncertainty represents a lower bound to the total model uncertainty assuming the input parameter uncertainties are characterized correctly. Each of the Monte Carlo runs was initialized in 1970 and integrated for 26 model years through the end of 1995. This was repeated 419 times using input parameter sets generated by Latin Hypercube Sampling. The standard deviation (a) of the Monte Carlo ensemble of total 03 trend predictions is used to quantify the model uncertainty. The 34% difference between the model trend in globally and annually averaged total O3 using nominal inputs and atmospheric trends calculated from Nimbus 7 and Meteor 3 total ozone mapping spectrometer (TOMS) version 7 data is less than the 46% calculated 1 (sigma), model uncertainty, so there is no significant difference between the modeled and observed trends. In the northern hemisphere midlatitude spring the modeled and observed total 03 trends differ by more than 1(sigma) but less than 2(sigma), which we refer to as marginal significance. We perform a multiple linear regression analysis of the runs which suggests that only a few of the model reactions contribute significantly to the variance in the model predictions. The lack of significance in these comparisons suggests that they are of questionable use as guides for continuing model development. Large model/measurement differences which are many multiples of the input parameter uncertainty are seen in the meridional gradients of the trend and the peak-to-peak variations in the trends over an annual cycle. These discrepancies unambiguously indicate model formulation problems and provide a measure of model performance which can be used in attempts to improve such models.

A New Formulation of the Filter-Error Method for Aerodynamic Parameter Estimation in Turbulence

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2015-01-01

A new formulation of the filter-error method for estimating aerodynamic parameters in nonlinear aircraft dynamic models during turbulence was developed and demonstrated. The approach uses an estimate of the measurement noise covariance to identify the model parameters, their uncertainties, and the process noise covariance, in a relaxation method analogous to the output-error method. Prior information on the model parameters and uncertainties can be supplied, and a post-estimation correction to the uncertainty was included to account for colored residuals not considered in the theory. No tuning parameters, needing adjustment by the analyst, are used in the estimation. The method was demonstrated in simulation using the NASA Generic Transport Model, then applied to the subscale T-2 jet-engine transport aircraft flight. Modeling results in different levels of turbulence were compared with results from time-domain output error and frequency- domain equation error methods to demonstrate the effectiveness of the approach.

Uncertainty characterization and quantification in air pollution models. Application to the ADMS-Urban model.

NASA Astrophysics Data System (ADS)

Debry, E.; Malherbe, L.; Schillinger, C.; Bessagnet, B.; Rouil, L.

2009-04-01

Evaluation of human exposure to atmospheric pollution usually requires the knowledge of pollutants concentrations in ambient air. In the framework of PAISA project, which studies the influence of socio-economical status on relationships between air pollution and short term health effects, the concentrations of gas and particle pollutants are computed over Strasbourg with the ADMS-Urban model. As for any modeling result, simulated concentrations come with uncertainties which have to be characterized and quantified. There are several sources of uncertainties related to input data and parameters, i.e. fields used to execute the model like meteorological fields, boundary conditions and emissions, related to the model formulation because of incomplete or inaccurate treatment of dynamical and chemical processes, and inherent to the stochastic behavior of atmosphere and human activities [1]. Our aim is here to assess the uncertainties of the simulated concentrations with respect to input data and model parameters. In this scope the first step consisted in bringing out the input data and model parameters that contribute most effectively to space and time variability of predicted concentrations. Concentrations of several pollutants were simulated for two months in winter 2004 and two months in summer 2004 over five areas of Strasbourg. The sensitivity analysis shows the dominating influence of boundary conditions and emissions. Among model parameters, the roughness and Monin-Obukhov lengths appear to have non neglectable local effects. Dry deposition is also an important dynamic process. The second step of the characterization and quantification of uncertainties consists in attributing a probability distribution to each input data and model parameter and in propagating the joint distribution of all data and parameters into the model so as to associate a probability distribution to the modeled concentrations. Several analytical and numerical methods exist to perform an uncertainty analysis. We chose the Monte Carlo method which has already been applied to atmospheric dispersion models [2, 3, 4]. The main advantage of this method is to be insensitive to the number of perturbed parameters but its drawbacks are its computation cost and its slow convergence. In order to speed up this one we used the method of antithetic variable which takes adavantage of the symmetry of probability laws. The air quality model simulations were carried out by the Association for study and watching of Atmospheric Pollution in Alsace (ASPA). The output concentrations distributions can then be updated with a Bayesian method. This work is part of an INERIS Research project also aiming at assessing the uncertainty of the CHIMERE dispersion model used in the Prev'Air forecasting platform (www.prevair.org) in order to deliver more accurate predictions. (1) Rao, K.S. Uncertainty Analysis in Atmospheric Dispersion Modeling, Pure and Applied Geophysics, 2005, 162, 1893-1917. (2) Beekmann, M. and Derognat, C. Monte Carlo uncertainty analysis of a regional-scale transport chemistry model constrained by measurements from the Atmospheric Pollution Over the PAris Area (ESQUIF) campaign, Journal of Geophysical Research, 2003, 108, 8559-8576. (3) Hanna, S.R. and Lu, Z. and Frey, H.C. and Wheeler, N. and Vukovich, J. and Arunachalam, S. and Fernau, M. and Hansen, D.A. Uncertainties in predicted ozone concentrations due to input uncertainties for the UAM-V photochemical grid model applied to the July 1995 OTAG domain, Atmospheric Environment, 2001, 35, 891-903. (4) Romanowicz, R. and Higson, H. and Teasdale, I. Bayesian uncertainty estimation methodology applied to air pollution modelling, Environmetrics, 2000, 11, 351-371.

Partitioning the Uncertainty in Estimates of Mean Basal Area Obtained from 10-year Diameter Growth Model Predictions

Treesearch

Ronald E. McRoberts

2005-01-01

Uncertainty in model-based predictions of individual tree diameter growth is attributed to three sources: measurement error for predictor variables, residual variability around model predictions, and uncertainty in model parameter estimates. Monte Carlo simulations are used to propagate the uncertainty from the three sources through a set of diameter growth models to...

Impact of state updating and multi-parametric ensemble for streamflow hindcasting in European river basins

NASA Astrophysics Data System (ADS)

Noh, S. J.; Rakovec, O.; Kumar, R.; Samaniego, L. E.

2015-12-01

Accurate and reliable streamflow prediction is essential to mitigate social and economic damage coming from water-related disasters such as flood and drought. Sequential data assimilation (DA) may facilitate improved streamflow prediction using real-time observations to correct internal model states. In conventional DA methods such as state updating, parametric uncertainty is often ignored mainly due to practical limitations of methodology to specify modeling uncertainty with limited ensemble members. However, if parametric uncertainty related with routing and runoff components is not incorporated properly, predictive uncertainty by model ensemble may be insufficient to capture dynamics of observations, which may deteriorate predictability. Recently, a multi-scale parameter regionalization (MPR) method was proposed to make hydrologic predictions at different scales using a same set of model parameters without losing much of the model performance. The MPR method incorporated within the mesoscale hydrologic model (mHM, http://www.ufz.de/mhm) could effectively represent and control uncertainty of high-dimensional parameters in a distributed model using global parameters. In this study, we evaluate impacts of streamflow data assimilation over European river basins. Especially, a multi-parametric ensemble approach is tested to consider the effects of parametric uncertainty in DA. Because augmentation of parameters is not required within an assimilation window, the approach could be more stable with limited ensemble members and have potential for operational uses. To consider the response times and non-Gaussian characteristics of internal hydrologic processes, lagged particle filtering is utilized. The presentation will be focused on gains and limitations of streamflow data assimilation and multi-parametric ensemble method over large-scale basins.

Aeroservoelastic Uncertainty Model Identification from Flight Data

NASA Technical Reports Server (NTRS)

Brenner, Martin J.

2001-01-01

Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust flight control system development. There has been a serious deficiency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from flight data using both parametric and nonparametric identification techniques. The model validation problem addressed in this paper is to identify aeroservoelastic models with associated uncertainty structures from a limited amount of controlled excitation inputs over an extensive flight envelope. The challenge to this problem is to update analytical models from flight data estimates while also deriving non-conservative uncertainty descriptions consistent with the flight data. Multisine control surface command inputs and control system feedbacks are used as signals in a wavelet-based modal parameter estimation procedure for model updates. Transfer function estimates are incorporated in a robust minimax estimation scheme to get input-output parameters and error bounds consistent with the data and model structure. Uncertainty estimates derived from the data in this manner provide an appropriate and relevant representation for model development and robust stability analysis. This model-plus-uncertainty identification procedure is applied to aeroservoelastic flight data from the NASA Dryden Flight Research Center F-18 Systems Research Aircraft.

Parameter optimization of a hydrologic model in a snow-dominated basin using a modular Python framework

NASA Astrophysics Data System (ADS)

Volk, J. M.; Turner, M. A.; Huntington, J. L.; Gardner, M.; Tyler, S.; Sheneman, L.

2016-12-01

Many distributed models that simulate watershed hydrologic processes require a collection of multi-dimensional parameters as input, some of which need to be calibrated before the model can be applied. The Precipitation Runoff Modeling System (PRMS) is a physically-based and spatially distributed hydrologic model that contains a considerable number of parameters that often need to be calibrated. Modelers can also benefit from uncertainty analysis of these parameters. To meet these needs, we developed a modular framework in Python to conduct PRMS parameter optimization, uncertainty analysis, interactive visual inspection of parameters and outputs, and other common modeling tasks. Here we present results for multi-step calibration of sensitive parameters controlling solar radiation, potential evapo-transpiration, and streamflow in a PRMS model that we applied to the snow-dominated Dry Creek watershed in Idaho. We also demonstrate how our modular approach enables the user to use a variety of parameter optimization and uncertainty methods or easily define their own, such as Monte Carlo random sampling, uniform sampling, or even optimization methods such as the downhill simplex method or its commonly used, more robust counterpart, shuffled complex evolution.

User Guidelines and Best Practices for CASL VUQ Analysis Using Dakota

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, Brian M.; Coleman, Kayla; Gilkey, Lindsay N.

Sandia’s Dakota software (available at http://dakota.sandia.gov) supports science and engineering transformation through advanced exploration of simulations. Specifically it manages and analyzes ensembles of simulations to provide broader and deeper perspective for analysts and decision makers. This enables them to enhance understanding of risk, improve products, and assess simulation credibility. In its simplest mode, Dakota can automate typical parameter variation studies through a generic interface to a physics-based computational model. This can lend efficiency and rigor to manual parameter perturbation studies already being conducted by analysts. However, Dakota also delivers advanced parametric analysis techniques enabling design exploration, optimization, model calibration, riskmore » analysis, and quantification of margins and uncertainty with such models. It directly supports verification and validation activities. Dakota algorithms enrich complex science and engineering models, enabling an analyst to answer crucial questions of - Sensitivity: Which are the most important input factors or parameters entering the simulation, and how do they influence key outputs?; Uncertainty: What is the uncertainty or variability in simulation output, given uncertainties in input parameters? How safe, reliable, robust, or variable is my system? (Quantification of margins and uncertainty, QMU); Optimization: What parameter values yield the best performing design or operating condition, given constraints? Calibration: What models and/or parameters best match experimental data? In general, Dakota is the Consortium for Advanced Simulation of Light Water Reactors (CASL) delivery vehicle for verification, validation, and uncertainty quantification (VUQ) algorithms. It permits ready application of the VUQ methods described above to simulation codes by CASL researchers, code developers, and application engineers.« less

Bayesian calibration of mechanistic aquatic biogeochemical models and benefits for environmental management

NASA Astrophysics Data System (ADS)

Arhonditsis, George B.; Papantou, Dimitra; Zhang, Weitao; Perhar, Gurbir; Massos, Evangelia; Shi, Molu

2008-09-01

Aquatic biogeochemical models have been an indispensable tool for addressing pressing environmental issues, e.g., understanding oceanic response to climate change, elucidation of the interplay between plankton dynamics and atmospheric CO 2 levels, and examination of alternative management schemes for eutrophication control. Their ability to form the scientific basis for environmental management decisions can be undermined by the underlying structural and parametric uncertainty. In this study, we outline how we can attain realistic predictive links between management actions and ecosystem response through a probabilistic framework that accommodates rigorous uncertainty analysis of a variety of error sources, i.e., measurement error, parameter uncertainty, discrepancy between model and natural system. Because model uncertainty analysis essentially aims to quantify the joint probability distribution of model parameters and to make inference about this distribution, we believe that the iterative nature of Bayes' Theorem is a logical means to incorporate existing knowledge and update the joint distribution as new information becomes available. The statistical methodology begins with the characterization of parameter uncertainty in the form of probability distributions, then water quality data are used to update the distributions, and yield posterior parameter estimates along with predictive uncertainty bounds. Our illustration is based on a six state variable (nitrate, ammonium, dissolved organic nitrogen, phytoplankton, zooplankton, and bacteria) ecological model developed for gaining insight into the mechanisms that drive plankton dynamics in a coastal embayment; the Gulf of Gera, Island of Lesvos, Greece. The lack of analytical expressions for the posterior parameter distributions was overcome using Markov chain Monte Carlo simulations; a convenient way to obtain representative samples of parameter values. The Bayesian calibration resulted in realistic reproduction of the key temporal patterns of the system, offered insights into the degree of information the data contain about model inputs, and also allowed the quantification of the dependence structure among the parameter estimates. Finally, our study uses two synthetic datasets to examine the ability of the updated model to provide estimates of predictive uncertainty for water quality variables of environmental management interest.

Buy now, saved later? The critical impact of time-to-pandemic uncertainty on pandemic cost-effectiveness analyses.

PubMed

Drake, Tom; Chalabi, Zaid; Coker, Richard

2015-02-01

Investment in pandemic preparedness is a long-term gamble, with the return on investment coming at an unknown point in the future. Many countries have chosen to stockpile key resources, and the number of pandemic economic evaluations has risen sharply since 2009. We assess the importance of uncertainty in time-to-pandemic (and associated discounting) in pandemic economic evaluation, a factor frequently neglected in the literature to-date. We use a probability tree model and Monte Carlo parameter sampling to consider the cost effectiveness of antiviral stockpiling in Cambodia under parameter uncertainty. Mean elasticity and mutual information (MI) are used to assess the importance of time-to-pandemic compared with other parameters. We also consider the sensitivity to choice of sampling distribution used to model time-to-pandemic uncertainty. Time-to-pandemic and discount rate are the primary drivers of sensitivity and uncertainty in pandemic cost effectiveness models. Base case cost effectiveness of antiviral stockpiling ranged between is US$112 and US$3599 per DALY averted using historical pandemic intervals for time-to-pandemic. The mean elasticities for time-to-pandemic and discount rate were greater than all other parameters. Similarly, the MI scores for time to pandemic and discount rate were greater than other parameters. Time-to-pandemic and discount rate were key drivers of uncertainty in cost-effectiveness results regardless of time-to-pandemic sampling distribution choice. Time-to-pandemic assumptions can "substantially" affect cost-effectiveness results and, in our model, is a greater contributor to uncertainty in cost-effectiveness results than any other parameter. We strongly recommend that cost-effectiveness models include probabilistic analysis of time-to-pandemic uncertainty. Published by Oxford University Press in association with The London School of Hygiene and Tropical Medicine © The Author 2013; all rights reserved.

A parallel calibration utility for WRF-Hydro on high performance computers

NASA Astrophysics Data System (ADS)

Wang, J.; Wang, C.; Kotamarthi, V. R.

2017-12-01

A successful modeling of complex hydrological processes comprises establishing an integrated hydrological model which simulates the hydrological processes in each water regime, calibrates and validates the model performance based on observation data, and estimates the uncertainties from different sources especially those associated with parameters. Such a model system requires large computing resources and often have to be run on High Performance Computers (HPC). The recently developed WRF-Hydro modeling system provides a significant advancement in the capability to simulate regional water cycles more completely. The WRF-Hydro model has a large range of parameters such as those in the input table files — GENPARM.TBL, SOILPARM.TBL and CHANPARM.TBL — and several distributed scaling factors such as OVROUGHRTFAC. These parameters affect the behavior and outputs of the model and thus may need to be calibrated against the observations in order to obtain a good modeling performance. Having a parameter calibration tool specifically for automate calibration and uncertainty estimates of WRF-Hydro model can provide significant convenience for the modeling community. In this study, we developed a customized tool using the parallel version of the model-independent parameter estimation and uncertainty analysis tool, PEST, to enabled it to run on HPC with PBS and SLURM workload manager and job scheduler. We also developed a series of PEST input file templates that are specifically for WRF-Hydro model calibration and uncertainty analysis. Here we will present a flood case study occurred in April 2013 over Midwest. The sensitivity and uncertainties are analyzed using the customized PEST tool we developed.

Improving Forecasts Through Realistic Uncertainty Estimates: A Novel Data Driven Method for Model Uncertainty Quantification in Data Assimilation

NASA Astrophysics Data System (ADS)

Pathiraja, S. D.; Moradkhani, H.; Marshall, L. A.; Sharma, A.; Geenens, G.

2016-12-01

Effective combination of model simulations and observations through Data Assimilation (DA) depends heavily on uncertainty characterisation. Many traditional methods for quantifying model uncertainty in DA require some level of subjectivity (by way of tuning parameters or by assuming Gaussian statistics). Furthermore, the focus is typically on only estimating the first and second moments. We propose a data-driven methodology to estimate the full distributional form of model uncertainty, i.e. the transition density p(xt|xt-1). All sources of uncertainty associated with the model simulations are considered collectively, without needing to devise stochastic perturbations for individual components (such as model input, parameter and structural uncertainty). A training period is used to derive the distribution of errors in observed variables conditioned on hidden states. Errors in hidden states are estimated from the conditional distribution of observed variables using non-linear optimization. The theory behind the framework and case study applications are discussed in detail. Results demonstrate improved predictions and more realistic uncertainty bounds compared to a standard perturbation approach.

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties.

PubMed

Hoffmann, Anna; Scherrer, Alexander; Küfer, Karl-Heinz

2015-01-01

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model. Copyright © 2014 Elsevier Inc. All rights reserved.

Numerical Simulation and Quantitative Uncertainty Assessment of Microchannel Flow

NASA Astrophysics Data System (ADS)

Debusschere, Bert; Najm, Habib; Knio, Omar; Matta, Alain; Ghanem, Roger; Le Maitre, Olivier

2002-11-01

This study investigates the effect of uncertainty in physical model parameters on computed electrokinetic flow of proteins in a microchannel with a potassium phosphate buffer. The coupled momentum, species transport, and electrostatic field equations give a detailed representation of electroosmotic and pressure-driven flow, including sample dispersion mechanisms. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. To quantify uncertainty, the governing equations are reformulated using a pseudo-spectral stochastic methodology, which uses polynomial chaos expansions to describe uncertain/stochastic model parameters, boundary conditions, and flow quantities. Integration of the resulting equations for the spectral mode strengths gives the evolution of all stochastic modes for all variables. Results show the spatiotemporal evolution of uncertainties in predicted quantities and highlight the dominant parameters contributing to these uncertainties during various flow phases. This work is supported by DARPA.

Probabilistic accounting of uncertainty in forecasts of species distributions under climate change

USGS Publications Warehouse

Wenger, Seth J.; Som, Nicholas A.; Dauwalter, Daniel C.; Isaak, Daniel J.; Neville, Helen M.; Luce, Charles H.; Dunham, Jason B.; Young, Michael K.; Fausch, Kurt D.; Rieman, Bruce E.

2013-01-01

Forecasts of species distributions under future climates are inherently uncertain, but there have been few attempts to describe this uncertainty comprehensively in a probabilistic manner. We developed a Monte Carlo approach that accounts for uncertainty within generalized linear regression models (parameter uncertainty and residual error), uncertainty among competing models (model uncertainty), and uncertainty in future climate conditions (climate uncertainty) to produce site-specific frequency distributions of occurrence probabilities across a species’ range. We illustrated the method by forecasting suitable habitat for bull trout (Salvelinus confluentus) in the Interior Columbia River Basin, USA, under recent and projected 2040s and 2080s climate conditions. The 95% interval of total suitable habitat under recent conditions was estimated at 30.1–42.5 thousand km; this was predicted to decline to 0.5–7.9 thousand km by the 2080s. Projections for the 2080s showed that the great majority of stream segments would be unsuitable with high certainty, regardless of the climate data set or bull trout model employed. The largest contributor to uncertainty in total suitable habitat was climate uncertainty, followed by parameter uncertainty and model uncertainty. Our approach makes it possible to calculate a full distribution of possible outcomes for a species, and permits ready graphical display of uncertainty for individual locations and of total habitat.

An uncertainty analysis of the hydrogen source term for a station blackout accident in Sequoyah using MELCOR 1.8.5

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gauntt, Randall O.; Bixler, Nathan E.; Wagner, Kenneth Charles

2014-03-01

A methodology for using the MELCOR code with the Latin Hypercube Sampling method was developed to estimate uncertainty in various predicted quantities such as hydrogen generation or release of fission products under severe accident conditions. In this case, the emphasis was on estimating the range of hydrogen sources in station blackout conditions in the Sequoyah Ice Condenser plant, taking into account uncertainties in the modeled physics known to affect hydrogen generation. The method uses user-specified likelihood distributions for uncertain model parameters, which may include uncertainties of a stochastic nature, to produce a collection of code calculations, or realizations, characterizing themore » range of possible outcomes. Forty MELCOR code realizations of Sequoyah were conducted that included 10 uncertain parameters, producing a range of in-vessel hydrogen quantities. The range of total hydrogen produced was approximately 583kg 131kg. Sensitivity analyses revealed expected trends with respected to the parameters of greatest importance, however, considerable scatter in results when plotted against any of the uncertain parameters was observed, with no parameter manifesting dominant effects on hydrogen generation. It is concluded that, with respect to the physics parameters investigated, in order to further reduce predicted hydrogen uncertainty, it would be necessary to reduce all physics parameter uncertainties similarly, bearing in mind that some parameters are inherently uncertain within a range. It is suspected that some residual uncertainty associated with modeling complex, coupled and synergistic phenomena, is an inherent aspect of complex systems and cannot be reduced to point value estimates. The probabilistic analyses such as the one demonstrated in this work are important to properly characterize response of complex systems such as severe accident progression in nuclear power plants.« less

Testing the robustness of management decisions to uncertainty: Everglades restoration scenarios.

PubMed

Fuller, Michael M; Gross, Louis J; Duke-Sylvester, Scott M; Palmer, Mark

2008-04-01

To effectively manage large natural reserves, resource managers must prepare for future contingencies while balancing the often conflicting priorities of different stakeholders. To deal with these issues, managers routinely employ models to project the response of ecosystems to different scenarios that represent alternative management plans or environmental forecasts. Scenario analysis is often used to rank such alternatives to aid the decision making process. However, model projections are subject to uncertainty in assumptions about model structure, parameter values, environmental inputs, and subcomponent interactions. We introduce an approach for testing the robustness of model-based management decisions to the uncertainty inherent in complex ecological models and their inputs. We use relative assessment to quantify the relative impacts of uncertainty on scenario ranking. To illustrate our approach we consider uncertainty in parameter values and uncertainty in input data, with specific examples drawn from the Florida Everglades restoration project. Our examples focus on two alternative 30-year hydrologic management plans that were ranked according to their overall impacts on wildlife habitat potential. We tested the assumption that varying the parameter settings and inputs of habitat index models does not change the rank order of the hydrologic plans. We compared the average projected index of habitat potential for four endemic species and two wading-bird guilds to rank the plans, accounting for variations in parameter settings and water level inputs associated with hypothetical future climates. Indices of habitat potential were based on projections from spatially explicit models that are closely tied to hydrology. For the American alligator, the rank order of the hydrologic plans was unaffected by substantial variation in model parameters. By contrast, simulated major shifts in water levels led to reversals in the ranks of the hydrologic plans in 24.1-30.6% of the projections for the wading bird guilds and several individual species. By exposing the differential effects of uncertainty, relative assessment can help resource managers assess the robustness of scenario choice in model-based policy decisions.

Quantification of the impact of precipitation spatial distribution uncertainty on predictive uncertainty of a snowmelt runoff model

NASA Astrophysics Data System (ADS)

Jacquin, A. P.

2012-04-01

This study is intended to quantify the impact of uncertainty about precipitation spatial distribution on predictive uncertainty of a snowmelt runoff model. This problem is especially relevant in mountain catchments with a sparse precipitation observation network and relative short precipitation records. The model analysed is a conceptual watershed model operating at a monthly time step. The model divides the catchment into five elevation zones, where the fifth zone corresponds to the catchment's glaciers. Precipitation amounts at each elevation zone i are estimated as the product between observed precipitation at a station and a precipitation factor FPi. If other precipitation data are not available, these precipitation factors must be adjusted during the calibration process and are thus seen as parameters of the model. In the case of the fifth zone, glaciers are seen as an inexhaustible source of water that melts when the snow cover is depleted.The catchment case study is Aconcagua River at Chacabuquito, located in the Andean region of Central Chile. The model's predictive uncertainty is measured in terms of the output variance of the mean squared error of the Box-Cox transformed discharge, the relative volumetric error, and the weighted average of snow water equivalent in the elevation zones at the end of the simulation period. Sobol's variance decomposition (SVD) method is used for assessing the impact of precipitation spatial distribution, represented by the precipitation factors FPi, on the models' predictive uncertainty. In the SVD method, the first order effect of a parameter (or group of parameters) indicates the fraction of predictive uncertainty that could be reduced if the true value of this parameter (or group) was known. Similarly, the total effect of a parameter (or group) measures the fraction of predictive uncertainty that would remain if the true value of this parameter (or group) was unknown, but all the remaining model parameters could be fixed. In this study, first order and total effects of the group of precipitation factors FP1- FP4, and the precipitation factor FP5, are calculated separately. First order and total effects of the group FP1- FP4 are much higher than first order and total effects of the factor FP5, which are negligible This situation is due to the fact that the actual value taken by FP5 does not have much influence in the contribution of the glacier zone to the catchment's output discharge, mainly limited by incident solar radiation. In addition to this, first order effects indicate that, in average, nearly 25% of predictive uncertainty could be reduced if the true values of the precipitation factors FPi could be known, but no information was available on the appropriate values for the remaining model parameters. Finally, the total effects of the precipitation factors FP1- FP4 are close to 41% in average, implying that even if the appropriate values for the remaining model parameters could be fixed, predictive uncertainty would be still quite high if the spatial distribution of precipitation remains unknown. Acknowledgements: This research was funded by FONDECYT, Research Project 1110279.

Study of the uncertainty in estimation of the exposure of non-human biota to ionising radiation.

PubMed

Avila, R; Beresford, N A; Agüero, A; Broed, R; Brown, J; Iospje, M; Robles, B; Suañez, A

2004-12-01

Uncertainty in estimations of the exposure of non-human biota to ionising radiation may arise from a number of sources including values of the model parameters, empirical data, measurement errors and biases in the sampling. The significance of the overall uncertainty of an exposure assessment will depend on how the estimated dose compares with reference doses used for risk characterisation. In this paper, we present the results of a study of the uncertainty in estimation of the exposure of non-human biota using some of the models and parameters recommended in the FASSET methodology. The study was carried out for semi-natural terrestrial, agricultural and marine ecosystems, and for four radionuclides (137Cs, 239Pu, 129I and 237Np). The parameters of the radionuclide transfer models showed the highest sensitivity and contributed the most to the uncertainty in the predictions of doses to biota. The most important ones were related to the bioavailability and mobility of radionuclides in the environment, for example soil-to-plant transfer factors, the bioaccumulation factors for marine biota and the gut uptake fraction for terrestrial mammals. In contrast, the dose conversion coefficients showed low sensitivity and contributed little to the overall uncertainty. Radiobiological effectiveness contributed to the overall uncertainty of the dose estimations for alpha emitters although to a lesser degree than a number of transfer model parameters.

Explicitly integrating parameter, input, and structure uncertainties into Bayesian Neural Networks for probabilistic hydrologic forecasting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xuesong; Liang, Faming; Yu, Beibei

2011-11-09

Estimating uncertainty of hydrologic forecasting is valuable to water resources and other relevant decision making processes. Recently, Bayesian Neural Networks (BNNs) have been proved powerful tools for quantifying uncertainty of streamflow forecasting. In this study, we propose a Markov Chain Monte Carlo (MCMC) framework to incorporate the uncertainties associated with input, model structure, and parameter into BNNs. This framework allows the structure of the neural networks to change by removing or adding connections between neurons and enables scaling of input data by using rainfall multipliers. The results show that the new BNNs outperform the BNNs that only consider uncertainties associatedmore » with parameter and model structure. Critical evaluation of posterior distribution of neural network weights, number of effective connections, rainfall multipliers, and hyper-parameters show that the assumptions held in our BNNs are not well supported. Further understanding of characteristics of different uncertainty sources and including output error into the MCMC framework are expected to enhance the application of neural networks for uncertainty analysis of hydrologic forecasting.« less

Introducing uncertainty analysis of nucleation and crystal growth models in Process Analytical Technology (PAT) system design of crystallization processes.

PubMed

Samad, Noor Asma Fazli Abdul; Sin, Gürkan; Gernaey, Krist V; Gani, Rafiqul

2013-11-01

This paper presents the application of uncertainty and sensitivity analysis as part of a systematic model-based process monitoring and control (PAT) system design framework for crystallization processes. For the uncertainty analysis, the Monte Carlo procedure is used to propagate input uncertainty, while for sensitivity analysis, global methods including the standardized regression coefficients (SRC) and Morris screening are used to identify the most significant parameters. The potassium dihydrogen phosphate (KDP) crystallization process is used as a case study, both in open-loop and closed-loop operation. In the uncertainty analysis, the impact on the predicted output of uncertain parameters related to the nucleation and the crystal growth model has been investigated for both a one- and two-dimensional crystal size distribution (CSD). The open-loop results show that the input uncertainties lead to significant uncertainties on the CSD, with appearance of a secondary peak due to secondary nucleation for both cases. The sensitivity analysis indicated that the most important parameters affecting the CSDs are nucleation order and growth order constants. In the proposed PAT system design (closed-loop), the target CSD variability was successfully reduced compared to the open-loop case, also when considering uncertainty in nucleation and crystal growth model parameters. The latter forms a strong indication of the robustness of the proposed PAT system design in achieving the target CSD and encourages its transfer to full-scale implementation. Copyright © 2013 Elsevier B.V. All rights reserved.

Tolerance and UQ4SIM: Nimble Uncertainty Documentation and Analysis Software

NASA Technical Reports Server (NTRS)

Kleb, Bil

2008-01-01

Ultimately, scientific numerical models need quantified output uncertainties so that modeling can evolve to better match reality. Documenting model input uncertainties and variabilities is a necessary first step toward that goal. Without known input parameter uncertainties, model sensitivities are all one can determine, and without code verification, output uncertainties are simply not reliable. The basic premise of uncertainty markup is to craft a tolerance and tagging mini-language that offers a natural, unobtrusive presentation and does not depend on parsing each type of input file format. Each file is marked up with tolerances and optionally, associated tags that serve to label the parameters and their uncertainties. The evolution of such a language, often called a Domain Specific Language or DSL, is given in [1], but in final form it parallels tolerances specified on an engineering drawing, e.g., 1 +/- 0.5, 5 +/- 10%, 2 +/- 10 where % signifies percent and o signifies order of magnitude. Tags, necessary for error propagation, can be added by placing a quotation-mark-delimited tag after the tolerance, e.g., 0.7 +/- 20% 'T_effective'. In addition, tolerances might have different underlying distributions, e.g., Uniform, Normal, or Triangular, or the tolerances may merely be intervals due to lack of knowledge (uncertainty). Finally, to address pragmatic considerations such as older models that require specific number-field formats, C-style format specifiers can be appended to the tolerance like so, 1.35 +/- 10U_3.2f. As an example of use, consider figure 1, where a chemical reaction input file is has been marked up to include tolerances and tags per table 1. Not only does the technique provide a natural method of specifying tolerances, but it also servers as in situ documentation of model uncertainties. This tolerance language comes with a utility to strip the tolerances (and tags), to provide a path to the nominal model parameter file. And, as shown in [1], having the ability to quickly mark and identify model parameter uncertainties facilitates error propagation, which in turn yield output uncertainties.

Parameter uncertainty analysis for the annual phosphorus loss estimator (APLE) model

USDA-ARS?s Scientific Manuscript database

Technical abstract: Models are often used to predict phosphorus (P) loss from agricultural fields. While it is commonly recognized that model predictions are inherently uncertain, few studies have addressed prediction uncertainties using P loss models. In this study, we conduct an uncertainty analys...

Characterizing uncertainty and variability in physiologically based pharmacokinetic models: state of the science and needs for research and implementation.

PubMed

Barton, Hugh A; Chiu, Weihsueh A; Setzer, R Woodrow; Andersen, Melvin E; Bailer, A John; Bois, Frédéric Y; Dewoskin, Robert S; Hays, Sean; Johanson, Gunnar; Jones, Nancy; Loizou, George; Macphail, Robert C; Portier, Christopher J; Spendiff, Martin; Tan, Yu-Mei

2007-10-01

Physiologically based pharmacokinetic (PBPK) models are used in mode-of-action based risk and safety assessments to estimate internal dosimetry in animals and humans. When used in risk assessment, these models can provide a basis for extrapolating between species, doses, and exposure routes or for justifying nondefault values for uncertainty factors. Characterization of uncertainty and variability is increasingly recognized as important for risk assessment; this represents a continuing challenge for both PBPK modelers and users. Current practices show significant progress in specifying deterministic biological models and nondeterministic (often statistical) models, estimating parameters using diverse data sets from multiple sources, using them to make predictions, and characterizing uncertainty and variability of model parameters and predictions. The International Workshop on Uncertainty and Variability in PBPK Models, held 31 Oct-2 Nov 2006, identified the state-of-the-science, needed changes in practice and implementation, and research priorities. For the short term, these include (1) multidisciplinary teams to integrate deterministic and nondeterministic/statistical models; (2) broader use of sensitivity analyses, including for structural and global (rather than local) parameter changes; and (3) enhanced transparency and reproducibility through improved documentation of model structure(s), parameter values, sensitivity and other analyses, and supporting, discrepant, or excluded data. Longer-term needs include (1) theoretical and practical methodological improvements for nondeterministic/statistical modeling; (2) better methods for evaluating alternative model structures; (3) peer-reviewed databases of parameters and covariates, and their distributions; (4) expanded coverage of PBPK models across chemicals with different properties; and (5) training and reference materials, such as cases studies, bibliographies/glossaries, model repositories, and enhanced software. The multidisciplinary dialogue initiated by this Workshop will foster the collaboration, research, data collection, and training necessary to make characterizing uncertainty and variability a standard practice in PBPK modeling and risk assessment.

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.; Chang, B.-C.; Fischl, Robert

1989-01-01

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Confronting the Uncertainty in Aerosol Forcing Using Comprehensive Observational Data

NASA Astrophysics Data System (ADS)

Johnson, J. S.; Regayre, L. A.; Yoshioka, M.; Pringle, K.; Sexton, D.; Lee, L.; Carslaw, K. S.

2017-12-01

The effect of aerosols on cloud droplet concentrations and radiative properties is the largest uncertainty in the overall radiative forcing of climate over the industrial period. In this study, we take advantage of a large perturbed parameter ensemble of simulations from the UK Met Office HadGEM-UKCA model (the aerosol component of the UK Earth System Model) to comprehensively sample uncertainty in aerosol forcing. Uncertain aerosol and atmospheric parameters cause substantial aerosol forcing uncertainty in climatically important regions. As the aerosol radiative forcing itself is unobservable, we investigate the potential for observations of aerosol and radiative properties to act as constraints on the large forcing uncertainty. We test how eight different theoretically perfect aerosol and radiation observations can constrain the forcing uncertainty over Europe. We find that the achievable constraint is weak unless many diverse observations are used simultaneously. This is due to the complex relationships between model output responses and the multiple interacting parameter uncertainties: compensating model errors mean there are many ways to produce the same model output (known as model equifinality) which impacts on the achievable constraint. However, using all eight observable quantities together we show that the aerosol forcing uncertainty can potentially be reduced by around 50%. This reduction occurs as we reduce a large sample of model variants (over 1 million) that cover the full parametric uncertainty to around 1% that are observationally plausible.Constraining the forcing uncertainty using real observations is a more complex undertaking, in which we must account for multiple further uncertainties including measurement uncertainties, structural model uncertainties and the model discrepancy from reality. Here, we make a first attempt to determine the true potential constraint on the forcing uncertainty from our model that is achievable using a comprehensive set of real aerosol and radiation observations taken from ground stations, flight campaigns and satellite. This research has been supported by the UK-China Research & Innovation Partnership Fund through the Met Office Climate Science for Service Partnership (CSSP) China as part of the Newton Fund, and by the NERC funded GASSP project.

Forecasting Responses of a Northern Peatland Carbon Cycle to Elevated CO2 and a Gradient of Experimental Warming

NASA Astrophysics Data System (ADS)

Jiang, Jiang; Huang, Yuanyuan; Ma, Shuang; Stacy, Mark; Shi, Zheng; Ricciuto, Daniel M.; Hanson, Paul J.; Luo, Yiqi

2018-03-01

The ability to forecast ecological carbon cycling is imperative to land management in a world where past carbon fluxes are no longer a clear guide in the Anthropocene. However, carbon-flux forecasting has not been practiced routinely like numerical weather prediction. This study explored (1) the relative contributions of model forcing data and parameters to uncertainty in forecasting flux- versus pool-based carbon cycle variables and (2) the time points when temperature and CO2 treatments may cause statistically detectable differences in those variables. We developed an online forecasting workflow (Ecological Platform for Assimilation of Data (EcoPAD)), which facilitates iterative data-model integration. EcoPAD automates data transfer from sensor networks, data assimilation, and ecological forecasting. We used the Spruce and Peatland Responses Under Changing Experiments data collected from 2011 to 2014 to constrain the parameters in the Terrestrial Ecosystem Model, forecast carbon cycle responses to elevated CO2 and a gradient of warming from 2015 to 2024, and specify uncertainties in the model output. Our results showed that data assimilation substantially reduces forecasting uncertainties. Interestingly, we found that the stochasticity of future external forcing contributed more to the uncertainty of forecasting future dynamics of C flux-related variables than model parameters. However, the parameter uncertainty primarily contributes to the uncertainty in forecasting C pool-related response variables. Given the uncertainties in forecasting carbon fluxes and pools, our analysis showed that statistically different responses of fast-turnover pools to various CO2 and warming treatments were observed sooner than slow-turnover pools. Our study has identified the sources of uncertainties in model prediction and thus leads to improve ecological carbon cycling forecasts in the future.

Sensitivity of land surface modeling to parameters: An uncertainty quantification method applied to the Community Land Model

NASA Astrophysics Data System (ADS)

Ricciuto, D. M.; Mei, R.; Mao, J.; Hoffman, F. M.; Kumar, J.

2015-12-01

Uncertainties in land parameters could have important impacts on simulated water and energy fluxes and land surface states, which will consequently affect atmospheric and biogeochemical processes. Therefore, quantification of such parameter uncertainties using a land surface model is the first step towards better understanding of predictive uncertainty in Earth system models. In this study, we applied a random-sampling, high-dimensional model representation (RS-HDMR) method to analyze the sensitivity of simulated photosynthesis, surface energy fluxes and surface hydrological components to selected land parameters in version 4.5 of the Community Land Model (CLM4.5). Because of the large computational expense of conducting ensembles of global gridded model simulations, we used the results of a previous cluster analysis to select one thousand representative land grid cells for simulation. Plant functional type (PFT)-specific uniform prior ranges for land parameters were determined using expert opinion and literature survey, and samples were generated with a quasi-Monte Carlo approach-Sobol sequence. Preliminary analysis of 1024 simulations suggested that four PFT-dependent parameters (including slope of the conductance-photosynthesis relationship, specific leaf area at canopy top, leaf C:N ratio and fraction of leaf N in RuBisco) are the dominant sensitive parameters for photosynthesis, surface energy and water fluxes across most PFTs, but with varying importance rankings. On the other hand, for surface ans sub-surface runoff, PFT-independent parameters, such as the depth-dependent decay factors for runoff, play more important roles than the previous four PFT-dependent parameters. Further analysis by conditioning the results on different seasons and years are being conducted to provide guidance on how climate variability and change might affect such sensitivity. This is the first step toward coupled simulations including biogeochemical processes, atmospheric processes or both to determine the full range of sensitivity of Earth system modeling to land-surface parameters. This can facilitate sampling strategies in measurement campaigns targeted at reduction of climate modeling uncertainties and can also provide guidance on land parameter calibration for simulation optimization.

Uncertainty, Sensitivity Analysis, and Causal Identification in the Arctic using a Perturbed Parameter Ensemble of the HiLAT Climate Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hunke, Elizabeth Clare; Urrego Blanco, Jorge Rolando; Urban, Nathan Mark

Coupled climate models have a large number of input parameters that can affect output uncertainty. We conducted a sensitivity analysis of sea ice proper:es and Arc:c related climate variables to 5 parameters in the HiLAT climate model: air-ocean turbulent exchange parameter (C), conversion of water vapor to clouds (cldfrc_rhminl) and of ice crystals to snow (micro_mg_dcs), snow thermal conduc:vity (ksno), and maximum snow grain size (rsnw_mlt). We used an elementary effect (EE) approach to rank their importance for output uncertainty. EE is an extension of one-at-a-time sensitivity analyses, but it is more efficient in sampling multi-dimensional parameter spaces. We lookedmore » for emerging relationships among climate variables across the model ensemble, and used causal discovery algorithms to establish potential pathways for those relationships.« less

Uncertainties propagation and global sensitivity analysis of the frequency response function of piezoelectric energy harvesters

NASA Astrophysics Data System (ADS)

Ruiz, Rafael O.; Meruane, Viviana

2017-06-01

The goal of this work is to describe a framework to propagate uncertainties in piezoelectric energy harvesters (PEHs). These uncertainties are related to the incomplete knowledge of the model parameters. The framework presented could be employed to conduct prior robust stochastic predictions. The prior analysis assumes a known probability density function for the uncertain variables and propagates the uncertainties to the output voltage. The framework is particularized to evaluate the behavior of the frequency response functions (FRFs) in PEHs, while its implementation is illustrated by the use of different unimorph and bimorph PEHs subjected to different scenarios: free of uncertainties, common uncertainties, and uncertainties as a product of imperfect clamping. The common variability associated with the PEH parameters are tabulated and reported. A global sensitivity analysis is conducted to identify the Sobol indices. Results indicate that the elastic modulus, density, and thickness of the piezoelectric layer are the most relevant parameters of the output variability. The importance of including the model parameter uncertainties in the estimation of the FRFs is revealed. In this sense, the present framework constitutes a powerful tool in the robust design and prediction of PEH performance.

SOARCA Peach Bottom Atomic Power Station Long-Term Station Blackout Uncertainty Analysis: Knowledge Advancement.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gauntt, Randall O.; Mattie, Patrick D.; Bixler, Nathan E.

2014-02-01

This paper describes the knowledge advancements from the uncertainty analysis for the State-of- the-Art Reactor Consequence Analyses (SOARCA) unmitigated long-term station blackout accident scenario at the Peach Bottom Atomic Power Station. This work assessed key MELCOR and MELCOR Accident Consequence Code System, Version 2 (MACCS2) modeling uncertainties in an integrated fashion to quantify the relative importance of each uncertain input on potential accident progression, radiological releases, and off-site consequences. This quantitative uncertainty analysis provides measures of the effects on consequences, of each of the selected uncertain parameters both individually and in interaction with other parameters. The results measure the modelmore » response (e.g., variance in the output) to uncertainty in the selected input. Investigation into the important uncertain parameters in turn yields insights into important phenomena for accident progression and off-site consequences. This uncertainty analysis confirmed the known importance of some parameters, such as failure rate of the Safety Relief Valve in accident progression modeling and the dry deposition velocity in off-site consequence modeling. The analysis also revealed some new insights, such as dependent effect of cesium chemical form for different accident progressions. (auth)« less

Quantifying Groundwater Model Uncertainty

NASA Astrophysics Data System (ADS)

Hill, M. C.; Poeter, E.; Foglia, L.

2007-12-01

Groundwater models are characterized by the (a) processes simulated, (b) boundary conditions, (c) initial conditions, (d) method of solving the equation, (e) parameterization, and (f) parameter values. Models are related to the system of concern using data, some of which form the basis of observations used most directly, through objective functions, to estimate parameter values. Here we consider situations in which parameter values are determined by minimizing an objective function. Other methods of model development are not considered because their ad hoc nature generally prohibits clear quantification of uncertainty. Quantifying prediction uncertainty ideally includes contributions from (a) to (f). The parameter values of (f) tend to be continuous with respect to both the simulated equivalents of the observations and the predictions, while many aspects of (a) through (e) are discrete. This fundamental difference means that there are options for evaluating the uncertainty related to parameter values that generally do not exist for other aspects of a model. While the methods available for (a) to (e) can be used for the parameter values (f), the inferential methods uniquely available for (f) generally are less computationally intensive and often can be used to considerable advantage. However, inferential approaches require calculation of sensitivities. Whether the numerical accuracy and stability of the model solution required for accurate sensitivities is more broadly important to other model uses is an issue that needs to be addressed. Alternative global methods can require 100 or even 1,000 times the number of runs needed by inferential methods, though methods of reducing the number of needed runs are being developed and tested. Here we present three approaches for quantifying model uncertainty and investigate their strengths and weaknesses. (1) Represent more aspects as parameters so that the computationally efficient methods can be broadly applied. This approach is attainable through universal model analysis software such as UCODE-2005, PEST, and joint use of these programs, which allow many aspects of a model to be defined as parameters. (2) Use highly parameterized models to quantify aspects of (e). While promising, this approach implicitly includes parameterizations that may be considered unreasonable if investigated explicitly, so that resulting measures of uncertainty may be too large. (3) Use a combination of inferential and global methods that can be facilitated using the new software MMA (Multi-Model Analysis), which is constructed using the JUPITER API. Here we consider issues related to the model discrimination criteria calculated by MMA.

Partitioning uncertainty in streamflow projections under nonstationary model conditions

NASA Astrophysics Data System (ADS)

Chawla, Ila; Mujumdar, P. P.

2018-02-01

Assessing the impacts of Land Use (LU) and climate change on future streamflow projections is necessary for efficient management of water resources. However, model projections are burdened with significant uncertainty arising from various sources. Most of the previous studies have considered climate models and scenarios as major sources of uncertainty, but uncertainties introduced by land use change and hydrologic model assumptions are rarely investigated. In this paper an attempt is made to segregate the contribution from (i) general circulation models (GCMs), (ii) emission scenarios, (iii) land use scenarios, (iv) stationarity assumption of the hydrologic model, and (v) internal variability of the processes, to overall uncertainty in streamflow projections using analysis of variance (ANOVA) approach. Generally, most of the impact assessment studies are carried out with unchanging hydrologic model parameters in future. It is, however, necessary to address the nonstationarity in model parameters with changing land use and climate. In this paper, a regression based methodology is presented to obtain the hydrologic model parameters with changing land use and climate scenarios in future. The Upper Ganga Basin (UGB) in India is used as a case study to demonstrate the methodology. The semi-distributed Variable Infiltration Capacity (VIC) model is set-up over the basin, under nonstationary conditions. Results indicate that model parameters vary with time, thereby invalidating the often-used assumption of model stationarity. The streamflow in UGB under the nonstationary model condition is found to reduce in future. The flows are also found to be sensitive to changes in land use. Segregation results suggest that model stationarity assumption and GCMs along with their interactions with emission scenarios, act as dominant sources of uncertainty. This paper provides a generalized framework for hydrologists to examine stationarity assumption of models before considering them for future streamflow projections and segregate the contribution of various sources to the uncertainty.

An improved state-parameter analysis of ecosystem models using data assimilation

USGS Publications Warehouse

Chen, M.; Liu, S.; Tieszen, L.L.; Hollinger, D.Y.

2008-01-01

Much of the effort spent in developing data assimilation methods for carbon dynamics analysis has focused on estimating optimal values for either model parameters or state variables. The main weakness of estimating parameter values alone (i.e., without considering state variables) is that all errors from input, output, and model structure are attributed to model parameter uncertainties. On the other hand, the accuracy of estimating state variables may be lowered if the temporal evolution of parameter values is not incorporated. This research develops a smoothed ensemble Kalman filter (SEnKF) by combining ensemble Kalman filter with kernel smoothing technique. SEnKF has following characteristics: (1) to estimate simultaneously the model states and parameters through concatenating unknown parameters and state variables into a joint state vector; (2) to mitigate dramatic, sudden changes of parameter values in parameter sampling and parameter evolution process, and control narrowing of parameter variance which results in filter divergence through adjusting smoothing factor in kernel smoothing algorithm; (3) to assimilate recursively data into the model and thus detect possible time variation of parameters; and (4) to address properly various sources of uncertainties stemming from input, output and parameter uncertainties. The SEnKF is tested by assimilating observed fluxes of carbon dioxide and environmental driving factor data from an AmeriFlux forest station located near Howland, Maine, USA, into a partition eddy flux model. Our analysis demonstrates that model parameters, such as light use efficiency, respiration coefficients, minimum and optimum temperatures for photosynthetic activity, and others, are highly constrained by eddy flux data at daily-to-seasonal time scales. The SEnKF stabilizes parameter values quickly regardless of the initial values of the parameters. Potential ecosystem light use efficiency demonstrates a strong seasonality. Results show that the simultaneous parameter estimation procedure significantly improves model predictions. Results also show that the SEnKF can dramatically reduce the variance in state variables stemming from the uncertainty of parameters and driving variables. The SEnKF is a robust and effective algorithm in evaluating and developing ecosystem models and in improving the understanding and quantification of carbon cycle parameters and processes. ?? 2008 Elsevier B.V.

Holistic uncertainty analysis in river basin modeling for climate vulnerability assessment

NASA Astrophysics Data System (ADS)

Taner, M. U.; Wi, S.; Brown, C.

2017-12-01

The challenges posed by uncertain future climate are a prominent concern for water resources managers. A number of frameworks exist for assessing the impacts of climate-related uncertainty, including internal climate variability and anthropogenic climate change, such as scenario-based approaches and vulnerability-based approaches. While in many cases climate uncertainty may be dominant, other factors such as future evolution of the river basin, hydrologic response and reservoir operations are potentially significant sources of uncertainty. While uncertainty associated with modeling hydrologic response has received attention, very little attention has focused on the range of uncertainty and possible effects of the water resources infrastructure and management. This work presents a holistic framework that allows analysis of climate, hydrologic and water management uncertainty in water resources systems analysis with the aid of a water system model designed to integrate component models for hydrology processes and water management activities. The uncertainties explored include those associated with climate variability and change, hydrologic model parameters, and water system operation rules. A Bayesian framework is used to quantify and model the uncertainties at each modeling steps in integrated fashion, including prior and the likelihood information about model parameters. The framework is demonstrated in a case study for the St. Croix Basin located at border of United States and Canada.

Optimisation of lateral car dynamics taking into account parameter uncertainties

NASA Astrophysics Data System (ADS)

Busch, Jochen; Bestle, Dieter

2014-02-01

Simulation studies on an active all-wheel-steering car show that disturbance of vehicle parameters have high influence on lateral car dynamics. This motivates the need of robust design against such parameter uncertainties. A specific parametrisation is established combining deterministic, velocity-dependent steering control parameters with partly uncertain, velocity-independent vehicle parameters for simultaneous use in a numerical optimisation process. Model-based objectives are formulated and summarised in a multi-objective optimisation problem where especially the lateral steady-state behaviour is improved by an adaption strategy based on measurable uncertainties. The normally distributed uncertainties are generated by optimal Latin hypercube sampling and a response surface based strategy helps to cut down time consuming model evaluations which offers the possibility to use a genetic optimisation algorithm. Optimisation results are discussed in different criterion spaces and the achieved improvements confirm the validity of the proposed procedure.

Quantifying uncertainty in Bayesian calibrated animal-to-human PBPK models with informative prior distributions

EPA Science Inventory

Understanding and quantifying the uncertainty of model parameters and predictions has gained more interest in recent years with the increased use of computational models in chemical risk assessment. Fully characterizing the uncertainty in risk metrics derived from linked quantita...

Uncertainty in predictions of forest carbon dynamics: separating driver error from model error.

PubMed

Spadavecchia, L; Williams, M; Law, B E

2011-07-01

We present an analysis of the relative magnitude and contribution of parameter and driver uncertainty to the confidence intervals on estimates of net carbon fluxes. Model parameters may be difficult or impractical to measure, while driver fields are rarely complete, with data gaps due to sensor failure and sparse observational networks. Parameters are generally derived through some optimization method, while driver fields may be interpolated from available data sources. For this study, we used data from a young ponderosa pine stand at Metolius, Central Oregon, and a simple daily model of coupled carbon and water fluxes (DALEC). An ensemble of acceptable parameterizations was generated using an ensemble Kalman filter and eddy covariance measurements of net C exchange. Geostatistical simulations generated an ensemble of meteorological driving variables for the site, consistent with the spatiotemporal autocorrelations inherent in the observational data from 13 local weather stations. Simulated meteorological data were propagated through the model to derive the uncertainty on the CO2 flux resultant from driver uncertainty typical of spatially extensive modeling studies. Furthermore, the model uncertainty was partitioned between temperature and precipitation. With at least one meteorological station within 25 km of the study site, driver uncertainty was relatively small ( 10% of the total net flux), while parameterization uncertainty was larger, 50% of the total net flux. The largest source of driver uncertainty was due to temperature (8% of the total flux). The combined effect of parameter and driver uncertainty was 57% of the total net flux. However, when the nearest meteorological station was > 100 km from the study site, uncertainty in net ecosystem exchange (NEE) predictions introduced by meteorological drivers increased by 88%. Precipitation estimates were a larger source of bias in NEE estimates than were temperature estimates, although the biases partly compensated for each other. The time scales on which precipitation errors occurred in the simulations were shorter than the temporal scales over which drought developed in the model, so drought events were reasonably simulated. The approach outlined here provides a means to assess the uncertainty and bias introduced by meteorological drivers in regional-scale ecological forecasting.

Statistical error model for a solar electric propulsion thrust subsystem

NASA Technical Reports Server (NTRS)

Bantell, M. H.

1973-01-01

The solar electric propulsion thrust subsystem statistical error model was developed as a tool for investigating the effects of thrust subsystem parameter uncertainties on navigation accuracy. The model is currently being used to evaluate the impact of electric engine parameter uncertainties on navigation system performance for a baseline mission to Encke's Comet in the 1980s. The data given represent the next generation in statistical error modeling for low-thrust applications. Principal improvements include the representation of thrust uncertainties and random process modeling in terms of random parametric variations in the thrust vector process for a multi-engine configuration.

Evaluating Uncertainty of Runoff Simulation using SWAT model of the Feilaixia Watershed in China Based on the GLUE Method

NASA Astrophysics Data System (ADS)

Chen, X.; Huang, G.

2017-12-01

In recent years, distributed hydrological models have been widely used in storm water management, water resources protection and so on. Therefore, how to evaluate the uncertainty of the model reasonably and efficiently becomes a hot topic today. In this paper, the soil and water assessment tool (SWAT) model is constructed for the study area of China's Feilaixia watershed, and the uncertainty of the runoff simulation is analyzed by GLUE method deeply. Taking the initial parameter range of GLUE method as the research core, the influence of different initial parameter ranges on model uncertainty is studied. In this paper, two sets of parameter ranges are chosen as the object of study, the first one (range 1) is recommended by SWAT-CUP and the second one (range 2) is calibrated by SUFI-2. The results showed that under the same number of simulations (10,000 times), the overall uncertainty obtained by the range 2 is less than the range 1. Specifically, the "behavioral" parameter sets for the range 2 is 10000 and for the range 1 is 4448. In the calibration and the validation, the ratio of P-factor to R-factor for range 1 is 1.387 and 1.391, and for range 2 is 1.405 and 1.462 respectively. In addition, the simulation result of range 2 is better with the NS and R2 slightly higher than range 1. Therefore, it can be concluded that using the parameter range calibrated by SUFI-2 as the initial parameter range for the GLUE is a way to effectively capture and evaluate the simulation uncertainty.

A fully-stochasticized, age-structured population model for population viability analysis of fish: Lower Missouri River endangered pallid sturgeon example

USGS Publications Warehouse

Wildhaber, Mark L.; Albers, Janice; Green, Nicholas; Moran, Edward H.

2017-01-01

We develop a fully-stochasticized, age-structured population model suitable for population viability analysis (PVA) of fish and demonstrate its use with the endangered pallid sturgeon (Scaphirhynchus albus) of the Lower Missouri River as an example. The model incorporates three levels of variance: parameter variance (uncertainty about the value of a parameter itself) applied at the iteration level, temporal variance (uncertainty caused by random environmental fluctuations over time) applied at the time-step level, and implicit individual variance (uncertainty caused by differences between individuals) applied within the time-step level. We found that population dynamics were most sensitive to survival rates, particularly age-2+ survival, and to fecundity-at-length. The inclusion of variance (unpartitioned or partitioned), stocking, or both generally decreased the influence of individual parameters on population growth rate. The partitioning of variance into parameter and temporal components had a strong influence on the importance of individual parameters, uncertainty of model predictions, and quasiextinction risk (i.e., pallid sturgeon population size falling below 50 age-1+ individuals). Our findings show that appropriately applying variance in PVA is important when evaluating the relative importance of parameters, and reinforce the need for better and more precise estimates of crucial life-history parameters for pallid sturgeon.

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

NASA Astrophysics Data System (ADS)

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-01

In Hezaveh et al. we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational-lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data, as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single variational parameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that the application of approximate Bayesian neural networks to astrophysical modeling problems can be a fast alternative to Monte Carlo Markov Chains, allowing orders of magnitude improvement in speed.

Effect of correlated observation error on parameters, predictions, and uncertainty

USGS Publications Warehouse

Tiedeman, Claire; Green, Christopher T.

2013-01-01

Correlations among observation errors are typically omitted when calculating observation weights for model calibration by inverse methods. We explore the effects of omitting these correlations on estimates of parameters, predictions, and uncertainties. First, we develop a new analytical expression for the difference in parameter variance estimated with and without error correlations for a simple one-parameter two-observation inverse model. Results indicate that omitting error correlations from both the weight matrix and the variance calculation can either increase or decrease the parameter variance, depending on the values of error correlation (ρ) and the ratio of dimensionless scaled sensitivities (rdss). For small ρ, the difference in variance is always small, but for large ρ, the difference varies widely depending on the sign and magnitude of rdss. Next, we consider a groundwater reactive transport model of denitrification with four parameters and correlated geochemical observation errors that are computed by an error-propagation approach that is new for hydrogeologic studies. We compare parameter estimates, predictions, and uncertainties obtained with and without the error correlations. Omitting the correlations modestly to substantially changes parameter estimates, and causes both increases and decreases of parameter variances, consistent with the analytical expression. Differences in predictions for the models calibrated with and without error correlations can be greater than parameter differences when both are considered relative to their respective confidence intervals. These results indicate that including observation error correlations in weighting for nonlinear regression can have important effects on parameter estimates, predictions, and their respective uncertainties.

Calibration-induced uncertainty of the EPIC model to estimate climate change impact on global maize yield

NASA Astrophysics Data System (ADS)

Xiong, Wei; Skalský, Rastislav; Porter, Cheryl H.; Balkovič, Juraj; Jones, James W.; Yang, Di

2016-09-01

Understanding the interactions between agricultural production and climate is necessary for sound decision-making in climate policy. Gridded and high-resolution crop simulation has emerged as a useful tool for building this understanding. Large uncertainty exists in this utilization, obstructing its capacity as a tool to devise adaptation strategies. Increasing focus has been given to sources of uncertainties for climate scenarios, input-data, and model, but uncertainties due to model parameter or calibration are still unknown. Here, we use publicly available geographical data sets as input to the Environmental Policy Integrated Climate model (EPIC) for simulating global-gridded maize yield. Impacts of climate change are assessed up to the year 2099 under a climate scenario generated by HadEM2-ES under RCP 8.5. We apply five strategies by shifting one specific parameter in each simulation to calibrate the model and understand the effects of calibration. Regionalizing crop phenology or harvest index appears effective to calibrate the model for the globe, but using various values of phenology generates pronounced difference in estimated climate impact. However, projected impacts of climate change on global maize production are consistently negative regardless of the parameter being adjusted. Different values of model parameter result in a modest uncertainty at global level, with difference of the global yield change less than 30% by the 2080s. The uncertainty subjects to decrease if applying model calibration or input data quality control. Calibration has a larger effect at local scales, implying the possible types and locations for adaptation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthias C. M. Troffaes; Gero Walter; Dana Kelly

In a standard Bayesian approach to the alpha-factor model for common-cause failure, a precise Dirichlet prior distribution models epistemic uncertainty in the alpha-factors. This Dirichlet prior is then updated with observed data to obtain a posterior distribution, which forms the basis for further inferences. In this paper, we adapt the imprecise Dirichlet model of Walley to represent epistemic uncertainty in the alpha-factors. In this approach, epistemic uncertainty is expressed more cautiously via lower and upper expectations for each alpha-factor, along with a learning parameter which determines how quickly the model learns from observed data. For this application, we focus onmore » elicitation of the learning parameter, and find that values in the range of 1 to 10 seem reasonable. The approach is compared with Kelly and Atwood's minimally informative Dirichlet prior for the alpha-factor model, which incorporated precise mean values for the alpha-factors, but which was otherwise quite diffuse. Next, we explore the use of a set of Gamma priors to model epistemic uncertainty in the marginal failure rate, expressed via a lower and upper expectation for this rate, again along with a learning parameter. As zero counts are generally less of an issue here, we find that the choice of this learning parameter is less crucial. Finally, we demonstrate how both epistemic uncertainty models can be combined to arrive at lower and upper expectations for all common-cause failure rates. Thereby, we effectively provide a full sensitivity analysis of common-cause failure rates, properly reflecting epistemic uncertainty of the analyst on all levels of the common-cause failure model.« less

Posterior uncertainty of GEOS-5 L-band radiative transfer model parameters and brightness temperatures after calibration with SMOS observations

NASA Astrophysics Data System (ADS)

De Lannoy, G. J.; Reichle, R. H.; Vrugt, J. A.

2012-12-01

Simulated L-band (1.4 GHz) brightness temperatures are very sensitive to the values of the parameters in the radiative transfer model (RTM). We assess the optimum RTM parameter values and their (posterior) uncertainty in the Goddard Earth Observing System (GEOS-5) land surface model using observations of multi-angular brightness temperature over North America from the Soil Moisture Ocean Salinity (SMOS) mission. Two different parameter estimation methods are being compared: (i) a particle swarm optimization (PSO) approach, and (ii) an MCMC simulation procedure using the differential evolution adaptive Metropolis (DREAM) algorithm. Our results demonstrate that both methods provide similar "optimal" parameter values. Yet, DREAM exhibits better convergence properties, resulting in a reduced spread of the posterior ensemble. The posterior parameter distributions derived with both methods are used for predictive uncertainty estimation of brightness temperature. This presentation will highlight our model-data synthesis framework and summarize our initial findings.

Accounting for Parameter Uncertainty in Complex Atmospheric Models, With an Application to Greenhouse Gas Emissions Evaluation

NASA Astrophysics Data System (ADS)

Swallow, B.; Rigby, M. L.; Rougier, J.; Manning, A.; Thomson, D.; Webster, H. N.; Lunt, M. F.; O'Doherty, S.

2016-12-01

In order to understand underlying processes governing environmental and physical phenomena, a complex mathematical model is usually required. However, there is an inherent uncertainty related to the parameterisation of unresolved processes in these simulators. Here, we focus on the specific problem of accounting for uncertainty in parameter values in an atmospheric chemical transport model. Systematic errors introduced by failing to account for these uncertainties have the potential to have a large effect on resulting estimates in unknown quantities of interest. One approach that is being increasingly used to address this issue is known as emulation, in which a large number of forward runs of the simulator are carried out, in order to approximate the response of the output to changes in parameters. However, due to the complexity of some models, it is often unfeasible to run large numbers of training runs that is usually required for full statistical emulators of the environmental processes. We therefore present a simplified model reduction method for approximating uncertainties in complex environmental simulators without the need for very large numbers of training runs. We illustrate the method through an application to the Met Office's atmospheric transport model NAME. We show how our parameter estimation framework can be incorporated into a hierarchical Bayesian inversion, and demonstrate the impact on estimates of UK methane emissions, using atmospheric mole fraction data. We conclude that accounting for uncertainties in the parameterisation of complex atmospheric models is vital if systematic errors are to be minimized and all relevant uncertainties accounted for. We also note that investigations of this nature can prove extremely useful in highlighting deficiencies in the simulator that might otherwise be missed.

Uncertainty and sensitivity analysis of fission gas behavior in engineering-scale fuel modeling

DOE PAGES

Pastore, Giovanni; Swiler, L. P.; Hales, Jason D.; ...

2014-10-12

The role of uncertainties in fission gas behavior calculations as part of engineering-scale nuclear fuel modeling is investigated using the BISON fuel performance code and a recently implemented physics-based model for the coupled fission gas release and swelling. Through the integration of BISON with the DAKOTA software, a sensitivity analysis of the results to selected model parameters is carried out based on UO2 single-pellet simulations covering different power regimes. The parameters are varied within ranges representative of the relative uncertainties and consistent with the information from the open literature. The study leads to an initial quantitative assessment of the uncertaintymore » in fission gas behavior modeling with the parameter characterization presently available. Also, the relative importance of the single parameters is evaluated. Moreover, a sensitivity analysis is carried out based on simulations of a fuel rod irradiation experiment, pointing out a significant impact of the considered uncertainties on the calculated fission gas release and cladding diametral strain. The results of the study indicate that the commonly accepted deviation between calculated and measured fission gas release by a factor of 2 approximately corresponds to the inherent modeling uncertainty at high fission gas release. Nevertheless, higher deviations may be expected for values around 10% and lower. Implications are discussed in terms of directions of research for the improved modeling of fission gas behavior for engineering purposes.« less

Harnessing the theoretical foundations of the exponential and beta-Poisson dose-response models to quantify parameter uncertainty using Markov Chain Monte Carlo.

PubMed

Schmidt, Philip J; Pintar, Katarina D M; Fazil, Aamir M; Topp, Edward

2013-09-01

Dose-response models are the essential link between exposure assessment and computed risk values in quantitative microbial risk assessment, yet the uncertainty that is inherent to computed risks because the dose-response model parameters are estimated using limited epidemiological data is rarely quantified. Second-order risk characterization approaches incorporating uncertainty in dose-response model parameters can provide more complete information to decisionmakers by separating variability and uncertainty to quantify the uncertainty in computed risks. Therefore, the objective of this work is to develop procedures to sample from posterior distributions describing uncertainty in the parameters of exponential and beta-Poisson dose-response models using Bayes's theorem and Markov Chain Monte Carlo (in OpenBUGS). The theoretical origins of the beta-Poisson dose-response model are used to identify a decomposed version of the model that enables Bayesian analysis without the need to evaluate Kummer confluent hypergeometric functions. Herein, it is also established that the beta distribution in the beta-Poisson dose-response model cannot address variation among individual pathogens, criteria to validate use of the conventional approximation to the beta-Poisson model are proposed, and simple algorithms to evaluate actual beta-Poisson probabilities of infection are investigated. The developed MCMC procedures are applied to analysis of a case study data set, and it is demonstrated that an important region of the posterior distribution of the beta-Poisson dose-response model parameters is attributable to the absence of low-dose data. This region includes beta-Poisson models for which the conventional approximation is especially invalid and in which many beta distributions have an extreme shape with questionable plausibility. © Her Majesty the Queen in Right of Canada 2013. Reproduced with the permission of the Minister of the Public Health Agency of Canada.

Modeling uncertainty: quicksand for water temperature modeling

USGS Publications Warehouse

Bartholow, John M.

2003-01-01

Uncertainty has been a hot topic relative to science generally, and modeling specifically. Modeling uncertainty comes in various forms: measured data, limited model domain, model parameter estimation, model structure, sensitivity to inputs, modelers themselves, and users of the results. This paper will address important components of uncertainty in modeling water temperatures, and discuss several areas that need attention as the modeling community grapples with how to incorporate uncertainty into modeling without getting stuck in the quicksand that prevents constructive contributions to policy making. The material, and in particular the reference, are meant to supplement the presentation given at this conference.

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS.

USGS Publications Warehouse

Cooley, Richard L.; Vecchia, Aldo V.

1987-01-01

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Uncertainty Quantification and Sensitivity Analysis in the CICE v5.1 Sea Ice Model

NASA Astrophysics Data System (ADS)

Urrego-Blanco, J. R.; Urban, N. M.

2015-12-01

Changes in the high latitude climate system have the potential to affect global climate through feedbacks with the atmosphere and connections with mid latitudes. Sea ice and climate models used to understand these changes have uncertainties that need to be characterized and quantified. In this work we characterize parametric uncertainty in Los Alamos Sea Ice model (CICE) and quantify the sensitivity of sea ice area, extent and volume with respect to uncertainty in about 40 individual model parameters. Unlike common sensitivity analyses conducted in previous studies where parameters are varied one-at-a-time, this study uses a global variance-based approach in which Sobol sequences are used to efficiently sample the full 40-dimensional parameter space. This approach requires a very large number of model evaluations, which are expensive to run. A more computationally efficient approach is implemented by training and cross-validating a surrogate (emulator) of the sea ice model with model output from 400 model runs. The emulator is used to make predictions of sea ice extent, area, and volume at several model configurations, which are then used to compute the Sobol sensitivity indices of the 40 parameters. A ranking based on the sensitivity indices indicates that model output is most sensitive to snow parameters such as conductivity and grain size, and the drainage of melt ponds. The main effects and interactions among the most influential parameters are also estimated by a non-parametric regression technique based on generalized additive models. It is recommended research to be prioritized towards more accurately determining these most influential parameters values by observational studies or by improving existing parameterizations in the sea ice model.

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

2014-01-01

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

Advances in Parameter and Uncertainty Quantification Using Bayesian Hierarchical Techniques with a Spatially Referenced Watershed Model (Invited)

NASA Astrophysics Data System (ADS)

Alexander, R. B.; Boyer, E. W.; Schwarz, G. E.; Smith, R. A.

2013-12-01

Estimating water and material stores and fluxes in watershed studies is frequently complicated by uncertainties in quantifying hydrological and biogeochemical effects of factors such as land use, soils, and climate. Although these process-related effects are commonly measured and modeled in separate catchments, researchers are especially challenged by their complexity across catchments and diverse environmental settings, leading to a poor understanding of how model parameters and prediction uncertainties vary spatially. To address these concerns, we illustrate the use of Bayesian hierarchical modeling techniques with a dynamic version of the spatially referenced watershed model SPARROW (SPAtially Referenced Regression On Watershed attributes). The dynamic SPARROW model is designed to predict streamflow and other water cycle components (e.g., evapotranspiration, soil and groundwater storage) for monthly varying hydrological regimes, using mechanistic functions, mass conservation constraints, and statistically estimated parameters. In this application, the model domain includes nearly 30,000 NHD (National Hydrologic Data) stream reaches and their associated catchments in the Susquehanna River Basin. We report the results of our comparisons of alternative models of varying complexity, including models with different explanatory variables as well as hierarchical models that account for spatial and temporal variability in model parameters and variance (error) components. The model errors are evaluated for changes with season and catchment size and correlations in time and space. The hierarchical models consist of a two-tiered structure in which climate forcing parameters are modeled as random variables, conditioned on watershed properties. Quantification of spatial and temporal variations in the hydrological parameters and model uncertainties in this approach leads to more efficient (lower variance) and less biased model predictions throughout the river network. Moreover, predictions of water-balance components are reported according to probabilistic metrics (e.g., percentiles, prediction intervals) that include both parameter and model uncertainties. These improvements in predictions of streamflow dynamics can inform the development of more accurate predictions of spatial and temporal variations in biogeochemical stores and fluxes (e.g., nutrients and carbon) in watersheds.

Bayesian Treatment of Uncertainty in Environmental Modeling: Optimization, Sampling and Data Assimilation Using the DREAM Software Package

NASA Astrophysics Data System (ADS)

Vrugt, J. A.

2012-12-01

In the past decade much progress has been made in the treatment of uncertainty in earth systems modeling. Whereas initial approaches has focused mostly on quantification of parameter and predictive uncertainty, recent methods attempt to disentangle the effects of parameter, forcing (input) data, model structural and calibration data errors. In this talk I will highlight some of our recent work involving theory, concepts and applications of Bayesian parameter and/or state estimation. In particular, new methods for sequential Monte Carlo (SMC) and Markov Chain Monte Carlo (MCMC) simulation will be presented with emphasis on massively parallel distributed computing and quantification of model structural errors. The theoretical and numerical developments will be illustrated using model-data synthesis problems in hydrology, hydrogeology and geophysics.

A geostatistics-informed hierarchical sensitivity analysis method for complex groundwater flow and transport modeling: GEOSTATISTICAL SENSITIVITY ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, Heng; Chen, Xingyuan; Ye, Ming

Sensitivity analysis is an important tool for quantifying uncertainty in the outputs of mathematical models, especially for complex systems with a high dimension of spatially correlated parameters. Variance-based global sensitivity analysis has gained popularity because it can quantify the relative contribution of uncertainty from different sources. However, its computational cost increases dramatically with the complexity of the considered model and the dimension of model parameters. In this study we developed a hierarchical sensitivity analysis method that (1) constructs an uncertainty hierarchy by analyzing the input uncertainty sources, and (2) accounts for the spatial correlation among parameters at each level ofmore » the hierarchy using geostatistical tools. The contribution of uncertainty source at each hierarchy level is measured by sensitivity indices calculated using the variance decomposition method. Using this methodology, we identified the most important uncertainty source for a dynamic groundwater flow and solute transport in model at the Department of Energy (DOE) Hanford site. The results indicate that boundary conditions and permeability field contribute the most uncertainty to the simulated head field and tracer plume, respectively. The relative contribution from each source varied spatially and temporally as driven by the dynamic interaction between groundwater and river water at the site. By using a geostatistical approach to reduce the number of realizations needed for the sensitivity analysis, the computational cost of implementing the developed method was reduced to a practically manageable level. The developed sensitivity analysis method is generally applicable to a wide range of hydrologic and environmental problems that deal with high-dimensional spatially-distributed parameters.« less

Accounting for uncertainty in model-based prevalence estimation: paratuberculosis control in dairy herds.

PubMed

Davidson, Ross S; McKendrick, Iain J; Wood, Joanna C; Marion, Glenn; Greig, Alistair; Stevenson, Karen; Sharp, Michael; Hutchings, Michael R

2012-09-10

A common approach to the application of epidemiological models is to determine a single (point estimate) parameterisation using the information available in the literature. However, in many cases there is considerable uncertainty about parameter values, reflecting both the incomplete nature of current knowledge and natural variation, for example between farms. Furthermore model outcomes may be highly sensitive to different parameter values. Paratuberculosis is an infection for which many of the key parameter values are poorly understood and highly variable, and for such infections there is a need to develop and apply statistical techniques which make maximal use of available data. A technique based on Latin hypercube sampling combined with a novel reweighting method was developed which enables parameter uncertainty and variability to be incorporated into a model-based framework for estimation of prevalence. The method was evaluated by applying it to a simulation of paratuberculosis in dairy herds which combines a continuous time stochastic algorithm with model features such as within herd variability in disease development and shedding, which have not been previously explored in paratuberculosis models. Generated sample parameter combinations were assigned a weight, determined by quantifying the model's resultant ability to reproduce prevalence data. Once these weights are generated the model can be used to evaluate other scenarios such as control options. To illustrate the utility of this approach these reweighted model outputs were used to compare standard test and cull control strategies both individually and in combination with simple husbandry practices that aim to reduce infection rates. The technique developed has been shown to be applicable to a complex model incorporating realistic control options. For models where parameters are not well known or subject to significant variability, the reweighting scheme allowed estimated distributions of parameter values to be combined with additional sources of information, such as that available from prevalence distributions, resulting in outputs which implicitly handle variation and uncertainty. This methodology allows for more robust predictions from modelling approaches by allowing for parameter uncertainty and combining different sources of information, and is thus expected to be useful in application to a large number of disease systems.

Linked Sensitivity Analysis, Calibration, and Uncertainty Analysis Using a System Dynamics Model for Stroke Comparative Effectiveness Research.

PubMed

Tian, Yuan; Hassmiller Lich, Kristen; Osgood, Nathaniel D; Eom, Kirsten; Matchar, David B

2016-11-01

As health services researchers and decision makers tackle more difficult problems using simulation models, the number of parameters and the corresponding degree of uncertainty have increased. This often results in reduced confidence in such complex models to guide decision making. To demonstrate a systematic approach of linked sensitivity analysis, calibration, and uncertainty analysis to improve confidence in complex models. Four techniques were integrated and applied to a System Dynamics stroke model of US veterans, which was developed to inform systemwide intervention and research planning: Morris method (sensitivity analysis), multistart Powell hill-climbing algorithm and generalized likelihood uncertainty estimation (calibration), and Monte Carlo simulation (uncertainty analysis). Of 60 uncertain parameters, sensitivity analysis identified 29 needing calibration, 7 that did not need calibration but significantly influenced key stroke outcomes, and 24 not influential to calibration or stroke outcomes that were fixed at their best guess values. One thousand alternative well-calibrated baselines were obtained to reflect calibration uncertainty and brought into uncertainty analysis. The initial stroke incidence rate among veterans was identified as the most influential uncertain parameter, for which further data should be collected. That said, accounting for current uncertainty, the analysis of 15 distinct prevention and treatment interventions provided a robust conclusion that hypertension control for all veterans would yield the largest gain in quality-adjusted life years. For complex health care models, a mixed approach was applied to examine the uncertainty surrounding key stroke outcomes and the robustness of conclusions. We demonstrate that this rigorous approach can be practical and advocate for such analysis to promote understanding of the limits of certainty in applying models to current decisions and to guide future data collection. © The Author(s) 2016.

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis ismore » conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. In conclusion, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.« less

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis ismore » conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. Finally, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.« less

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

NASA Astrophysics Data System (ADS)

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; Geraci, Gianluca; Eldred, Michael S.; Vane, Zachary P.; Lacaze, Guilhem; Oefelein, Joseph C.; Najm, Habib N.

2018-03-01

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the systems stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

DOE PAGES

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; ...

2018-02-09

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis ismore » conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. In conclusion, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.« less

Validation and uncertainty analysis of a pre-treatment 2D dose prediction model

NASA Astrophysics Data System (ADS)

Baeza, Jose A.; Wolfs, Cecile J. A.; Nijsten, Sebastiaan M. J. J. G.; Verhaegen, Frank

2018-02-01

Independent verification of complex treatment delivery with megavolt photon beam radiotherapy (RT) has been effectively used to detect and prevent errors. This work presents the validation and uncertainty analysis of a model that predicts 2D portal dose images (PDIs) without a patient or phantom in the beam. The prediction model is based on an exponential point dose model with separable primary and secondary photon fluence components. The model includes a scatter kernel, off-axis ratio map, transmission values and penumbra kernels for beam-delimiting components. These parameters were derived through a model fitting procedure supplied with point dose and dose profile measurements of radiation fields. The model was validated against a treatment planning system (TPS; Eclipse) and radiochromic film measurements for complex clinical scenarios, including volumetric modulated arc therapy (VMAT). Confidence limits on fitted model parameters were calculated based on simulated measurements. A sensitivity analysis was performed to evaluate the effect of the parameter uncertainties on the model output. For the maximum uncertainty, the maximum deviating measurement sets were propagated through the fitting procedure and the model. The overall uncertainty was assessed using all simulated measurements. The validation of the prediction model against the TPS and the film showed a good agreement, with on average 90.8% and 90.5% of pixels passing a (2%,2 mm) global gamma analysis respectively, with a low dose threshold of 10%. The maximum and overall uncertainty of the model is dependent on the type of clinical plan used as input. The results can be used to study the robustness of the model. A model for predicting accurate 2D pre-treatment PDIs in complex RT scenarios can be used clinically and its uncertainties can be taken into account.

Hybrid Gibbs Sampling and MCMC for CMB Analysis at Small Angular Scales

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Eriksen, H. K.; Wandelt, B. D.; Gorski, K. M.; Huey, G.; O'Dwyer, I. J.; Dickinson, C.; Banday, A. J.; Lawrence, C. R.

2008-01-01

A) Gibbs Sampling has now been validated as an efficient, statistically exact, and practically useful method for "low-L" (as demonstrated on WMAP temperature polarization data). B) We are extending Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters for the entire range of angular scales relevant for Planck. C) Made possible by inclusion of foreground model parameters in Gibbs sampling and hybrid MCMC and Gibbs sampling for the low signal to noise (high-L) regime. D) Future items to be included in the Bayesian framework include: 1) Integration with Hybrid Likelihood (or posterior) code for cosmological parameters; 2) Include other uncertainties in instrumental systematics? (I.e. beam uncertainties, noise estimation, calibration errors, other).

Parameter and model uncertainty in a life-table model for fine particles (PM2.5): a statistical modeling study

PubMed Central

Tainio, Marko; Tuomisto, Jouni T; Hänninen, Otto; Ruuskanen, Juhani; Jantunen, Matti J; Pekkanen, Juha

2007-01-01

Background The estimation of health impacts involves often uncertain input variables and assumptions which have to be incorporated into the model structure. These uncertainties may have significant effects on the results obtained with model, and, thus, on decision making. Fine particles (PM2.5) are believed to cause major health impacts, and, consequently, uncertainties in their health impact assessment have clear relevance to policy-making. We studied the effects of various uncertain input variables by building a life-table model for fine particles. Methods Life-expectancy of the Helsinki metropolitan area population and the change in life-expectancy due to fine particle exposures were predicted using a life-table model. A number of parameter and model uncertainties were estimated. Sensitivity analysis for input variables was performed by calculating rank-order correlations between input and output variables. The studied model uncertainties were (i) plausibility of mortality outcomes and (ii) lag, and parameter uncertainties (iii) exposure-response coefficients for different mortality outcomes, and (iv) exposure estimates for different age groups. The monetary value of the years-of-life-lost and the relative importance of the uncertainties related to monetary valuation were predicted to compare the relative importance of the monetary valuation on the health effect uncertainties. Results The magnitude of the health effects costs depended mostly on discount rate, exposure-response coefficient, and plausibility of the cardiopulmonary mortality. Other mortality outcomes (lung cancer, other non-accidental and infant mortality) and lag had only minor impact on the output. The results highlight the importance of the uncertainties associated with cardiopulmonary mortality in the fine particle impact assessment when compared with other uncertainties. Conclusion When estimating life-expectancy, the estimates used for cardiopulmonary exposure-response coefficient, discount rate, and plausibility require careful assessment, while complicated lag estimates can be omitted without this having any major effect on the results. PMID:17714598

Parameter and model uncertainty in a life-table model for fine particles (PM2.5): a statistical modeling study.

PubMed

Tainio, Marko; Tuomisto, Jouni T; Hänninen, Otto; Ruuskanen, Juhani; Jantunen, Matti J; Pekkanen, Juha

2007-08-23

The estimation of health impacts involves often uncertain input variables and assumptions which have to be incorporated into the model structure. These uncertainties may have significant effects on the results obtained with model, and, thus, on decision making. Fine particles (PM2.5) are believed to cause major health impacts, and, consequently, uncertainties in their health impact assessment have clear relevance to policy-making. We studied the effects of various uncertain input variables by building a life-table model for fine particles. Life-expectancy of the Helsinki metropolitan area population and the change in life-expectancy due to fine particle exposures were predicted using a life-table model. A number of parameter and model uncertainties were estimated. Sensitivity analysis for input variables was performed by calculating rank-order correlations between input and output variables. The studied model uncertainties were (i) plausibility of mortality outcomes and (ii) lag, and parameter uncertainties (iii) exposure-response coefficients for different mortality outcomes, and (iv) exposure estimates for different age groups. The monetary value of the years-of-life-lost and the relative importance of the uncertainties related to monetary valuation were predicted to compare the relative importance of the monetary valuation on the health effect uncertainties. The magnitude of the health effects costs depended mostly on discount rate, exposure-response coefficient, and plausibility of the cardiopulmonary mortality. Other mortality outcomes (lung cancer, other non-accidental and infant mortality) and lag had only minor impact on the output. The results highlight the importance of the uncertainties associated with cardiopulmonary mortality in the fine particle impact assessment when compared with other uncertainties. When estimating life-expectancy, the estimates used for cardiopulmonary exposure-response coefficient, discount rate, and plausibility require careful assessment, while complicated lag estimates can be omitted without this having any major effect on the results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vrugt, Jasper A; Robinson, Bruce A; Ter Braak, Cajo J F

In recent years, a strong debate has emerged in the hydrologic literature regarding what constitutes an appropriate framework for uncertainty estimation. Particularly, there is strong disagreement whether an uncertainty framework should have its roots within a proper statistical (Bayesian) context, or whether such a framework should be based on a different philosophy and implement informal measures and weaker inference to summarize parameter and predictive distributions. In this paper, we compare a formal Bayesian approach using Markov Chain Monte Carlo (MCMC) with generalized likelihood uncertainty estimation (GLUE) for assessing uncertainty in conceptual watershed modeling. Our formal Bayesian approach is implemented usingmore » the recently developed differential evolution adaptive metropolis (DREAM) MCMC scheme with a likelihood function that explicitly considers model structural, input and parameter uncertainty. Our results demonstrate that DREAM and GLUE can generate very similar estimates of total streamflow uncertainty. This suggests that formal and informal Bayesian approaches have more common ground than the hydrologic literature and ongoing debate might suggest. The main advantage of formal approaches is, however, that they attempt to disentangle the effect of forcing, parameter and model structural error on total predictive uncertainty. This is key to improving hydrologic theory and to better understand and predict the flow of water through catchments.« less

Evaluation of Uncertainty in Constituent Input Parameters for Modeling the Fate of RDX

DTIC Science & Technology

2015-07-01

exercise was to evaluate the importance of chemical -specific model input parameters, the impacts of their uncertainty, and the potential benefits of... chemical -specific inputs for RDX that were determined to be sensitive with relatively high uncertainty: these included the soil-water linear...Koc for organic chemicals . The EFS values provided for log Koc of RDX were 1.72 and 1.95. OBJECTIVE: TREECS™ (http://el.erdc.usace.army.mil/treecs

Estimation of parameter uncertainty for an activated sludge model using Bayesian inference: a comparison with the frequentist method.

PubMed

Zonta, Zivko J; Flotats, Xavier; Magrí, Albert

2014-08-01

The procedure commonly used for the assessment of the parameters included in activated sludge models (ASMs) relies on the estimation of their optimal value within a confidence region (i.e. frequentist inference). Once optimal values are estimated, parameter uncertainty is computed through the covariance matrix. However, alternative approaches based on the consideration of the model parameters as probability distributions (i.e. Bayesian inference), may be of interest. The aim of this work is to apply (and compare) both Bayesian and frequentist inference methods when assessing uncertainty for an ASM-type model, which considers intracellular storage and biomass growth, simultaneously. Practical identifiability was addressed exclusively considering respirometric profiles based on the oxygen uptake rate and with the aid of probabilistic global sensitivity analysis. Parameter uncertainty was thus estimated according to both the Bayesian and frequentist inferential procedures. Results were compared in order to evidence the strengths and weaknesses of both approaches. Since it was demonstrated that Bayesian inference could be reduced to a frequentist approach under particular hypotheses, the former can be considered as a more generalist methodology. Hence, the use of Bayesian inference is encouraged for tackling inferential issues in ASM environments.

Hard and Soft Constraints in Reliability-Based Design Optimization

NASA Technical Reports Server (NTRS)

Crespo, L.uis G.; Giesy, Daniel P.; Kenny, Sean P.

2006-01-01

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

Monitoring and modeling as a continuing learning process: the use of hydrological models in a general probabilistic framework.

NASA Astrophysics Data System (ADS)

Baroni, G.; Gräff, T.; Reinstorf, F.; Oswald, S. E.

2012-04-01

Nowadays uncertainty and sensitivity analysis are considered basic tools for the assessment of hydrological models and the evaluation of the most important sources of uncertainty. In this context, in the last decades several methods have been developed and applied in different hydrological conditions. However, in most of the cases, the studies have been done by investigating mainly the influence of the parameter uncertainty on the simulated outputs and few approaches tried to consider also other sources of uncertainty i.e. input and model structure. Moreover, several constrains arise when spatially distributed parameters are involved. To overcome these limitations a general probabilistic framework based on Monte Carlo simulations and the Sobol method has been proposed. In this study, the general probabilistic framework was applied at field scale using a 1D physical-based hydrological model (SWAP). Furthermore, the framework was extended at catchment scale in combination with a spatially distributed hydrological model (SHETRAN). The models are applied in two different experimental sites in Germany: a relatively flat cropped field close to Potsdam (Brandenburg) and a small mountainous catchment with agricultural land use (Schaefertal, Harz Mountains). For both cases, input and parameters are considered as major sources of uncertainty. Evaluation of the models was based on soil moisture detected at plot scale in different depths and, for the catchment site, also with daily discharge values. The study shows how the framework can take into account all the various sources of uncertainty i.e. input data, parameters (either in scalar or spatially distributed form) and model structures. The framework can be used in a loop in order to optimize further monitoring activities used to improve the performance of the model. In the particular applications, the results show how the sources of uncertainty are specific for each process considered. The influence of the input data as well as the presence of compensating errors become clear by the different processes simulated.

The integrated effects of future climate and hydrologic uncertainty on sustainable flood risk management

NASA Astrophysics Data System (ADS)

Steinschneider, S.; Wi, S.; Brown, C. M.

2013-12-01

Flood risk management performance is investigated within the context of integrated climate and hydrologic modeling uncertainty to explore system robustness. The research question investigated is whether structural and hydrologic parameterization uncertainties are significant relative to other uncertainties such as climate change when considering water resources system performance. Two hydrologic models are considered, a conceptual, lumped parameter model that preserves the water balance and a physically-based model that preserves both water and energy balances. In the conceptual model, parameter and structural uncertainties are quantified and propagated through the analysis using a Bayesian modeling framework with an innovative error model. Mean climate changes and internal climate variability are explored using an ensemble of simulations from a stochastic weather generator. The approach presented can be used to quantify the sensitivity of flood protection adequacy to different sources of uncertainty in the climate and hydrologic system, enabling the identification of robust projects that maintain adequate performance despite the uncertainties. The method is demonstrated in a case study for the Coralville Reservoir on the Iowa River, where increased flooding over the past several decades has raised questions about potential impacts of climate change on flood protection adequacy.

Mapping (dis)agreement in hydrologic projections

NASA Astrophysics Data System (ADS)

Melsen, Lieke A.; Addor, Nans; Mizukami, Naoki; Newman, Andrew J.; Torfs, Paul J. J. F.; Clark, Martyn P.; Uijlenhoet, Remko; Teuling, Adriaan J.

2018-03-01

Hydrologic projections are of vital socio-economic importance. However, they are also prone to uncertainty. In order to establish a meaningful range of storylines to support water managers in decision making, we need to reveal the relevant sources of uncertainty. Here, we systematically and extensively investigate uncertainty in hydrologic projections for 605 basins throughout the contiguous US. We show that in the majority of the basins, the sign of change in average annual runoff and discharge timing for the period 2070-2100 compared to 1985-2008 differs among combinations of climate models, hydrologic models, and parameters. Mapping the results revealed that different sources of uncertainty dominate in different regions. Hydrologic model induced uncertainty in the sign of change in mean runoff was related to snow processes and aridity, whereas uncertainty in both mean runoff and discharge timing induced by the climate models was related to disagreement among the models regarding the change in precipitation. Overall, disagreement on the sign of change was more widespread for the mean runoff than for the discharge timing. The results demonstrate the need to define a wide range of quantitative hydrologic storylines, including parameter, hydrologic model, and climate model forcing uncertainty, to support water resource planning.

Quantifying uncertainty in NDSHA estimates due to earthquake catalogue

NASA Astrophysics Data System (ADS)

Magrin, Andrea; Peresan, Antonella; Vaccari, Franco; Panza, Giuliano

2014-05-01

The procedure for the neo-deterministic seismic zoning, NDSHA, is based on the calculation of synthetic seismograms by the modal summation technique. This approach makes use of information about the space distribution of large magnitude earthquakes, which can be defined based on seismic history and seismotectonics, as well as incorporating information from a wide set of geological and geophysical data (e.g., morphostructural features and ongoing deformation processes identified by earth observations). Hence the method does not make use of attenuation models (GMPE), which may be unable to account for the complexity of the product between seismic source tensor and medium Green function and are often poorly constrained by the available observations. NDSHA defines the hazard from the envelope of the values of ground motion parameters determined considering a wide set of scenario earthquakes; accordingly, the simplest outcome of this method is a map where the maximum of a given seismic parameter is associated to each site. In NDSHA uncertainties are not statistically treated as in PSHA, where aleatory uncertainty is traditionally handled with probability density functions (e.g., for magnitude and distance random variables) and epistemic uncertainty is considered by applying logic trees that allow the use of alternative models and alternative parameter values of each model, but the treatment of uncertainties is performed by sensitivity analyses for key modelling parameters. To fix the uncertainty related to a particular input parameter is an important component of the procedure. The input parameters must account for the uncertainty in the prediction of fault radiation and in the use of Green functions for a given medium. A key parameter is the magnitude of sources used in the simulation that is based on catalogue informations, seismogenic zones and seismogenic nodes. Because the largest part of the existing catalogues is based on macroseismic intensity, a rough estimate of ground motion error can therefore be the factor of 2, intrinsic in MCS scale. We tested this hypothesis by the analysis of uncertainty in ground motion maps due to the catalogue random errors in magnitude and localization.

Uncertainties in Galactic Chemical Evolution Models

DOE PAGES

Cote, Benoit; Ritter, Christian; Oshea, Brian W.; ...

2016-06-15

Here we use a simple one-zone galactic chemical evolution model to quantify the uncertainties generated by the input parameters in numerical predictions for a galaxy with properties similar to those of the Milky Way. We compiled several studies from the literature to gather the current constraints for our simulations regarding the typical value and uncertainty of the following seven basic parameters: the lower and upper mass limits of the stellar initial mass function (IMF), the slope of the high-mass end of the stellar IMF, the slope of the delay-time distribution function of Type Ia supernovae (SNe Ia), the number ofmore » SNe Ia per M ⊙ formed, the total stellar mass formed, and the final mass of gas. We derived a probability distribution function to express the range of likely values for every parameter, which were then included in a Monte Carlo code to run several hundred simulations with randomly selected input parameters. This approach enables us to analyze the predicted chemical evolution of 16 elements in a statistical manner by identifying the most probable solutions along with their 68% and 95% confidence levels. Our results show that the overall uncertainties are shaped by several input parameters that individually contribute at different metallicities, and thus at different galactic ages. The level of uncertainty then depends on the metallicity and is different from one element to another. Among the seven input parameters considered in this work, the slope of the IMF and the number of SNe Ia are currently the two main sources of uncertainty. The thicknesses of the uncertainty bands bounded by the 68% and 95% confidence levels are generally within 0.3 and 0.6 dex, respectively. When looking at the evolution of individual elements as a function of galactic age instead of metallicity, those same thicknesses range from 0.1 to 0.6 dex for the 68% confidence levels and from 0.3 to 1.0 dex for the 95% confidence levels. The uncertainty in our chemical evolution model does not include uncertainties relating to stellar yields, star formation and merger histories, and modeling assumptions.« less

Spatial variability versus parameter uncertainty in freshwater fate and exposure factors of chemicals.

PubMed

Nijhof, Carl O P; Huijbregts, Mark A J; Golsteijn, Laura; van Zelm, Rosalie

2016-04-01

We compared the influence of spatial variability in environmental characteristics and the uncertainty in measured substance properties of seven chemicals on freshwater fate factors (FFs), representing the residence time in the freshwater environment, and on exposure factors (XFs), representing the dissolved fraction of a chemical. The influence of spatial variability was quantified using the SimpleBox model in which Europe was divided in 100 × 100 km regions, nested in a regional (300 × 300 km) and supra-regional (500 × 500 km) scale. Uncertainty in substance properties was quantified by means of probabilistic modelling. Spatial variability and parameter uncertainty were expressed by the ratio k of the 95%ile and 5%ile of the FF and XF. Our analysis shows that spatial variability ranges in FFs of persistent chemicals that partition predominantly into one environmental compartment was up to 2 orders of magnitude larger compared to uncertainty. For the other (less persistent) chemicals, uncertainty in the FF was up to 1 order of magnitude larger than spatial variability. Variability and uncertainty in freshwater XFs of the seven chemicals was negligible (k < 1.5). We found that, depending on the chemical and emission scenario, accounting for region-specific environmental characteristics in multimedia fate modelling, as well as accounting for parameter uncertainty, can have a significant influence on freshwater fate factor predictions. Therefore, we conclude that it is important that fate factors should not only account for parameter uncertainty, but for spatial variability as well, as this further increases the reliability of ecotoxicological impacts in LCA. Copyright © 2016 Elsevier Ltd. All rights reserved.

Uncertainty Analysis of Air Radiation for Lunar Return Shock Layers

NASA Technical Reports Server (NTRS)

Kleb, Bil; Johnston, Christopher O.

2008-01-01

By leveraging a new uncertainty markup technique, two risk analysis methods are used to compute the uncertainty of lunar-return shock layer radiation predicted by the High temperature Aerothermodynamic Radiation Algorithm (HARA). The effects of epistemic uncertainty, or uncertainty due to a lack of knowledge, is considered for the following modeling parameters: atomic line oscillator strengths, atomic line Stark broadening widths, atomic photoionization cross sections, negative ion photodetachment cross sections, molecular bands oscillator strengths, and electron impact excitation rates. First, a simplified shock layer problem consisting of two constant-property equilibrium layers is considered. The results of this simplified problem show that the atomic nitrogen oscillator strengths and Stark broadening widths in both the vacuum ultraviolet and infrared spectral regions, along with the negative ion continuum, are the dominant uncertainty contributors. Next, three variable property stagnation-line shock layer cases are analyzed: a typical lunar return case and two Fire II cases. For the near-equilibrium lunar return and Fire 1643-second cases, the resulting uncertainties are very similar to the simplified case. Conversely, the relatively nonequilibrium 1636-second case shows significantly larger influence from electron impact excitation rates of both atoms and molecules. For all cases, the total uncertainty in radiative heat flux to the wall due to epistemic uncertainty in modeling parameters is 30% as opposed to the erroneously-small uncertainty levels (plus or minus 6%) found when treating model parameter uncertainties as aleatory (due to chance) instead of epistemic (due to lack of knowledge).

Comparison of different uncertainty techniques in urban stormwater quantity and quality modelling.

PubMed

Dotto, Cintia B S; Mannina, Giorgio; Kleidorfer, Manfred; Vezzaro, Luca; Henrichs, Malte; McCarthy, David T; Freni, Gabriele; Rauch, Wolfgang; Deletic, Ana

2012-05-15

Urban drainage models are important tools used by both practitioners and scientists in the field of stormwater management. These models are often conceptual and usually require calibration using local datasets. The quantification of the uncertainty associated with the models is a must, although it is rarely practiced. The International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, has been working on the development of a framework for defining and assessing uncertainties in the field of urban drainage modelling. A part of that work is the assessment and comparison of different techniques generally used in the uncertainty assessment of the parameters of water models. This paper compares a number of these techniques: the Generalized Likelihood Uncertainty Estimation (GLUE), the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA), an approach based on a multi-objective auto-calibration (a multialgorithm, genetically adaptive multi-objective method, AMALGAM) and a Bayesian approach based on a simplified Markov Chain Monte Carlo method (implemented in the software MICA). To allow a meaningful comparison among the different uncertainty techniques, common criteria have been set for the likelihood formulation, defining the number of simulations, and the measure of uncertainty bounds. Moreover, all the uncertainty techniques were implemented for the same case study, in which the same stormwater quantity and quality model was used alongside the same dataset. The comparison results for a well-posed rainfall/runoff model showed that the four methods provide similar probability distributions of model parameters, and model prediction intervals. For ill-posed water quality model the differences between the results were much wider; and the paper provides the specific advantages and disadvantages of each method. In relation to computational efficiency (i.e. number of iterations required to generate the probability distribution of parameters), it was found that SCEM-UA and AMALGAM produce results quicker than GLUE in terms of required number of simulations. However, GLUE requires the lowest modelling skills and is easy to implement. All non-Bayesian methods have problems with the way they accept behavioural parameter sets, e.g. GLUE, SCEM-UA and AMALGAM have subjective acceptance thresholds, while MICA has usually problem with its hypothesis on normality of residuals. It is concluded that modellers should select the method which is most suitable for the system they are modelling (e.g. complexity of the model's structure including the number of parameters), their skill/knowledge level, the available information, and the purpose of their study. Copyright © 2012 Elsevier Ltd. All rights reserved.

Developing a non-point source P loss indicator in R and its parameter uncertainty assessment using GLUE: a case study in northern China.

PubMed

Su, Jingjun; Du, Xinzhong; Li, Xuyong

2018-05-16

Uncertainty analysis is an important prerequisite for model application. However, the existing phosphorus (P) loss indexes or indicators were rarely evaluated. This study applied generalized likelihood uncertainty estimation (GLUE) method to assess the uncertainty of parameters and modeling outputs of a non-point source (NPS) P indicator constructed in R language. And the influences of subjective choices of likelihood formulation and acceptability threshold of GLUE on model outputs were also detected. The results indicated the following. (1) Parameters RegR 2 , RegSDR 2 , PlossDP fer , PlossDP man , DPDR, and DPR were highly sensitive to overall TP simulation and their value ranges could be reduced by GLUE. (2) Nash efficiency likelihood (L 1 ) seemed to present better ability in accentuating high likelihood value simulations than the exponential function (L 2 ) did. (3) The combined likelihood integrating the criteria of multiple outputs acted better than single likelihood in model uncertainty assessment in terms of reducing the uncertainty band widths and assuring the fitting goodness of whole model outputs. (4) A value of 0.55 appeared to be a modest choice of threshold value to balance the interests between high modeling efficiency and high bracketing efficiency. Results of this study could provide (1) an option to conduct NPS modeling under one single computer platform, (2) important references to the parameter setting for NPS model development in similar regions, (3) useful suggestions for the application of GLUE method in studies with different emphases according to research interests, and (4) important insights into the watershed P management in similar regions.

An Applied Framework for Incorporating Multiple Sources of Uncertainty in Fisheries Stock Assessments.

PubMed

Scott, Finlay; Jardim, Ernesto; Millar, Colin P; Cerviño, Santiago

2016-01-01

Estimating fish stock status is very challenging given the many sources and high levels of uncertainty surrounding the biological processes (e.g. natural variability in the demographic rates), model selection (e.g. choosing growth or stock assessment models) and parameter estimation. Incorporating multiple sources of uncertainty in a stock assessment allows advice to better account for the risks associated with proposed management options, promoting decisions that are more robust to such uncertainty. However, a typical assessment only reports the model fit and variance of estimated parameters, thereby underreporting the overall uncertainty. Additionally, although multiple candidate models may be considered, only one is selected as the 'best' result, effectively rejecting the plausible assumptions behind the other models. We present an applied framework to integrate multiple sources of uncertainty in the stock assessment process. The first step is the generation and conditioning of a suite of stock assessment models that contain different assumptions about the stock and the fishery. The second step is the estimation of parameters, including fitting of the stock assessment models. The final step integrates across all of the results to reconcile the multi-model outcome. The framework is flexible enough to be tailored to particular stocks and fisheries and can draw on information from multiple sources to implement a broad variety of assumptions, making it applicable to stocks with varying levels of data availability The Iberian hake stock in International Council for the Exploration of the Sea (ICES) Divisions VIIIc and IXa is used to demonstrate the framework, starting from length-based stock and indices data. Process and model uncertainty are considered through the growth, natural mortality, fishing mortality, survey catchability and stock-recruitment relationship. Estimation uncertainty is included as part of the fitting process. Simple model averaging is used to integrate across the results and produce a single assessment that considers the multiple sources of uncertainty.

Uncertainty analyses of the calibrated parameter values of a water quality model

NASA Astrophysics Data System (ADS)

Rode, M.; Suhr, U.; Lindenschmidt, K.-E.

2003-04-01

For river basin management water quality models are increasingly used for the analysis and evaluation of different management measures. However substantial uncertainties exist in parameter values depending on the available calibration data. In this paper an uncertainty analysis for a water quality model is presented, which considers the impact of available model calibration data and the variance of input variables. The investigation was conducted based on four extensive flowtime related longitudinal surveys in the River Elbe in the years 1996 to 1999 with varying discharges and seasonal conditions. For the model calculations the deterministic model QSIM of the BfG (Germany) was used. QSIM is a one dimensional water quality model and uses standard algorithms for hydrodynamics and phytoplankton dynamics in running waters, e.g. Michaelis Menten/Monod kinetics, which are used in a wide range of models. The multi-objective calibration of the model was carried out with the nonlinear parameter estimator PEST. The results show that for individual flow time related measuring surveys very good agreements between model calculation and measured values can be obtained. If these parameters are applied to deviating boundary conditions, substantial errors in model calculation can occur. These uncertainties can be decreased with an increased calibration database. More reliable model parameters can be identified, which supply reasonable results for broader boundary conditions. The extension of the application of the parameter set on a wider range of water quality conditions leads to a slight reduction of the model precision for the specific water quality situation. Moreover the investigations show that highly variable water quality variables like the algal biomass always allow a smaller forecast accuracy than variables with lower coefficients of variation like e.g. nitrate.

A methodology for computing uncertainty bounds of multivariable systems based on sector stability theory concepts

NASA Technical Reports Server (NTRS)

Waszak, Martin R.

1992-01-01

The application of a sector-based stability theory approach to the formulation of useful uncertainty descriptions for linear, time-invariant, multivariable systems is explored. A review of basic sector properties and sector-based approach are presented first. The sector-based approach is then applied to several general forms of parameter uncertainty to investigate its advantages and limitations. The results indicate that the sector uncertainty bound can be used effectively to evaluate the impact of parameter uncertainties on the frequency response of the design model. Inherent conservatism is a potential limitation of the sector-based approach, especially for highly dependent uncertain parameters. In addition, the representation of the system dynamics can affect the amount of conservatism reflected in the sector bound. Careful application of the model can help to reduce this conservatism, however, and the solution approach has some degrees of freedom that may be further exploited to reduce the conservatism.

Quantifying and Reducing Curve-Fitting Uncertainty in Isc

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campanelli, Mark; Duck, Benjamin; Emery, Keith

2015-06-14

Current-voltage (I-V) curve measurements of photovoltaic (PV) devices are used to determine performance parameters and to establish traceable calibration chains. Measurement standards specify localized curve fitting methods, e.g., straight-line interpolation/extrapolation of the I-V curve points near short-circuit current, Isc. By considering such fits as statistical linear regressions, uncertainties in the performance parameters are readily quantified. However, the legitimacy of such a computed uncertainty requires that the model be a valid (local) representation of the I-V curve and that the noise be sufficiently well characterized. Using more data points often has the advantage of lowering the uncertainty. However, more data pointsmore » can make the uncertainty in the fit arbitrarily small, and this fit uncertainty misses the dominant residual uncertainty due to so-called model discrepancy. Using objective Bayesian linear regression for straight-line fits for Isc, we investigate an evidence-based method to automatically choose data windows of I-V points with reduced model discrepancy. We also investigate noise effects. Uncertainties, aligned with the Guide to the Expression of Uncertainty in Measurement (GUM), are quantified throughout.« less

Quantifying and Reducing Curve-Fitting Uncertainty in Isc: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campanelli, Mark; Duck, Benjamin; Emery, Keith

Current-voltage (I-V) curve measurements of photovoltaic (PV) devices are used to determine performance parameters and to establish traceable calibration chains. Measurement standards specify localized curve fitting methods, e.g., straight-line interpolation/extrapolation of the I-V curve points near short-circuit current, Isc. By considering such fits as statistical linear regressions, uncertainties in the performance parameters are readily quantified. However, the legitimacy of such a computed uncertainty requires that the model be a valid (local) representation of the I-V curve and that the noise be sufficiently well characterized. Using more data points often has the advantage of lowering the uncertainty. However, more data pointsmore » can make the uncertainty in the fit arbitrarily small, and this fit uncertainty misses the dominant residual uncertainty due to so-called model discrepancy. Using objective Bayesian linear regression for straight-line fits for Isc, we investigate an evidence-based method to automatically choose data windows of I-V points with reduced model discrepancy. We also investigate noise effects. Uncertainties, aligned with the Guide to the Expression of Uncertainty in Measurement (GUM), are quantified throughout.« less

Effects of uncertainties in hydrological modelling. A case study of a mountainous catchment in Southern Norway

NASA Astrophysics Data System (ADS)

Engeland, Kolbjørn; Steinsland, Ingelin; Johansen, Stian Solvang; Petersen-Øverleir, Asgeir; Kolberg, Sjur

2016-05-01

In this study, we explore the effect of uncertainty and poor observation quality on hydrological model calibration and predictions. The Osali catchment in Western Norway was selected as case study and an elevation distributed HBV-model was used. We systematically evaluated the effect of accounting for uncertainty in parameters, precipitation input, temperature input and streamflow observations. For precipitation and temperature we accounted for the interpolation uncertainty, and for streamflow we accounted for rating curve uncertainty. Further, the effects of poorer quality of precipitation input and streamflow observations were explored. Less information about precipitation was obtained by excluding the nearest precipitation station from the analysis, while reduced information about the streamflow was obtained by omitting the highest and lowest streamflow observations when estimating the rating curve. The results showed that including uncertainty in the precipitation and temperature inputs has a negligible effect on the posterior distribution of parameters and for the Nash-Sutcliffe (NS) efficiency for the predicted flows, while the reliability and the continuous rank probability score (CRPS) improves. Less information in precipitation input resulted in a shift in the water balance parameter Pcorr, a model producing smoother streamflow predictions, giving poorer NS and CRPS, but higher reliability. The effect of calibrating the hydrological model using streamflow observations based on different rating curves is mainly seen as variability in the water balance parameter Pcorr. When evaluating predictions, the best evaluation scores were not achieved for the rating curve used for calibration, but for rating curves giving smoother streamflow observations. Less information in streamflow influenced the water balance parameter Pcorr, and increased the spread in evaluation scores by giving both better and worse scores.

Parameter Uncertainty Analysis Using Monte Carlo Simulations for a Regional-Scale Groundwater Model

NASA Astrophysics Data System (ADS)

Zhang, Y.; Pohlmann, K.

2016-12-01

Regional-scale grid-based groundwater models for flow and transport often contain multiple types of parameters that can intensify the challenge of parameter uncertainty analysis. We propose a Monte Carlo approach to systematically quantify the influence of various types of model parameters on groundwater flux and contaminant travel times. The Monte Carlo simulations were conducted based on the steady-state conversion of the original transient model, which was then combined with the PEST sensitivity analysis tool SENSAN and particle tracking software MODPATH. Results identified hydrogeologic units whose hydraulic conductivity can significantly affect groundwater flux, and thirteen out of 173 model parameters that can cause large variation in travel times for contaminant particles originating from given source zones.

Sources of Uncertainty in the Prediction of LAI / fPAR from MODIS

NASA Technical Reports Server (NTRS)

Dungan, Jennifer L.; Ganapol, Barry D.; Brass, James A. (Technical Monitor)

2002-01-01

To explicate the sources of uncertainty in the prediction of biophysical variables over space, consider the general equation: where z is a variable with values on some nominal, ordinal, interval or ratio scale; y is a vector of input variables; u is the spatial support of y and z ; x and u are the spatial locations of y and z , respectively; f is a model and B is the vector of the parameters of this model. Any y or z has a value and a spatial extent which is called its support. Viewed in this way, categories of uncertainty are from variable (e.g. measurement), parameter, positional. support and model (e.g. structural) sources. The prediction of Leaf Area Index (LAI) and the fraction of absorbed photosynthetically active radiation (fPAR) are examples of z variables predicted using model(s) as a function of y variables and spatially constant parameters. The MOD15 algorithm is an example of f, called f(sub 1), with parameters including those defined by one of six biome types and solar and view angles. The Leaf Canopy Model (LCM)2, a nested model that combines leaf radiative transfer with a full canopy reflectance model through the phase function, is a simpler though similar radiative transfer approach to f(sub 1). In a previous study, MOD15 and LCM2 gave similar results for the broadleaf forest biome. Differences between these two models can be used to consider the structural uncertainty in prediction results. In an effort to quantify each of the five sources of uncertainty and rank their relative importance for the LAI/fPAR prediction problem, we used recent data for an EOS Core Validation Site in the broadleaf biome with coincident surface reflectance, vegetation index, fPAR and LAI products from the Moderate Resolution Imaging Spectrometer (MODIS). Uncertainty due to support on the input reflectance variable was characterized using Landsat ETM+ data. Input uncertainties were propagated through the LCM2 model and compared with published uncertainties from the MOD15 algorithm.

Inferring pathological states in cortical neuron microcircuits.

PubMed

Rydzewski, Jakub; Nowak, Wieslaw; Nicosia, Giuseppe

2015-12-07

The brain activity is to a large extent determined by states of neural cortex microcircuits. Unfortunately, accuracy of results from neural circuits׳ mathematical models is often biased by the presence of uncertainties in underlying experimental data. Moreover, due to problems with uncertainties identification in a multidimensional parameters space, it is almost impossible to classify states of the neural cortex, which correspond to a particular set of the parameters. Here, we develop a complete methodology for determining uncertainties and the novel protocol for classifying all states in any neuroinformatic model. Further, we test this protocol on the mathematical, nonlinear model of such a microcircuit developed by Giugliano et al. (2008) and applied in the experimental data analysis of Huntington׳s disease. Up to now, the link between parameter domains in the mathematical model of Huntington׳s disease and the pathological states in cortical microcircuits has remained unclear. In this paper we precisely identify all the uncertainties, the most crucial input parameters and domains that drive the system into an unhealthy state. The scheme proposed here is general and can be easily applied to other mathematical models of biological phenomena. Copyright © 2015 Elsevier Ltd. All rights reserved.

Novel Method for Incorporating Model Uncertainties into Gravitational Wave Parameter Estimates

NASA Astrophysics Data System (ADS)

Moore, Christopher J.; Gair, Jonathan R.

2014-12-01

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications, these models are incomplete, which both reduces the prospects of detection and leads to a systematic error in the parameter estimates. In the analysis of data from gravitational wave detectors, for example, accurate waveform templates can be computed using numerical methods, but the prohibitive cost of these simulations means this can only be done for a small handful of parameters. In this Letter, a novel method to fold model uncertainties into data analysis is proposed; the waveform uncertainty is analytically marginalized over using with a prior distribution constructed by using Gaussian process regression to interpolate the waveform difference from a small training set of accurate templates. The method is well motivated, easy to implement, and no more computationally expensive than standard techniques. The new method is shown to perform extremely well when applied to a toy problem. While we use the application to gravitational wave data analysis to motivate and illustrate the technique, it can be applied in any context where model uncertainties exist.

Using CV-GLUE procedure in analysis of wetland model predictive uncertainty.

PubMed

Huang, Chun-Wei; Lin, Yu-Pin; Chiang, Li-Chi; Wang, Yung-Chieh

2014-07-01

This study develops a procedure that is related to Generalized Likelihood Uncertainty Estimation (GLUE), called the CV-GLUE procedure, for assessing the predictive uncertainty that is associated with different model structures with varying degrees of complexity. The proposed procedure comprises model calibration, validation, and predictive uncertainty estimation in terms of a characteristic coefficient of variation (characteristic CV). The procedure first performed two-stage Monte-Carlo simulations to ensure predictive accuracy by obtaining behavior parameter sets, and then the estimation of CV-values of the model outcomes, which represent the predictive uncertainties for a model structure of interest with its associated behavior parameter sets. Three commonly used wetland models (the first-order K-C model, the plug flow with dispersion model, and the Wetland Water Quality Model; WWQM) were compared based on data that were collected from a free water surface constructed wetland with paddy cultivation in Taipei, Taiwan. The results show that the first-order K-C model, which is simpler than the other two models, has greater predictive uncertainty. This finding shows that predictive uncertainty does not necessarily increase with the complexity of the model structure because in this case, the more simplistic representation (first-order K-C model) of reality results in a higher uncertainty in the prediction made by the model. The CV-GLUE procedure is suggested to be a useful tool not only for designing constructed wetlands but also for other aspects of environmental management. Copyright © 2014 Elsevier Ltd. All rights reserved.

Combined Estimation of Hydrogeologic Conceptual Model and Parameter Uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Meyer, Philip D.; Ye, Ming; Neuman, Shlomo P.

2004-03-01

The objective of the research described in this report is the development and application of a methodology for comprehensively assessing the hydrogeologic uncertainties involved in dose assessment, including uncertainties associated with conceptual models, parameters, and scenarios. This report describes and applies a statistical method to quantitatively estimate the combined uncertainty in model predictions arising from conceptual model and parameter uncertainties. The method relies on model averaging to combine the predictions of a set of alternative models. Implementation is driven by the available data. When there is minimal site-specific data the method can be carried out with prior parameter estimates basedmore » on generic data and subjective prior model probabilities. For sites with observations of system behavior (and optionally data characterizing model parameters), the method uses model calibration to update the prior parameter estimates and model probabilities based on the correspondence between model predictions and site observations. The set of model alternatives can contain both simplified and complex models, with the requirement that all models be based on the same set of data. The method was applied to the geostatistical modeling of air permeability at a fractured rock site. Seven alternative variogram models of log air permeability were considered to represent data from single-hole pneumatic injection tests in six boreholes at the site. Unbiased maximum likelihood estimates of variogram and drift parameters were obtained for each model. Standard information criteria provided an ambiguous ranking of the models, which would not justify selecting one of them and discarding all others as is commonly done in practice. Instead, some of the models were eliminated based on their negligibly small updated probabilities and the rest were used to project the measured log permeabilities by kriging onto a rock volume containing the six boreholes. These four projections, and associated kriging variances, were averaged using the posterior model probabilities as weights. Finally, cross-validation was conducted by eliminating from consideration all data from one borehole at a time, repeating the above process, and comparing the predictive capability of the model-averaged result with that of each individual model. Using two quantitative measures of comparison, the model-averaged result was superior to any individual geostatistical model of log permeability considered.« less

Quantifying parameter uncertainty in stochastic models using the Box Cox transformation

NASA Astrophysics Data System (ADS)

Thyer, Mark; Kuczera, George; Wang, Q. J.

2002-08-01

The Box-Cox transformation is widely used to transform hydrological data to make it approximately Gaussian. Bayesian evaluation of parameter uncertainty in stochastic models using the Box-Cox transformation is hindered by the fact that there is no analytical solution for the posterior distribution. However, the Markov chain Monte Carlo method known as the Metropolis algorithm can be used to simulate the posterior distribution. This method properly accounts for the nonnegativity constraint implicit in the Box-Cox transformation. Nonetheless, a case study using the AR(1) model uncovered a practical problem with the implementation of the Metropolis algorithm. The use of a multivariate Gaussian jump distribution resulted in unacceptable convergence behaviour. This was rectified by developing suitable parameter transformations for the mean and variance of the AR(1) process to remove the strong nonlinear dependencies with the Box-Cox transformation parameter. Applying this methodology to the Sydney annual rainfall data and the Burdekin River annual runoff data illustrates the efficacy of these parameter transformations and demonstrate the value of quantifying parameter uncertainty.

A Bayesian Network Based Global Sensitivity Analysis Method for Identifying Dominant Processes in a Multi-physics Model

NASA Astrophysics Data System (ADS)

Dai, H.; Chen, X.; Ye, M.; Song, X.; Zachara, J. M.

2016-12-01

Sensitivity analysis has been an important tool in groundwater modeling to identify the influential parameters. Among various sensitivity analysis methods, the variance-based global sensitivity analysis has gained popularity for its model independence characteristic and capability of providing accurate sensitivity measurements. However, the conventional variance-based method only considers uncertainty contribution of single model parameters. In this research, we extended the variance-based method to consider more uncertainty sources and developed a new framework to allow flexible combinations of different uncertainty components. We decompose the uncertainty sources into a hierarchical three-layer structure: scenario, model and parametric. Furthermore, each layer of uncertainty source is capable of containing multiple components. An uncertainty and sensitivity analysis framework was then constructed following this three-layer structure using Bayesian network. Different uncertainty components are represented as uncertain nodes in this network. Through the framework, variance-based sensitivity analysis can be implemented with great flexibility of using different grouping strategies for uncertainty components. The variance-based sensitivity analysis thus is improved to be able to investigate the importance of an extended range of uncertainty sources: scenario, model, and other different combinations of uncertainty components which can represent certain key model system processes (e.g., groundwater recharge process, flow reactive transport process). For test and demonstration purposes, the developed methodology was implemented into a test case of real-world groundwater reactive transport modeling with various uncertainty sources. The results demonstrate that the new sensitivity analysis method is able to estimate accurate importance measurements for any uncertainty sources which were formed by different combinations of uncertainty components. The new methodology can provide useful information for environmental management and decision-makers to formulate policies and strategies.

Sensitivity analysis and uncertainty estimation in ash concentration simulations and tephra deposit daily forecasted at Mt. Etna, in Italy

NASA Astrophysics Data System (ADS)

Prestifilippo, Michele; Scollo, Simona; Tarantola, Stefano

2015-04-01

The uncertainty in volcanic ash forecasts may depend on our knowledge of the model input parameters and our capability to represent the dynamic of an incoming eruption. Forecasts help governments to reduce risks associated with volcanic eruptions and for this reason different kinds of analysis that help to understand the effect that each input parameter has on model outputs are necessary. We present an iterative approach based on the sequential combination of sensitivity analysis, parameter estimation procedure and Monte Carlo-based uncertainty analysis, applied to the lagrangian volcanic ash dispersal model PUFF. We modify the main input parameters as the total mass, the total grain-size distribution, the plume thickness, the shape of the eruption column, the sedimentation models and the diffusion coefficient, perform thousands of simulations and analyze the results. The study is carried out on two different Etna scenarios: the sub-plinian eruption of 22 July 1998 that formed an eruption column rising 12 km above sea level and lasted some minutes and the lava fountain eruption having features similar to the 2011-2013 events that produced eruption column high up to several kilometers above sea level and lasted some hours. Sensitivity analyses and uncertainty estimation results help us to address the measurements that volcanologists should perform during volcanic crisis to reduce the model uncertainty.

Ensemble-based flash-flood modelling: Taking into account hydrodynamic parameters and initial soil moisture uncertainties

NASA Astrophysics Data System (ADS)

Edouard, Simon; Vincendon, Béatrice; Ducrocq, Véronique

2018-05-01

Intense precipitation events in the Mediterranean often lead to devastating flash floods (FF). FF modelling is affected by several kinds of uncertainties and Hydrological Ensemble Prediction Systems (HEPS) are designed to take those uncertainties into account. The major source of uncertainty comes from rainfall forcing and convective-scale meteorological ensemble prediction systems can manage it for forecasting purpose. But other sources are related to the hydrological modelling part of the HEPS. This study focuses on the uncertainties arising from the hydrological model parameters and initial soil moisture with aim to design an ensemble-based version of an hydrological model dedicated to Mediterranean fast responding rivers simulations, the ISBA-TOP coupled system. The first step consists in identifying the parameters that have the strongest influence on FF simulations by assuming perfect precipitation. A sensitivity study is carried out first using a synthetic framework and then for several real events and several catchments. Perturbation methods varying the most sensitive parameters as well as initial soil moisture allow designing an ensemble-based version of ISBA-TOP. The first results of this system on some real events are presented. The direct perspective of this work will be to drive this ensemble-based version with the members of a convective-scale meteorological ensemble prediction system to design a complete HEPS for FF forecasting.

Bayesian Assessment of the Uncertainties of Estimates of a Conceptual Rainfall-Runoff Model Parameters

NASA Astrophysics Data System (ADS)

Silva, F. E. O. E.; Naghettini, M. D. C.; Fernandes, W.

2014-12-01

This paper evaluated the uncertainties associated with the estimation of the parameters of a conceptual rainfall-runoff model, through the use of Bayesian inference techniques by Monte Carlo simulation. The Pará River sub-basin, located in the upper São Francisco river basin, in southeastern Brazil, was selected for developing the studies. In this paper, we used the Rio Grande conceptual hydrologic model (EHR/UFMG, 2001) and the Markov Chain Monte Carlo simulation method named DREAM (VRUGT, 2008a). Two probabilistic models for the residues were analyzed: (i) the classic [Normal likelihood - r ≈ N (0, σ²)]; and (ii) a generalized likelihood (SCHOUPS & VRUGT, 2010), in which it is assumed that the differences between observed and simulated flows are correlated, non-stationary, and distributed as a Skew Exponential Power density. The assumptions made for both models were checked to ensure that the estimation of uncertainties in the parameters was not biased. The results showed that the Bayesian approach proved to be adequate to the proposed objectives, enabling and reinforcing the importance of assessing the uncertainties associated with hydrological modeling.

Estimation of environment-related properties of chemicals for design of sustainable processes: development of group-contribution+ (GC+) property models and uncertainty analysis.

PubMed

Hukkerikar, Amol Shivajirao; Kalakul, Sawitree; Sarup, Bent; Young, Douglas M; Sin, Gürkan; Gani, Rafiqul

2012-11-26

The aim of this work is to develop group-contribution(+) (GC(+)) method (combined group-contribution (GC) method and atom connectivity index (CI) method) based property models to provide reliable estimations of environment-related properties of organic chemicals together with uncertainties of estimated property values. For this purpose, a systematic methodology for property modeling and uncertainty analysis is used. The methodology includes a parameter estimation step to determine parameters of property models and an uncertainty analysis step to establish statistical information about the quality of parameter estimation, such as the parameter covariance, the standard errors in predicted properties, and the confidence intervals. For parameter estimation, large data sets of experimentally measured property values of a wide range of chemicals (hydrocarbons, oxygenated chemicals, nitrogenated chemicals, poly functional chemicals, etc.) taken from the database of the US Environmental Protection Agency (EPA) and from the database of USEtox is used. For property modeling and uncertainty analysis, the Marrero and Gani GC method and atom connectivity index method have been considered. In total, 22 environment-related properties, which include the fathead minnow 96-h LC(50), Daphnia magna 48-h LC(50), oral rat LD(50), aqueous solubility, bioconcentration factor, permissible exposure limit (OSHA-TWA), photochemical oxidation potential, global warming potential, ozone depletion potential, acidification potential, emission to urban air (carcinogenic and noncarcinogenic), emission to continental rural air (carcinogenic and noncarcinogenic), emission to continental fresh water (carcinogenic and noncarcinogenic), emission to continental seawater (carcinogenic and noncarcinogenic), emission to continental natural soil (carcinogenic and noncarcinogenic), and emission to continental agricultural soil (carcinogenic and noncarcinogenic) have been modeled and analyzed. The application of the developed property models for the estimation of environment-related properties and uncertainties of the estimated property values is highlighted through an illustrative example. The developed property models provide reliable estimates of environment-related properties needed to perform process synthesis, design, and analysis of sustainable chemical processes and allow one to evaluate the effect of uncertainties of estimated property values on the calculated performance of processes giving useful insights into quality and reliability of the design of sustainable processes.

Modelling uncertainties and possible future trends of precipitation and temperature for 10 sub-basins in Columbia River Basin (CRB)

NASA Astrophysics Data System (ADS)

Ahmadalipour, A.; Rana, A.; Qin, Y.; Moradkhani, H.

2014-12-01

Trends and changes in future climatic parameters, such as, precipitation and temperature have been a central part of climate change studies. In the present work, we have analyzed the seasonal and yearly trends and uncertainties of prediction in all the 10 sub-basins of Columbia River Basin (CRB) for future time period of 2010-2099. The work is carried out using 2 different sets of statistically downscaled Global Climate Model (GCMs) projection datasets i.e. Bias correction and statistical downscaling (BCSD) generated at Portland State University and The Multivariate Adaptive Constructed Analogs (MACA) generated at University of Idaho. The analysis is done for with 10 GCM downscaled products each from CMIP5 daily dataset totaling to 40 different downscaled products for robust analysis. Summer, winter and yearly trend analysis is performed for all the 10 sub-basins using linear regression (significance tested by student t test) and Mann Kendall test (0.05 percent significance level), for precipitation (P), temperature maximum (Tmax) and temperature minimum (Tmin). Thereafter, all the parameters are modelled for uncertainty, across all models, in all the 10 sub-basins and across the CRB for future scenario periods. Results have indicated in varied degree of trends for all the sub-basins, mostly pointing towards a significant increase in all three climatic parameters, for all the seasons and yearly considerations. Uncertainty analysis have reveled very high change in all the parameters across models and sub-basins under consideration. Basin wide uncertainty analysis is performed to corroborate results from smaller, sub-basin scale. Similar trends and uncertainties are reported on the larger scale as well. Interestingly, both trends and uncertainties are higher during winter period than during summer, contributing to large part of the yearly change.

PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON UNCERTAINTY, SENSITIVITY, AND PARAMETER ESTIMATION FOR MULTIMEDIA ENVIRONMENTAL MODELING. EPA/600/R-04/117, NUREG/CP-0187, ERDC SR-04-2.

EPA Science Inventory

An International Workshop on Uncertainty, Sensitivity, and Parameter Estimation for Multimedia Environmental Modeling was held August 1921, 2003, at the U.S. Nuclear Regulatory Commission Headquarters in Rockville, Maryland, USA. The workshop was organized and convened by the Fe...

Exemplifying the Effects of Parameterization Shortcomings in the Numerical Simulation of Geological Energy and Mass Storage

NASA Astrophysics Data System (ADS)

Dethlefsen, Frank; Tilmann Pfeiffer, Wolf; Schäfer, Dirk

2016-04-01

Numerical simulations of hydraulic, thermal, geomechanical, or geochemical (THMC-) processes in the subsurface have been conducted for decades. Often, such simulations are commenced by applying a parameter set that is as realistic as possible. Then, a base scenario is calibrated on field observations. Finally, scenario simulations can be performed, for instance to forecast the system behavior after varying input data. In the context of subsurface energy and mass storage, however, these model calibrations based on field data are often not available, as these storage actions have not been carried out so far. Consequently, the numerical models merely rely on the parameter set initially selected, and uncertainties as a consequence of a lack of parameter values or process understanding may not be perceivable, not mentioning quantifiable. Therefore, conducting THMC simulations in the context of energy and mass storage deserves a particular review of the model parameterization with its input data, and such a review so far hardly exists to the required extent. Variability or aleatory uncertainty exists for geoscientific parameter values in general, and parameters for that numerous data points are available, such as aquifer permeabilities, may be described statistically thereby exhibiting statistical uncertainty. In this case, sensitivity analyses for quantifying the uncertainty in the simulation resulting from varying this parameter can be conducted. There are other parameters, where the lack of data quantity and quality implies a fundamental changing of ongoing processes when such a parameter value is varied in numerical scenario simulations. As an example for such a scenario uncertainty, varying the capillary entry pressure as one of the multiphase flow parameters can either allow or completely inhibit the penetration of an aquitard by gas. As the last example, the uncertainty of cap-rock fault permeabilities and consequently potential leakage rates of stored gases into shallow compartments are regarded as recognized ignorance by the authors of this study, as no realistic approach exists to determine this parameter and values are best guesses only. In addition to these aleatory uncertainties, an equivalent classification is possible for rating epistemic uncertainties describing the degree of understanding processes such as the geochemical and hydraulic effects following potential gas intrusions from deeper reservoirs into shallow aquifers. As an outcome of this grouping of uncertainties, prediction errors of scenario simulations can be calculated by sensitivity analyses, if the uncertainties are identified as statistical. However, if scenario uncertainties exist or even recognized ignorance has to be attested to a parameter or a process in question, the outcomes of simulations mainly depend on the decision of the modeler by choosing parameter values or by interpreting the occurring of processes. In that case, the informative value of numerical simulations is limited by ambiguous simulation results, which cannot be refined without improving the geoscientific database through laboratory or field studies on a longer term basis, so that the effects of the subsurface use may be predicted realistically. This discussion, amended by a compilation of available geoscientific data to parameterize such simulations, will be presented in this study.

Methodology for Uncertainty Analysis of Dynamic Computational Toxicology Models

EPA Science Inventory

The task of quantifying the uncertainty in both parameter estimates and model predictions has become more important with the increased use of dynamic computational toxicology models by the EPA. Dynamic toxicological models include physiologically-based pharmacokinetic (PBPK) mode...

Aerial robot intelligent control method based on back-stepping

NASA Astrophysics Data System (ADS)

Zhou, Jian; Xue, Qian

2018-05-01

The aerial robot is characterized as strong nonlinearity, high coupling and parameter uncertainty, a self-adaptive back-stepping control method based on neural network is proposed in this paper. The uncertain part of the aerial robot model is compensated online by the neural network of Cerebellum Model Articulation Controller and robust control items are designed to overcome the uncertainty error of the system during online learning. At the same time, particle swarm algorithm is used to optimize and fix parameters so as to improve the dynamic performance, and control law is obtained by the recursion of back-stepping regression. Simulation results show that the designed control law has desired attitude tracking performance and good robustness in case of uncertainties and large errors in the model parameters.

Static and Dynamic Model Update of an Inflatable/Rigidizable Torus Structure

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Reaves, mercedes C.

2006-01-01

The present work addresses the development of an experimental and computational procedure for validating finite element models. A torus structure, part of an inflatable/rigidizable Hexapod, is used to demonstrate the approach. Because of fabrication, materials, and geometric uncertainties, a statistical approach combined with optimization is used to modify key model parameters. Static test results are used to update stiffness parameters and dynamic test results are used to update the mass distribution. Updated parameters are computed using gradient and non-gradient based optimization algorithms. Results show significant improvements in model predictions after parameters are updated. Lessons learned in the areas of test procedures, modeling approaches, and uncertainties quantification are presented.

Are Subject-Specific Musculoskeletal Models Robust to the Uncertainties in Parameter Identification?

PubMed Central

Valente, Giordano; Pitto, Lorenzo; Testi, Debora; Seth, Ajay; Delp, Scott L.; Stagni, Rita; Viceconti, Marco; Taddei, Fulvia

2014-01-01

Subject-specific musculoskeletal modeling can be applied to study musculoskeletal disorders, allowing inclusion of personalized anatomy and properties. Independent of the tools used for model creation, there are unavoidable uncertainties associated with parameter identification, whose effect on model predictions is still not fully understood. The aim of the present study was to analyze the sensitivity of subject-specific model predictions (i.e., joint angles, joint moments, muscle and joint contact forces) during walking to the uncertainties in the identification of body landmark positions, maximum muscle tension and musculotendon geometry. To this aim, we created an MRI-based musculoskeletal model of the lower limbs, defined as a 7-segment, 10-degree-of-freedom articulated linkage, actuated by 84 musculotendon units. We then performed a Monte-Carlo probabilistic analysis perturbing model parameters according to their uncertainty, and solving a typical inverse dynamics and static optimization problem using 500 models that included the different sets of perturbed variable values. Model creation and gait simulations were performed by using freely available software that we developed to standardize the process of model creation, integrate with OpenSim and create probabilistic simulations of movement. The uncertainties in input variables had a moderate effect on model predictions, as muscle and joint contact forces showed maximum standard deviation of 0.3 times body-weight and maximum range of 2.1 times body-weight. In addition, the output variables significantly correlated with few input variables (up to 7 out of 312) across the gait cycle, including the geometry definition of larger muscles and the maximum muscle tension in limited gait portions. Although we found subject-specific models not markedly sensitive to parameter identification, researchers should be aware of the model precision in relation to the intended application. In fact, force predictions could be affected by an uncertainty in the same order of magnitude of its value, although this condition has low probability to occur. PMID:25390896

Model structures amplify uncertainty in predicted soil carbon responses to climate change.

PubMed

Shi, Zheng; Crowell, Sean; Luo, Yiqi; Moore, Berrien

2018-06-04

Large model uncertainty in projected future soil carbon (C) dynamics has been well documented. However, our understanding of the sources of this uncertainty is limited. Here we quantify the uncertainties arising from model parameters, structures and their interactions, and how those uncertainties propagate through different models to projections of future soil carbon stocks. Both the vertically resolved model and the microbial explicit model project much greater uncertainties to climate change than the conventional soil C model, with both positive and negative C-climate feedbacks, whereas the conventional model consistently predicts positive soil C-climate feedback. Our findings suggest that diverse model structures are necessary to increase confidence in soil C projection. However, the larger uncertainty in the complex models also suggests that we need to strike a balance between model complexity and the need to include diverse model structures in order to forecast soil C dynamics with high confidence and low uncertainty.

Computational solution verification and validation applied to a thermal model of a ruggedized instrumentation package

DOE PAGES

Scott, Sarah Nicole; Templeton, Jeremy Alan; Hough, Patricia Diane; ...

2014-01-01

This study details a methodology for quantification of errors and uncertainties of a finite element heat transfer model applied to a Ruggedized Instrumentation Package (RIP). The proposed verification and validation (V&V) process includes solution verification to examine errors associated with the code's solution techniques, and model validation to assess the model's predictive capability for quantities of interest. The model was subjected to mesh resolution and numerical parameters sensitivity studies to determine reasonable parameter values and to understand how they change the overall model response and performance criteria. To facilitate quantification of the uncertainty associated with the mesh, automatic meshing andmore » mesh refining/coarsening algorithms were created and implemented on the complex geometry of the RIP. Automated software to vary model inputs was also developed to determine the solution’s sensitivity to numerical and physical parameters. The model was compared with an experiment to demonstrate its accuracy and determine the importance of both modelled and unmodelled physics in quantifying the results' uncertainty. An emphasis is placed on automating the V&V process to enable uncertainty quantification within tight development schedules.« less

Characterizing Uncertainty and Variability in PBPK Models ...

EPA Pesticide Factsheets

Mode-of-action based risk and safety assessments can rely upon tissue dosimetry estimates in animals and humans obtained from physiologically-based pharmacokinetic (PBPK) modeling. However, risk assessment also increasingly requires characterization of uncertainty and variability; such characterization for PBPK model predictions represents a continuing challenge to both modelers and users. Current practices show significant progress in specifying deterministic biological models and the non-deterministic (often statistical) models, estimating their parameters using diverse data sets from multiple sources, and using them to make predictions and characterize uncertainty and variability. The International Workshop on Uncertainty and Variability in PBPK Models, held Oct 31-Nov 2, 2006, sought to identify the state-of-the-science in this area and recommend priorities for research and changes in practice and implementation. For the short term, these include: (1) multidisciplinary teams to integrate deterministic and non-deterministic/statistical models; (2) broader use of sensitivity analyses, including for structural and global (rather than local) parameter changes; and (3) enhanced transparency and reproducibility through more complete documentation of the model structure(s) and parameter values, the results of sensitivity and other analyses, and supporting, discrepant, or excluded data. Longer-term needs include: (1) theoretic and practical methodological impro

Spectral optimization and uncertainty quantification in combustion modeling

NASA Astrophysics Data System (ADS)

Sheen, David Allan

Reliable simulations of reacting flow systems require a well-characterized, detailed chemical model as a foundation. Accuracy of such a model can be assured, in principle, by a multi-parameter optimization against a set of experimental data. However, the inherent uncertainties in the rate evaluations and experimental data leave a model still characterized by some finite kinetic rate parameter space. Without a careful analysis of how this uncertainty space propagates into the model's predictions, those predictions can at best be trusted only qualitatively. In this work, the Method of Uncertainty Minimization using Polynomial Chaos Expansions is proposed to quantify these uncertainties. In this method, the uncertainty in the rate parameters of the as-compiled model is quantified. Then, the model is subjected to a rigorous multi-parameter optimization, as well as a consistency-screening process. Lastly, the uncertainty of the optimized model is calculated using an inverse spectral optimization technique, and then propagated into a range of simulation conditions. An as-compiled, detailed H2/CO/C1-C4 kinetic model is combined with a set of ethylene combustion data to serve as an example. The idea that the hydrocarbon oxidation model should be understood and developed in a hierarchical fashion has been a major driving force in kinetics research for decades. How this hierarchical strategy works at a quantitative level, however, has never been addressed. In this work, we use ethylene and propane combustion as examples and explore the question of hierarchical model development quantitatively. The Method of Uncertainty Minimization using Polynomial Chaos Expansions is utilized to quantify the amount of information that a particular combustion experiment, and thereby each data set, contributes to the model. This knowledge is applied to explore the relationships among the combustion chemistry of hydrogen/carbon monoxide, ethylene, and larger alkanes. Frequently, new data will become available, and it will be desirable to know the effect that inclusion of these data has on the optimized model. Two cases are considered here. In the first, a study of H2/CO mass burning rates has recently been published, wherein the experimentally-obtained results could not be reconciled with any extant H2/CO oxidation model. It is shown in that an optimized H2/CO model can be developed that will reproduce the results of the new experimental measurements. In addition, the high precision of the new experiments provide a strong constraint on the reaction rate parameters of the chemistry model, manifested in a significant improvement in the precision of simulations. In the second case, species time histories were measured during n-heptane oxidation behind reflected shock waves. The highly precise nature of these measurements is expected to impose critical constraints on chemical kinetic models of hydrocarbon combustion. The results show that while an as-compiled, prior reaction model of n-alkane combustion can be accurate in its prediction of the detailed species profiles, the kinetic parameter uncertainty in the model remains to be too large to obtain a precise prediction of the data. Constraining the prior model against the species time histories within the measurement uncertainties led to notable improvements in the precision of model predictions against the species data as well as the global combustion properties considered. Lastly, we show that while the capability of the multispecies measurement presents a step-change in our precise knowledge of the chemical processes in hydrocarbon combustion, accurate data of global combustion properties are still necessary to predict fuel combustion.

Assimilating multi-source uncertainties of a parsimonious conceptual hydrological model using hierarchical Bayesian modeling

Treesearch

Wei Wu; James Clark; James Vose

2010-01-01

Hierarchical Bayesian (HB) modeling allows for multiple sources of uncertainty by factoring complex relationships into conditional distributions that can be used to draw inference and make predictions. We applied an HB model to estimate the parameters and state variables of a parsimonious hydrological model – GR4J – by coherently assimilating the uncertainties from the...

Effect of soil property uncertainties on permafrost thaw projections: a calibration-constrained analysis

NASA Astrophysics Data System (ADS)

Harp, D. R.; Atchley, A. L.; Painter, S. L.; Coon, E. T.; Wilson, C. J.; Romanovsky, V. E.; Rowland, J. C.

2016-02-01

The effects of soil property uncertainties on permafrost thaw projections are studied using a three-phase subsurface thermal hydrology model and calibration-constrained uncertainty analysis. The null-space Monte Carlo method is used to identify soil hydrothermal parameter combinations that are consistent with borehole temperature measurements at the study site, the Barrow Environmental Observatory. Each parameter combination is then used in a forward projection of permafrost conditions for the 21st century (from calendar year 2006 to 2100) using atmospheric forcings from the Community Earth System Model (CESM) in the Representative Concentration Pathway (RCP) 8.5 greenhouse gas concentration trajectory. A 100-year projection allows for the evaluation of predictive uncertainty (due to soil property (parametric) uncertainty) and the inter-annual climate variability due to year to year differences in CESM climate forcings. After calibrating to measured borehole temperature data at this well-characterized site, soil property uncertainties are still significant and result in significant predictive uncertainties in projected active layer thickness and annual thaw depth-duration even with a specified future climate. Inter-annual climate variability in projected soil moisture content and Stefan number are small. A volume- and time-integrated Stefan number decreases significantly, indicating a shift in subsurface energy utilization in the future climate (latent heat of phase change becomes more important than heat conduction). Out of 10 soil parameters, ALT, annual thaw depth-duration, and Stefan number are highly dependent on mineral soil porosity, while annual mean liquid saturation of the active layer is highly dependent on the mineral soil residual saturation and moderately dependent on peat residual saturation. By comparing the ensemble statistics to the spread of projected permafrost metrics using different climate models, we quantify the relative magnitude of soil property uncertainty to another source of permafrost uncertainty, structural climate model uncertainty. We show that the effect of calibration-constrained uncertainty in soil properties, although significant, is less than that produced by structural climate model uncertainty for this location.

Binary variable multiple-model multiple imputation to address missing data mechanism uncertainty: Application to a smoking cessation trial

PubMed Central

Siddique, Juned; Harel, Ofer; Crespi, Catherine M.; Hedeker, Donald

2014-01-01

The true missing data mechanism is never known in practice. We present a method for generating multiple imputations for binary variables that formally incorporates missing data mechanism uncertainty. Imputations are generated from a distribution of imputation models rather than a single model, with the distribution reflecting subjective notions of missing data mechanism uncertainty. Parameter estimates and standard errors are obtained using rules for nested multiple imputation. Using simulation, we investigate the impact of missing data mechanism uncertainty on post-imputation inferences and show that incorporating this uncertainty can increase the coverage of parameter estimates. We apply our method to a longitudinal smoking cessation trial where nonignorably missing data were a concern. Our method provides a simple approach for formalizing subjective notions regarding nonresponse and can be implemented using existing imputation software. PMID:24634315

Modeling Input Errors to Improve Uncertainty Estimates for Sediment Transport Model Predictions

NASA Astrophysics Data System (ADS)

Jung, J. Y.; Niemann, J. D.; Greimann, B. P.

2016-12-01

Bayesian methods using Markov chain Monte Carlo algorithms have recently been applied to sediment transport models to assess the uncertainty in the model predictions due to the parameter values. Unfortunately, the existing approaches can only attribute overall uncertainty to the parameters. This limitation is critical because no model can produce accurate forecasts if forced with inaccurate input data, even if the model is well founded in physical theory. In this research, an existing Bayesian method is modified to consider the potential errors in input data during the uncertainty evaluation process. The input error is modeled using Gaussian distributions, and the means and standard deviations are treated as uncertain parameters. The proposed approach is tested by coupling it to the Sedimentation and River Hydraulics - One Dimension (SRH-1D) model and simulating a 23-km reach of the Tachia River in Taiwan. The Wu equation in SRH-1D is used for computing the transport capacity for a bed material load of non-cohesive material. Three types of input data are considered uncertain: (1) the input flowrate at the upstream boundary, (2) the water surface elevation at the downstream boundary, and (3) the water surface elevation at a hydraulic structure in the middle of the reach. The benefits of modeling the input errors in the uncertainty analysis are evaluated by comparing the accuracy of the most likely forecast and the coverage of the observed data by the credible intervals to those of the existing method. The results indicate that the internal boundary condition has the largest uncertainty among those considered. Overall, the uncertainty estimates from the new method are notably different from those of the existing method for both the calibration and forecast periods.

Overall uncertainty study of the hydrological impacts of climate change for a Canadian watershed

NASA Astrophysics Data System (ADS)

Chen, Jie; Brissette, FrançOis P.; Poulin, Annie; Leconte, Robert

2011-12-01

General circulation models (GCMs) and greenhouse gas emissions scenarios (GGES) are generally considered to be the two major sources of uncertainty in quantifying the climate change impacts on hydrology. Other sources of uncertainty have been given less attention. This study considers overall uncertainty by combining results from an ensemble of two GGES, six GCMs, five GCM initial conditions, four downscaling techniques, three hydrological model structures, and 10 sets of hydrological model parameters. Each climate projection is equally weighted to predict the hydrology on a Canadian watershed for the 2081-2100 horizon. The results show that the choice of GCM is consistently a major contributor to uncertainty. However, other sources of uncertainty, such as the choice of a downscaling method and the GCM initial conditions, also have a comparable or even larger uncertainty for some hydrological variables. Uncertainties linked to GGES and the hydrological model structure are somewhat less than those related to GCMs and downscaling techniques. Uncertainty due to the hydrological model parameter selection has the least important contribution among all the variables considered. Overall, this research underlines the importance of adequately covering all sources of uncertainty. A failure to do so may result in moderately to severely biased climate change impact studies. Results further indicate that the major contributors to uncertainty vary depending on the hydrological variables selected, and that the methodology presented in this paper is successful at identifying the key sources of uncertainty to consider for a climate change impact study.

Automating calibration, sensitivity and uncertainty analysis of complex models using the R package Flexible Modeling Environment (FME): SWAT as an example

USGS Publications Warehouse

Wu, Y.; Liu, S.

2012-01-01

Parameter optimization and uncertainty issues are a great challenge for the application of large environmental models like the Soil and Water Assessment Tool (SWAT), which is a physically-based hydrological model for simulating water and nutrient cycles at the watershed scale. In this study, we present a comprehensive modeling environment for SWAT, including automated calibration, and sensitivity and uncertainty analysis capabilities through integration with the R package Flexible Modeling Environment (FME). To address challenges (e.g., calling the model in R and transferring variables between Fortran and R) in developing such a two-language coupling framework, 1) we converted the Fortran-based SWAT model to an R function (R-SWAT) using the RFortran platform, and alternatively 2) we compiled SWAT as a Dynamic Link Library (DLL). We then wrapped SWAT (via R-SWAT) with FME to perform complex applications including parameter identifiability, inverse modeling, and sensitivity and uncertainty analysis in the R environment. The final R-SWAT-FME framework has the following key functionalities: automatic initialization of R, running Fortran-based SWAT and R commands in parallel, transferring parameters and model output between SWAT and R, and inverse modeling with visualization. To examine this framework and demonstrate how it works, a case study simulating streamflow in the Cedar River Basin in Iowa in the United Sates was used, and we compared it with the built-in auto-calibration tool of SWAT in parameter optimization. Results indicate that both methods performed well and similarly in searching a set of optimal parameters. Nonetheless, the R-SWAT-FME is more attractive due to its instant visualization, and potential to take advantage of other R packages (e.g., inverse modeling and statistical graphics). The methods presented in the paper are readily adaptable to other model applications that require capability for automated calibration, and sensitivity and uncertainty analysis.

Assessment of Spatial Transferability of Process-Based Hydrological Model Parameters in Two Neighboring Catchments in the Himalayan Region

NASA Astrophysics Data System (ADS)

Nepal, S.

2016-12-01

The spatial transferability of the model parameters of the process-oriented distributed J2000 hydrological model was investigated in two glaciated sub-catchments of the Koshi river basin in eastern Nepal. The basins had a high degree of similarity with respect to their static landscape features. The model was first calibrated (1986-1991) and validated (1992-1997) in the Dudh Koshi sub-catchment. The calibrated and validated model parameters were then transferred to the nearby Tamor catchment (2001-2009). A sensitivity and uncertainty analysis was carried out for both sub-catchments to discover the sensitivity range of the parameters in the two catchments. The model represented the overall hydrograph well in both sub-catchments, including baseflow and medium range flows (rising and recession limbs). The efficiency results according to both Nash-Sutcliffe and the coefficient of determination was above 0.84 in both cases. The sensitivity analysis showed that the same parameter was most sensitive for Nash-Sutcliffe (ENS) and Log Nash-Sutcliffe (LNS) efficiencies in both catchments. However, there were some differences in sensitivity to ENS and LNS for moderate and low sensitive parameters, although the majority (13 out of 16 for ENS and 16 out of 16 for LNS) had a sensitivity response in a similar range. A generalized likelihood uncertainty estimation (GLUE) result suggest that most of the time the observed runoff is within the parameter uncertainty range, although occasionally the values lie outside the uncertainty range, especially during flood peaks and more in the Tamor. This may be due to the limited input data resulting from the small number of precipitation stations and lack of representative stations in high-altitude areas, as well as to model structural uncertainty. The results indicate that transfer of the J2000 parameters to a neighboring catchment in the Himalayan region with similar physiographic landscape characteristics is viable. This indicates the possibility of applying process-based J2000 model be to the ungauged catchments in the Himalayan region, which could provide important insights into the hydrological system dynamics and provide much needed information to support water resources planning and management.

Particle Dark Matter constraints: the effect of Galactic uncertainties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benito, Maria; Bernal, Nicolás; Iocco, Fabio

2017-02-01

Collider, space, and Earth based experiments are now able to probe several extensions of the Standard Model of particle physics which provide viable dark matter candidates. Direct and indirect dark matter searches rely on inputs of astrophysical nature, such as the local dark matter density or the shape of the dark matter density profile in the target in object. The determination of these quantities is highly affected by astrophysical uncertainties. The latter, especially those for our own Galaxy, are ill-known, and often not fully accounted for when analyzing the phenomenology of particle physics models. In this paper we present amore » systematic, quantitative estimate of how astrophysical uncertainties on Galactic quantities (such as the local galactocentric distance, circular velocity, or the morphology of the stellar disk and bulge) propagate to the determination of the phenomenology of particle physics models, thus eventually affecting the determination of new physics parameters. We present results in the context of two specific extensions of the Standard Model (the Singlet Scalar and the Inert Doublet) that we adopt as case studies for their simplicity in illustrating the magnitude and impact of such uncertainties on the parameter space of the particle physics model itself. Our findings point toward very relevant effects of current Galactic uncertainties on the determination of particle physics parameters, and urge a systematic estimate of such uncertainties in more complex scenarios, in order to achieve constraints on the determination of new physics that realistically include all known uncertainties.« less

The Value of Information in Decision-Analytic Modeling for Malaria Vector Control in East Africa.

PubMed

Kim, Dohyeong; Brown, Zachary; Anderson, Richard; Mutero, Clifford; Miranda, Marie Lynn; Wiener, Jonathan; Kramer, Randall

2017-02-01

Decision analysis tools and mathematical modeling are increasingly emphasized in malaria control programs worldwide to improve resource allocation and address ongoing challenges with sustainability. However, such tools require substantial scientific evidence, which is costly to acquire. The value of information (VOI) has been proposed as a metric for gauging the value of reduced model uncertainty. We apply this concept to an evidenced-based Malaria Decision Analysis Support Tool (MDAST) designed for application in East Africa. In developing MDAST, substantial gaps in the scientific evidence base were identified regarding insecticide resistance in malaria vector control and the effectiveness of alternative mosquito control approaches, including larviciding. We identify four entomological parameters in the model (two for insecticide resistance and two for larviciding) that involve high levels of uncertainty and to which outputs in MDAST are sensitive. We estimate and compare a VOI for combinations of these parameters in evaluating three policy alternatives relative to a status quo policy. We find having perfect information on the uncertain parameters could improve program net benefits by up to 5-21%, with the highest VOI associated with jointly eliminating uncertainty about reproductive speed of malaria-transmitting mosquitoes and initial efficacy of larviciding at reducing the emergence of new adult mosquitoes. Future research on parameter uncertainty in decision analysis of malaria control policy should investigate the VOI with respect to other aspects of malaria transmission (such as antimalarial resistance), the costs of reducing uncertainty in these parameters, and the extent to which imperfect information about these parameters can improve payoffs. © 2016 Society for Risk Analysis.

Sources of Uncertainty in Predicting Land Surface Fluxes Using Diverse Data and Models

NASA Technical Reports Server (NTRS)

Dungan, Jennifer L.; Wang, Weile; Michaelis, Andrew; Votava, Petr; Nemani, Ramakrishma

2010-01-01

In the domain of predicting land surface fluxes, models are used to bring data from large observation networks and satellite remote sensing together to make predictions about present and future states of the Earth. Characterizing the uncertainty about such predictions is a complex process and one that is not yet fully understood. Uncertainty exists about initialization, measurement and interpolation of input variables; model parameters; model structure; and mixed spatial and temporal supports. Multiple models or structures often exist to describe the same processes. Uncertainty about structure is currently addressed by running an ensemble of different models and examining the distribution of model outputs. To illustrate structural uncertainty, a multi-model ensemble experiment we have been conducting using the Terrestrial Observation and Prediction System (TOPS) will be discussed. TOPS uses public versions of process-based ecosystem models that use satellite-derived inputs along with surface climate data and land surface characterization to produce predictions of ecosystem fluxes including gross and net primary production and net ecosystem exchange. Using the TOPS framework, we have explored the uncertainty arising from the application of models with different assumptions, structures, parameters, and variable definitions. With a small number of models, this only begins to capture the range of possible spatial fields of ecosystem fluxes. Few attempts have been made to systematically address the components of uncertainty in such a framework. We discuss the characterization of uncertainty for this approach including both quantifiable and poorly known aspects.

A conceptual precipitation-runoff modeling suite: Model selection, calibration and predictive uncertainty assessment

Treesearch

Tyler Jon Smith

2008-01-01

In Montana and much of the Rocky Mountain West, the single most important parameter in forecasting the controls on regional water resources is snowpack. Despite the heightened importance of snowpack, few studies have considered the representation of uncertainty in coupled snowmelt/hydrologic conceptual models. Uncertainty estimation provides a direct interpretation of...

Uncertainty in eddy covariance measurements and its application to physiological models

Treesearch

D.Y. Hollinger; A.D. Richardson; A.D. Richardson

2005-01-01

Flux data are noisy, and this uncertainty is largely due to random measurement error. Knowledge of uncertainty is essential for the statistical evaluation of modeled andmeasured fluxes, for comparison of parameters derived by fitting models to measured fluxes and in formal data-assimilation efforts. We used the difference between simultaneous measurements from two...

Uncertainty assessment of a model for biological nitrogen and phosphorus removal: Application to a large wastewater treatment plant

NASA Astrophysics Data System (ADS)

Mannina, Giorgio; Cosenza, Alida; Viviani, Gaspare

In the last few years, the use of mathematical models in WasteWater Treatment Plant (WWTP) processes has become a common way to predict WWTP behaviour. However, mathematical models generally demand advanced input for their implementation that must be evaluated by an extensive data-gathering campaign, which cannot always be carried out. This fact, together with the intrinsic complexity of the model structure, leads to model results that may be very uncertain. Quantification of the uncertainty is imperative. However, despite the importance of uncertainty quantification, only few studies have been carried out in the wastewater treatment field, and those studies only included a few of the sources of model uncertainty. Seeking the development of the area, the paper presents the uncertainty assessment of a mathematical model simulating biological nitrogen and phosphorus removal. The uncertainty assessment was conducted according to the Generalised Likelihood Uncertainty Estimation (GLUE) methodology that has been scarcely applied in wastewater field. The model was based on activated-sludge models 1 (ASM) and 2 (ASM2). Different approaches can be used for uncertainty analysis. The GLUE methodology requires a large number of Monte Carlo simulations in which a random sampling of individual parameters drawn from probability distributions is used to determine a set of parameter values. Using this approach, model reliability was evaluated based on its capacity to globally limit the uncertainty. The method was applied to a large full-scale WWTP for which quantity and quality data was gathered. The analysis enabled to gain useful insights for WWTP modelling identifying the crucial aspects where higher uncertainty rely and where therefore, more efforts should be provided in terms of both data gathering and modelling practises.

Constraints on CDM cosmology from galaxy power spectrum, CMB and SNIa evolution

NASA Astrophysics Data System (ADS)

Ferramacho, L. D.; Blanchard, A.; Zolnierowski, Y.

2009-05-01

Aims: We examine the constraints that can be obtained on standard cold dark matter models from the most currently used data set: CMB anisotropies, type Ia supernovae and the SDSS luminous red galaxies. We also examine how these constraints are widened when the equation of state parameter w and the curvature parameter Ωk are left as free parameters. Finally, we investigate the impact on these constraints of a possible form of evolution in SNIa intrinsic luminosity. Methods: We obtained our results from MCMC analysis using the full likelihood of each data set. Results: For the ΛCDM model, our “vanilla” model, cosmological parameters are tightly constrained and consistent with current estimates from various methods. When the dark energy parameter w is free we find that the constraints remain mostly unchanged, i.e. changes are smaller than the 1 sigma uncertainties. Similarly, relaxing the assumption of a flat universe leads to nearly identical constraints on the dark energy density parameter of the universe Ω_Λ , baryon density of the universe Ω_b, the optical depth τ, the index of the power spectrum of primordial fluctuations n_S, with most one sigma uncertainties better than 5%. More significant changes appear on other parameters: while preferred values are almost unchanged, uncertainties for the physical dark matter density Ω_ch^2, Hubble constant H0 and σ8 are typically twice as large. The constraint on the age of the Universe, which is very accurate for the vanilla model, is the most degraded. We found that different methodological approaches on large scale structure estimates lead to appreciable differences in preferred values and uncertainty widths. We found that possible evolution in SNIa intrinsic luminosity does not alter these constraints by much, except for w, for which the uncertainty is twice as large. At the same time, this possible evolution is severely constrained. Conclusions: We conclude that systematic uncertainties for some estimated quantities are similar or larger than statistical ones.

Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field

NASA Astrophysics Data System (ADS)

Huang, Ai-Jun; Wang, Dong; Wang, Jia-Ming; Shi, Jia-Dong; Sun, Wen-Yang; Ye, Liu

2017-08-01

In this work, we investigate the quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg XX model with inhomogeneous magnetic field. It has been found that larger coupling strength J between the two spin-chain qubits can effectively reduce the entropic uncertainty. Besides, we observe the mechanics of how the inhomogeneous field influences the uncertainty, and find out that when the inhomogeneous field parameter b<1, the uncertainty will decrease with the decrease of the inhomogeneous field parameter b, conversely, the uncertainty will increase with decreasing b under the condition that b>1. Intriguingly, the entropic uncertainty can shrink to zero when the coupling coefficients are relatively large, while the entropic uncertainty only reduces to 1 with the increase of the homogeneous magnetic field. Additionally, we observe the purity of the state and Bell non-locality and obtain that the entropic uncertainty is anticorrelated with both the purity and Bell non-locality of the evolution state.

Joint analysis of input and parametric uncertainties in watershed water quality modeling: A formal Bayesian approach

NASA Astrophysics Data System (ADS)

Han, Feng; Zheng, Yi

2018-06-01

Significant Input uncertainty is a major source of error in watershed water quality (WWQ) modeling. It remains challenging to address the input uncertainty in a rigorous Bayesian framework. This study develops the Bayesian Analysis of Input and Parametric Uncertainties (BAIPU), an approach for the joint analysis of input and parametric uncertainties through a tight coupling of Markov Chain Monte Carlo (MCMC) analysis and Bayesian Model Averaging (BMA). The formal likelihood function for this approach is derived considering a lag-1 autocorrelated, heteroscedastic, and Skew Exponential Power (SEP) distributed error model. A series of numerical experiments were performed based on a synthetic nitrate pollution case and on a real study case in the Newport Bay Watershed, California. The Soil and Water Assessment Tool (SWAT) and Differential Evolution Adaptive Metropolis (DREAM(ZS)) were used as the representative WWQ model and MCMC algorithm, respectively. The major findings include the following: (1) the BAIPU can be implemented and used to appropriately identify the uncertain parameters and characterize the predictive uncertainty; (2) the compensation effect between the input and parametric uncertainties can seriously mislead the modeling based management decisions, if the input uncertainty is not explicitly accounted for; (3) the BAIPU accounts for the interaction between the input and parametric uncertainties and therefore provides more accurate calibration and uncertainty results than a sequential analysis of the uncertainties; and (4) the BAIPU quantifies the credibility of different input assumptions on a statistical basis and can be implemented as an effective inverse modeling approach to the joint inference of parameters and inputs.

Modeling and Bayesian parameter estimation for shape memory alloy bending actuators

NASA Astrophysics Data System (ADS)

Crews, John H.; Smith, Ralph C.

2012-04-01

In this paper, we employ a homogenized energy model (HEM) for shape memory alloy (SMA) bending actuators. Additionally, we utilize a Bayesian method for quantifying parameter uncertainty. The system consists of a SMA wire attached to a flexible beam. As the actuator is heated, the beam bends, providing endoscopic motion. The model parameters are fit to experimental data using an ordinary least-squares approach. The uncertainty in the fit model parameters is then quantified using Markov Chain Monte Carlo (MCMC) methods. The MCMC algorithm provides bounds on the parameters, which will ultimately be used in robust control algorithms. One purpose of the paper is to test the feasibility of the Random Walk Metropolis algorithm, the MCMC method used here.

Modelling uncertainties in the diffusion-advection equation for radon transport in soil using interval arithmetic.

PubMed

Chakraverty, S; Sahoo, B K; Rao, T D; Karunakar, P; Sapra, B K

2018-02-01

Modelling radon transport in the earth crust is a useful tool to investigate the changes in the geo-physical processes prior to earthquake event. Radon transport is modeled generally through the deterministic advection-diffusion equation. However, in order to determine the magnitudes of parameters governing these processes from experimental measurements, it is necessary to investigate the role of uncertainties in these parameters. Present paper investigates this aspect by combining the concept of interval uncertainties in transport parameters such as soil diffusivity, advection velocity etc, occurring in the radon transport equation as applied to soil matrix. The predictions made with interval arithmetic have been compared and discussed with the results of classical deterministic model. The practical applicability of the model is demonstrated through a case study involving radon flux measurements at the soil surface with an accumulator deployed in steady-state mode. It is possible to detect the presence of very low levels of advection processes by applying uncertainty bounds on the variations in the observed concentration data in the accumulator. The results are further discussed. Copyright © 2017 Elsevier Ltd. All rights reserved.

Effects of Parameter Uncertainty on Long-Term Simulations of Lake Alkalinity

NASA Astrophysics Data System (ADS)

Lee, Sijin; Georgakakos, Konstantine P.; Schnoor, Jerald L.

1990-03-01

A first-order second-moment uncertainty analysis has been applied to two lakes in the Adirondack Park, New York, to assess the long-term response of lakes to acid deposition. Uncertainty due to parameter error and initial condition error was considered. Because the enhanced trickle-down (ETD) model is calibrated with only 3 years of field data and is used to simulate a 50-year period, the uncertainty in the lake alkalinity prediction is relatively large. When a best estimate of parameter uncertainty is used, the annual average alkalinity is predicted to be -11 ±28 μeq/L for Lake Woods and 142 ± 139 μeq/L for Lake Panther after 50 years. Hydrologic parameters and chemical weathering rate constants contributed most to the uncertainty of the simulations. Results indicate that the uncertainty in long-range predictions of lake alkalinity increased significantly over a 5- to 10-year period and then reached a steady state.

Balancing the stochastic description of uncertainties as a function of hydrologic model complexity

NASA Astrophysics Data System (ADS)

Del Giudice, D.; Reichert, P.; Albert, C.; Kalcic, M.; Logsdon Muenich, R.; Scavia, D.; Bosch, N. S.; Michalak, A. M.

2016-12-01

Uncertainty analysis is becoming an important component of forecasting water and pollutant fluxes in urban and rural environments. Properly accounting for errors in the modeling process can help to robustly assess the uncertainties associated with the inputs (e.g. precipitation) and outputs (e.g. runoff) of hydrological models. In recent years we have investigated several Bayesian methods to infer the parameters of a mechanistic hydrological model along with those of the stochastic error component. The latter describes the uncertainties of model outputs and possibly inputs. We have adapted our framework to a variety of applications, ranging from predicting floods in small stormwater systems to nutrient loads in large agricultural watersheds. Given practical constraints, we discuss how in general the number of quantities to infer probabilistically varies inversely with the complexity of the mechanistic model. Most often, when evaluating a hydrological model of intermediate complexity, we can infer the parameters of the model as well as of the output error model. Describing the output errors as a first order autoregressive process can realistically capture the "downstream" effect of inaccurate inputs and structure. With simpler runoff models we can additionally quantify input uncertainty by using a stochastic rainfall process. For complex hydrologic transport models, instead, we show that keeping model parameters fixed and just estimating time-dependent output uncertainties could be a viable option. The common goal across all these applications is to create time-dependent prediction intervals which are both reliable (cover the nominal amount of validation data) and precise (are as narrow as possible). In conclusion, we recommend focusing both on the choice of the hydrological model and of the probabilistic error description. The latter can include output uncertainty only, if the model is computationally-expensive, or, with simpler models, it can separately account for different sources of errors like in the inputs and the structure of the model.

Robust sensor fault detection and isolation of gas turbine engines subjected to time-varying parameter uncertainties

NASA Astrophysics Data System (ADS)

Pourbabaee, Bahareh; Meskin, Nader; Khorasani, Khashayar

2016-08-01

In this paper, a novel robust sensor fault detection and isolation (FDI) strategy using the multiple model-based (MM) approach is proposed that remains robust with respect to both time-varying parameter uncertainties and process and measurement noise in all the channels. The scheme is composed of robust Kalman filters (RKF) that are constructed for multiple piecewise linear (PWL) models that are constructed at various operating points of an uncertain nonlinear system. The parameter uncertainty is modeled by using a time-varying norm bounded admissible structure that affects all the PWL state space matrices. The robust Kalman filter gain matrices are designed by solving two algebraic Riccati equations (AREs) that are expressed as two linear matrix inequality (LMI) feasibility conditions. The proposed multiple RKF-based FDI scheme is simulated for a single spool gas turbine engine to diagnose various sensor faults despite the presence of parameter uncertainties, process and measurement noise. Our comparative studies confirm the superiority of our proposed FDI method when compared to the methods that are available in the literature.

An uncertainty model of acoustic metamaterials with random parameters

NASA Astrophysics Data System (ADS)

He, Z. C.; Hu, J. Y.; Li, Eric

2018-01-01

Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully.

Constraining uncertainties in water supply reliability in a tropical data scarce basin

NASA Astrophysics Data System (ADS)

Kaune, Alexander; Werner, Micha; Rodriguez, Erasmo; de Fraiture, Charlotte

2015-04-01

Assessing the water supply reliability in river basins is essential for adequate planning and development of irrigated agriculture and urban water systems. In many cases hydrological models are applied to determine the surface water availability in river basins. However, surface water availability and variability is often not appropriately quantified due to epistemic uncertainties, leading to water supply insecurity. The objective of this research is to determine the water supply reliability in order to support planning and development of irrigated agriculture in a tropical, data scarce environment. The approach proposed uses a simple hydrological model, but explicitly includes model parameter uncertainty. A transboundary river basin in the tropical region of Colombia and Venezuela with an approximately area of 2100 km² was selected as a case study. The Budyko hydrological framework was extended to consider climatological input variability and model parameter uncertainty, and through this the surface water reliability to satisfy the irrigation and urban demand was estimated. This provides a spatial estimate of the water supply reliability across the basin. For the middle basin the reliability was found to be less than 30% for most of the months when the water is extracted from an upstream source. Conversely, the monthly water supply reliability was high (r>98%) in the lower basin irrigation areas when water was withdrawn from a source located further downstream. Including model parameter uncertainty provides a complete estimate of the water supply reliability, but that estimate is influenced by the uncertainty in the model. Reducing the uncertainty in the model through improved data and perhaps improved model structure will improve the estimate of the water supply reliability allowing better planning of irrigated agriculture and dependable water allocation decisions.

Calibrating the sqHIMMELI v1.0 wetland methane emission model with hierarchical modeling and adaptive MCMC

NASA Astrophysics Data System (ADS)

Susiluoto, Jouni; Raivonen, Maarit; Backman, Leif; Laine, Marko; Makela, Jarmo; Peltola, Olli; Vesala, Timo; Aalto, Tuula

2018-03-01

Estimating methane (CH4) emissions from natural wetlands is complex, and the estimates contain large uncertainties. The models used for the task are typically heavily parameterized and the parameter values are not well known. In this study, we perform a Bayesian model calibration for a new wetland CH4 emission model to improve the quality of the predictions and to understand the limitations of such models.The detailed process model that we analyze contains descriptions for CH4 production from anaerobic respiration, CH4 oxidation, and gas transportation by diffusion, ebullition, and the aerenchyma cells of vascular plants. The processes are controlled by several tunable parameters. We use a hierarchical statistical model to describe the parameters and obtain the posterior distributions of the parameters and uncertainties in the processes with adaptive Markov chain Monte Carlo (MCMC), importance resampling, and time series analysis techniques. For the estimation, the analysis utilizes measurement data from the Siikaneva flux measurement site in southern Finland. The uncertainties related to the parameters and the modeled processes are described quantitatively. At the process level, the flux measurement data are able to constrain the CH4 production processes, methane oxidation, and the different gas transport processes. The posterior covariance structures explain how the parameters and the processes are related. Additionally, the flux and flux component uncertainties are analyzed both at the annual and daily levels. The parameter posterior densities obtained provide information regarding importance of the different processes, which is also useful for development of wetland methane emission models other than the square root HelsinkI Model of MEthane buiLd-up and emIssion for peatlands (sqHIMMELI). The hierarchical modeling allows us to assess the effects of some of the parameters on an annual basis. The results of the calibration and the cross validation suggest that the early spring net primary production could be used to predict parameters affecting the annual methane production. Even though the calibration is specific to the Siikaneva site, the hierarchical modeling approach is well suited for larger-scale studies and the results of the estimation pave way for a regional or global-scale Bayesian calibration of wetland emission models.

Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling

NASA Astrophysics Data System (ADS)

Sutton, Jonathan E.; Guo, Wei; Katsoulakis, Markos A.; Vlachos, Dionisios G.

2016-04-01

Kinetic models based on first principles are becoming common place in heterogeneous catalysis because of their ability to interpret experimental data, identify the rate-controlling step, guide experiments and predict novel materials. To overcome the tremendous computational cost of estimating parameters of complex networks on metal catalysts, approximate quantum mechanical calculations are employed that render models potentially inaccurate. Here, by introducing correlative global sensitivity analysis and uncertainty quantification, we show that neglecting correlations in the energies of species and reactions can lead to an incorrect identification of influential parameters and key reaction intermediates and reactions. We rationalize why models often underpredict reaction rates and show that, despite the uncertainty being large, the method can, in conjunction with experimental data, identify influential missing reaction pathways and provide insights into the catalyst active site and the kinetic reliability of a model. The method is demonstrated in ethanol steam reforming for hydrogen production for fuel cells.

Variability And Uncertainty Analysis Of Contaminant Transport Model Using Fuzzy Latin Hypercube Sampling Technique

NASA Astrophysics Data System (ADS)

Kumar, V.; Nayagum, D.; Thornton, S.; Banwart, S.; Schuhmacher2, M.; Lerner, D.

2006-12-01

Characterization of uncertainty associated with groundwater quality models is often of critical importance, as for example in cases where environmental models are employed in risk assessment. Insufficient data, inherent variability and estimation errors of environmental model parameters introduce uncertainty into model predictions. However, uncertainty analysis using conventional methods such as standard Monte Carlo sampling (MCS) may not be efficient, or even suitable, for complex, computationally demanding models and involving different nature of parametric variability and uncertainty. General MCS or variant of MCS such as Latin Hypercube Sampling (LHS) assumes variability and uncertainty as a single random entity and the generated samples are treated as crisp assuming vagueness as randomness. Also when the models are used as purely predictive tools, uncertainty and variability lead to the need for assessment of the plausible range of model outputs. An improved systematic variability and uncertainty analysis can provide insight into the level of confidence in model estimates, and can aid in assessing how various possible model estimates should be weighed. The present study aims to introduce, Fuzzy Latin Hypercube Sampling (FLHS), a hybrid approach of incorporating cognitive and noncognitive uncertainties. The noncognitive uncertainty such as physical randomness, statistical uncertainty due to limited information, etc can be described by its own probability density function (PDF); whereas the cognitive uncertainty such estimation error etc can be described by the membership function for its fuzziness and confidence interval by ?-cuts. An important property of this theory is its ability to merge inexact generated data of LHS approach to increase the quality of information. The FLHS technique ensures that the entire range of each variable is sampled with proper incorporation of uncertainty and variability. A fuzzified statistical summary of the model results will produce indices of sensitivity and uncertainty that relate the effects of heterogeneity and uncertainty of input variables to model predictions. The feasibility of the method is validated to assess uncertainty propagation of parameter values for estimation of the contamination level of a drinking water supply well due to transport of dissolved phenolics from a contaminated site in the UK.

Evaluation of incremental reactivity and its uncertainty in Southern California.

PubMed

Martien, Philip T; Harley, Robert A; Milford, Jana B; Russell, Armistead G

2003-04-15

The incremental reactivity (IR) and relative incremental reactivity (RIR) of carbon monoxide and 30 individual volatile organic compounds (VOC) were estimated for the South Coast Air Basin using two photochemical air quality models: a 3-D, grid-based model and a vertically resolved trajectory model. Both models include an extended version of the SAPRC99 chemical mechanism. For the 3-D modeling, the decoupled direct method (DDM-3D) was used to assess reactivities. The trajectory model was applied to estimate uncertainties in reactivities due to uncertainties in chemical rate parameters, deposition parameters, and emission rates using Monte Carlo analysis with Latin hypercube sampling. For most VOC, RIRs were found to be consistent in rankings with those produced by Carter using a box model. However, 3-D simulations show that coastal regions, upwind of most of the emissions, have comparatively low IR but higher RIR than predicted by box models for C4-C5 alkenes and carbonyls that initiate the production of HOx radicals. Biogenic VOC emissions were found to have a lower RIR than predicted by box model estimates, because emissions of these VOC were mostly downwind of the areas of primary ozone production. Uncertainties in RIR of individual VOC were found to be dominated by uncertainties in the rate parameters of their primary oxidation reactions. The coefficient of variation (COV) of most RIR values ranged from 20% to 30%, whereas the COV of absolute incremental reactivity ranged from about 30% to 40%. In general, uncertainty and variability both decreased when relative rather than absolute reactivity metrics were used.

'spup' - an R package for uncertainty propagation in spatial environmental modelling

NASA Astrophysics Data System (ADS)

Sawicka, Kasia; Heuvelink, Gerard

2016-04-01

Computer models have become a crucial tool in engineering and environmental sciences for simulating the behaviour of complex static and dynamic systems. However, while many models are deterministic, the uncertainty in their predictions needs to be estimated before they are used for decision support. Currently, advances in uncertainty propagation and assessment have been paralleled by a growing number of software tools for uncertainty analysis, but none has gained recognition for a universal applicability, including case studies with spatial models and spatial model inputs. Due to the growing popularity and applicability of the open source R programming language we undertook a project to develop an R package that facilitates uncertainty propagation analysis in spatial environmental modelling. In particular, the 'spup' package provides functions for examining the uncertainty propagation starting from input data and model parameters, via the environmental model onto model predictions. The functions include uncertainty model specification, stochastic simulation and propagation of uncertainty using Monte Carlo (MC) techniques, as well as several uncertainty visualization functions. Uncertain environmental variables are represented in the package as objects whose attribute values may be uncertain and described by probability distributions. Both numerical and categorical data types are handled. Spatial auto-correlation within an attribute and cross-correlation between attributes is also accommodated for. For uncertainty propagation the package has implemented the MC approach with efficient sampling algorithms, i.e. stratified random sampling and Latin hypercube sampling. The design includes facilitation of parallel computing to speed up MC computation. The MC realizations may be used as an input to the environmental models called from R, or externally. Selected static and interactive visualization methods that are understandable by non-experts with limited background in statistics can be used to summarize and visualize uncertainty about the measured input, model parameters and output of the uncertainty propagation. We demonstrate that the 'spup' package is an effective and easy tool to apply and can be used in multi-disciplinary research and model-based decision support.

'spup' - an R package for uncertainty propagation analysis in spatial environmental modelling

NASA Astrophysics Data System (ADS)

Sawicka, Kasia; Heuvelink, Gerard

2017-04-01

Computer models have become a crucial tool in engineering and environmental sciences for simulating the behaviour of complex static and dynamic systems. However, while many models are deterministic, the uncertainty in their predictions needs to be estimated before they are used for decision support. Currently, advances in uncertainty propagation and assessment have been paralleled by a growing number of software tools for uncertainty analysis, but none has gained recognition for a universal applicability and being able to deal with case studies with spatial models and spatial model inputs. Due to the growing popularity and applicability of the open source R programming language we undertook a project to develop an R package that facilitates uncertainty propagation analysis in spatial environmental modelling. In particular, the 'spup' package provides functions for examining the uncertainty propagation starting from input data and model parameters, via the environmental model onto model predictions. The functions include uncertainty model specification, stochastic simulation and propagation of uncertainty using Monte Carlo (MC) techniques, as well as several uncertainty visualization functions. Uncertain environmental variables are represented in the package as objects whose attribute values may be uncertain and described by probability distributions. Both numerical and categorical data types are handled. Spatial auto-correlation within an attribute and cross-correlation between attributes is also accommodated for. For uncertainty propagation the package has implemented the MC approach with efficient sampling algorithms, i.e. stratified random sampling and Latin hypercube sampling. The design includes facilitation of parallel computing to speed up MC computation. The MC realizations may be used as an input to the environmental models called from R, or externally. Selected visualization methods that are understandable by non-experts with limited background in statistics can be used to summarize and visualize uncertainty about the measured input, model parameters and output of the uncertainty propagation. We demonstrate that the 'spup' package is an effective and easy tool to apply and can be used in multi-disciplinary research and model-based decision support.

Effect of Fault Parameter Uncertainties on PSHA explored by Monte Carlo Simulations: A case study for southern Apennines, Italy

NASA Astrophysics Data System (ADS)

Akinci, A.; Pace, B.

2017-12-01

In this study, we discuss the seismic hazard variability of peak ground acceleration (PGA) at 475 years return period in the Southern Apennines of Italy. The uncertainty and parametric sensitivity are presented to quantify the impact of the several fault parameters on ground motion predictions for 10% exceedance in 50-year hazard. A time-independent PSHA model is constructed based on the long-term recurrence behavior of seismogenic faults adopting the characteristic earthquake model for those sources capable of rupturing the entire fault segment with a single maximum magnitude. The fault-based source model uses the dimensions and slip rates of mapped fault to develop magnitude-frequency estimates for characteristic earthquakes. Variability of the selected fault parameter is given with a truncated normal random variable distribution presented by standard deviation about a mean value. A Monte Carlo approach, based on the random balanced sampling by logic tree, is used in order to capture the uncertainty in seismic hazard calculations. For generating both uncertainty and sensitivity maps, we perform 200 simulations for each of the fault parameters. The results are synthesized both in frequency-magnitude distribution of modeled faults as well as the different maps: the overall uncertainty maps provide a confidence interval for the PGA values and the parameter uncertainty maps determine the sensitivity of hazard assessment to variability of every logic tree branch. These branches of logic tree, analyzed through the Monte Carlo approach, are maximum magnitudes, fault length, fault width, fault dip and slip rates. The overall variability of these parameters is determined by varying them simultaneously in the hazard calculations while the sensitivity of each parameter to overall variability is determined varying each of the fault parameters while fixing others. However, in this study we do not investigate the sensitivity of mean hazard results to the consideration of different GMPEs. Distribution of possible seismic hazard results is illustrated by 95% confidence factor map, which indicates the dispersion about mean value, and coefficient of variation map, which shows percent variability. The results of our study clearly illustrate the influence of active fault parameters to probabilistic seismic hazard maps.

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, Heng; Ye, Ming; Walker, Anthony P.

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averagingmore » methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.« less

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.; Chang, B.-C.; Fischl, Robert

1991-01-01

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Assessing the reliability of dose coefficients for exposure to radioiodine by members of the public, accounting for dosimetric and risk model uncertainties.

PubMed

Puncher, M; Zhang, W; Harrison, J D; Wakeford, R

2017-06-26

Assessments of risk to a specific population group resulting from internal exposure to a particular radionuclide can be used to assess the reliability of the appropriate International Commission on Radiological Protection (ICRP) dose coefficients used as a radiation protection device for the specified exposure pathway. An estimate of the uncertainty on the associated risk is important for informing judgments on reliability; a derived uncertainty factor, UF, is an estimate of the 95% probable geometric difference between the best risk estimate and the nominal risk and is a useful tool for making this assessment. This paper describes the application of parameter uncertainty analysis to quantify uncertainties resulting from internal exposures to radioiodine by members of the public, specifically 1, 10 and 20-year old females from the population of England and Wales. Best estimates of thyroid cancer incidence risk (lifetime attributable risk) are calculated for ingestion or inhalation of 129 I and 131 I, accounting for uncertainties in biokinetic model and cancer risk model parameter values. These estimates are compared with the equivalent ICRP derived nominal age-, sex- and population-averaged estimates of excess thyroid cancer incidence to obtain UFs. Derived UF values for ingestion or inhalation of 131 I for 1 year, 10-year and 20-year olds are around 28, 12 and 6, respectively, when compared with ICRP Publication 103 nominal values, and 9, 7 and 14, respectively, when compared with ICRP Publication 60 values. Broadly similar results were obtained for 129 I. The uncertainties on risk estimates are largely determined by uncertainties on risk model parameters rather than uncertainties on biokinetic model parameters. An examination of the sensitivity of the results to the risk models and populations used in the calculations show variations in the central estimates of risk of a factor of around 2-3. It is assumed that the direct proportionality of excess thyroid cancer risk and dose observed at low to moderate acute doses and incorporated in the risk models also applies to very small doses received at very low dose rates; the uncertainty in this assumption is considerable, but largely unquantifiable. The UF values illustrate the need for an informed approach to the use of ICRP dose and risk coefficients.

A software tool to assess uncertainty in transient-storage model parameters using Monte Carlo simulations

USGS Publications Warehouse

Ward, Adam S.; Kelleher, Christa A.; Mason, Seth J. K.; Wagener, Thorsten; McIntyre, Neil; McGlynn, Brian L.; Runkel, Robert L.; Payn, Robert A.

2017-01-01

Researchers and practitioners alike often need to understand and characterize how water and solutes move through a stream in terms of the relative importance of in-stream and near-stream storage and transport processes. In-channel and subsurface storage processes are highly variable in space and time and difficult to measure. Storage estimates are commonly obtained using transient-storage models (TSMs) of the experimentally obtained solute-tracer test data. The TSM equations represent key transport and storage processes with a suite of numerical parameters. Parameter values are estimated via inverse modeling, in which parameter values are iteratively changed until model simulations closely match observed solute-tracer data. Several investigators have shown that TSM parameter estimates can be highly uncertain. When this is the case, parameter values cannot be used reliably to interpret stream-reach functioning. However, authors of most TSM studies do not evaluate or report parameter certainty. Here, we present a software tool linked to the One-dimensional Transport with Inflow and Storage (OTIS) model that enables researchers to conduct uncertainty analyses via Monte-Carlo parameter sampling and to visualize uncertainty and sensitivity results. We demonstrate application of our tool to 2 case studies and compare our results to output obtained from more traditional implementation of the OTIS model. We conclude by suggesting best practices for transient-storage modeling and recommend that future applications of TSMs include assessments of parameter certainty to support comparisons and more reliable interpretations of transport processes.

Finding optimal vaccination strategies under parameter uncertainty using stochastic programming.

PubMed

Tanner, Matthew W; Sattenspiel, Lisa; Ntaimo, Lewis

2008-10-01

We present a stochastic programming framework for finding the optimal vaccination policy for controlling infectious disease epidemics under parameter uncertainty. Stochastic programming is a popular framework for including the effects of parameter uncertainty in a mathematical optimization model. The problem is initially formulated to find the minimum cost vaccination policy under a chance-constraint. The chance-constraint requires that the probability that R(*)

A physics-based probabilistic forecasting model for rainfall-induced shallow landslides at regional scale

NASA Astrophysics Data System (ADS)

Zhang, Shaojie; Zhao, Luqiang; Delgado-Tellez, Ricardo; Bao, Hongjun

2018-03-01

Conventional outputs of physics-based landslide forecasting models are presented as deterministic warnings by calculating the safety factor (Fs) of potentially dangerous slopes. However, these models are highly dependent on variables such as cohesion force and internal friction angle which are affected by a high degree of uncertainty especially at a regional scale, resulting in unacceptable uncertainties of Fs. Under such circumstances, the outputs of physical models are more suitable if presented in the form of landslide probability values. In order to develop such models, a method to link the uncertainty of soil parameter values with landslide probability is devised. This paper proposes the use of Monte Carlo methods to quantitatively express uncertainty by assigning random values to physical variables inside a defined interval. The inequality Fs < 1 is tested for each pixel in n simulations which are integrated in a unique parameter. This parameter links the landslide probability to the uncertainties of soil mechanical parameters and is used to create a physics-based probabilistic forecasting model for rainfall-induced shallow landslides. The prediction ability of this model was tested in a case study, in which simulated forecasting of landslide disasters associated with heavy rainfalls on 9 July 2013 in the Wenchuan earthquake region of Sichuan province, China, was performed. The proposed model successfully forecasted landslides in 159 of the 176 disaster points registered by the geo-environmental monitoring station of Sichuan province. Such testing results indicate that the new model can be operated in a highly efficient way and show more reliable results, attributable to its high prediction accuracy. Accordingly, the new model can be potentially packaged into a forecasting system for shallow landslides providing technological support for the mitigation of these disasters at regional scale.

Parameterization and Uncertainty Analysis of SWAT model in Hydrological Simulation of Chaohe River Basin

NASA Astrophysics Data System (ADS)

Jie, M.; Zhang, J.; Guo, B. B.

2017-12-01

As a typical distributed hydrological model, the SWAT model also has a challenge in calibrating parameters and analysis their uncertainty. This paper chooses the Chaohe River Basin China as the study area, through the establishment of the SWAT model, loading the DEM data of the Chaohe river basin, the watershed is automatically divided into several sub-basins. Analyzing the land use, soil and slope which are on the basis of the sub-basins and calculating the hydrological response unit (HRU) of the study area, after running SWAT model, the runoff simulation values in the watershed are obtained. On this basis, using weather data, known daily runoff of three hydrological stations, combined with the SWAT-CUP automatic program and the manual adjustment method are used to analyze the multi-site calibration of the model parameters. Furthermore, the GLUE algorithm is used to analyze the parameters uncertainty of the SWAT model. Through the sensitivity analysis, calibration and uncertainty study of SWAT, the results indicate that the parameterization of the hydrological characteristics of the Chaohe river is successful and feasible which can be used to simulate the Chaohe river basin.

The impact of lake and reservoir parameterization on global streamflow simulation.

PubMed

Zajac, Zuzanna; Revilla-Romero, Beatriz; Salamon, Peter; Burek, Peter; Hirpa, Feyera A; Beck, Hylke

2017-05-01

Lakes and reservoirs affect the timing and magnitude of streamflow, and are therefore essential hydrological model components, especially in the context of global flood forecasting. However, the parameterization of lake and reservoir routines on a global scale is subject to considerable uncertainty due to lack of information on lake hydrographic characteristics and reservoir operating rules. In this study we estimated the effect of lakes and reservoirs on global daily streamflow simulations of a spatially-distributed LISFLOOD hydrological model. We applied state-of-the-art global sensitivity and uncertainty analyses for selected catchments to examine the effect of uncertain lake and reservoir parameterization on model performance. Streamflow observations from 390 catchments around the globe and multiple performance measures were used to assess model performance. Results indicate a considerable geographical variability in the lake and reservoir effects on the streamflow simulation. Nash-Sutcliffe Efficiency (NSE) and Kling-Gupta Efficiency (KGE) metrics improved for 65% and 38% of catchments respectively, with median skill score values of 0.16 and 0.2 while scores deteriorated for 28% and 52% of the catchments, with median values -0.09 and -0.16, respectively. The effect of reservoirs on extreme high flows was substantial and widespread in the global domain, while the effect of lakes was spatially limited to a few catchments. As indicated by global sensitivity analysis, parameter uncertainty substantially affected uncertainty of model performance. Reservoir parameters often contributed to this uncertainty, although the effect varied widely among catchments. The effect of reservoir parameters on model performance diminished with distance downstream of reservoirs in favor of other parameters, notably groundwater-related parameters and channel Manning's roughness coefficient. This study underscores the importance of accounting for lakes and, especially, reservoirs and using appropriate parameterization in large-scale hydrological simulations.

Analysis of the uncertainties in the physical calculations of water-moderated power reactors of the VVER type by the parameters of models of preparing few-group constants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bryukhin, V. V., E-mail: bryuhin@yandex.ru; Kurakin, K. Yu.; Uvakin, M. A.

The article covers the uncertainty analysis of the physical calculations of the VVER reactor core for different meshes of the reference values of the feedback parameters (FBP). Various numbers of nodes of the parametric axes of FBPs and different ranges between them are investigated. The uncertainties of the dynamic calculations are analyzed using RTS RCCA ejection as an example within the framework of the model with the boundary conditions at the core inlet and outlet.

Parameter Uncertainty on AGCM-simulated Tropical Cyclones

NASA Astrophysics Data System (ADS)

He, F.

2015-12-01

This work studies the parameter uncertainty on tropical cyclone (TC) simulations in Atmospheric General Circulation Models (AGCMs) using the Reed-Jablonowski TC test case, which is illustrated in Community Atmosphere Model (CAM). It examines the impact from 24 parameters across the physical parameterization schemes that represent the convection, turbulence, precipitation and cloud processes in AGCMs. The one-at-a-time (OAT) sensitivity analysis method first quantifies their relative importance on TC simulations and identifies the key parameters to the six different TC characteristics: intensity, precipitation, longwave cloud radiative forcing (LWCF), shortwave cloud radiative forcing (SWCF), cloud liquid water path (LWP) and ice water path (IWP). Then, 8 physical parameters are chosen and perturbed using the Latin-Hypercube Sampling (LHS) method. The comparison between OAT ensemble run and LHS ensemble run shows that the simulated TC intensity is mainly affected by the parcel fractional mass entrainment rate in Zhang-McFarlane (ZM) deep convection scheme. The nonlinear interactive effect among different physical parameters is negligible on simulated TC intensity. In contrast, this nonlinear interactive effect plays a significant role in other simulated tropical cyclone characteristics (precipitation, LWCF, SWCF, LWP and IWP) and greatly enlarge their simulated uncertainties. The statistical emulator Extended Multivariate Adaptive Regression Splines (EMARS) is applied to characterize the response functions for nonlinear effect. Last, we find that the intensity uncertainty caused by physical parameters is in a degree comparable to uncertainty caused by model structure (e.g. grid) and initial conditions (e.g. sea surface temperature, atmospheric moisture). These findings suggest the importance of using the perturbed physics ensemble (PPE) method to revisit tropical cyclone prediction under climate change scenario.

A new software for deformation source optimization, the Bayesian Earthquake Analysis Tool (BEAT)

NASA Astrophysics Data System (ADS)

Vasyura-Bathke, H.; Dutta, R.; Jonsson, S.; Mai, P. M.

2017-12-01

Modern studies of crustal deformation and the related source estimation, including magmatic and tectonic sources, increasingly use non-linear optimization strategies to estimate geometric and/or kinematic source parameters and often consider both jointly, geodetic and seismic data. Bayesian inference is increasingly being used for estimating posterior distributions of deformation source model parameters, given measured/estimated/assumed data and model uncertainties. For instance, some studies consider uncertainties of a layered medium and propagate these into source parameter uncertainties, while others use informative priors to reduce the model parameter space. In addition, innovative sampling algorithms have been developed to efficiently explore the high-dimensional parameter spaces. Compared to earlier studies, these improvements have resulted in overall more robust source model parameter estimates that include uncertainties. However, the computational burden of these methods is high and estimation codes are rarely made available along with the published results. Even if the codes are accessible, it is usually challenging to assemble them into a single optimization framework as they are typically coded in different programing languages. Therefore, further progress and future applications of these methods/codes are hampered, while reproducibility and validation of results has become essentially impossible. In the spirit of providing open-access and modular codes to facilitate progress and reproducible research in deformation source estimations, we undertook the effort of developing BEAT, a python package that comprises all the above-mentioned features in one single programing environment. The package builds on the pyrocko seismological toolbox (www.pyrocko.org), and uses the pymc3 module for Bayesian statistical model fitting. BEAT is an open-source package (https://github.com/hvasbath/beat), and we encourage and solicit contributions to the project. Here, we present our strategy for developing BEAT and show application examples; especially the effect of including the model prediction uncertainty of the velocity model in following source optimizations: full moment tensor, Mogi source, moderate strike-slip earth-quake.

Using Uncertainty Quantification to Guide Development and Improvements of a Regional-Scale Model of the Coastal Lowlands Aquifer System Spanning Texas, Louisiana, Mississippi, Alabama and Florida

NASA Astrophysics Data System (ADS)

Foster, L. K.; Clark, B. R.; Duncan, L. L.; Tebo, D. T.; White, J.

2017-12-01

Several historical groundwater models exist within the Coastal Lowlands Aquifer System (CLAS), which spans the Gulf Coastal Plain in Texas, Louisiana, Mississippi, Alabama, and Florida. The largest of these models, called the Gulf Coast Regional Aquifer System Analysis (RASA) model, has been brought into a new framework using the Newton formulation for MODFLOW-2005 (MODFLOW-NWT) and serves as the starting point of a new investigation underway by the U.S. Geological Survey to improve understanding of the CLAS and provide predictions of future groundwater availability within an uncertainty quantification (UQ) framework. The use of an UQ framework will not only provide estimates of water-level observation worth, hydraulic parameter uncertainty, boundary-condition uncertainty, and uncertainty of future potential predictions, but it will also guide the model development process. Traditionally, model development proceeds from dataset construction to the process of deterministic history matching, followed by deterministic predictions using the model. This investigation will combine the use of UQ with existing historical models of the study area to assess in a quantitative framework the effect model package and property improvements have on the ability to represent past-system states, as well as the effect on the model's ability to make certain predictions of water levels, water budgets, and base-flow estimates. Estimates of hydraulic property information and boundary conditions from the existing models and literature, forming the prior, will be used to make initial estimates of model forecasts and their corresponding uncertainty, along with an uncalibrated groundwater model run within an unconstrained Monte Carlo analysis. First-Order Second-Moment (FOSM) analysis will also be used to investigate parameter and predictive uncertainty, and guide next steps in model development prior to rigorous history matching by using PEST++ parameter estimation code.

A structured analysis of uncertainty surrounding modeled impacts of groundwater-extraction rules

NASA Astrophysics Data System (ADS)

Guillaume, Joseph H. A.; Qureshi, M. Ejaz; Jakeman, Anthony J.

2012-08-01

Integrating economic and groundwater models for groundwater-management can help improve understanding of trade-offs involved between conflicting socioeconomic and biophysical objectives. However, there is significant uncertainty in most strategic decision-making situations, including in the models constructed to represent them. If not addressed, this uncertainty may be used to challenge the legitimacy of the models and decisions made using them. In this context, a preliminary uncertainty analysis was conducted of a dynamic coupled economic-groundwater model aimed at assessing groundwater extraction rules. The analysis demonstrates how a variety of uncertainties in such a model can be addressed. A number of methods are used including propagation of scenarios and bounds on parameters, multiple models, block bootstrap time-series sampling and robust linear regression for model calibration. These methods are described within the context of a theoretical uncertainty management framework, using a set of fundamental uncertainty management tasks and an uncertainty typology.

A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties

NASA Astrophysics Data System (ADS)

Lü, Hui; Shangguan, Wen-Bin; Yu, Dejie

2017-09-01

Automotive brake systems are always subjected to various types of uncertainties and two types of random-fuzzy uncertainties may exist in the brakes. In this paper, a unified approach is proposed for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties. In the proposed approach, two uncertainty analysis models with mixed variables are introduced to model the random-fuzzy uncertainties. The first one is the random and fuzzy model, in which random variables and fuzzy variables exist simultaneously and independently. The second one is the fuzzy random model, in which uncertain parameters are all treated as random variables while their distribution parameters are expressed as fuzzy numbers. Firstly, the fuzziness is discretized by using α-cut technique and the two uncertainty analysis models are simplified into random-interval models. Afterwards, by temporarily neglecting interval uncertainties, the random-interval models are degraded into random models, in which the expectations, variances, reliability indexes and reliability probabilities of system stability functions are calculated. And then, by reconsidering the interval uncertainties, the bounds of the expectations, variances, reliability indexes and reliability probabilities are computed based on Taylor series expansion. Finally, by recomposing the analysis results at each α-cut level, the fuzzy reliability indexes and probabilities can be obtained, by which the brake squeal instability can be evaluated. The proposed approach gives a general framework to deal with both types of random-fuzzy uncertainties that may exist in the brakes and its effectiveness is demonstrated by numerical examples. It will be a valuable supplement to the systematic study of brake squeal considering uncertainty.

Joint inversion of regional and teleseismic earthquake waveforms

NASA Astrophysics Data System (ADS)

Baker, Mark R.; Doser, Diane I.

1988-03-01

A least squares joint inversion technique for regional and teleseismic waveforms is presented. The mean square error between seismograms and synthetics is minimized using true amplitudes. Matching true amplitudes in modeling requires meaningful estimates of modeling uncertainties and of seismogram signal-to-noise ratios. This also permits calculating linearized uncertainties on the solution based on accuracy and resolution. We use a priori estimates of earthquake parameters to stabilize unresolved parameters, and for comparison with a posteriori uncertainties. We verify the technique on synthetic data, and on the 1983 Borah Peak, Idaho (M = 7.3), earthquake. We demonstrate the inversion on the August 1954 Rainbow Mountain, Nevada (M = 6.8), earthquake and find parameters consistent with previous studies.

Mass discharge estimation from contaminated sites: Multi-model solutions for assessment of conceptual uncertainty

NASA Astrophysics Data System (ADS)

Thomsen, N. I.; Troldborg, M.; McKnight, U. S.; Binning, P. J.; Bjerg, P. L.

2012-04-01

Mass discharge estimates are increasingly being used in the management of contaminated sites. Such estimates have proven useful for supporting decisions related to the prioritization of contaminated sites in a groundwater catchment. Potential management options can be categorised as follows: (1) leave as is, (2) clean up, or (3) further investigation needed. However, mass discharge estimates are often very uncertain, which may hamper the management decisions. If option 1 is incorrectly chosen soil and water quality will decrease, threatening or destroying drinking water resources. The risk of choosing option 2 is to spend money on remediating a site that does not pose a problem. Choosing option 3 will often be safest, but may not be the optimal economic solution. Quantification of the uncertainty in mass discharge estimates can therefore greatly improve the foundation for selecting the appropriate management option. The uncertainty of mass discharge estimates depends greatly on the extent of the site characterization. A good approach for uncertainty estimation will be flexible with respect to the investigation level, and account for both parameter and conceptual model uncertainty. We propose a method for quantifying the uncertainty of dynamic mass discharge estimates from contaminant point sources on the local scale. The method considers both parameter and conceptual uncertainty through a multi-model approach. The multi-model approach evaluates multiple conceptual models for the same site. The different conceptual models consider different source characterizations and hydrogeological descriptions. The idea is to include a set of essentially different conceptual models where each model is believed to be realistic representation of the given site, based on the current level of information. Parameter uncertainty is quantified using Monte Carlo simulations. For each conceptual model we calculate a transient mass discharge estimate with uncertainty bounds resulting from the parametric uncertainty. To quantify the conceptual uncertainty from a given site, we combine the outputs from the different conceptual models using Bayesian model averaging. The weight for each model is obtained by integrating available data and expert knowledge using Bayesian belief networks. The multi-model approach is applied to a contaminated site. At the site a DNAPL (dense non aqueous phase liquid) spill consisting of PCE (perchloroethylene) has contaminated a fractured clay till aquitard overlaying a limestone aquifer. The exact shape and nature of the source is unknown and so is the importance of transport in the fractures. The result of the multi-model approach is a visual representation of the uncertainty of the mass discharge estimates for the site which can be used to support the management options.

Estimating parameters of hidden Markov models based on marked individuals: use of robust design data

USGS Publications Warehouse

Kendall, William L.; White, Gary C.; Hines, James E.; Langtimm, Catherine A.; Yoshizaki, Jun

2012-01-01

Development and use of multistate mark-recapture models, which provide estimates of parameters of Markov processes in the face of imperfect detection, have become common over the last twenty years. Recently, estimating parameters of hidden Markov models, where the state of an individual can be uncertain even when it is detected, has received attention. Previous work has shown that ignoring state uncertainty biases estimates of survival and state transition probabilities, thereby reducing the power to detect effects. Efforts to adjust for state uncertainty have included special cases and a general framework for a single sample per period of interest. We provide a flexible framework for adjusting for state uncertainty in multistate models, while utilizing multiple sampling occasions per period of interest to increase precision and remove parameter redundancy. These models also produce direct estimates of state structure for each primary period, even for the case where there is just one sampling occasion. We apply our model to expected value data, and to data from a study of Florida manatees, to provide examples of the improvement in precision due to secondary capture occasions. We also provide user-friendly software to implement these models. This general framework could also be used by practitioners to consider constrained models of particular interest, or model the relationship between within-primary period parameters (e.g., state structure) and between-primary period parameters (e.g., state transition probabilities).

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

DOE PAGES

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

2017-11-15

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Uncertainties in Parameters Estimated with Neural Networks: Application to Strong Gravitational Lensing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perreault Levasseur, Laurence; Hezaveh, Yashar D.; Wechsler, Risa H.

In Hezaveh et al. (2017) we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for obtaining the uncertainties of these parameters. We review the framework of variational inference to obtain approximate posteriors of Bayesian neural networks and apply it to a network trained to estimate the parameters of the Singular Isothermal Ellipsoid plus external shear and total flux magnification. We show that the method can capture the uncertainties due to different levels of noise in the input data,more » as well as training and architecture-related errors made by the network. To evaluate the accuracy of the resulting uncertainties, we calculate the coverage probabilities of marginalized distributions for each lensing parameter. By tuning a single hyperparameter, the dropout rate, we obtain coverage probabilities approximately equal to the confidence levels for which they were calculated, resulting in accurate and precise uncertainty estimates. Our results suggest that neural networks can be a fast alternative to Monte Carlo Markov Chains for parameter uncertainty estimation in many practical applications, allowing more than seven orders of magnitude improvement in speed.« less

Development and comparison in uncertainty assessment based Bayesian modularization method in hydrological modeling

NASA Astrophysics Data System (ADS)

Li, Lu; Xu, Chong-Yu; Engeland, Kolbjørn

2013-04-01

SummaryWith respect to model calibration, parameter estimation and analysis of uncertainty sources, various regression and probabilistic approaches are used in hydrological modeling. A family of Bayesian methods, which incorporates different sources of information into a single analysis through Bayes' theorem, is widely used for uncertainty assessment. However, none of these approaches can well treat the impact of high flows in hydrological modeling. This study proposes a Bayesian modularization uncertainty assessment approach in which the highest streamflow observations are treated as suspect information that should not influence the inference of the main bulk of the model parameters. This study includes a comprehensive comparison and evaluation of uncertainty assessments by our new Bayesian modularization method and standard Bayesian methods using the Metropolis-Hastings (MH) algorithm with the daily hydrological model WASMOD. Three likelihood functions were used in combination with standard Bayesian method: the AR(1) plus Normal model independent of time (Model 1), the AR(1) plus Normal model dependent on time (Model 2) and the AR(1) plus Multi-normal model (Model 3). The results reveal that the Bayesian modularization method provides the most accurate streamflow estimates measured by the Nash-Sutcliffe efficiency and provide the best in uncertainty estimates for low, medium and entire flows compared to standard Bayesian methods. The study thus provides a new approach for reducing the impact of high flows on the discharge uncertainty assessment of hydrological models via Bayesian method.

Using an ensemble smoother to evaluate parameter uncertainty of an integrated hydrological model of Yanqi basin

NASA Astrophysics Data System (ADS)

Li, Ning; McLaughlin, Dennis; Kinzelbach, Wolfgang; Li, WenPeng; Dong, XinGuang

2015-10-01

Model uncertainty needs to be quantified to provide objective assessments of the reliability of model predictions and of the risk associated with management decisions that rely on these predictions. This is particularly true in water resource studies that depend on model-based assessments of alternative management strategies. In recent decades, Bayesian data assimilation methods have been widely used in hydrology to assess uncertain model parameters and predictions. In this case study, a particular data assimilation algorithm, the Ensemble Smoother with Multiple Data Assimilation (ESMDA) (Emerick and Reynolds, 2012), is used to derive posterior samples of uncertain model parameters and forecasts for a distributed hydrological model of Yanqi basin, China. This model is constructed using MIKESHE/MIKE11software, which provides for coupling between surface and subsurface processes (DHI, 2011a-d). The random samples in the posterior parameter ensemble are obtained by using measurements to update 50 prior parameter samples generated with a Latin Hypercube Sampling (LHS) procedure. The posterior forecast samples are obtained from model runs that use the corresponding posterior parameter samples. Two iterative sample update methods are considered: one based on an a perturbed observation Kalman filter update and one based on a square root Kalman filter update. These alternatives give nearly the same results and converge in only two iterations. The uncertain parameters considered include hydraulic conductivities, drainage and river leakage factors, van Genuchten soil property parameters, and dispersion coefficients. The results show that the uncertainty in many of the parameters is reduced during the smoother updating process, reflecting information obtained from the observations. Some of the parameters are insensitive and do not benefit from measurement information. The correlation coefficients among certain parameters increase in each iteration, although they generally stay below 0.50.

Identification procedure for epistemic uncertainties using inverse fuzzy arithmetic

NASA Astrophysics Data System (ADS)

Haag, T.; Herrmann, J.; Hanss, M.

2010-10-01

For the mathematical representation of systems with epistemic uncertainties, arising, for example, from simplifications in the modeling procedure, models with fuzzy-valued parameters prove to be a suitable and promising approach. In practice, however, the determination of these parameters turns out to be a non-trivial problem. The identification procedure to appropriately update these parameters on the basis of a reference output (measurement or output of an advanced model) requires the solution of an inverse problem. Against this background, an inverse method for the computation of the fuzzy-valued parameters of a model with epistemic uncertainties is presented. This method stands out due to the fact that it only uses feedforward simulations of the model, based on the transformation method of fuzzy arithmetic, along with the reference output. An inversion of the system equations is not necessary. The advancement of the method presented in this paper consists of the identification of multiple input parameters based on a single reference output or measurement. An optimization is used to solve the resulting underdetermined problems by minimizing the uncertainty of the identified parameters. Regions where the identification procedure is reliable are determined by the computation of a feasibility criterion which is also based on the output data of the transformation method only. For a frequency response function of a mechanical system, this criterion allows a restriction of the identification process to some special range of frequency where its solution can be guaranteed. Finally, the practicability of the method is demonstrated by covering the measured output of a fluid-filled piping system by the corresponding uncertain FE model in a conservative way.

Effect of pesticide fate parameters and their uncertainty on the selection of 'worst-case' scenarios of pesticide leaching to groundwater.

PubMed

Vanderborght, Jan; Tiktak, Aaldrik; Boesten, Jos J T I; Vereecken, Harry

2011-03-01

For the registration of pesticides in the European Union, model simulations for worst-case scenarios are used to demonstrate that leaching concentrations to groundwater do not exceed a critical threshold. A worst-case scenario is a combination of soil and climate properties for which predicted leaching concentrations are higher than a certain percentile of the spatial concentration distribution within a region. The derivation of scenarios is complicated by uncertainty about soil and pesticide fate parameters. As the ranking of climate and soil property combinations according to predicted leaching concentrations is different for different pesticides, the worst-case scenario for one pesticide may misrepresent the worst case for another pesticide, which leads to 'scenario uncertainty'. Pesticide fate parameter uncertainty led to higher concentrations in the higher percentiles of spatial concentration distributions, especially for distributions in smaller and more homogeneous regions. The effect of pesticide fate parameter uncertainty on the spatial concentration distribution was small when compared with the uncertainty of local concentration predictions and with the scenario uncertainty. Uncertainty in pesticide fate parameters and scenario uncertainty can be accounted for using higher percentiles of spatial concentration distributions and considering a range of pesticides for the scenario selection. Copyright © 2010 Society of Chemical Industry.

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

DOE PAGES

Safta, Cosmin; Sargsyan, Khachik; Najm, Habib N.; ...

2015-01-01

In this study, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory–epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

Probabilistic methods for sensitivity analysis and calibration in the NASA challenge problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Safta, Cosmin; Sargsyan, Khachik; Najm, Habib N.

In this study, a series of algorithms are proposed to address the problems in the NASA Langley Research Center Multidisciplinary Uncertainty Quantification Challenge. A Bayesian approach is employed to characterize and calibrate the epistemic parameters based on the available data, whereas a variance-based global sensitivity analysis is used to rank the epistemic and aleatory model parameters. A nested sampling of the aleatory–epistemic space is proposed to propagate uncertainties from model parameters to output quantities of interest.

Use of Linear Prediction Uncertainty Analysis to Guide Conditioning of Models Simulating Surface-Water/Groundwater Interactions

NASA Astrophysics Data System (ADS)

Hughes, J. D.; White, J.; Doherty, J.

2011-12-01

Linear prediction uncertainty analysis in a Bayesian framework was applied to guide the conditioning of an integrated surface water/groundwater model that will be used to predict the effects of groundwater withdrawals on surface-water and groundwater flows. Linear prediction uncertainty analysis is an effective approach for identifying (1) raw and processed data most effective for model conditioning prior to inversion, (2) specific observations and periods of time critically sensitive to specific predictions, and (3) additional observation data that would reduce model uncertainty relative to specific predictions. We present results for a two-dimensional groundwater model of a 2,186 km2 area of the Biscayne aquifer in south Florida implicitly coupled to a surface-water routing model of the actively managed canal system. The model domain includes 5 municipal well fields withdrawing more than 1 Mm3/day and 17 operable surface-water control structures that control freshwater releases from the Everglades and freshwater discharges to Biscayne Bay. More than 10 years of daily observation data from 35 groundwater wells and 24 surface water gages are available to condition model parameters. A dense parameterization was used to fully characterize the contribution of the inversion null space to predictive uncertainty and included bias-correction parameters. This approach allows better resolution of the boundary between the inversion null space and solution space. Bias-correction parameters (e.g., rainfall, potential evapotranspiration, and structure flow multipliers) absorb information that is present in structural noise that may otherwise contaminate the estimation of more physically-based model parameters. This allows greater precision in predictions that are entirely solution-space dependent, and reduces the propensity for bias in predictions that are not. Results show that application of this analysis is an effective means of identifying those surface-water and groundwater data, both raw and processed, that minimize predictive uncertainty, while simultaneously identifying the maximum solution-space dimensionality of the inverse problem supported by the data.

Hydrologic Model Selection using Markov chain Monte Carlo methods

NASA Astrophysics Data System (ADS)

Marshall, L.; Sharma, A.; Nott, D.

2002-12-01

Estimation of parameter uncertainty (and in turn model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modelling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve random sampling of the posterior distribution. This study presents an adaptive MCMC sampling algorithm which has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. The MCMC sampling technique is used to compare six alternative configurations of a commonly used conceptual rainfall-runoff model, the Australian Water Balance Model (AWBM), using 11 years of daily rainfall runoff data from the Bass river catchment in Australia. The alternative configurations considered fall into two classes - those that consider model errors to be independent of prior values, and those that model the errors as an autoregressive process. Each such class consists of three formulations that represent increasing levels of complexity (and parameterisation) of the original model structure. The results from this study point both to the importance of using Bayesian approaches in evaluating model performance, as well as the simplicity of the MCMC sampling framework that has the ability to bring such approaches within the reach of the applied hydrological community.

A Bayesian Alternative for Multi-objective Ecohydrological Model Specification

NASA Astrophysics Data System (ADS)

Tang, Y.; Marshall, L. A.; Sharma, A.; Ajami, H.

2015-12-01

Process-based ecohydrological models combine the study of hydrological, physical, biogeochemical and ecological processes of the catchments, which are usually more complex and parametric than conceptual hydrological models. Thus, appropriate calibration objectives and model uncertainty analysis are essential for ecohydrological modeling. In recent years, Bayesian inference has become one of the most popular tools for quantifying the uncertainties in hydrological modeling with the development of Markov Chain Monte Carlo (MCMC) techniques. Our study aims to develop appropriate prior distributions and likelihood functions that minimize the model uncertainties and bias within a Bayesian ecohydrological framework. In our study, a formal Bayesian approach is implemented in an ecohydrological model which combines a hydrological model (HyMOD) and a dynamic vegetation model (DVM). Simulations focused on one objective likelihood (Streamflow/LAI) and multi-objective likelihoods (Streamflow and LAI) with different weights are compared. Uniform, weakly informative and strongly informative prior distributions are used in different simulations. The Kullback-leibler divergence (KLD) is used to measure the dis(similarity) between different priors and corresponding posterior distributions to examine the parameter sensitivity. Results show that different prior distributions can strongly influence posterior distributions for parameters, especially when the available data is limited or parameters are insensitive to the available data. We demonstrate differences in optimized parameters and uncertainty limits in different cases based on multi-objective likelihoods vs. single objective likelihoods. We also demonstrate the importance of appropriately defining the weights of objectives in multi-objective calibration according to different data types.

Probabilistic accounting of uncertainty in forecasts of species distributions under climate change

Treesearch

Seth J. Wenger; Nicholas A. Som; Daniel C. Dauwalter; Daniel J. Isaak; Helen M. Neville; Charles H. Luce; Jason B. Dunham; Michael K. Young; Kurt D. Fausch; Bruce E. Rieman

2013-01-01

Forecasts of species distributions under future climates are inherently uncertain, but there have been few attempts to describe this uncertainty comprehensively in a probabilistic manner. We developed a Monte Carlo approach that accounts for uncertainty within generalized linear regression models (parameter uncertainty and residual error), uncertainty among competing...

Uncertainty Analysis of Inertial Model Attitude Sensor Calibration and Application with a Recommended New Calibration Method

NASA Technical Reports Server (NTRS)

Tripp, John S.; Tcheng, Ping

1999-01-01

Statistical tools, previously developed for nonlinear least-squares estimation of multivariate sensor calibration parameters and the associated calibration uncertainty analysis, have been applied to single- and multiple-axis inertial model attitude sensors used in wind tunnel testing to measure angle of attack and roll angle. The analysis provides confidence and prediction intervals of calibrated sensor measurement uncertainty as functions of applied input pitch and roll angles. A comparative performance study of various experimental designs for inertial sensor calibration is presented along with corroborating experimental data. The importance of replicated calibrations over extended time periods has been emphasized; replication provides independent estimates of calibration precision and bias uncertainties, statistical tests for calibration or modeling bias uncertainty, and statistical tests for sensor parameter drift over time. A set of recommendations for a new standardized model attitude sensor calibration method and usage procedures is included. The statistical information provided by these procedures is necessary for the uncertainty analysis of aerospace test results now required by users of industrial wind tunnel test facilities.

Hard Constraints in Optimization Under Uncertainty

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

2008-01-01

This paper proposes a methodology for the analysis and design of systems subject to parametric uncertainty where design requirements are specified via hard inequality constraints. Hard constraints are those that must be satisfied for all parameter realizations within a given uncertainty model. Uncertainty models given by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles, are the focus of this paper. These models, which are also quite practical, allow for a rigorous mathematical treatment within the proposed framework. Hard constraint feasibility is determined by sizing the largest uncertainty set for which the design requirements are satisfied. Analytically verifiable assessments of robustness are attained by comparing this set with the actual uncertainty model. Strategies that enable the comparison of the robustness characteristics of competing design alternatives, the description and approximation of the robust design space, and the systematic search for designs with improved robustness are also proposed. Since the problem formulation is generic and the tools derived only require standard optimization algorithms for their implementation, this methodology is applicable to a broad range of engineering problems.

A python framework for environmental model uncertainty analysis

USGS Publications Warehouse

White, Jeremy; Fienen, Michael N.; Doherty, John E.

2016-01-01

We have developed pyEMU, a python framework for Environmental Modeling Uncertainty analyses, open-source tool that is non-intrusive, easy-to-use, computationally efficient, and scalable to highly-parameterized inverse problems. The framework implements several types of linear (first-order, second-moment (FOSM)) and non-linear uncertainty analyses. The FOSM-based analyses can also be completed prior to parameter estimation to help inform important modeling decisions, such as parameterization and objective function formulation. Complete workflows for several types of FOSM-based and non-linear analyses are documented in example notebooks implemented using Jupyter that are available in the online pyEMU repository. Example workflows include basic parameter and forecast analyses, data worth analyses, and error-variance analyses, as well as usage of parameter ensemble generation and management capabilities. These workflows document the necessary steps and provides insights into the results, with the goal of educating users not only in how to apply pyEMU, but also in the underlying theory of applied uncertainty quantification.

A fractional factorial probabilistic collocation method for uncertainty propagation of hydrologic model parameters in a reduced dimensional space

NASA Astrophysics Data System (ADS)

Wang, S.; Huang, G. H.; Huang, W.; Fan, Y. R.; Li, Z.

2015-10-01

In this study, a fractional factorial probabilistic collocation method is proposed to reveal statistical significance of hydrologic model parameters and their multi-level interactions affecting model outputs, facilitating uncertainty propagation in a reduced dimensional space. The proposed methodology is applied to the Xiangxi River watershed in China to demonstrate its validity and applicability, as well as its capability of revealing complex and dynamic parameter interactions. A set of reduced polynomial chaos expansions (PCEs) only with statistically significant terms can be obtained based on the results of factorial analysis of variance (ANOVA), achieving a reduction of uncertainty in hydrologic predictions. The predictive performance of reduced PCEs is verified by comparing against standard PCEs and the Monte Carlo with Latin hypercube sampling (MC-LHS) method in terms of reliability, sharpness, and Nash-Sutcliffe efficiency (NSE). Results reveal that the reduced PCEs are able to capture hydrologic behaviors of the Xiangxi River watershed, and they are efficient functional representations for propagating uncertainties in hydrologic predictions.

Reduced uncertainty of regional scale CLM predictions of net carbon fluxes and leaf area indices with estimated plant-specific parameters

NASA Astrophysics Data System (ADS)

Post, Hanna; Hendricks Franssen, Harrie-Jan; Han, Xujun; Baatz, Roland; Montzka, Carsten; Schmidt, Marius; Vereecken, Harry

2016-04-01

Reliable estimates of carbon fluxes and states at regional scales are required to reduce uncertainties in regional carbon balance estimates and to support decision making in environmental politics. In this work the Community Land Model version 4.5 (CLM4.5-BGC) was applied at a high spatial resolution (1 km2) for the Rur catchment in western Germany. In order to improve the model-data consistency of net ecosystem exchange (NEE) and leaf area index (LAI) for this study area, five plant functional type (PFT)-specific CLM4.5-BGC parameters were estimated with time series of half-hourly NEE data for one year in 2011/2012, using the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, a Markov Chain Monte Carlo (MCMC) approach. The parameters were estimated separately for four different plant functional types (needleleaf evergreen temperate tree, broadleaf deciduous temperate tree, C3-grass and C3-crop) at four different sites. The four sites are located inside or close to the Rur catchment. We evaluated modeled NEE for one year in 2012/2013 with NEE measured at seven eddy covariance sites in the catchment, including the four parameter estimation sites. Modeled LAI was evaluated by means of LAI derived from remotely sensed RapidEye images of about 18 days in 2011/2012. Performance indices were based on a comparison between measurements and (i) a reference run with CLM default parameters, and (ii) a 60 instance CLM ensemble with parameters sampled from the DREAM posterior probability density functions (pdfs). The difference between the observed and simulated NEE sum reduced 23% if estimated parameters instead of default parameters were used as input. The mean absolute difference between modeled and measured LAI was reduced by 59% on average. Simulated LAI was not only improved in terms of the absolute value but in some cases also in terms of the timing (beginning of vegetation onset), which was directly related to a substantial improvement of the NEE estimates in spring. In order to obtain a more comprehensive estimate of the model uncertainty, a second CLM ensemble was set up, where initial conditions and atmospheric forcings were perturbed in addition to the parameter estimates. This resulted in very high standard deviations (STD) of the modeled annual NEE sums for C3-grass and C3-crop PFTs, ranging between 24.1 and 225.9 gC m-2 y-1, compared to STD = 0.1 - 3.4 gC m-2 y-1 (effect of parameter uncertainty only, without additional perturbation of initial states and atmospheric forcings). The higher spread of modeled NEE for the C3-crop and C3-grass indicated that the model uncertainty was notably higher for those PFTs compared to the forest-PFTs. Our findings highlight the potential of parameter and uncertainty estimation to support the understanding and further development of land surface models such as CLM.

A Bayesian approach to model structural error and input variability in groundwater modeling

NASA Astrophysics Data System (ADS)

Xu, T.; Valocchi, A. J.; Lin, Y. F. F.; Liang, F.

2015-12-01

Effective water resource management typically relies on numerical models to analyze groundwater flow and solute transport processes. Model structural error (due to simplification and/or misrepresentation of the "true" environmental system) and input forcing variability (which commonly arises since some inputs are uncontrolled or estimated with high uncertainty) are ubiquitous in groundwater models. Calibration that overlooks errors in model structure and input data can lead to biased parameter estimates and compromised predictions. We present a fully Bayesian approach for a complete assessment of uncertainty for spatially distributed groundwater models. The approach explicitly recognizes stochastic input and uses data-driven error models based on nonparametric kernel methods to account for model structural error. We employ exploratory data analysis to assist in specifying informative prior for error models to improve identifiability. The inference is facilitated by an efficient sampling algorithm based on DREAM-ZS and a parameter subspace multiple-try strategy to reduce the required number of forward simulations of the groundwater model. We demonstrate the Bayesian approach through a synthetic case study of surface-ground water interaction under changing pumping conditions. It is found that explicit treatment of errors in model structure and input data (groundwater pumping rate) has substantial impact on the posterior distribution of groundwater model parameters. Using error models reduces predictive bias caused by parameter compensation. In addition, input variability increases parametric and predictive uncertainty. The Bayesian approach allows for a comparison among the contributions from various error sources, which could inform future model improvement and data collection efforts on how to best direct resources towards reducing predictive uncertainty.

The Impact of Uncertain Physical Parameters on HVAC Demand Response

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Yannan; Elizondo, Marcelo A.; Lu, Shuai

HVAC units are currently one of the major resources providing demand response (DR) in residential buildings. Models of HVAC with DR function can improve understanding of its impact on power system operations and facilitate the deployment of DR technologies. This paper investigates the importance of various physical parameters and their distributions to the HVAC response to DR signals, which is a key step to the construction of HVAC models for a population of units with insufficient data. These parameters include the size of floors, insulation efficiency, the amount of solid mass in the house, and efficiency of the HVAC units.more » These parameters are usually assumed to follow Gaussian or Uniform distributions. We study the effect of uncertainty in the chosen parameter distributions on the aggregate HVAC response to DR signals, during transient phase and in steady state. We use a quasi-Monte Carlo sampling method with linear regression and Prony analysis to evaluate sensitivity of DR output to the uncertainty in the distribution parameters. The significance ranking on the uncertainty sources is given for future guidance in the modeling of HVAC demand response.« less

Uncertainty analysis of vegetation distribution in the northern high latitudes during the 21st century with a dynamic vegetation model.

PubMed

Jiang, Yueyang; Zhuang, Qianlai; Schaphoff, Sibyll; Sitch, Stephen; Sokolov, Andrei; Kicklighter, David; Melillo, Jerry

2012-03-01

This study aims to assess how high-latitude vegetation may respond under various climate scenarios during the 21st century with a focus on analyzing model parameters induced uncertainty and how this uncertainty compares to the uncertainty induced by various climates. The analysis was based on a set of 10,000 Monte Carlo ensemble Lund-Potsdam-Jena (LPJ) simulations for the northern high latitudes (45(o)N and polewards) for the period 1900-2100. The LPJ Dynamic Global Vegetation Model (LPJ-DGVM) was run under contemporary and future climates from four Special Report Emission Scenarios (SRES), A1FI, A2, B1, and B2, based on the Hadley Centre General Circulation Model (GCM), and six climate scenarios, X901M, X902L, X903H, X904M, X905L, and X906H from the Integrated Global System Model (IGSM) at the Massachusetts Institute of Technology (MIT). In the current dynamic vegetation model, some parameters are more important than others in determining the vegetation distribution. Parameters that control plant carbon uptake and light-use efficiency have the predominant influence on the vegetation distribution of both woody and herbaceous plant functional types. The relative importance of different parameters varies temporally and spatially and is influenced by climate inputs. In addition to climate, these parameters play an important role in determining the vegetation distribution in the region. The parameter-based uncertainties contribute most to the total uncertainty. The current warming conditions lead to a complexity of vegetation responses in the region. Temperate trees will be more sensitive to climate variability, compared with boreal forest trees and C3 perennial grasses. This sensitivity would result in a unanimous northward greenness migration due to anomalous warming in the northern high latitudes. Temporally, boreal needleleaved evergreen plants are projected to decline considerably, and a large portion of C3 perennial grass is projected to disappear by the end of the 21st century. In contrast, the area of temperate trees would increase, especially under the most extreme A1FI scenario. As the warming continues, the northward greenness expansion in the Arctic region could continue.

Uncertainty Quantification in High Throughput Screening ...

EPA Pesticide Factsheets

Using uncertainty quantification, we aim to improve the quality of modeling data from high throughput screening assays for use in risk assessment. ToxCast is a large-scale screening program that analyzes thousands of chemicals using over 800 assays representing hundreds of biochemical and cellular processes, including endocrine disruption, cytotoxicity, and zebrafish development. Over 2.6 million concentration response curves are fit to models to extract parameters related to potency and efficacy. Models built on ToxCast results are being used to rank and prioritize the toxicological risk of tested chemicals and to predict the toxicity of tens of thousands of chemicals not yet tested in vivo. However, the data size also presents challenges. When fitting the data, the choice of models, model selection strategy, and hit call criteria must reflect the need for computational efficiency and robustness, requiring hard and somewhat arbitrary cutoffs. When coupled with unavoidable noise in the experimental concentration response data, these hard cutoffs cause uncertainty in model parameters and the hit call itself. The uncertainty will then propagate through all of the models built on the data. Left unquantified, this uncertainty makes it difficult to fully interpret the data for risk assessment. We used bootstrap resampling methods to quantify the uncertainty in fitting models to the concentration response data. Bootstrap resampling determines confidence intervals for

Calibration of Predictor Models Using Multiple Validation Experiments

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.; Giesy, Daniel P.

2015-01-01

This paper presents a framework for calibrating computational models using data from several and possibly dissimilar validation experiments. The offset between model predictions and observations, which might be caused by measurement noise, model-form uncertainty, and numerical error, drives the process by which uncertainty in the models parameters is characterized. The resulting description of uncertainty along with the computational model constitute a predictor model. Two types of predictor models are studied: Interval Predictor Models (IPMs) and Random Predictor Models (RPMs). IPMs use sets to characterize uncertainty, whereas RPMs use random vectors. The propagation of a set through a model makes the response an interval valued function of the state, whereas the propagation of a random vector yields a random process. Optimization-based strategies for calculating both types of predictor models are proposed. Whereas the formulations used to calculate IPMs target solutions leading to the interval value function of minimal spread containing all observations, those for RPMs seek to maximize the models' ability to reproduce the distribution of observations. Regarding RPMs, we choose a structure for the random vector (i.e., the assignment of probability to points in the parameter space) solely dependent on the prediction error. As such, the probabilistic description of uncertainty is not a subjective assignment of belief, nor is it expected to asymptotically converge to a fixed value, but instead it casts the model's ability to reproduce the experimental data. This framework enables evaluating the spread and distribution of the predicted response of target applications depending on the same parameters beyond the validation domain.

Uncertainty and sensitivity assessments of an agricultural-hydrological model (RZWQM2) using the GLUE method

NASA Astrophysics Data System (ADS)

Sun, Mei; Zhang, Xiaolin; Huo, Zailin; Feng, Shaoyuan; Huang, Guanhua; Mao, Xiaomin

2016-03-01

Quantitatively ascertaining and analyzing the effects of model uncertainty on model reliability is a focal point for agricultural-hydrological models due to more uncertainties of inputs and processes. In this study, the generalized likelihood uncertainty estimation (GLUE) method with Latin hypercube sampling (LHS) was used to evaluate the uncertainty of the RZWQM-DSSAT (RZWQM2) model outputs responses and the sensitivity of 25 parameters related to soil properties, nutrient transport and crop genetics. To avoid the one-sided risk of model prediction caused by using a single calibration criterion, the combined likelihood (CL) function integrated information concerning water, nitrogen, and crop production was introduced in GLUE analysis for the predictions of the following four model output responses: the total amount of water content (T-SWC) and the nitrate nitrogen (T-NIT) within the 1-m soil profile, the seed yields of waxy maize (Y-Maize) and winter wheat (Y-Wheat). In the process of evaluating RZWQM2, measurements and meteorological data were obtained from a field experiment that involved a winter wheat and waxy maize crop rotation system conducted from 2003 to 2004 in southern Beijing. The calibration and validation results indicated that RZWQM2 model can be used to simulate the crop growth and water-nitrogen migration and transformation in wheat-maize crop rotation planting system. The results of uncertainty analysis using of GLUE method showed T-NIT was sensitive to parameters relative to nitrification coefficient, maize growth characteristics on seedling period, wheat vernalization period, and wheat photoperiod. Parameters on soil saturated hydraulic conductivity, nitrogen nitrification and denitrification, and urea hydrolysis played an important role in crop yield component. The prediction errors for RZWQM2 outputs with CL function were relatively lower and uniform compared with other likelihood functions composed of individual calibration criterion. This new and successful application of the GLUE method for determining the uncertainty and sensitivity of the RZWQM2 could provide a reference for the optimization of model parameters with different emphases according to research interests.

Modelling of the X,Y,Z positioning errors and uncertainty evaluation for the LNE’s mAFM using the Monte Carlo method

NASA Astrophysics Data System (ADS)

Ceria, Paul; Ducourtieux, Sebastien; Boukellal, Younes; Allard, Alexandre; Fischer, Nicolas; Feltin, Nicolas

2017-03-01

In order to evaluate the uncertainty budget of the LNE’s mAFM, a reference instrument dedicated to the calibration of nanoscale dimensional standards, a numerical model has been developed to evaluate the measurement uncertainty of the metrology loop involved in the XYZ positioning of the tip relative to the sample. The objective of this model is to overcome difficulties experienced when trying to evaluate some uncertainty components which cannot be experimentally determined and more specifically, the one linked to the geometry of the metrology loop. The model is based on object-oriented programming and developed under Matlab. It integrates one hundred parameters that allow the control of the geometry of the metrology loop without using analytical formulae. The created objects, mainly the reference and the mobile prism and their mirrors, the interferometers and their laser beams, can be moved and deformed freely to take into account several error sources. The Monte Carlo method is then used to determine the positioning uncertainty of the instrument by randomly drawing the parameters according to their associated tolerances and their probability density functions (PDFs). The whole process follows Supplement 2 to ‘The Guide to the Expression of the Uncertainty in Measurement’ (GUM). Some advanced statistical tools like Morris design and Sobol indices are also used to provide a sensitivity analysis by identifying the most influential parameters and quantifying their contribution to the XYZ positioning uncertainty. The approach validated in the paper shows that the actual positioning uncertainty is about 6 nm. As the final objective is to reach 1 nm, we engage in a discussion to estimate the most effective way to reduce the uncertainty.

A General Approach for Specifying Informative Prior Distributions for PBPK Model Parameters

EPA Science Inventory

Characterization of uncertainty in model predictions is receiving more interest as more models are being used in applications that are critical to human health. For models in which parameters reflect biological characteristics, it is often possible to provide estimates of paramet...

What’s Driving Uncertainty? The Model or the Model Parameters (What’s Driving Uncertainty? The influences of model and model parameters in data analysis)

DOE PAGES

Anderson-Cook, Christine Michaela

2017-03-01

Here, one of the substantial improvements to the practice of data analysis in recent decades is the change from reporting just a point estimate for a parameter or characteristic, to now including a summary of uncertainty for that estimate. Understanding the precision of the estimate for the quantity of interest provides better understanding of what to expect and how well we are able to predict future behavior from the process. For example, when we report a sample average as an estimate of the population mean, it is good practice to also provide a confidence interval (or credible interval, if youmore » are doing a Bayesian analysis) to accompany that summary. This helps to calibrate what ranges of values are reasonable given the variability observed in the sample and the amount of data that were included in producing the summary.« less

Performance Assessment Uncertainty Analysis for Japan's HLW Program Feasibility Study (H12)

DOE Office of Scientific and Technical Information (OSTI.GOV)

BABA,T.; ISHIGURO,K.; ISHIHARA,Y.

1999-08-30

Most HLW programs in the world recognize that any estimate of long-term radiological performance must be couched in terms of the uncertainties derived from natural variation, changes through time and lack of knowledge about the essential processes. The Japan Nuclear Cycle Development Institute followed a relatively standard procedure to address two major categories of uncertainty. First, a FEatures, Events and Processes (FEPs) listing, screening and grouping activity was pursued in order to define the range of uncertainty in system processes as well as possible variations in engineering design. A reference and many alternative cases representing various groups of FEPs weremore » defined and individual numerical simulations performed for each to quantify the range of conceptual uncertainty. Second, parameter distributions were developed for the reference case to represent the uncertainty in the strength of these processes, the sequencing of activities and geometric variations. Both point estimates using high and low values for individual parameters as well as a probabilistic analysis were performed to estimate parameter uncertainty. A brief description of the conceptual model uncertainty analysis is presented. This paper focuses on presenting the details of the probabilistic parameter uncertainty assessment.« less

Input Uncertainty and its Implications on Parameter Assessment in Hydrologic and Hydroclimatic Modelling Studies

NASA Astrophysics Data System (ADS)

Chowdhury, S.; Sharma, A.

2005-12-01

Hydrological model inputs are often derived from measurements at point locations taken at discrete time steps. The nature of uncertainty associated with such inputs is thus a function of the quality and number of measurements available in time. A change in these characteristics (such as a change in the number of rain-gauge inputs used to derive spatially averaged rainfall) results in inhomogeneity in the associated distributional profile. Ignoring such uncertainty can lead to models that aim to simulate based on the observed input variable instead of the true measurement, resulting in a biased representation of the underlying system dynamics as well as an increase in both bias and the predictive uncertainty in simulations. This is especially true of cases where the nature of uncertainty likely in the future is significantly different to that in the past. Possible examples include situations where the accuracy of the catchment averaged rainfall has increased substantially due to an increase in the rain-gauge density, or accuracy of climatic observations (such as sea surface temperatures) increased due to the use of more accurate remote sensing technologies. We introduce here a method to ascertain the true value of parameters in the presence of additive uncertainty in model inputs. This method, known as SIMulation EXtrapolation (SIMEX, [Cook, 1994]) operates on the basis of an empirical relationship between parameters and the level of additive input noise (or uncertainty). The method starts with generating a series of alternate realisations of model inputs by artificially adding white noise in increasing multiples of the known error variance. The alternate realisations lead to alternate sets of parameters that are increasingly biased with respect to the truth due to the increased variability in the inputs. Once several such realisations have been drawn, one is able to formulate an empirical relationship between the parameter values and the level of additive noise present. SIMEX is based on theory that the trend in alternate parameters can be extrapolated back to the notional error free zone. We illustrate the utility of SIMEX in a synthetic rainfall-runoff modelling scenario and an application to study the dependence of uncertain distributed sea surface temperature anomalies with an indicator of the El Nino Southern Oscillation, the Southern Oscillation Index (SOI). The errors in rainfall data and its affect is explored using Sacramento rainfall runoff model. The rainfall uncertainty is assumed to be multiplicative and temporally invariant. The model used to relate the sea surface temperature anomalies (SSTA) to the SOI is assumed to be of a linear form. The nature of uncertainty in the SSTA is additive and varies with time. The SIMEX framework allows assessment of the relationship between the error free inputs and response. Cook, J.R., Stefanski, L. A., Simulation-Extrapolation Estimation in Parametric Measurement Error Models, Journal of the American Statistical Association, 89 (428), 1314-1328, 1994.

Evaluation of five dry particle deposition parameterizations for incorporation into atmospheric transport models

NASA Astrophysics Data System (ADS)

Khan, Tanvir R.; Perlinger, Judith A.

2017-10-01

Despite considerable effort to develop mechanistic dry particle deposition parameterizations for atmospheric transport models, current knowledge has been inadequate to propose quantitative measures of the relative performance of available parameterizations. In this study, we evaluated the performance of five dry particle deposition parameterizations developed by Zhang et al. (2001) (Z01), Petroff and Zhang (2010) (PZ10), Kouznetsov and Sofiev (2012) (KS12), Zhang and He (2014) (ZH14), and Zhang and Shao (2014) (ZS14), respectively. The evaluation was performed in three dimensions: model ability to reproduce observed deposition velocities, Vd (accuracy); the influence of imprecision in input parameter values on the modeled Vd (uncertainty); and identification of the most influential parameter(s) (sensitivity). The accuracy of the modeled Vd was evaluated using observations obtained from five land use categories (LUCs): grass, coniferous and deciduous forests, natural water, and ice/snow. To ascertain the uncertainty in modeled Vd, and quantify the influence of imprecision in key model input parameters, a Monte Carlo uncertainty analysis was performed. The Sobol' sensitivity analysis was conducted with the objective to determine the parameter ranking from the most to the least influential. Comparing the normalized mean bias factors (indicators of accuracy), we find that the ZH14 parameterization is the most accurate for all LUCs except for coniferous forest, for which it is second most accurate. From Monte Carlo simulations, the estimated mean normalized uncertainties in the modeled Vd obtained for seven particle sizes (ranging from 0.005 to 2.5 µm) for the five LUCs are 17, 12, 13, 16, and 27 % for the Z01, PZ10, KS12, ZH14, and ZS14 parameterizations, respectively. From the Sobol' sensitivity results, we suggest that the parameter rankings vary by particle size and LUC for a given parameterization. Overall, for dp = 0.001 to 1.0 µm, friction velocity was one of the three most influential parameters in all parameterizations. For giant particles (dp = 10 µm), relative humidity was the most influential parameter. Because it is the least complex of the five parameterizations, and it has the greatest accuracy and least uncertainty, we propose that the ZH14 parameterization is currently superior for incorporation into atmospheric transport models.

Sparse Polynomial Chaos Surrogate for ACME Land Model via Iterative Bayesian Compressive Sensing

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Ricciuto, D. M.; Safta, C.; Debusschere, B.; Najm, H. N.; Thornton, P. E.

2015-12-01

For computationally expensive climate models, Monte-Carlo approaches of exploring the input parameter space are often prohibitive due to slow convergence with respect to ensemble size. To alleviate this, we build inexpensive surrogates using uncertainty quantification (UQ) methods employing Polynomial Chaos (PC) expansions that approximate the input-output relationships using as few model evaluations as possible. However, when many uncertain input parameters are present, such UQ studies suffer from the curse of dimensionality. In particular, for 50-100 input parameters non-adaptive PC representations have infeasible numbers of basis terms. To this end, we develop and employ Weighted Iterative Bayesian Compressive Sensing to learn the most important input parameter relationships for efficient, sparse PC surrogate construction with posterior uncertainty quantified due to insufficient data. Besides drastic dimensionality reduction, the uncertain surrogate can efficiently replace the model in computationally intensive studies such as forward uncertainty propagation and variance-based sensitivity analysis, as well as design optimization and parameter estimation using observational data. We applied the surrogate construction and variance-based uncertainty decomposition to Accelerated Climate Model for Energy (ACME) Land Model for several output QoIs at nearly 100 FLUXNET sites covering multiple plant functional types and climates, varying 65 input parameters over broad ranges of possible values. This work is supported by the U.S. Department of Energy, Office of Science, Biological and Environmental Research, Accelerated Climate Modeling for Energy (ACME) project. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Inferring soil salinity in a drip irrigation system from multi-configuration EMI measurements using adaptive Markov chain Monte Carlo

NASA Astrophysics Data System (ADS)

Zaib Jadoon, Khan; Umer Altaf, Muhammad; McCabe, Matthew Francis; Hoteit, Ibrahim; Muhammad, Nisar; Moghadas, Davood; Weihermüller, Lutz

2017-10-01

A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In MCMC the posterior distribution is computed using Bayes' rule. The electromagnetic forward model based on the full solution of Maxwell's equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD Mini-Explorer. Uncertainty in the parameters for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness as compared to layers electrical conductivity are not very informative and are therefore difficult to resolve. Application of the proposed MCMC-based inversion to field measurements in a drip irrigation system demonstrates that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provides useful insight about parameter uncertainty for the assessment of the model outputs.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Evaluation of Uncertainty in Constituent Input Parameters for Modeling the Fate of IMX 101 Components

DTIC Science & Technology

2017-05-01

ER D C/ EL T R- 17 -7 Environmental Security Technology Certification Program (ESTCP) Evaluation of Uncertainty in Constituent Input...Environmental Security Technology Certification Program (ESTCP) ERDC/EL TR-17-7 May 2017 Evaluation of Uncertainty in Constituent Input Parameters...Environmental Evaluation and Characterization Sys- tem (TREECS™) was applied to a groundwater site and a surface water site to evaluate the sensitivity

Understanding identifiability as a crucial step in uncertainty assessment

NASA Astrophysics Data System (ADS)

Jakeman, A. J.; Guillaume, J. H. A.; Hill, M. C.; Seo, L.

2016-12-01

The topic of identifiability analysis offers concepts and approaches to identify why unique model parameter values cannot be identified, and can suggest possible responses that either increase uniqueness or help to understand the effect of non-uniqueness on predictions. Identifiability analysis typically involves evaluation of the model equations and the parameter estimation process. Non-identifiability can have a number of undesirable effects. In terms of model parameters these effects include: parameters not being estimated uniquely even with ideal data; wildly different values being returned for different initialisations of a parameter optimisation algorithm; and parameters not being physically meaningful in a model attempting to represent a process. This presentation illustrates some of the drastic consequences of ignoring model identifiability analysis. It argues for a more cogent framework and use of identifiability analysis as a way of understanding model limitations and systematically learning about sources of uncertainty and their importance. The presentation specifically distinguishes between five sources of parameter non-uniqueness (and hence uncertainty) within the modelling process, pragmatically capturing key distinctions within existing identifiability literature. It enumerates many of the various approaches discussed in the literature. Admittedly, improving identifiability is often non-trivial. It requires thorough understanding of the cause of non-identifiability, and the time, knowledge and resources to collect or select new data, modify model structures or objective functions, or improve conditioning. But ignoring these problems is not a viable solution. Even simple approaches such as fixing parameter values or naively using a different model structure may have significant impacts on results which are too often overlooked because identifiability analysis is neglected.

Uncertainty analysis on simple mass balance model to calculate critical loads for soil acidity.

PubMed

Li, Harbin; McNulty, Steven G

2007-10-01

Simple mass balance equations (SMBE) of critical acid loads (CAL) in forest soil were developed to assess potential risks of air pollutants to ecosystems. However, to apply SMBE reliably at large scales, SMBE must be tested for adequacy and uncertainty. Our goal was to provide a detailed analysis of uncertainty in SMBE so that sound strategies for scaling up CAL estimates to the national scale could be developed. Specifically, we wanted to quantify CAL uncertainty under natural variability in 17 model parameters, and determine their relative contributions in predicting CAL. Results indicated that uncertainty in CAL came primarily from components of base cation weathering (BC(w); 49%) and acid neutralizing capacity (46%), whereas the most critical parameters were BC(w) base rate (62%), soil depth (20%), and soil temperature (11%). Thus, improvements in estimates of these factors are crucial to reducing uncertainty and successfully scaling up SMBE for national assessments of CAL.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks.

PubMed

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-08-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

Efficient Characterization of Parametric Uncertainty of Complex (Bio)chemical Networks

PubMed Central

Schillings, Claudia; Sunnåker, Mikael; Stelling, Jörg; Schwab, Christoph

2015-01-01

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is “non-intrusive” and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design. PMID:26317784

Predicting long-range transport: a systematic evaluation of two multimedia transport models.

PubMed

Bennett, D H; Scheringer, M; McKone, T E; Hungerbühler, K

2001-03-15

The United Nations Environment Program has recently developed criteria to identify and restrict chemicals with a potential for persistence and long-range transport (persistent organic pollutants or POPs). There are many stakeholders involved, and the issues are not only scientific but also include social, economic, and political factors. This work focuses on one aspect of the POPs debate, the criteria for determining the potential for long-range transport (LRT). Our goal is to determine if current models are reliable enough to support decisions that classify a chemical based on the LRT potential. We examine the robustness of two multimedia fate models for determining the relative ranking and absolute spatial range of various chemicals in the environment. We also consider the effect of parameter uncertainties and the model uncertainty associated with the selection of an algorithm for gas-particle partitioning on the model results. Given the same chemical properties, both models give virtually the same ranking. However, when chemical parameter uncertainties and model uncertainties such as particle partitioning are considered, the spatial range distributions obtained for the individual chemicals overlap, preventing a distinct rank order. The absolute values obtained for the predicted spatial range or travel distance differ significantly between the two models for the uncertainties evaluated. We find that to evaluate a chemical when large and unresolved uncertainties exist, it is more informative to use two or more models and include multiple types of uncertainty. Model differences and uncertainties must be explicitly confronted to determine how the limitations of scientific knowledge impact predictions in the decision-making process.

Uncertainty evaluation of nuclear reaction model parameters using integral and microscopic measurements. Covariances evaluation with CONRAD code

NASA Astrophysics Data System (ADS)

de Saint Jean, C.; Habert, B.; Archier, P.; Noguere, G.; Bernard, D.; Tommasi, J.; Blaise, P.

2010-10-01

In the [eV;MeV] energy range, modelling of the neutron induced reactions are based on nuclear reaction models having parameters. Estimation of co-variances on cross sections or on nuclear reaction model parameters is a recurrent puzzle in nuclear data evaluation. Major breakthroughs were asked by nuclear reactor physicists to assess proper uncertainties to be used in applications. In this paper, mathematical methods developped in the CONRAD code[2] will be presented to explain the treatment of all type of uncertainties, including experimental ones (statistical and systematic) and propagate them to nuclear reaction model parameters or cross sections. Marginalization procedure will thus be exposed using analytical or Monte-Carlo solutions. Furthermore, one major drawback found by reactor physicist is the fact that integral or analytical experiments (reactor mock-up or simple integral experiment, e.g. ICSBEP, …) were not taken into account sufficiently soon in the evaluation process to remove discrepancies. In this paper, we will describe a mathematical framework to take into account properly this kind of information.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Uncertainty and sensitivity analysis of control strategies using the benchmark simulation model No1 (BSM1).

PubMed

Flores-Alsina, Xavier; Rodriguez-Roda, Ignasi; Sin, Gürkan; Gernaey, Krist V

2009-01-01

The objective of this paper is to perform an uncertainty and sensitivity analysis of the predictions of the Benchmark Simulation Model (BSM) No. 1, when comparing four activated sludge control strategies. The Monte Carlo simulation technique is used to evaluate the uncertainty in the BSM1 predictions, considering the ASM1 bio-kinetic parameters and influent fractions as input uncertainties while the Effluent Quality Index (EQI) and the Operating Cost Index (OCI) are focused on as model outputs. The resulting Monte Carlo simulations are presented using descriptive statistics indicating the degree of uncertainty in the predicted EQI and OCI. Next, the Standard Regression Coefficients (SRC) method is used for sensitivity analysis to identify which input parameters influence the uncertainty in the EQI predictions the most. The results show that control strategies including an ammonium (S(NH)) controller reduce uncertainty in both overall pollution removal and effluent total Kjeldahl nitrogen. Also, control strategies with an external carbon source reduce the effluent nitrate (S(NO)) uncertainty increasing both their economical cost and variability as a trade-off. Finally, the maximum specific autotrophic growth rate (micro(A)) causes most of the variance in the effluent for all the evaluated control strategies. The influence of denitrification related parameters, e.g. eta(g) (anoxic growth rate correction factor) and eta(h) (anoxic hydrolysis rate correction factor), becomes less important when a S(NO) controller manipulating an external carbon source addition is implemented.

Considering the ranges of uncertainties in the New Probabilistic Seismic Hazard Assessment of Germany - Version 2016

NASA Astrophysics Data System (ADS)

Grunthal, Gottfried; Stromeyer, Dietrich; Bosse, Christian; Cotton, Fabrice; Bindi, Dino

2017-04-01

The seismic load parameters for the upcoming National Annex to the Eurocode 8 result from the reassessment of the seismic hazard supported by the German Institution for Civil Engineering . This 2016 version of hazard assessment for Germany as target area was based on a comprehensive involvement of all accessible uncertainties in models and parameters into the approach and the provision of a rational framework for facilitating the uncertainties in a transparent way. The developed seismic hazard model represents significant improvements; i.e. it is based on updated and extended databases, comprehensive ranges of models, robust methods and a selection of a set of ground motion prediction equations of their latest generation. The output specifications were designed according to the user oriented needs as suggested by two review teams supervising the entire project. In particular, seismic load parameters were calculated for rock conditions with a vS30 of 800 ms-1 for three hazard levels (10%, 5% and 2% probability of occurrence or exceedance within 50 years) in form of, e.g., uniform hazard spectra (UHS) based on 19 sprectral periods in the range of 0.01 - 3s, seismic hazard maps for spectral response accelerations for different spectral periods or for macroseismic intensities. The developed hazard model consists of a logic tree with 4040 end branches and essential innovations employed to capture epistemic uncertainties and aleatory variabilities. The computation scheme enables the sound calculation of the mean and any quantile of required seismic load parameters. Mean, median and 84th percentiles of load parameters were provided together with the full calculation model to clearly illustrate the uncertainties of such a probabilistic assessment for a region of a low-to-moderate level of seismicity. The regional variations of these uncertainties (e.g. ratios between the mean and median hazard estimations) were analyzed and discussed.

Strict Constraint Feasibility in Analysis and Design of Uncertain Systems

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Giesy, Daniel P.; Kenny, Sean P.

2006-01-01

This paper proposes a methodology for the analysis and design optimization of models subject to parametric uncertainty, where hard inequality constraints are present. Hard constraints are those that must be satisfied for all parameter realizations prescribed by the uncertainty model. Emphasis is given to uncertainty models prescribed by norm-bounded perturbations from a nominal parameter value, i.e., hyper-spheres, and by sets of independently bounded uncertain variables, i.e., hyper-rectangles. These models make it possible to consider sets of parameters having comparable as well as dissimilar levels of uncertainty. Two alternative formulations for hyper-rectangular sets are proposed, one based on a transformation of variables and another based on an infinity norm approach. The suite of tools developed enable us to determine if the satisfaction of hard constraints is feasible by identifying critical combinations of uncertain parameters. Since this practice is performed without sampling or partitioning the parameter space, the resulting assessments of robustness are analytically verifiable. Strategies that enable the comparison of the robustness of competing design alternatives, the approximation of the robust design space, and the systematic search for designs with improved robustness characteristics are also proposed. Since the problem formulation is generic and the solution methods only require standard optimization algorithms for their implementation, the tools developed are applicable to a broad range of problems in several disciplines.

Uncertainty Quantification of Evapotranspiration and Infiltration from Modeling and Historic Time Series at the Savannah River F-Area

NASA Astrophysics Data System (ADS)

Faybishenko, B.; Flach, G. P.

2012-12-01

The objectives of this presentation are: (a) to illustrate the application of Monte Carlo and fuzzy-probabilistic approaches for uncertainty quantification (UQ) in predictions of potential evapotranspiration (PET), actual evapotranspiration (ET), and infiltration (I), using uncertain hydrological or meteorological time series data, and (b) to compare the results of these calculations with those from field measurements at the U.S. Department of Energy Savannah River Site (SRS), near Aiken, South Carolina, USA. The UQ calculations include the evaluation of aleatory (parameter uncertainty) and epistemic (model) uncertainties. The effect of aleatory uncertainty is expressed by assigning the probability distributions of input parameters, using historical monthly averaged data from the meteorological station at the SRS. The combined effect of aleatory and epistemic uncertainties on the UQ of PET, ET, and Iis then expressed by aggregating the results of calculations from multiple models using a p-box and fuzzy numbers. The uncertainty in PETis calculated using the Bair-Robertson, Blaney-Criddle, Caprio, Hargreaves-Samani, Hamon, Jensen-Haise, Linacre, Makkink, Priestly-Taylor, Penman, Penman-Monteith, Thornthwaite, and Turc models. Then, ET is calculated from the modified Budyko model, followed by calculations of I from the water balance equation. We show that probabilistic and fuzzy-probabilistic calculations using multiple models generate the PET, ET, and Idistributions, which are well within the range of field measurements. We also show that a selection of a subset of models can be used to constrain the uncertainty quantification of PET, ET, and I.

Parameter and input data uncertainty estimation for the assessment of water resources in two sub-basins of the Limpopo River Basin

NASA Astrophysics Data System (ADS)

Oosthuizen, Nadia; Hughes, Denis A.; Kapangaziwiri, Evison; Mwenge Kahinda, Jean-Marc; Mvandaba, Vuyelwa

2018-05-01

The demand for water resources is rapidly growing, placing more strain on access to water and its management. In order to appropriately manage water resources, there is a need to accurately quantify available water resources. Unfortunately, the data required for such assessment are frequently far from sufficient in terms of availability and quality, especially in southern Africa. In this study, the uncertainty related to the estimation of water resources of two sub-basins of the Limpopo River Basin - the Mogalakwena in South Africa and the Shashe shared between Botswana and Zimbabwe - is assessed. Input data (and model parameters) are significant sources of uncertainty that should be quantified. In southern Africa water use data are among the most unreliable sources of model input data because available databases generally consist of only licensed information and actual use is generally unknown. The study assesses how these uncertainties impact the estimation of surface water resources of the sub-basins. Data on farm reservoirs and irrigated areas from various sources were collected and used to run the model. Many farm dams and large irrigation areas are located in the upper parts of the Mogalakwena sub-basin. Results indicate that water use uncertainty is small. Nevertheless, the medium to low flows are clearly impacted. The simulated mean monthly flows at the outlet of the Mogalakwena sub-basin were between 22.62 and 24.68 Mm3 per month when incorporating only the uncertainty related to the main physical runoff generating parameters. The range of total predictive uncertainty of the model increased to between 22.15 and 24.99 Mm3 when water use data such as small farm and large reservoirs and irrigation were included. For the Shashe sub-basin incorporating only uncertainty related to the main runoff parameters resulted in mean monthly flows between 11.66 and 14.54 Mm3. The range of predictive uncertainty changed to between 11.66 and 17.72 Mm3 after the uncertainty in water use information was added.

Uncertainty in tsunami sediment transport modeling

USGS Publications Warehouse

Jaffe, Bruce E.; Goto, Kazuhisa; Sugawara, Daisuke; Gelfenbaum, Guy R.; La Selle, SeanPaul M.

2016-01-01

Erosion and deposition from tsunamis record information about tsunami hydrodynamics and size that can be interpreted to improve tsunami hazard assessment. We explore sources and methods for quantifying uncertainty in tsunami sediment transport modeling. Uncertainty varies with tsunami, study site, available input data, sediment grain size, and model. Although uncertainty has the potential to be large, published case studies indicate that both forward and inverse tsunami sediment transport models perform well enough to be useful for deciphering tsunami characteristics, including size, from deposits. New techniques for quantifying uncertainty, such as Ensemble Kalman Filtering inversion, and more rigorous reporting of uncertainties will advance the science of tsunami sediment transport modeling. Uncertainty may be decreased with additional laboratory studies that increase our understanding of the semi-empirical parameters and physics of tsunami sediment transport, standardized benchmark tests to assess model performance, and development of hybrid modeling approaches to exploit the strengths of forward and inverse models.

Probabilistic evaluation of damage potential in earthquake-induced liquefaction in a 3-D soil deposit

NASA Astrophysics Data System (ADS)

Halder, A.; Miller, F. J.

1982-03-01

A probabilistic model to evaluate the risk of liquefaction at a site and to limit or eliminate damage during earthquake induced liquefaction is proposed. The model is extended to consider three dimensional nonhomogeneous soil properties. The parameters relevant to the liquefaction phenomenon are identified, including: (1) soil parameters; (2) parameters required to consider laboratory test and sampling effects; and (3) loading parameters. The fundamentals of risk based design concepts pertient to liquefaction are reviewed. A detailed statistical evaluation of the soil parameters in the proposed liquefaction model is provided and the uncertainty associated with the estimation of in situ relative density is evaluated for both direct and indirect methods. It is found that the liquefaction potential the uncertainties in the load parameters could be higher than those in the resistance parameters.

Data and Model Uncertainties associated with Biogeochemical Groundwater Remediation and their impact on Decision Analysis

NASA Astrophysics Data System (ADS)

Pandey, S.; Vesselinov, V. V.; O'Malley, D.; Karra, S.; Hansen, S. K.

2016-12-01

Models and data are used to characterize the extent of contamination and remediation, both of which are dependent upon the complex interplay of processes ranging from geochemical reactions, microbial metabolism, and pore-scale mixing to heterogeneous flow and external forcings. Characterization is wrought with important uncertainties related to the model itself (e.g. conceptualization, model implementation, parameter values) and the data used for model calibration (e.g. sparsity, measurement errors). This research consists of two primary components: (1) Developing numerical models that incorporate the complex hydrogeology and biogeochemistry that drive groundwater contamination and remediation; (2) Utilizing novel techniques for data/model-based analyses (such as parameter calibration and uncertainty quantification) to aid in decision support for optimal uncertainty reduction related to characterization and remediation of contaminated sites. The reactive transport models are developed using PFLOTRAN and are capable of simulating a wide range of biogeochemical and hydrologic conditions that affect the migration and remediation of groundwater contaminants under diverse field conditions. Data/model-based analyses are achieved using MADS, which utilizes Bayesian methods and Information Gap theory to address the data/model uncertainties discussed above. We also use these tools to evaluate different models, which vary in complexity, in order to weigh and rank models based on model accuracy (in representation of existing observations), model parsimony (everything else being equal, models with smaller number of model parameters are preferred), and model robustness (related to model predictions of unknown future states). These analyses are carried out on synthetic problems, but are directly related to real-world problems; for example, the modeled processes and data inputs are consistent with the conditions at the Los Alamos National Laboratory contamination sites (RDX and Chromium).

Uncertainty Estimation in Elastic Full Waveform Inversion by Utilising the Hessian Matrix

NASA Astrophysics Data System (ADS)

Hagen, V. S.; Arntsen, B.; Raknes, E. B.

2017-12-01

Elastic Full Waveform Inversion (EFWI) is a computationally intensive iterative method for estimating elastic model parameters. A key element of EFWI is the numerical solution of the elastic wave equation which lies as a foundation to quantify the mismatch between synthetic (modelled) and true (real) measured seismic data. The misfit between the modelled and true receiver data is used to update the parameter model to yield a better fit between the modelled and true receiver signal. A common approach to the EFWI model update problem is to use a conjugate gradient search method. In this approach the resolution and cross-coupling for the estimated parameter update can be found by computing the full Hessian matrix. Resolution of the estimated model parameters depend on the chosen parametrisation, acquisition geometry, and temporal frequency range. Although some understanding has been gained, it is still not clear which elastic parameters can be reliably estimated under which conditions. With few exceptions, previous analyses have been based on arguments using radiation pattern analysis. We use the known adjoint-state technique with an expansion to compute the Hessian acting on a model perturbation to conduct our study. The Hessian is used to infer parameter resolution and cross-coupling for different selections of models, acquisition geometries, and data types, including streamer and ocean bottom seismic recordings. Information about the model uncertainty is obtained from the exact Hessian, and is essential when evaluating the quality of estimated parameters due to the strong influence of source-receiver geometry and frequency content. Investigation is done on both a homogeneous model and the Gullfaks model where we illustrate the influence of offset on parameter resolution and cross-coupling as a way of estimating uncertainty.

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

NASA Astrophysics Data System (ADS)

Feng, Jinchao; Lansford, Joshua; Mironenko, Alexander; Pourkargar, Davood Babaei; Vlachos, Dionisios G.; Katsoulakis, Markos A.

2018-03-01

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

Towards robust quantification and reduction of uncertainty in hydrologic predictions: Integration of particle Markov chain Monte Carlo and factorial polynomial chaos expansion

NASA Astrophysics Data System (ADS)

Wang, S.; Huang, G. H.; Baetz, B. W.; Ancell, B. C.

2017-05-01

The particle filtering techniques have been receiving increasing attention from the hydrologic community due to its ability to properly estimate model parameters and states of nonlinear and non-Gaussian systems. To facilitate a robust quantification of uncertainty in hydrologic predictions, it is necessary to explicitly examine the forward propagation and evolution of parameter uncertainties and their interactions that affect the predictive performance. This paper presents a unified probabilistic framework that merges the strengths of particle Markov chain Monte Carlo (PMCMC) and factorial polynomial chaos expansion (FPCE) algorithms to robustly quantify and reduce uncertainties in hydrologic predictions. A Gaussian anamorphosis technique is used to establish a seamless bridge between the data assimilation using the PMCMC and the uncertainty propagation using the FPCE through a straightforward transformation of posterior distributions of model parameters. The unified probabilistic framework is applied to the Xiangxi River watershed of the Three Gorges Reservoir (TGR) region in China to demonstrate its validity and applicability. Results reveal that the degree of spatial variability of soil moisture capacity is the most identifiable model parameter with the fastest convergence through the streamflow assimilation process. The potential interaction between the spatial variability in soil moisture conditions and the maximum soil moisture capacity has the most significant effect on the performance of streamflow predictions. In addition, parameter sensitivities and interactions vary in magnitude and direction over time due to temporal and spatial dynamics of hydrologic processes.

An optimization based sampling approach for multiple metrics uncertainty analysis using generalized likelihood uncertainty estimation

NASA Astrophysics Data System (ADS)

Zhou, Rurui; Li, Yu; Lu, Di; Liu, Haixing; Zhou, Huicheng

2016-09-01

This paper investigates the use of an epsilon-dominance non-dominated sorted genetic algorithm II (ɛ-NSGAII) as a sampling approach with an aim to improving sampling efficiency for multiple metrics uncertainty analysis using Generalized Likelihood Uncertainty Estimation (GLUE). The effectiveness of ɛ-NSGAII based sampling is demonstrated compared with Latin hypercube sampling (LHS) through analyzing sampling efficiency, multiple metrics performance, parameter uncertainty and flood forecasting uncertainty with a case study of flood forecasting uncertainty evaluation based on Xinanjiang model (XAJ) for Qing River reservoir, China. Results obtained demonstrate the following advantages of the ɛ-NSGAII based sampling approach in comparison to LHS: (1) The former performs more effective and efficient than LHS, for example the simulation time required to generate 1000 behavioral parameter sets is shorter by 9 times; (2) The Pareto tradeoffs between metrics are demonstrated clearly with the solutions from ɛ-NSGAII based sampling, also their Pareto optimal values are better than those of LHS, which means better forecasting accuracy of ɛ-NSGAII parameter sets; (3) The parameter posterior distributions from ɛ-NSGAII based sampling are concentrated in the appropriate ranges rather than uniform, which accords with their physical significance, also parameter uncertainties are reduced significantly; (4) The forecasted floods are close to the observations as evaluated by three measures: the normalized total flow outside the uncertainty intervals (FOUI), average relative band-width (RB) and average deviation amplitude (D). The flood forecasting uncertainty is also reduced a lot with ɛ-NSGAII based sampling. This study provides a new sampling approach to improve multiple metrics uncertainty analysis under the framework of GLUE, and could be used to reveal the underlying mechanisms of parameter sets under multiple conflicting metrics in the uncertainty analysis process.

Estimating the Uncertainty In Diameter Growth Model Predictions and Its Effects On The Uncertainty of Annual Inventory Estimates

Treesearch

Ronald E. McRoberts; Veronica C. Lessard

2001-01-01

Uncertainty in diameter growth predictions is attributed to three general sources: measurement error or sampling variability in predictor variables, parameter covariances, and residual or unexplained variation around model expectations. Using measurement error and sampling variability distributions obtained from the literature and Monte Carlo simulation methods, the...

Quantifying parametric uncertainty in the Rothermel model

Treesearch

S. Goodrick

2008-01-01

The purpose of the present work is to quantify parametric uncertainty in the Rothermel wildland fire spreadmodel (implemented in software such as fire spread models in the United States. This model consists of a non-linear system of equations that relates environmentalvariables (input parameter groups...

UNCERTAINTY AND SENSITIVITY ANALYSES FOR VERY HIGH ORDER MODELS

EPA Science Inventory

While there may in many cases be high potential for exposure of humans and ecosystems to chemicals released from a source, the degree to which this potential is realized is often uncertain. Conceptually, uncertainties are divided among parameters, model, and modeler during simula...

Hierarchical Bayesian Model Averaging for Chance Constrained Remediation Designs

NASA Astrophysics Data System (ADS)

Chitsazan, N.; Tsai, F. T.

2012-12-01

Groundwater remediation designs are heavily relying on simulation models which are subjected to various sources of uncertainty in their predictions. To develop a robust remediation design, it is crucial to understand the effect of uncertainty sources. In this research, we introduce a hierarchical Bayesian model averaging (HBMA) framework to segregate and prioritize sources of uncertainty in a multi-layer frame, where each layer targets a source of uncertainty. The HBMA framework provides an insight to uncertainty priorities and propagation. In addition, HBMA allows evaluating model weights in different hierarchy levels and assessing the relative importance of models in each level. To account for uncertainty, we employ a chance constrained (CC) programming for stochastic remediation design. Chance constrained programming was implemented traditionally to account for parameter uncertainty. Recently, many studies suggested that model structure uncertainty is not negligible compared to parameter uncertainty. Using chance constrained programming along with HBMA can provide a rigorous tool for groundwater remediation designs under uncertainty. In this research, the HBMA-CC was applied to a remediation design in a synthetic aquifer. The design was to develop a scavenger well approach to mitigate saltwater intrusion toward production wells. HBMA was employed to assess uncertainties from model structure, parameter estimation and kriging interpolation. An improved harmony search optimization method was used to find the optimal location of the scavenger well. We evaluated prediction variances of chloride concentration at the production wells through the HBMA framework. The results showed that choosing the single best model may lead to a significant error in evaluating prediction variances for two reasons. First, considering the single best model, variances that stem from uncertainty in the model structure will be ignored. Second, considering the best model with non-dominant model weight may underestimate or overestimate prediction variances by ignoring other plausible propositions. Chance constraints allow developing a remediation design with a desirable reliability. However, considering the single best model, the calculated reliability will be different from the desirable reliability. We calculated the reliability of the design for the models at different levels of HBMA. The results showed that by moving toward the top layers of HBMA, the calculated reliability converges to the chosen reliability. We employed the chance constrained optimization along with the HBMA framework to find the optimal location and pumpage for the scavenger well. The results showed that using models at different levels in the HBMA framework, the optimal location of the scavenger well remained the same, but the optimal extraction rate was altered. Thus, we concluded that the optimal pumping rate was sensitive to the prediction variance. Also, the prediction variance was changed by using different extraction rate. Using very high extraction rate will cause prediction variances of chloride concentration at the production wells to approach zero regardless of which HBMA models used.

Evaluation and uncertainty analysis of regional-scale CLM4.5 net carbon flux estimates

NASA Astrophysics Data System (ADS)

Post, Hanna; Hendricks Franssen, Harrie-Jan; Han, Xujun; Baatz, Roland; Montzka, Carsten; Schmidt, Marius; Vereecken, Harry

2018-01-01

Modeling net ecosystem exchange (NEE) at the regional scale with land surface models (LSMs) is relevant for the estimation of regional carbon balances, but studies on it are very limited. Furthermore, it is essential to better understand and quantify the uncertainty of LSMs in order to improve them. An important key variable in this respect is the prognostic leaf area index (LAI), which is very sensitive to forcing data and strongly affects the modeled NEE. We applied the Community Land Model (CLM4.5-BGC) to the Rur catchment in western Germany and compared estimated and default ecological key parameters for modeling carbon fluxes and LAI. The parameter estimates were previously estimated with the Markov chain Monte Carlo (MCMC) approach DREAM(zs) for four of the most widespread plant functional types in the catchment. It was found that the catchment-scale annual NEE was strongly positive with default parameter values but negative (and closer to observations) with the estimated values. Thus, the estimation of CLM parameters with local NEE observations can be highly relevant when determining regional carbon balances. To obtain a more comprehensive picture of model uncertainty, CLM ensembles were set up with perturbed meteorological input and uncertain initial states in addition to uncertain parameters. C3 grass and C3 crops were particularly sensitive to the perturbed meteorological input, which resulted in a strong increase in the standard deviation of the annual NEE sum (σ ∑ NEE) for the different ensemble members from ˜ 2 to 3 g C m-2 yr-1 (with uncertain parameters) to ˜ 45 g C m-2 yr-1 (C3 grass) and ˜ 75 g C m-2 yr-1 (C3 crops) with perturbed forcings. This increase in uncertainty is related to the impact of the meteorological forcings on leaf onset and senescence, and enhanced/reduced drought stress related to perturbation of precipitation. The NEE uncertainty for the forest plant functional type (PFT) was considerably lower (σ ∑ NEE ˜ 4.0-13.5 g C m-2 yr-1 with perturbed parameters, meteorological forcings and initial states). We conclude that LAI and NEE uncertainty with CLM is clearly underestimated if uncertain meteorological forcings and initial states are not taken into account.

Sensitivity of Asteroid Impact Risk to Uncertainty in Asteroid Properties and Entry Parameters

NASA Astrophysics Data System (ADS)

Wheeler, Lorien; Mathias, Donovan; Dotson, Jessie L.; NASA Asteroid Threat Assessment Project

2017-10-01

A central challenge in assessing the threat posed by asteroids striking Earth is the large amount of uncertainty inherent throughout all aspects of the problem. Many asteroid properties are not well characterized and can range widely from strong, dense, monolithic irons to loosely bound, highly porous rubble piles. Even for an object of known properties, the specific entry velocity, angle, and impact location can swing the potential consequence from no damage to causing millions of casualties. Due to the extreme rarity of large asteroid strikes, there are also large uncertainties in how different types of asteroids will interact with the atmosphere during entry, how readily they may break up or ablate, and how much surface damage will be caused by the resulting airbursts or impacts.In this work, we use our Probabilistic Asteroid Impact Risk (PAIR) model to investigate the sensitivity of asteroid impact damage to uncertainties in key asteroid properties, entry parameters, or modeling assumptions. The PAIR model combines physics-based analytic models of asteroid entry and damage in a probabilistic Monte Carlo framework to assess the risk posed by a wide range of potential impacts. The model samples from uncertainty distributions of asteroid properties and entry parameters to generate millions of specific impact cases, and models the atmospheric entry and damage for each case, including blast overpressure, thermal radiation, tsunami inundation, and global effects. To assess the risk sensitivity, we alternately fix and vary the different input parameters and compare the effect on the resulting range of damage produced. The goal of these studies is to help guide future efforts in asteroid characterization and model refinement by determining which properties most significantly affect the potential risk.

Impact of uncertainties in free stream conditions on the aerodynamics of a rectangular cylinder

NASA Astrophysics Data System (ADS)

Mariotti, Alessandro; Shoeibi Omrani, Pejman; Witteveen, Jeroen; Salvetti, Maria Vittoria

2015-11-01

The BARC benchmark deals with the flow around a rectangular cylinder with chord-to-depth ratio equal to 5. This flow configuration is of practical interest for civil and industrial structures and it is characterized by massively separated flow and unsteadiness. In a recent review of BARC results, significant dispersion was observed both in experimental and numerical predictions of some flow quantities, which are extremely sensitive to various uncertainties, which may be present in experiments and simulations. Besides modeling and numerical errors, in simulations it is difficult to exactly reproduce the experimental conditions due to uncertainties in the set-up parameters, which sometimes cannot be exactly controlled or characterized. Probabilistic methods and URANS simulations are used to investigate the impact of the uncertainties in the following set-up parameters: the angle of incidence, the free stream longitudinal turbulence intensity and length scale. Stochastic collocation is employed to perform the probabilistic propagation of the uncertainty. The discretization and modeling errors are estimated by repeating the same analysis for different grids and turbulence models. The results obtained for different assumed PDF of the set-up parameters are also compared.

Trans-dimensional matched-field geoacoustic inversion with hierarchical error models and interacting Markov chains.

PubMed

Dettmer, Jan; Dosso, Stan E

2012-10-01

This paper develops a trans-dimensional approach to matched-field geoacoustic inversion, including interacting Markov chains to improve efficiency and an autoregressive model to account for correlated errors. The trans-dimensional approach and hierarchical seabed model allows inversion without assuming any particular parametrization by relaxing model specification to a range of plausible seabed models (e.g., in this case, the number of sediment layers is an unknown parameter). Data errors are addressed by sampling statistical error-distribution parameters, including correlated errors (covariance), by applying a hierarchical autoregressive error model. The well-known difficulty of low acceptance rates for trans-dimensional jumps is addressed with interacting Markov chains, resulting in a substantial increase in efficiency. The trans-dimensional seabed model and the hierarchical error model relax the degree of prior assumptions required in the inversion, resulting in substantially improved (more realistic) uncertainty estimates and a more automated algorithm. In particular, the approach gives seabed parameter uncertainty estimates that account for uncertainty due to prior model choice (layering and data error statistics). The approach is applied to data measured on a vertical array in the Mediterranean Sea.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cote, Benoit; Ritter, Christian; Oshea, Brian W.

Here we use a simple one-zone galactic chemical evolution model to quantify the uncertainties generated by the input parameters in numerical predictions for a galaxy with properties similar to those of the Milky Way. We compiled several studies from the literature to gather the current constraints for our simulations regarding the typical value and uncertainty of the following seven basic parameters: the lower and upper mass limits of the stellar initial mass function (IMF), the slope of the high-mass end of the stellar IMF, the slope of the delay-time distribution function of Type Ia supernovae (SNe Ia), the number ofmore » SNe Ia per M ⊙ formed, the total stellar mass formed, and the final mass of gas. We derived a probability distribution function to express the range of likely values for every parameter, which were then included in a Monte Carlo code to run several hundred simulations with randomly selected input parameters. This approach enables us to analyze the predicted chemical evolution of 16 elements in a statistical manner by identifying the most probable solutions along with their 68% and 95% confidence levels. Our results show that the overall uncertainties are shaped by several input parameters that individually contribute at different metallicities, and thus at different galactic ages. The level of uncertainty then depends on the metallicity and is different from one element to another. Among the seven input parameters considered in this work, the slope of the IMF and the number of SNe Ia are currently the two main sources of uncertainty. The thicknesses of the uncertainty bands bounded by the 68% and 95% confidence levels are generally within 0.3 and 0.6 dex, respectively. When looking at the evolution of individual elements as a function of galactic age instead of metallicity, those same thicknesses range from 0.1 to 0.6 dex for the 68% confidence levels and from 0.3 to 1.0 dex for the 95% confidence levels. The uncertainty in our chemical evolution model does not include uncertainties relating to stellar yields, star formation and merger histories, and modeling assumptions.« less

Evaluation of calibration efficacy under different levels of uncertainty

DOE PAGES

Heo, Yeonsook; Graziano, Diane J.; Guzowski, Leah; ...

2014-06-10

This study examines how calibration performs under different levels of uncertainty in model input data. It specifically assesses the efficacy of Bayesian calibration to enhance the reliability of EnergyPlus model predictions. A Bayesian approach can be used to update uncertain values of parameters, given measured energy-use data, and to quantify the associated uncertainty.We assess the efficacy of Bayesian calibration under a controlled virtual-reality setup, which enables rigorous validation of the accuracy of calibration results in terms of both calibrated parameter values and model predictions. Case studies demonstrate the performance of Bayesian calibration of base models developed from audit data withmore » differing levels of detail in building design, usage, and operation.« less

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

NASA Astrophysics Data System (ADS)

Feyen, Luc; Caers, Jef

2006-06-01

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.

Uncertainties in the Antarctic Ice Sheet Contribution to Sea Level Rise: Exploration of Model Response to Errors in Climate Forcing, Boundary Conditions, and Internal Parameters

NASA Astrophysics Data System (ADS)

Schlegel, N.; Seroussi, H. L.; Boening, C.; Larour, E. Y.; Limonadi, D.; Schodlok, M.; Watkins, M. M.

2017-12-01

The Jet Propulsion Laboratory-University of California at Irvine Ice Sheet System Model (ISSM) is a thermo-mechanical 2D/3D parallelized finite element software used to physically model the continental-scale flow of ice at high resolutions. Embedded into ISSM are uncertainty quantification (UQ) tools, based on the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) software. ISSM-DAKOTA offers various UQ methods for the investigation of how errors in model input impact uncertainty in simulation results. We utilize these tools to regionally sample model input and key parameters, based on specified bounds of uncertainty, and run a suite of continental-scale 100-year ISSM forward simulations of the Antarctic Ice Sheet. Resulting diagnostics (e.g., spread in local mass flux and regional mass balance) inform our conclusion about which parameters and/or forcing has the greatest impact on century-scale model simulations of ice sheet evolution. The results allow us to prioritize the key datasets and measurements that are critical for the minimization of ice sheet model uncertainty. Overall, we find that Antartica's total sea level contribution is strongly affected by grounding line retreat, which is driven by the magnitude of ice shelf basal melt rates and by errors in bedrock topography. In addition, results suggest that after 100 years of simulation, Thwaites glacier is the most significant source of model uncertainty, and its drainage basin has the largest potential for future sea level contribution. This work is performed at and supported by the California Institute of Technology's Jet Propulsion Laboratory. Supercomputing time is also supported through a contract with the National Aeronautics and Space Administration's Cryosphere program.

Using FOSM-Based Data Worth Analyses to Design Geophysical Surveys to Reduce Uncertainty in a Regional Groundwater Model Update

NASA Astrophysics Data System (ADS)

Smith, B. D.; White, J.; Kress, W. H.; Clark, B. R.; Barlow, J.

2016-12-01

Hydrogeophysical surveys have become an integral part of understanding hydrogeological frameworks used in groundwater models. Regional models cover a large area where water well data is, at best, scattered and irregular. Since budgets are finite, priorities must be assigned to select optimal areas for geophysical surveys. For airborne electromagnetic (AEM) geophysical surveys, optimization of mapping depth and line spacing needs to take in account the objectives of the groundwater models. The approach discussed here uses a first-order, second-moment (FOSM) uncertainty analyses which assumes an approximate linear relation between model parameters and observations. This assumption allows FOSM analyses to be applied to estimate the value of increased parameter knowledge to reduce forecast uncertainty. FOSM is used to facilitate optimization of yet-to-be-completed geophysical surveying to reduce model forecast uncertainty. The main objective of geophysical surveying is assumed to estimate values and spatial variation in hydrologic parameters (i.e. hydraulic conductivity) as well as map lower permeability layers that influence the spatial distribution of recharge flux. The proposed data worth analysis was applied to Mississippi Embayment Regional Aquifer Study (MERAS) which is being updated. The objective of MERAS is to assess the ground-water availability (status and trends) of the Mississippi embayment aquifer system. The study area covers portions of eight states including Alabama, Arkansas, Illinois, Kentucky, Louisiana, Mississippi, Missouri, and Tennessee. The active model grid covers approximately 70,000 square miles, and incorporates some 6,000 miles of major rivers and over 100,000 water wells. In the FOSM analysis, a dense network of pilot points was used to capture uncertainty in hydraulic conductivity and recharge. To simulate the effect of AEM flight lines, the prior uncertainty for hydraulic conductivity and recharge pilots along potential flight lines was reduced. The FOSM forecast uncertainty estimates were then recalculated and compared to the base forecast uncertainty estimates. The resulting reduction in forecast uncertainty is a measure of the effect on the model from the AEM survey. Iterations through this process, results in optimization of flight line location.

A Bayesian Hierarchical Modeling Approach to Predicting Flow in Ungauged Basins

NASA Astrophysics Data System (ADS)

Gronewold, A.; Alameddine, I.; Anderson, R. M.

2009-12-01

Recent innovative approaches to identifying and applying regression-based relationships between land use patterns (such as increasing impervious surface area and decreasing vegetative cover) and rainfall-runoff model parameters represent novel and promising improvements to predicting flow from ungauged basins. In particular, these approaches allow for predicting flows under uncertain and potentially variable future conditions due to rapid land cover changes, variable climate conditions, and other factors. Despite the broad range of literature on estimating rainfall-runoff model parameters, however, the absence of a robust set of modeling tools for identifying and quantifying uncertainties in (and correlation between) rainfall-runoff model parameters represents a significant gap in current hydrological modeling research. Here, we build upon a series of recent publications promoting novel Bayesian and probabilistic modeling strategies for quantifying rainfall-runoff model parameter estimation uncertainty. Our approach applies alternative measures of rainfall-runoff model parameter joint likelihood (including Nash-Sutcliffe efficiency, among others) to simulate samples from the joint parameter posterior probability density function. We then use these correlated samples as response variables in a Bayesian hierarchical model with land use coverage data as predictor variables in order to develop a robust land use-based tool for forecasting flow in ungauged basins while accounting for, and explicitly acknowledging, parameter estimation uncertainty. We apply this modeling strategy to low-relief coastal watersheds of Eastern North Carolina, an area representative of coastal resource waters throughout the world because of its sensitive embayments and because of the abundant (but currently threatened) natural resources it hosts. Consequently, this area is the subject of several ongoing studies and large-scale planning initiatives, including those conducted through the United States Environmental Protection Agency (USEPA) total maximum daily load (TMDL) program, as well as those addressing coastal population dynamics and sea level rise. Our approach has several advantages, including the propagation of parameter uncertainty through a nonparametric probability distribution which avoids common pitfalls of fitting parameters and model error structure to a predetermined parametric distribution function. In addition, by explicitly acknowledging correlation between model parameters (and reflecting those correlations in our predictive model) our model yields relatively efficient prediction intervals (unlike those in the current literature which are often unnecessarily large, and may lead to overly-conservative management actions). Finally, our model helps improve understanding of the rainfall-runoff process by identifying model parameters (and associated catchment attributes) which are most sensitive to current and future land use change patterns. Disclaimer: Although this work was reviewed by EPA and approved for publication, it may not necessarily reflect official Agency policy.

Volcano deformation source parameters estimated from InSAR: Sensitivities to uncertainties in seismic tomography

USGS Publications Warehouse

Masterlark, Timothy; Donovan, Theodore; Feigl, Kurt L.; Haney, Matt; Thurber, Clifford H.; Tung, Sui

2016-01-01

The eruption cycle of a volcano is controlled in part by the upward migration of magma. The characteristics of the magma flux produce a deformation signature at the Earth's surface. Inverse analyses use geodetic data to estimate strategic controlling parameters that describe the position and pressurization of a magma chamber at depth. The specific distribution of material properties controls how observed surface deformation translates to source parameter estimates. Seismic tomography models describe the spatial distributions of material properties that are necessary for accurate models of volcano deformation. This study investigates how uncertainties in seismic tomography models propagate into variations in the estimates of volcano deformation source parameters inverted from geodetic data. We conduct finite element model-based nonlinear inverse analyses of interferometric synthetic aperture radar (InSAR) data for Okmok volcano, Alaska, as an example. We then analyze the estimated parameters and their uncertainties to characterize the magma chamber. Analyses are performed separately for models simulating a pressurized chamber embedded in a homogeneous domain as well as for a domain having a heterogeneous distribution of material properties according to seismic tomography. The estimated depth of the source is sensitive to the distribution of material properties. The estimated depths for the homogeneous and heterogeneous domains are 2666 ± 42 and 3527 ± 56 m below mean sea level, respectively (99% confidence). A Monte Carlo analysis indicates that uncertainties of the seismic tomography cannot account for this discrepancy at the 99% confidence level. Accounting for the spatial distribution of elastic properties according to seismic tomography significantly improves the fit of the deformation model predictions and significantly influences estimates for parameters that describe the location of a pressurized magma chamber.

On how to avoid input and structural uncertainties corrupt the inference of hydrological parameters using a Bayesian framework

NASA Astrophysics Data System (ADS)

Hernández, Mario R.; Francés, Félix

2015-04-01

One phase of the hydrological models implementation process, significantly contributing to the hydrological predictions uncertainty, is the calibration phase in which values of the unknown model parameters are tuned by optimizing an objective function. An unsuitable error model (e.g. Standard Least Squares or SLS) introduces noise into the estimation of the parameters. The main sources of this noise are the input errors and the hydrological model structural deficiencies. Thus, the biased calibrated parameters cause the divergence model phenomenon, where the errors variance of the (spatially and temporally) forecasted flows far exceeds the errors variance in the fitting period, and provoke the loss of part or all of the physical meaning of the modeled processes. In other words, yielding a calibrated hydrological model which works well, but not for the right reasons. Besides, an unsuitable error model yields a non-reliable predictive uncertainty assessment. Hence, with the aim of prevent all these undesirable effects, this research focuses on the Bayesian joint inference (BJI) of both the hydrological and error model parameters, considering a general additive (GA) error model that allows for correlation, non-stationarity (in variance and bias) and non-normality of model residuals. As hydrological model, it has been used a conceptual distributed model called TETIS, with a particular split structure of the effective model parameters. Bayesian inference has been performed with the aid of a Markov Chain Monte Carlo (MCMC) algorithm called Dream-ZS. MCMC algorithm quantifies the uncertainty of the hydrological and error model parameters by getting the joint posterior probability distribution, conditioned on the observed flows. The BJI methodology is a very powerful and reliable tool, but it must be used correctly this is, if non-stationarity in errors variance and bias is modeled, the Total Laws must be taken into account. The results of this research show that the application of BJI with a GA error model outperforms the hydrological parameters robustness (diminishing the divergence model phenomenon) and improves the reliability of the streamflow predictive distribution, in respect of the results of a bad error model as SLS. Finally, the most likely prediction in a validation period, for both BJI+GA and SLS error models shows a similar performance.

Uncertainty analysis of signal deconvolution using a measured instrument response function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hartouni, E. P.; Beeman, B.; Caggiano, J. A.

2016-10-05

A common analysis procedure minimizes the ln-likelihood that a set of experimental observables matches a parameterized model of the observation. The model includes a description of the underlying physical process as well as the instrument response function (IRF). Here, we investigate the National Ignition Facility (NIF) neutron time-of-flight (nTOF) spectrometers, the IRF is constructed from measurements and models. IRF measurements have a finite precision that can make significant contributions to the uncertainty estimate of the physical model’s parameters. Finally, we apply a Bayesian analysis to properly account for IRF uncertainties in calculating the ln-likelihood function used to find the optimummore » physical parameters.« less

Systematic Uncertainties in High-Energy Hadronic Interaction Models

NASA Astrophysics Data System (ADS)

Zha, M.; Knapp, J.; Ostapchenko, S.

2003-07-01

Hadronic interaction models for cosmic ray energies are uncertain since our knowledge of hadronic interactions is extrap olated from accelerator experiments at much lower energies. At present most high-energy models are based on Grib ov-Regge theory of multi-Pomeron exchange, which provides a theoretical framework to evaluate cross-sections and particle production. While experimental data constrain some of the model parameters, others are not well determined and are therefore a source of systematic uncertainties. In this paper we evaluate the variation of results obtained with the QGSJET model, when modifying parameters relating to three ma jor sources of uncertainty: the form of the parton structure function, the role of diffractive interactions, and the string hadronisation. Results on inelastic cross sections, on secondary particle production and on the air shower development are discussed.

Robust control of seismically excited cable stayed bridges with MR dampers

NASA Astrophysics Data System (ADS)

YeganehFallah, Arash; Khajeh Ahamd Attari, Nader

2017-03-01

In recent decades active and semi-active structural control are becoming attractive alternatives for enhancing performance of civil infrastructures subjected to seismic and winds loads. However, in order to have reliable active and semi-active control, there is a need to include information of uncertainties in design of the controller. In real world for civil structures, parameters such as loading places, stiffness, mass and damping are time variant and uncertain. These uncertainties in many cases model as parametric uncertainties. The motivation of this research is to design a robust controller for attenuating the vibrational responses of civil infrastructures, regarding their dynamical uncertainties. Uncertainties in structural dynamic’s parameters are modeled as affine uncertainties in state space modeling. These uncertainties are decoupled from the system through Linear Fractional Transformation (LFT) and are assumed to be unknown input to the system but norm bounded. The robust H ∞ controller is designed for the decoupled system to regulate the evaluation outputs and it is robust to effects of uncertainties, disturbance and sensors noise. The cable stayed bridge benchmark which is equipped with MR damper is considered for the numerical simulation. The simulated results show that the proposed robust controller can effectively mitigate undesired uncertainties effects on systems’ responds under seismic loading.

On the quantification and efficient propagation of imprecise probabilities resulting from small datasets

NASA Astrophysics Data System (ADS)

Zhang, Jiaxin; Shields, Michael D.

2018-01-01

This paper addresses the problem of uncertainty quantification and propagation when data for characterizing probability distributions are scarce. We propose a methodology wherein the full uncertainty associated with probability model form and parameter estimation are retained and efficiently propagated. This is achieved by applying the information-theoretic multimodel inference method to identify plausible candidate probability densities and associated probabilities that each method is the best model in the Kullback-Leibler sense. The joint parameter densities for each plausible model are then estimated using Bayes' rule. We then propagate this full set of probability models by estimating an optimal importance sampling density that is representative of all plausible models, propagating this density, and reweighting the samples according to each of the candidate probability models. This is in contrast with conventional methods that try to identify a single probability model that encapsulates the full uncertainty caused by lack of data and consequently underestimate uncertainty. The result is a complete probabilistic description of both aleatory and epistemic uncertainty achieved with several orders of magnitude reduction in computational cost. It is shown how the model can be updated to adaptively accommodate added data and added candidate probability models. The method is applied for uncertainty analysis of plate buckling strength where it is demonstrated how dataset size affects the confidence (or lack thereof) we can place in statistical estimates of response when data are lacking.

A new moving strategy for the sequential Monte Carlo approach in optimizing the hydrological model parameters

NASA Astrophysics Data System (ADS)

Zhu, Gaofeng; Li, Xin; Ma, Jinzhu; Wang, Yunquan; Liu, Shaomin; Huang, Chunlin; Zhang, Kun; Hu, Xiaoli

2018-04-01

Sequential Monte Carlo (SMC) samplers have become increasing popular for estimating the posterior parameter distribution with the non-linear dependency structures and multiple modes often present in hydrological models. However, the explorative capabilities and efficiency of the sampler depends strongly on the efficiency in the move step of SMC sampler. In this paper we presented a new SMC sampler entitled the Particle Evolution Metropolis Sequential Monte Carlo (PEM-SMC) algorithm, which is well suited to handle unknown static parameters of hydrologic model. The PEM-SMC sampler is inspired by the works of Liang and Wong (2001) and operates by incorporating the strengths of the genetic algorithm, differential evolution algorithm and Metropolis-Hasting algorithm into the framework of SMC. We also prove that the sampler admits the target distribution to be a stationary distribution. Two case studies including a multi-dimensional bimodal normal distribution and a conceptual rainfall-runoff hydrologic model by only considering parameter uncertainty and simultaneously considering parameter and input uncertainty show that PEM-SMC sampler is generally superior to other popular SMC algorithms in handling the high dimensional problems. The study also indicated that it may be important to account for model structural uncertainty by using multiplier different hydrological models in the SMC framework in future study.

Development of a Framework for Model-Based Analysis, Uncertainty Quantification, and Robust Control Design of Nonlinear Smart Composite Systems

DTIC Science & Technology

2015-06-04

control, vibration and noise control, health monitoring, and energy harvesting . However, these advantages come at the cost of rate-dependent hysteresis...configuration used for energy harvesting . Uncertainty Quantification Uncertainty quantification is pursued in two steps: (i) determination of densities...Crews and R.C. Smith, “Quantification of parameter and model uncertainty for shape mem- ory alloy bending actuators,” Journal of Intelligent material

Parameter Uncertainty for Aircraft Aerodynamic Modeling using Recursive Least Squares

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2016-01-01

A real-time method was demonstrated for determining accurate uncertainty levels of stability and control derivatives estimated using recursive least squares and time-domain data. The method uses a recursive formulation of the residual autocorrelation to account for colored residuals, which are routinely encountered in aircraft parameter estimation and change the predicted uncertainties. Simulation data and flight test data for a subscale jet transport aircraft were used to demonstrate the approach. Results showed that the corrected uncertainties matched the observed scatter in the parameter estimates, and did so more accurately than conventional uncertainty estimates that assume white residuals. Only small differences were observed between batch estimates and recursive estimates at the end of the maneuver. It was also demonstrated that the autocorrelation could be reduced to a small number of lags to minimize computation and memory storage requirements without significantly degrading the accuracy of predicted uncertainty levels.

Multiscale Informatics for Low-Temperature Propane Oxidation: Further Complexities in Studies of Complex Reactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burke, Michael P.; Goldsmith, C. Franklin; Klippenstein, Stephen J.

2015-07-16

We have developed a multi-scale approach (Burke, M. P.; Klippenstein, S. J.; Harding, L. B. Proc. Combust. Inst. 2013, 34, 547–555.) to kinetic model formulation that directly incorporates elementary kinetic theories as a means to provide reliable, physics-based extrapolation to unexplored conditions. Here, we extend and generalize the multi-scale modeling strategy to treat systems of considerable complexity – involving multi-well reactions, potentially missing reactions, non-statistical product branching ratios, and non-Boltzmann (i.e. non-thermal) reactant distributions. The methodology is demonstrated here for a subsystem of low-temperature propane oxidation, as a representative system for low-temperature fuel oxidation. A multi-scale model is assembled andmore » informed by a wide variety of targets that include ab initio calculations of molecular properties, rate constant measurements of isolated reactions, and complex systems measurements. Active model parameters are chosen to accommodate both “parametric” and “structural” uncertainties. Theoretical parameters (e.g. barrier heights) are included as active model parameters to account for parametric uncertainties in the theoretical treatment; experimental parameters (e.g. initial temperatures) are included to account for parametric uncertainties in the physical models of the experiments. RMG software is used to assess potential structural uncertainties due to missing reactions. Additionally, branching ratios among product channels are included as active model parameters to account for structural uncertainties related to difficulties in modeling sequences of multiple chemically activated steps. The approach is demonstrated here for interpreting time-resolved measurements of OH, HO2, n-propyl, i-propyl, propene, oxetane, and methyloxirane from photolysis-initiated low-temperature oxidation of propane at pressures from 4 to 60 Torr and temperatures from 300 to 700 K. In particular, the multi-scale informed model provides a consistent quantitative explanation of both ab initio calculations and time-resolved species measurements. The present results show that interpretations of OH measurements are significantly more complicated than previously thought – in addition to barrier heights for key transition states considered previously, OH profiles also depend on additional theoretical parameters for R + O2 reactions, secondary reactions, QOOH + O2 reactions, and treatment of non-Boltzmann reaction sequences. Extraction of physically rigorous information from those measurements may require more sophisticated treatment of all of those model aspects, as well as additional experimental data under more conditions, to discriminate among possible interpretations and ensure model reliability. Keywords: Optimization, Uncertainty quantification, Chemical mechanism, Low-Temperature Oxidation, Non-Boltzmann« less

A Bayesian ensemble data assimilation to constrain model parameters and land-use carbon emissions

NASA Astrophysics Data System (ADS)

Lienert, Sebastian; Joos, Fortunat

2018-05-01

A dynamic global vegetation model (DGVM) is applied in a probabilistic framework and benchmarking system to constrain uncertain model parameters by observations and to quantify carbon emissions from land-use and land-cover change (LULCC). Processes featured in DGVMs include parameters which are prone to substantial uncertainty. To cope with these uncertainties Latin hypercube sampling (LHS) is used to create a 1000-member perturbed parameter ensemble, which is then evaluated with a diverse set of global and spatiotemporally resolved observational constraints. We discuss the performance of the constrained ensemble and use it to formulate a new best-guess version of the model (LPX-Bern v1.4). The observationally constrained ensemble is used to investigate historical emissions due to LULCC (ELUC) and their sensitivity to model parametrization. We find a global ELUC estimate of 158 (108, 211) PgC (median and 90 % confidence interval) between 1800 and 2016. We compare ELUC to other estimates both globally and regionally. Spatial patterns are investigated and estimates of ELUC of the 10 countries with the largest contribution to the flux over the historical period are reported. We consider model versions with and without additional land-use processes (shifting cultivation and wood harvest) and find that the difference in global ELUC is on the same order of magnitude as parameter-induced uncertainty and in some cases could potentially even be offset with appropriate parameter choice.

A Simplified Model of Choice Behavior under Uncertainty

PubMed Central

Lin, Ching-Hung; Lin, Yu-Kai; Song, Tzu-Jiun; Huang, Jong-Tsun; Chiu, Yao-Chu

2016-01-01

The Iowa Gambling Task (IGT) has been standardized as a clinical assessment tool (Bechara, 2007). Nonetheless, numerous research groups have attempted to modify IGT models to optimize parameters for predicting the choice behavior of normal controls and patients. A decade ago, most researchers considered the expected utility (EU) model (Busemeyer and Stout, 2002) to be the optimal model for predicting choice behavior under uncertainty. However, in recent years, studies have demonstrated that models with the prospect utility (PU) function are more effective than the EU models in the IGT (Ahn et al., 2008). Nevertheless, after some preliminary tests based on our behavioral dataset and modeling, it was determined that the Ahn et al. (2008) PU model is not optimal due to some incompatible results. This study aims to modify the Ahn et al. (2008) PU model to a simplified model and used the IGT performance of 145 subjects as the benchmark data for comparison. In our simplified PU model, the best goodness-of-fit was found mostly as the value of α approached zero. More specifically, we retested the key parameters α, λ, and A in the PU model. Notably, the influence of the parameters α, λ, and A has a hierarchical power structure in terms of manipulating the goodness-of-fit in the PU model. Additionally, we found that the parameters λ and A may be ineffective when the parameter α is close to zero in the PU model. The present simplified model demonstrated that decision makers mostly adopted the strategy of gain-stay loss-shift rather than foreseeing the long-term outcome. However, there are other behavioral variables that are not well revealed under these dynamic-uncertainty situations. Therefore, the optimal behavioral models may not have been found yet. In short, the best model for predicting choice behavior under dynamic-uncertainty situations should be further evaluated. PMID:27582715

Comparison of two optimization algorithms for fuzzy finite element model updating for damage detection in a wind turbine blade

NASA Astrophysics Data System (ADS)

Turnbull, Heather; Omenzetter, Piotr

2018-03-01

vDifficulties associated with current health monitoring and inspection practices combined with harsh, often remote, operational environments of wind turbines highlight the requirement for a non-destructive evaluation system capable of remotely monitoring the current structural state of turbine blades. This research adopted a physics based structural health monitoring methodology through calibration of a finite element model using inverse techniques. A 2.36m blade from a 5kW turbine was used as an experimental specimen, with operational modal analysis techniques utilised to realize the modal properties of the system. Modelling the experimental responses as fuzzy numbers using the sub-level technique, uncertainty in the response parameters was propagated back through the model and into the updating parameters. Initially, experimental responses of the blade were obtained, with a numerical model of the blade created and updated. Deterministic updating was carried out through formulation and minimisation of a deterministic objective function using both firefly algorithm and virus optimisation algorithm. Uncertainty in experimental responses were modelled using triangular membership functions, allowing membership functions of updating parameters (Young's modulus and shear modulus) to be obtained. Firefly algorithm and virus optimisation algorithm were again utilised, however, this time in the solution of fuzzy objective functions. This enabled uncertainty associated with updating parameters to be quantified. Varying damage location and severity was simulated experimentally through addition of small masses to the structure intended to cause a structural alteration. A damaged model was created, modelling four variable magnitude nonstructural masses at predefined points and updated to provide a deterministic damage prediction and information in relation to the parameters uncertainty via fuzzy updating.

Scaling of Precipitation Extremes Modelled by Generalized Pareto Distribution

NASA Astrophysics Data System (ADS)

Rajulapati, C. R.; Mujumdar, P. P.

2017-12-01

Precipitation extremes are often modelled with data from annual maximum series or peaks over threshold series. The Generalized Pareto Distribution (GPD) is commonly used to fit the peaks over threshold series. Scaling of precipitation extremes from larger time scales to smaller time scales when the extremes are modelled with the GPD is burdened with difficulties arising from varying thresholds for different durations. In this study, the scale invariance theory is used to develop a disaggregation model for precipitation extremes exceeding specified thresholds. A scaling relationship is developed for a range of thresholds obtained from a set of quantiles of non-zero precipitation of different durations. The GPD parameters and exceedance rate parameters are modelled by the Bayesian approach and the uncertainty in scaling exponent is quantified. A quantile based modification in the scaling relationship is proposed for obtaining the varying thresholds and exceedance rate parameters for shorter durations. The disaggregation model is applied to precipitation datasets of Berlin City, Germany and Bangalore City, India. From both the applications, it is observed that the uncertainty in the scaling exponent has a considerable effect on uncertainty in scaled parameters and return levels of shorter durations.

A Probabilistic Approach to Model Update

NASA Technical Reports Server (NTRS)

Horta, Lucas G.; Reaves, Mercedes C.; Voracek, David F.

2001-01-01

Finite element models are often developed for load validation, structural certification, response predictions, and to study alternate design concepts. In rare occasions, models developed with a nominal set of parameters agree with experimental data without the need to update parameter values. Today, model updating is generally heuristic and often performed by a skilled analyst with in-depth understanding of the model assumptions. Parameter uncertainties play a key role in understanding the model update problem and therefore probabilistic analysis tools, developed for reliability and risk analysis, may be used to incorporate uncertainty in the analysis. In this work, probability analysis (PA) tools are used to aid the parameter update task using experimental data and some basic knowledge of potential error sources. Discussed here is the first application of PA tools to update parameters of a finite element model for a composite wing structure. Static deflection data at six locations are used to update five parameters. It is shown that while prediction of individual response values may not be matched identically, the system response is significantly improved with moderate changes in parameter values.

Groundwater flow and transport modeling

USGS Publications Warehouse

Konikow, Leonard F.; Mercer, J.W.

1988-01-01

Deterministic, distributed-parameter, numerical simulation models for analyzing groundwater flow and transport problems have come to be used almost routinely during the past decade. A review of the theoretical basis and practical use of groundwater flow and solute transport models is used to illustrate the state-of-the-art. Because of errors and uncertainty in defining model parameters, models must be calibrated to obtain a best estimate of the parameters. For flow modeling, data generally are sufficient to allow calibration. For solute-transport modeling, lack of data not only limits calibration, but also causes uncertainty in process description. Where data are available, model reliability should be assessed on the basis of sensitivity tests and measures of goodness-of-fit. Some of these concepts are demonstrated by using two case histories. ?? 1988.

Sensitivity Analysis of the Bone Fracture Risk Model

NASA Technical Reports Server (NTRS)

Lewandowski, Beth; Myers, Jerry; Sibonga, Jean Diane

2017-01-01

Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.

Made-to-measure modelling of observed galaxy dynamics

NASA Astrophysics Data System (ADS)

Bovy, Jo; Kawata, Daisuke; Hunt, Jason A. S.

2018-01-01

Amongst dynamical modelling techniques, the made-to-measure (M2M) method for modelling steady-state systems is amongst the most flexible, allowing non-parametric distribution functions in complex gravitational potentials to be modelled efficiently using N-body particles. Here, we propose and test various improvements to the standard M2M method for modelling observed data, illustrated using the simple set-up of a one-dimensional harmonic oscillator. We demonstrate that nuisance parameters describing the modelled system's orientation with respect to the observer - e.g. an external galaxy's inclination or the Sun's position in the Milky Way - as well as the parameters of an external gravitational field can be optimized simultaneously with the particle weights. We develop a method for sampling from the high-dimensional uncertainty distribution of the particle weights. We combine this in a Gibbs sampler with samplers for the nuisance and potential parameters to explore the uncertainty distribution of the full set of parameters. We illustrate our M2M improvements by modelling the vertical density and kinematics of F-type stars in Gaia DR1. The novel M2M method proposed here allows full probabilistic modelling of steady-state dynamical systems, allowing uncertainties on the non-parametric distribution function and on nuisance parameters to be taken into account when constraining the dark and baryonic masses of stellar systems.

Quantifying sampling noise and parametric uncertainty in atomistic-to-continuum simulations using surrogate models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salloum, Maher N.; Sargsyan, Khachik; Jones, Reese E.

2015-08-11

We present a methodology to assess the predictive fidelity of multiscale simulations by incorporating uncertainty in the information exchanged between the components of an atomistic-to-continuum simulation. We account for both the uncertainty due to finite sampling in molecular dynamics (MD) simulations and the uncertainty in the physical parameters of the model. Using Bayesian inference, we represent the expensive atomistic component by a surrogate model that relates the long-term output of the atomistic simulation to its uncertain inputs. We then present algorithms to solve for the variables exchanged across the atomistic-continuum interface in terms of polynomial chaos expansions (PCEs). We alsomore » consider a simple Couette flow where velocities are exchanged between the atomistic and continuum components, while accounting for uncertainty in the atomistic model parameters and the continuum boundary conditions. Results show convergence of the coupling algorithm at a reasonable number of iterations. As a result, the uncertainty in the obtained variables significantly depends on the amount of data sampled from the MD simulations and on the width of the time averaging window used in the MD simulations.« less

Fuel cycle cost uncertainty from nuclear fuel cycle comparison

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, J.; McNelis, D.; Yim, M.S.

2013-07-01

This paper examined the uncertainty in fuel cycle cost (FCC) calculation by considering both model and parameter uncertainty. Four different fuel cycle options were compared in the analysis including the once-through cycle (OT), the DUPIC cycle, the MOX cycle and a closed fuel cycle with fast reactors (FR). The model uncertainty was addressed by using three different FCC modeling approaches with and without the time value of money consideration. The relative ratios of FCC in comparison to OT did not change much by using different modeling approaches. This observation was consistent with the results of the sensitivity study for themore » discount rate. Two different sets of data with uncertainty range of unit costs were used to address the parameter uncertainty of the FCC calculation. The sensitivity study showed that the dominating contributor to the total variance of FCC is the uranium price. In general, the FCC of OT was found to be the lowest followed by FR, MOX, and DUPIC. But depending on the uranium price, the FR cycle was found to have lower FCC over OT. The reprocessing cost was also found to have a major impact on FCC.« less

Hydrological model parameter dimensionality is a weak measure of prediction uncertainty

NASA Astrophysics Data System (ADS)

Pande, S.; Arkesteijn, L.; Savenije, H.; Bastidas, L. A.

2015-04-01

This paper shows that instability of hydrological system representation in response to different pieces of information and associated prediction uncertainty is a function of model complexity. After demonstrating the connection between unstable model representation and model complexity, complexity is analyzed in a step by step manner. This is done measuring differences between simulations of a model under different realizations of input forcings. Algorithms are then suggested to estimate model complexity. Model complexities of the two model structures, SAC-SMA (Sacramento Soil Moisture Accounting) and its simplified version SIXPAR (Six Parameter Model), are computed on resampled input data sets from basins that span across the continental US. The model complexities for SIXPAR are estimated for various parameter ranges. It is shown that complexity of SIXPAR increases with lower storage capacity and/or higher recession coefficients. Thus it is argued that a conceptually simple model structure, such as SIXPAR, can be more complex than an intuitively more complex model structure, such as SAC-SMA for certain parameter ranges. We therefore contend that magnitudes of feasible model parameters influence the complexity of the model selection problem just as parameter dimensionality (number of parameters) does and that parameter dimensionality is an incomplete indicator of stability of hydrological model selection and prediction problems.

Gradient-based model calibration with proxy-model assistance

NASA Astrophysics Data System (ADS)

Burrows, Wesley; Doherty, John

2016-02-01

Use of a proxy model in gradient-based calibration and uncertainty analysis of a complex groundwater model with large run times and problematic numerical behaviour is described. The methodology is general, and can be used with models of all types. The proxy model is based on a series of analytical functions that link all model outputs used in the calibration process to all parameters requiring estimation. In enforcing history-matching constraints during the calibration and post-calibration uncertainty analysis processes, the proxy model is run for the purposes of populating the Jacobian matrix, while the original model is run when testing parameter upgrades; the latter process is readily parallelized. Use of a proxy model in this fashion dramatically reduces the computational burden of complex model calibration and uncertainty analysis. At the same time, the effect of model numerical misbehaviour on calculation of local gradients is mitigated, this allowing access to the benefits of gradient-based analysis where lack of integrity in finite-difference derivatives calculation would otherwise have impeded such access. Construction of a proxy model, and its subsequent use in calibration of a complex model, and in analysing the uncertainties of predictions made by that model, is implemented in the PEST suite.

Assessment of uncertainties in radiation-induced cancer risk predictions at clinically relevant doses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nguyen, J.; Moteabbed, M.; Paganetti, H., E-mail: hpaganetti@mgh.harvard.edu

2015-01-15

Purpose: Theoretical dose–response models offer the possibility to assess second cancer induction risks after external beam therapy. The parameters used in these models are determined with limited data from epidemiological studies. Risk estimations are thus associated with considerable uncertainties. This study aims at illustrating uncertainties when predicting the risk for organ-specific second cancers in the primary radiation field illustrated by choosing selected treatment plans for brain cancer patients. Methods: A widely used risk model was considered in this study. The uncertainties of the model parameters were estimated with reported data of second cancer incidences for various organs. Standard error propagationmore » was then subsequently applied to assess the uncertainty in the risk model. Next, second cancer risks of five pediatric patients treated for cancer in the head and neck regions were calculated. For each case, treatment plans for proton and photon therapy were designed to estimate the uncertainties (a) in the lifetime attributable risk (LAR) for a given treatment modality and (b) when comparing risks of two different treatment modalities. Results: Uncertainties in excess of 100% of the risk were found for almost all organs considered. When applied to treatment plans, the calculated LAR values have uncertainties of the same magnitude. A comparison between cancer risks of different treatment modalities, however, does allow statistically significant conclusions. In the studied cases, the patient averaged LAR ratio of proton and photon treatments was 0.35, 0.56, and 0.59 for brain carcinoma, brain sarcoma, and bone sarcoma, respectively. Their corresponding uncertainties were estimated to be potentially below 5%, depending on uncertainties in dosimetry. Conclusions: The uncertainty in the dose–response curve in cancer risk models makes it currently impractical to predict the risk for an individual external beam treatment. On the other hand, the ratio of absolute risks between two modalities is less sensitive to the uncertainties in the risk model and can provide statistically significant estimates.« less

Optimal radiotherapy dose schedules under parametric uncertainty

NASA Astrophysics Data System (ADS)

Badri, Hamidreza; Watanabe, Yoichi; Leder, Kevin

2016-01-01

We consider the effects of parameter uncertainty on the optimal radiation schedule in the context of the linear-quadratic model. Our interest arises from the observation that if inter-patient variability in normal and tumor tissue radiosensitivity or sparing factor of the organs-at-risk (OAR) are not accounted for during radiation scheduling, the performance of the therapy may be strongly degraded or the OAR may receive a substantially larger dose than the allowable threshold. This paper proposes a stochastic radiation scheduling concept to incorporate inter-patient variability into the scheduling optimization problem. Our method is based on a probabilistic approach, where the model parameters are given by a set of random variables. Our probabilistic formulation ensures that our constraints are satisfied with a given probability, and that our objective function achieves a desired level with a stated probability. We used a variable transformation to reduce the resulting optimization problem to two dimensions. We showed that the optimal solution lies on the boundary of the feasible region and we implemented a branch and bound algorithm to find the global optimal solution. We demonstrated how the configuration of optimal schedules in the presence of uncertainty compares to optimal schedules in the absence of uncertainty (conventional schedule). We observed that in order to protect against the possibility of the model parameters falling into a region where the conventional schedule is no longer feasible, it is required to avoid extremal solutions, i.e. a single large dose or very large total dose delivered over a long period. Finally, we performed numerical experiments in the setting of head and neck tumors including several normal tissues to reveal the effect of parameter uncertainty on optimal schedules and to evaluate the sensitivity of the solutions to the choice of key model parameters.

Accounting for uncertainty in pedotransfer functions in vulnerability assessments of pesticide leaching to groundwater.

PubMed

Stenemo, Fredrik; Jarvis, Nicholas

2007-09-01

A simulation tool for site-specific vulnerability assessments of pesticide leaching to groundwater was developed, based on the pesticide fate and transport model MACRO, parameterized using pedotransfer functions and reasonable worst-case parameter values. The effects of uncertainty in the pedotransfer functions on simulation results were examined for 48 combinations of soils, pesticides and application timings, by sampling pedotransfer function regression errors and propagating them through the simulation model in a Monte Carlo analysis. An uncertainty factor, f(u), was derived, defined as the ratio between the concentration simulated with no errors, c(sim), and the 80th percentile concentration for the scenario. The pedotransfer function errors caused a large variation in simulation results, with f(u) ranging from 1.14 to 1440, with a median of 2.8. A non-linear relationship was found between f(u) and c(sim), which can be used to account for parameter uncertainty by correcting the simulated concentration, c(sim), to an estimated 80th percentile value. For fine-textured soils, the predictions were most sensitive to errors in the pedotransfer functions for two parameters regulating macropore flow (the saturated matrix hydraulic conductivity, K(b), and the effective diffusion pathlength, d) and two water retention function parameters (van Genuchten's N and alpha parameters). For coarse-textured soils, the model was also sensitive to errors in the exponent in the degradation water response function and the dispersivity, in addition to K(b), but showed little sensitivity to d. To reduce uncertainty in model predictions, improved pedotransfer functions for K(b), d, N and alpha would therefore be most useful. 2007 Society of Chemical Industry

Adaptive back-stepping control of the harmonic drive system with LuGre model-based friction compensation

NASA Astrophysics Data System (ADS)

Liu, Sen; Gang, Tieqiang

2018-03-01

Harmonic drives are widely used in aerospace and industrial robots. Flexibility, friction and parameter uncertainty will result in transmission performance degradation. In this paper, an adaptive back-stepping method with friction compensation is proposed to improve the tracking performance of the harmonic drive system. The nonlinear friction is described by LuGre model and compensated with a friction observer, and the uncertainty of model parameters is resolved by adaptive parameter estimation method. By using Lyapunov stability theory, it is proved that all the errors of the closed-loop system are uniformly ultimately bounded. Simulations illustrate the effectiveness of our friction compensation method.

Will hydrologists learn from the world around them?: Empiricism, models, uncertainty and stationarity (Invited)

NASA Astrophysics Data System (ADS)

Lall, U.

2010-12-01

To honor the passing this year of eminent hydrologists, Dooge, Klemes and Shiklomanov, I offer an irreverent look at the issues of uncertainty and stationarity as the hydrologic industry prepares climate change products. In an AGU keynote, Dooge said that the principle of mass balance was the only hydrologic law. It was not clear how one should apply it. Klemes observed that Rippl’s 1872 mass curve analyses could essentially subsume many of the advances in stochastic modeling and reservoir optimization. Shiklomanov tackled data challenges to present a comprehensive view of the world’s water supply and demand highlighting the imbalance and sustainability challenge we face. He did not characterize the associated uncertainties. It is remarkable how little data can provide insights, while at times much information from models and data hihglights uncertainty. Hydrologists have focused on parameter uncertainties in hydrologic models. The indeterminacy of the typical situation offered Beven the opportunity to coin the term equifinality. However, this ignores the fact that the traditional continuum model fails us across scales if we don’t re-derive the correct averaged equations accounting for subscale heterogeneity. Nevertheless, the operating paradigm here has been a stimulus response model y = f(x,P), where y are the observations of the state variables, x are observations of hydrologic drivers, P are model parameters, and f(.,.) is an appropriate differential or integral transform. The uncertainty analyses then focuses on P, such that the resulting field of y is approximately unbiased and has minimum variance or maximum likelihood. The parameters P are usually time invariant, and x and/or f(.,.) are expected to account for changes in the boundary conditions. Thus the dynamics is stationary, while the time series of either x or y may not be. Given the lack of clarity as to whether the dynamical system or the trajectory is stationary it is amusing that the paper ”Stationarity is Dead” that implicitly uses changes in time series properties and boundary conditions as its basis gets much press. To avoid the stationarity dilemma, hydrologists are willing to take climate model outputs, rather than an analysis based on historical climate. Uncertainty analysis is viewed as the appropriate shrinkage of the spread across models and ensembles by clever averaging after bias corrections of the model output - a process I liken to transforming elephants into mice. Since it is someone else’s model, we abandon the seemingly good sense of seeking the best parameters P that reproduce the data y. We now seek to fit a model y = T{f1(x,P1),f2(x,P2)…}, where we don’t question the parameter or model but simply fudge the outputs to what was observed. Clearly, we can’t become climate modelers and must work with what we are dealt. By the way, doesn’t this uncertainty analysis and reduction process involve an assumption of stationarity? So, how should hydrologists navigate this muddle of uncertainty and stationarity? I offer some ideas tying to modeling purpose, and advocate a greater effort on diagnostic analyses that provide insights into how hydrologic dynamics co-evolve with climate at a variety of space and time scales. Are there natural bounds or structure to systemic uncertainty and predictability, and what are the key carriers of hydrologic information?

Prediction and assimilation of surf-zone processes using a Bayesian network: Part I: Forward models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

Prediction of coastal processes, including waves, currents, and sediment transport, can be obtained from a variety of detailed geophysical-process models with many simulations showing significant skill. This capability supports a wide range of research and applied efforts that can benefit from accurate numerical predictions. However, the predictions are only as accurate as the data used to drive the models and, given the large temporal and spatial variability of the surf zone, inaccuracies in data are unavoidable such that useful predictions require corresponding estimates of uncertainty. We demonstrate how a Bayesian-network model can be used to provide accurate predictions of wave-height evolution in the surf zone given very sparse and/or inaccurate boundary-condition data. The approach is based on a formal treatment of a data-assimilation problem that takes advantage of significant reduction of the dimensionality of the model system. We demonstrate that predictions of a detailed geophysical model of the wave evolution are reproduced accurately using a Bayesian approach. In this surf-zone application, forward prediction skill was 83%, and uncertainties in the model inputs were accurately transferred to uncertainty in output variables. We also demonstrate that if modeling uncertainties were not conveyed to the Bayesian network (i.e., perfect data or model were assumed), then overly optimistic prediction uncertainties were computed. More consistent predictions and uncertainties were obtained by including model-parameter errors as a source of input uncertainty. Improved predictions (skill of 90%) were achieved because the Bayesian network simultaneously estimated optimal parameters while predicting wave heights.

Inexact nonlinear improved fuzzy chance-constrained programming model for irrigation water management under uncertainty

NASA Astrophysics Data System (ADS)

Zhang, Chenglong; Zhang, Fan; Guo, Shanshan; Liu, Xiao; Guo, Ping

2018-01-01

An inexact nonlinear mλ-measure fuzzy chance-constrained programming (INMFCCP) model is developed for irrigation water allocation under uncertainty. Techniques of inexact quadratic programming (IQP), mλ-measure, and fuzzy chance-constrained programming (FCCP) are integrated into a general optimization framework. The INMFCCP model can deal with not only nonlinearities in the objective function, but also uncertainties presented as discrete intervals in the objective function, variables and left-hand side constraints and fuzziness in the right-hand side constraints. Moreover, this model improves upon the conventional fuzzy chance-constrained programming by introducing a linear combination of possibility measure and necessity measure with varying preference parameters. To demonstrate its applicability, the model is then applied to a case study in the middle reaches of Heihe River Basin, northwest China. An interval regression analysis method is used to obtain interval crop water production functions in the whole growth period under uncertainty. Therefore, more flexible solutions can be generated for optimal irrigation water allocation. The variation of results can be examined by giving different confidence levels and preference parameters. Besides, it can reflect interrelationships among system benefits, preference parameters, confidence levels and the corresponding risk levels. Comparison between interval crop water production functions and deterministic ones based on the developed INMFCCP model indicates that the former is capable of reflecting more complexities and uncertainties in practical application. These results can provide more reliable scientific basis for supporting irrigation water management in arid areas.

Uncertainty analysis of gross primary production partitioned from net ecosystem exchange measurements

NASA Astrophysics Data System (ADS)

Raj, R.; Hamm, N. A. S.; van der Tol, C.; Stein, A.

2015-08-01

Gross primary production (GPP), separated from flux tower measurements of net ecosystem exchange (NEE) of CO2, is used increasingly to validate process-based simulators and remote sensing-derived estimates of simulated GPP at various time steps. Proper validation should include the uncertainty associated with this separation at different time steps. This can be achieved by using a Bayesian framework. In this study, we estimated the uncertainty in GPP at half hourly time steps. We used a non-rectangular hyperbola (NRH) model to separate GPP from flux tower measurements of NEE at the Speulderbos forest site, The Netherlands. The NRH model included the variables that influence GPP, in particular radiation, and temperature. In addition, the NRH model provided a robust empirical relationship between radiation and GPP by including the degree of curvature of the light response curve. Parameters of the NRH model were fitted to the measured NEE data for every 10-day period during the growing season (April to October) in 2009. Adopting a Bayesian approach, we defined the prior distribution of each NRH parameter. Markov chain Monte Carlo (MCMC) simulation was used to update the prior distribution of each NRH parameter. This allowed us to estimate the uncertainty in the separated GPP at half-hourly time steps. This yielded the posterior distribution of GPP at each half hour and allowed the quantification of uncertainty. The time series of posterior distributions thus obtained allowed us to estimate the uncertainty at daily time steps. We compared the informative with non-informative prior distributions of the NRH parameters. The results showed that both choices of prior produced similar posterior distributions GPP. This will provide relevant and important information for the validation of process-based simulators in the future. Furthermore, the obtained posterior distributions of NEE and the NRH parameters are of interest for a range of applications.

Quantifying the Uncertainty in Discharge Data Using Hydraulic Knowledge and Uncertain Gaugings

NASA Astrophysics Data System (ADS)

Renard, B.; Le Coz, J.; Bonnifait, L.; Branger, F.; Le Boursicaud, R.; Horner, I.; Mansanarez, V.; Lang, M.

2014-12-01

River discharge is a crucial variable for Hydrology: as the output variable of most hydrologic models, it is used for sensitivity analyses, model structure identification, parameter estimation, data assimilation, prediction, etc. A major difficulty stems from the fact that river discharge is not measured continuously. Instead, discharge time series used by hydrologists are usually based on simple stage-discharge relations (rating curves) calibrated using a set of direct stage-discharge measurements (gaugings). In this presentation, we present a Bayesian approach to build such hydrometric rating curves, to estimate the associated uncertainty and to propagate this uncertainty to discharge time series. The three main steps of this approach are described: (1) Hydraulic analysis: identification of the hydraulic controls that govern the stage-discharge relation, identification of the rating curve equation and specification of prior distributions for the rating curve parameters; (2) Rating curve estimation: Bayesian inference of the rating curve parameters, accounting for the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions; (3) Uncertainty propagation: quantification of the uncertainty in discharge time series, accounting for both the rating curve uncertainties and the uncertainty of recorded stage values. In addition, we also discuss current research activities, including the treatment of non-univocal stage-discharge relationships (e.g. due to hydraulic hysteresis, vegetation growth, sudden change of the geometry of the section, etc.).

Experimental and modeling uncertainties in the validation of lower hybrid current drive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poli, F. M.; Bonoli, P. T.; Chilenski, M.

Our work discusses sources of uncertainty in the validation of lower hybrid wave current drive simulations against experiments, by evolving self-consistently the magnetic equilibrium and the heating and current drive profiles, calculated with a combined toroidal ray tracing code and 3D Fokker–Planck solver. The simulations indicate a complex interplay of elements, where uncertainties in the input plasma parameters, in the models and in the transport solver combine and compensate each other, at times. It is concluded that ray-tracing calculations should include a realistic representation of the density and temperature in the region between the confined plasma and the wall, whichmore » is especially important in regimes where the LH waves are weakly damped and undergo multiple reflections from the plasma boundary. Uncertainties introduced in the processing of diagnostic data as well as uncertainties introduced by model approximations are assessed. We show that, by comparing the evolution of the plasma parameters in self-consistent simulations with available data, inconsistencies can be identified and limitations in the models or in the experimental data assessed.« less

Experimental and modeling uncertainties in the validation of lower hybrid current drive

DOE PAGES

Poli, F. M.; Bonoli, P. T.; Chilenski, M.; ...

2016-07-28

Our work discusses sources of uncertainty in the validation of lower hybrid wave current drive simulations against experiments, by evolving self-consistently the magnetic equilibrium and the heating and current drive profiles, calculated with a combined toroidal ray tracing code and 3D Fokker–Planck solver. The simulations indicate a complex interplay of elements, where uncertainties in the input plasma parameters, in the models and in the transport solver combine and compensate each other, at times. It is concluded that ray-tracing calculations should include a realistic representation of the density and temperature in the region between the confined plasma and the wall, whichmore » is especially important in regimes where the LH waves are weakly damped and undergo multiple reflections from the plasma boundary. Uncertainties introduced in the processing of diagnostic data as well as uncertainties introduced by model approximations are assessed. We show that, by comparing the evolution of the plasma parameters in self-consistent simulations with available data, inconsistencies can be identified and limitations in the models or in the experimental data assessed.« less

Sensitivity Analysis and Parameter Estimation for a Reactive Transport Model of Uranium Bioremediation

NASA Astrophysics Data System (ADS)

Meyer, P. D.; Yabusaki, S.; Curtis, G. P.; Ye, M.; Fang, Y.

2011-12-01

A three-dimensional, variably-saturated flow and multicomponent biogeochemical reactive transport model of uranium bioremediation was used to generate synthetic data . The 3-D model was based on a field experiment at the U.S. Dept. of Energy Rifle Integrated Field Research Challenge site that used acetate biostimulation of indigenous metal reducing bacteria to catalyze the conversion of aqueous uranium in the +6 oxidation state to immobile solid-associated uranium in the +4 oxidation state. A key assumption in past modeling studies at this site was that a comprehensive reaction network could be developed largely through one-dimensional modeling. Sensitivity analyses and parameter estimation were completed for a 1-D reactive transport model abstracted from the 3-D model to test this assumption, to identify parameters with the greatest potential to contribute to model predictive uncertainty, and to evaluate model structure and data limitations. Results showed that sensitivities of key biogeochemical concentrations varied in space and time, that model nonlinearities and/or parameter interactions have a significant impact on calculated sensitivities, and that the complexity of the model's representation of processes affecting Fe(II) in the system may make it difficult to correctly attribute observed Fe(II) behavior to modeled processes. Non-uniformity of the 3-D simulated groundwater flux and averaging of the 3-D synthetic data for use as calibration targets in the 1-D modeling resulted in systematic errors in the 1-D model parameter estimates and outputs. This occurred despite using the same reaction network for 1-D modeling as used in the data-generating 3-D model. Predictive uncertainty of the 1-D model appeared to be significantly underestimated by linear parameter uncertainty estimates.

Probabilistic migration modelling focused on functional barrier efficiency and low migration concepts in support of risk assessment.

PubMed

Brandsch, Rainer

2017-10-01

Migration modelling provides reliable migration estimates from food-contact materials (FCM) to food or food simulants based on mass-transfer parameters like diffusion and partition coefficients related to individual materials. In most cases, mass-transfer parameters are not readily available from the literature and for this reason are estimated with a given uncertainty. Historically, uncertainty was accounted for by introducing upper limit concepts first, turning out to be of limited applicability due to highly overestimated migration results. Probabilistic migration modelling gives the possibility to consider uncertainty of the mass-transfer parameters as well as other model inputs. With respect to a functional barrier, the most important parameters among others are the diffusion properties of the functional barrier and its thickness. A software tool that accepts distribution as inputs and is capable of applying Monte Carlo methods, i.e., random sampling from the input distributions of the relevant parameters (i.e., diffusion coefficient and layer thickness), predicts migration results with related uncertainty and confidence intervals. The capabilities of probabilistic migration modelling are presented in the view of three case studies (1) sensitivity analysis, (2) functional barrier efficiency and (3) validation by experimental testing. Based on the predicted migration by probabilistic migration modelling and related exposure estimates, safety evaluation of new materials in the context of existing or new packaging concepts is possible. Identifying associated migration risk and potential safety concerns in the early stage of packaging development is possible. Furthermore, dedicated material selection exhibiting required functional barrier efficiency under application conditions becomes feasible. Validation of the migration risk assessment by probabilistic migration modelling through a minimum of dedicated experimental testing is strongly recommended.

Analytic uncertainty and sensitivity analysis of models with input correlations

NASA Astrophysics Data System (ADS)

Zhu, Yueying; Wang, Qiuping A.; Li, Wei; Cai, Xu

2018-03-01

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated parameters are often happened in practical applications. In the present paper, an analytic method is built for the uncertainty and sensitivity analysis of models in the presence of input correlations. With the method, it is straightforward to identify the importance of the independence and correlations of input variables in determining the model response. This allows one to decide whether or not the input correlations should be considered in practice. Numerical examples suggest the effectiveness and validation of our analytic method in the analysis of general models. A practical application of the method is also proposed to the uncertainty and sensitivity analysis of a deterministic HIV model.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

Uncertainty analysis of gross primary production partitioned from net ecosystem exchange measurements

NASA Astrophysics Data System (ADS)

Raj, Rahul; Hamm, Nicholas Alexander Samuel; van der Tol, Christiaan; Stein, Alfred

2016-03-01

Gross primary production (GPP) can be separated from flux tower measurements of net ecosystem exchange (NEE) of CO2. This is used increasingly to validate process-based simulators and remote-sensing-derived estimates of simulated GPP at various time steps. Proper validation includes the uncertainty associated with this separation. In this study, uncertainty assessment was done in a Bayesian framework. It was applied to data from the Speulderbos forest site, The Netherlands. We estimated the uncertainty in GPP at half-hourly time steps, using a non-rectangular hyperbola (NRH) model for its separation from the flux tower measurements. The NRH model provides a robust empirical relationship between radiation and GPP. It includes the degree of curvature of the light response curve, radiation and temperature. Parameters of the NRH model were fitted to the measured NEE data for every 10-day period during the growing season (April to October) in 2009. We defined the prior distribution of each NRH parameter and used Markov chain Monte Carlo (MCMC) simulation to estimate the uncertainty in the separated GPP from the posterior distribution at half-hourly time steps. This time series also allowed us to estimate the uncertainty at daily time steps. We compared the informative with the non-informative prior distributions of the NRH parameters and found that both choices produced similar posterior distributions of GPP. This will provide relevant and important information for the validation of process-based simulators in the future. Furthermore, the obtained posterior distributions of NEE and the NRH parameters are of interest for a range of applications.

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

NASA Astrophysics Data System (ADS)

Riva, Fabio; Milanese, Lucio; Ricci, Paolo

2017-10-01

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the model equations in terms of Chebyshev polynomials is discussed. This methodology, based on the work by Scheffel [Am. J. Comput. Math. 2, 173-193 (2012)], approximates the model equation solution with a semi-analytic expression that depends explicitly on time, spatial coordinates, and input parameters. By employing a weighted residual method, a set of nonlinear algebraic equations for the coefficients appearing in the Chebyshev decomposition is then obtained. The methodology is applied to a two-dimensional Braginskii model used to simulate plasma turbulence in basic plasma physics experiments and in the scrape-off layer of tokamaks, in order to study the impact on the simulation results of the input parameter that describes the parallel losses. The uncertainty that characterizes the time-averaged density gradient lengths, time-averaged densities, and fluctuation density level are evaluated. A reasonable estimate of the uncertainty of these distributions can be obtained with a single reduced-cost simulation.

Uncertainty analysis of multi-rate kinetics of uranium desorption from sediments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Xiaoying; Liu, Chongxuan; Hu, Bill X.

2014-01-01

A multi-rate expression for uranyl [U(VI)] surface complexation reactions has been proposed to describe diffusion-limited U(VI) sorption/desorption in heterogeneous subsurface sediments. An important assumption in the rate expression is that its rate constants follow a certain type probability distribution. In this paper, a Bayes-based, Differential Evolution Markov Chain method was used to assess the distribution assumption and to analyze parameter and model structure uncertainties. U(VI) desorption from a contaminated sediment at the US Hanford 300 Area, Washington was used as an example for detail analysis. The results indicated that: 1) the rate constants in the multi-rate expression contain uneven uncertaintiesmore » with slower rate constants having relative larger uncertainties; 2) the lognormal distribution is an effective assumption for the rate constants in the multi-rate model to simualte U(VI) desorption; 3) however, long-term prediction and its uncertainty may be significantly biased by the lognormal assumption for the smaller rate constants; and 4) both parameter and model structure uncertainties can affect the extrapolation of the multi-rate model with a larger uncertainty from the model structure. The results provide important insights into the factors contributing to the uncertainties of the multi-rate expression commonly used to describe the diffusion or mixing-limited sorption/desorption of both organic and inorganic contaminants in subsurface sediments.« less

Optimal control problems of epidemic systems with parameter uncertainties: application to a malaria two-age-classes transmission model with asymptomatic carriers.

PubMed

Mwanga, Gasper G; Haario, Heikki; Capasso, Vicenzo

2015-03-01

The main scope of this paper is to study the optimal control practices of malaria, by discussing the implementation of a catalog of optimal control strategies in presence of parameter uncertainties, which is typical of infectious diseases data. In this study we focus on a deterministic mathematical model for the transmission of malaria, including in particular asymptomatic carriers and two age classes in the human population. A partial qualitative analysis of the relevant ODE system has been carried out, leading to a realistic threshold parameter. For the deterministic model under consideration, four possible control strategies have been analyzed: the use of Long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic and asymptomatic individuals. The numerical results show that using optimal control the disease can be brought to a stable disease free equilibrium when all four controls are used. The Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures is determined. The numerical simulations of the optimal control in the presence of parameter uncertainty demonstrate the robustness of the optimal control: the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the designing of cost-effective strategies for disease controls with multiple interventions, even under considerable uncertainty of model parameters. Copyright © 2014 Elsevier Inc. All rights reserved.

Bayesian Methods for Effective Field Theories

NASA Astrophysics Data System (ADS)

Wesolowski, Sarah

Microscopic predictions of the properties of atomic nuclei have reached a high level of precision in the past decade. This progress mandates improved uncertainty quantification (UQ) for a robust comparison of experiment with theory. With the uncertainty from many-body methods under control, calculations are now sensitive to the input inter-nucleon interactions. These interactions include parameters that must be fit to experiment, inducing both uncertainty from the fit and from missing physics in the operator structure of the Hamiltonian. Furthermore, the implementation of the inter-nucleon interactions is not unique, which presents the additional problem of assessing results using different interactions. Effective field theories (EFTs) take advantage of a separation of high- and low-energy scales in the problem to form a power-counting scheme that allows the organization of terms in the Hamiltonian based on their expected contribution to observable predictions. This scheme gives a natural framework for quantification of uncertainty due to missing physics. The free parameters of the EFT, called the low-energy constants (LECs), must be fit to data, but in a properly constructed EFT these constants will be natural-sized, i.e., of order unity. The constraints provided by the EFT, namely the size of the systematic uncertainty from truncation of the theory and the natural size of the LECs, are assumed information even before a calculation is performed or a fit is done. Bayesian statistical methods provide a framework for treating uncertainties that naturally incorporates prior information as well as putting stochastic and systematic uncertainties on an equal footing. For EFT UQ Bayesian methods allow the relevant EFT properties to be incorporated quantitatively as prior probability distribution functions (pdfs). Following the logic of probability theory, observable quantities and underlying physical parameters such as the EFT breakdown scale may be expressed as pdfs that incorporate the prior pdfs. Problems of model selection, such as distinguishing between competing EFT implementations, are also natural in a Bayesian framework. In this thesis we focus on two complementary topics for EFT UQ using Bayesian methods--quantifying EFT truncation uncertainty and parameter estimation for LECs. Using the order-by-order calculations and underlying EFT constraints as prior information, we show how to estimate EFT truncation uncertainties. We then apply the result to calculating truncation uncertainties on predictions of nucleon-nucleon scattering in chiral effective field theory. We apply model-checking diagnostics to our calculations to ensure that the statistical model of truncation uncertainty produces consistent results. A framework for EFT parameter estimation based on EFT convergence properties and naturalness is developed which includes a series of diagnostics to ensure the extraction of the maximum amount of available information from data to estimate LECs with minimal bias. We develop this framework using model EFTs and apply it to the problem of extrapolating lattice quantum chromodynamics results for the nucleon mass. We then apply aspects of the parameter estimation framework to perform case studies in chiral EFT parameter estimation, investigating a possible operator redundancy at fourth order in the chiral expansion and the appropriate inclusion of truncation uncertainty in estimating LECs.

Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis.

PubMed

Hock, Sabrina; Hasenauer, Jan; Theis, Fabian J

2013-01-01

Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.

CXTFIT/Excel A modular adaptable code for parameter estimation, sensitivity analysis and uncertainty analysis for laboratory or field tracer experiments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Guoping; Mayes, Melanie; Parker, Jack C

2010-01-01

We implemented the widely used CXTFIT code in Excel to provide flexibility and added sensitivity and uncertainty analysis functions to improve transport parameter estimation and to facilitate model discrimination for multi-tracer experiments on structured soils. Analytical solutions for one-dimensional equilibrium and nonequilibrium convection dispersion equations were coded as VBA functions so that they could be used as ordinary math functions in Excel for forward predictions. Macros with user-friendly interfaces were developed for optimization, sensitivity analysis, uncertainty analysis, error propagation, response surface calculation, and Monte Carlo analysis. As a result, any parameter with transformations (e.g., dimensionless, log-transformed, species-dependent reactions, etc.) couldmore » be estimated with uncertainty and sensitivity quantification for multiple tracer data at multiple locations and times. Prior information and observation errors could be incorporated into the weighted nonlinear least squares method with a penalty function. Users are able to change selected parameter values and view the results via embedded graphics, resulting in a flexible tool applicable to modeling transport processes and to teaching students about parameter estimation. The code was verified by comparing to a number of benchmarks with CXTFIT 2.0. It was applied to improve parameter estimation for four typical tracer experiment data sets in the literature using multi-model evaluation and comparison. Additional examples were included to illustrate the flexibilities and advantages of CXTFIT/Excel. The VBA macros were designed for general purpose and could be used for any parameter estimation/model calibration when the forward solution is implemented in Excel. A step-by-step tutorial, example Excel files and the code are provided as supplemental material.« less

Predicting minimum uncertainties in the inversion of ocean color geophysical parameters based on Cramer-Rao bounds.

PubMed

Jay, Sylvain; Guillaume, Mireille; Chami, Malik; Minghelli, Audrey; Deville, Yannick; Lafrance, Bruno; Serfaty, Véronique

2018-01-22

We present an analytical approach based on Cramer-Rao Bounds (CRBs) to investigate the uncertainties in estimated ocean color parameters resulting from the propagation of uncertainties in the bio-optical reflectance modeling through the inversion process. Based on given bio-optical and noise probabilistic models, CRBs can be computed efficiently for any set of ocean color parameters and any sensor configuration, directly providing the minimum estimation variance that can be possibly attained by any unbiased estimator of any targeted parameter. Here, CRBs are explicitly developed using (1) two water reflectance models corresponding to deep and shallow waters, resp., and (2) four probabilistic models describing the environmental noises observed within four Sentinel-2 MSI, HICO, Sentinel-3 OLCI and MODIS images, resp. For both deep and shallow waters, CRBs are shown to be consistent with the experimental estimation variances obtained using two published remote-sensing methods, while not requiring one to perform any inversion. CRBs are also used to investigate to what extent perfect a priori knowledge on one or several geophysical parameters can improve the estimation of remaining unknown parameters. For example, using pre-existing knowledge of bathymetry (e.g., derived from LiDAR) within the inversion is shown to greatly improve the retrieval of bottom cover for shallow waters. Finally, CRBs are shown to provide valuable information on the best estimation performances that may be achieved with the MSI, HICO, OLCI and MODIS configurations for a variety of oceanic, coastal and inland waters. CRBs are thus demonstrated to be an informative and efficient tool to characterize minimum uncertainties in inverted ocean color geophysical parameters.

Multi-criteria evaluation of wastewater treatment plant control strategies under uncertainty.

PubMed

Flores-Alsina, Xavier; Rodríguez-Roda, Ignasi; Sin, Gürkan; Gernaey, Krist V

2008-11-01

The evaluation of activated sludge control strategies in wastewater treatment plants (WWTP) via mathematical modelling is a complex activity because several objectives; e.g. economic, environmental, technical and legal; must be taken into account at the same time, i.e. the evaluation of the alternatives is a multi-criteria problem. Activated sludge models are not well characterized and some of the parameters can present uncertainty, e.g. the influent fractions arriving to the facility and the effect of either temperature or toxic compounds on the kinetic parameters, having a strong influence in the model predictions used during the evaluation of the alternatives and affecting the resulting rank of preferences. Using a simplified version of the IWA Benchmark Simulation Model No. 2 as a case study, this article shows the variations in the decision making when the uncertainty in activated sludge model (ASM) parameters is either included or not during the evaluation of WWTP control strategies. This paper comprises two main sections. Firstly, there is the evaluation of six WWTP control strategies using multi-criteria decision analysis setting the ASM parameters at their default value. In the following section, the uncertainty is introduced, i.e. input uncertainty, which is characterized by probability distribution functions based on the available process knowledge. Next, Monte Carlo simulations are run to propagate input through the model and affect the different outcomes. Thus (i) the variation in the overall degree of satisfaction of the control objectives for the generated WWTP control strategies is quantified, (ii) the contributions of environmental, legal, technical and economic objectives to the existing variance are identified and finally (iii) the influence of the relative importance of the control objectives during the selection of alternatives is analyzed. The results show that the control strategies with an external carbon source reduce the output uncertainty in the criteria used to quantify the degree of satisfaction of environmental, technical and legal objectives, but increasing the economical costs and their variability as a trade-off. Also, it is shown how a preliminary selected alternative with cascade ammonium controller becomes less desirable when input uncertainty is included, having simpler alternatives more chance of success.

Fukushima Daiichi unit 1 uncertainty analysis--Preliminary selection of uncertain parameters and analysis methodology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardoni, Jeffrey N.; Kalinich, Donald A.

2014-02-01

Sandia National Laboratories (SNL) plans to conduct uncertainty analyses (UA) on the Fukushima Daiichi unit (1F1) plant with the MELCOR code. The model to be used was developed for a previous accident reconstruction investigation jointly sponsored by the US Department of Energy (DOE) and Nuclear Regulatory Commission (NRC). However, that study only examined a handful of various model inputs and boundary conditions, and the predictions yielded only fair agreement with plant data and current release estimates. The goal of this uncertainty study is to perform a focused evaluation of uncertainty in core melt progression behavior and its effect on keymore » figures-of-merit (e.g., hydrogen production, vessel lower head failure, etc.). In preparation for the SNL Fukushima UA work, a scoping study has been completed to identify important core melt progression parameters for the uncertainty analysis. The study also lays out a preliminary UA methodology.« less

Transient Inverse Calibration of Site-Wide Groundwater Model to Hanford Operational Impacts from 1943 to 1996--Alternative Conceptual Model Considering Interaction with Uppermost Basalt Confined Aquifer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vermeul, Vincent R.; Cole, Charles R.; Bergeron, Marcel P.

2001-08-29

The baseline three-dimensional transient inverse model for the estimation of site-wide scale flow parameters, including their uncertainties, using data on the transient behavior of the unconfined aquifer system over the entire historical period of Hanford operations, has been modified to account for the effects of basalt intercommunication between the Hanford unconfined aquifer and the underlying upper basalt confined aquifer. Both the baseline and alternative conceptual models (ACM-1) considered only the groundwater flow component and corresponding observational data in the 3-Dl transient inverse calibration efforts. Subsequent efforts will examine both groundwater flow and transport. Comparisons of goodness of fit measures andmore » parameter estimation results for the ACM-1 transient inverse calibrated model with those from previous site-wide groundwater modeling efforts illustrate that the new 3-D transient inverse model approach will strengthen the technical defensibility of the final model(s) and provide the ability to incorporate uncertainty in predictions related to both conceptual model and parameter uncertainty. These results, however, indicate that additional improvements are required to the conceptual model framework. An investigation was initiated at the end of this basalt inverse modeling effort to determine whether facies-based zonation would improve specific yield parameter estimation results (ACM-2). A description of the justification and methodology to develop this zonation is discussed.« less

Towards Characterization, Modeling, and Uncertainty Quantification in Multi-scale Mechanics of Oragnic-rich Shales

NASA Astrophysics Data System (ADS)

Abedi, S.; Mashhadian, M.; Noshadravan, A.

2015-12-01

Increasing the efficiency and sustainability in operation of hydrocarbon recovery from organic-rich shales requires a fundamental understanding of chemomechanical properties of organic-rich shales. This understanding is manifested in form of physics-bases predictive models capable of capturing highly heterogeneous and multi-scale structure of organic-rich shale materials. In this work we present a framework of experimental characterization, micromechanical modeling, and uncertainty quantification that spans from nanoscale to macroscale. Application of experiments such as coupled grid nano-indentation and energy dispersive x-ray spectroscopy and micromechanical modeling attributing the role of organic maturity to the texture of the material, allow us to identify unique clay mechanical properties among different samples that are independent of maturity of shale formations and total organic content. The results can then be used to inform the physically-based multiscale model for organic rich shales consisting of three levels that spans from the scale of elementary building blocks (e.g. clay minerals in clay-dominated formations) of organic rich shales to the scale of the macroscopic inorganic/organic hard/soft inclusion composite. Although this approach is powerful in capturing the effective properties of organic-rich shale in an average sense, it does not account for the uncertainty in compositional and mechanical model parameters. Thus, we take this model one step forward by systematically incorporating the main sources of uncertainty in modeling multiscale behavior of organic-rich shales. In particular we account for the uncertainty in main model parameters at different scales such as porosity, elastic properties and mineralogy mass percent. To that end, we use Maximum Entropy Principle and random matrix theory to construct probabilistic descriptions of model inputs based on available information. The Monte Carlo simulation is then carried out to propagate the uncertainty and consequently construct probabilistic descriptions of properties at multiple length-scales. The combination of experimental characterization and stochastic multi-scale modeling presented in this work improves the robustness in the prediction of essential subsurface parameters in engineering scale.

Uncertainty analysis of vegetation distribution in the northern high latitudes during the 21st century with a dynamic vegetation model

PubMed Central

Jiang, Yueyang; Zhuang, Qianlai; Schaphoff, Sibyll; Sitch, Stephen; Sokolov, Andrei; Kicklighter, David; Melillo, Jerry

2012-01-01

This study aims to assess how high-latitude vegetation may respond under various climate scenarios during the 21st century with a focus on analyzing model parameters induced uncertainty and how this uncertainty compares to the uncertainty induced by various climates. The analysis was based on a set of 10,000 Monte Carlo ensemble Lund-Potsdam-Jena (LPJ) simulations for the northern high latitudes (45oN and polewards) for the period 1900–2100. The LPJ Dynamic Global Vegetation Model (LPJ-DGVM) was run under contemporary and future climates from four Special Report Emission Scenarios (SRES), A1FI, A2, B1, and B2, based on the Hadley Centre General Circulation Model (GCM), and six climate scenarios, X901M, X902L, X903H, X904M, X905L, and X906H from the Integrated Global System Model (IGSM) at the Massachusetts Institute of Technology (MIT). In the current dynamic vegetation model, some parameters are more important than others in determining the vegetation distribution. Parameters that control plant carbon uptake and light-use efficiency have the predominant influence on the vegetation distribution of both woody and herbaceous plant functional types. The relative importance of different parameters varies temporally and spatially and is influenced by climate inputs. In addition to climate, these parameters play an important role in determining the vegetation distribution in the region. The parameter-based uncertainties contribute most to the total uncertainty. The current warming conditions lead to a complexity of vegetation responses in the region. Temperate trees will be more sensitive to climate variability, compared with boreal forest trees and C3 perennial grasses. This sensitivity would result in a unanimous northward greenness migration due to anomalous warming in the northern high latitudes. Temporally, boreal needleleaved evergreen plants are projected to decline considerably, and a large portion of C3 perennial grass is projected to disappear by the end of the 21st century. In contrast, the area of temperate trees would increase, especially under the most extreme A1FI scenario. As the warming continues, the northward greenness expansion in the Arctic region could continue. PMID:22822437

Uncertainty Quantification given Discontinuous Climate Model Response and a Limited Number of Model Runs

NASA Astrophysics Data System (ADS)

Sargsyan, K.; Safta, C.; Debusschere, B.; Najm, H.

2010-12-01

Uncertainty quantification in complex climate models is challenged by the sparsity of available climate model predictions due to the high computational cost of model runs. Another feature that prevents classical uncertainty analysis from being readily applicable is bifurcative behavior in climate model response with respect to certain input parameters. A typical example is the Atlantic Meridional Overturning Circulation. The predicted maximum overturning stream function exhibits discontinuity across a curve in the space of two uncertain parameters, namely climate sensitivity and CO2 forcing. We outline a methodology for uncertainty quantification given discontinuous model response and a limited number of model runs. Our approach is two-fold. First we detect the discontinuity with Bayesian inference, thus obtaining a probabilistic representation of the discontinuity curve shape and location for arbitrarily distributed input parameter values. Then, we construct spectral representations of uncertainty, using Polynomial Chaos (PC) expansions on either side of the discontinuity curve, leading to an averaged-PC representation of the forward model that allows efficient uncertainty quantification. The approach is enabled by a Rosenblatt transformation that maps each side of the discontinuity to regular domains where desirable orthogonality properties for the spectral bases hold. We obtain PC modes by either orthogonal projection or Bayesian inference, and argue for a hybrid approach that targets a balance between the accuracy provided by the orthogonal projection and the flexibility provided by the Bayesian inference - where the latter allows obtaining reasonable expansions without extra forward model runs. The model output, and its associated uncertainty at specific design points, are then computed by taking an ensemble average over PC expansions corresponding to possible realizations of the discontinuity curve. The methodology is tested on synthetic examples of discontinuous model data with adjustable sharpness and structure. This work was supported by the Sandia National Laboratories Seniors’ Council LDRD (Laboratory Directed Research and Development) program. Sandia National Laboratories is a multi-program laboratory operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

Influence of model reduction on uncertainty of flood inundation predictions

NASA Astrophysics Data System (ADS)

Romanowicz, R. J.; Kiczko, A.; Osuch, M.

2012-04-01

Derivation of flood risk maps requires an estimation of the maximum inundation extent for a flood with an assumed probability of exceedence, e.g. a 100 or 500 year flood. The results of numerical simulations of flood wave propagation are used to overcome the lack of relevant observations. In practice, deterministic 1-D models are used for flow routing, giving a simplified image of a flood wave propagation process. The solution of a 1-D model depends on the simplifications to the model structure, the initial and boundary conditions and the estimates of model parameters which are usually identified using the inverse problem based on the available noisy observations. Therefore, there is a large uncertainty involved in the derivation of flood risk maps. In this study we examine the influence of model structure simplifications on estimates of flood extent for the urban river reach. As the study area we chose the Warsaw reach of the River Vistula, where nine bridges and several dikes are located. The aim of the study is to examine the influence of water structures on the derived model roughness parameters, with all the bridges and dikes taken into account, with a reduced number and without any water infrastructure. The results indicate that roughness parameter values of a 1-D HEC-RAS model can be adjusted for the reduction in model structure. However, the price we pay is the model robustness. Apart from a relatively simple question regarding reducing model structure, we also try to answer more fundamental questions regarding the relative importance of input, model structure simplification, parametric and rating curve uncertainty to the uncertainty of flood extent estimates. We apply pseudo-Bayesian methods of uncertainty estimation and Global Sensitivity Analysis as the main methodological tools. The results indicate that the uncertainties have a substantial influence on flood risk assessment. In the paper we present a simplified methodology allowing the influence of that uncertainty to be assessed. This work was supported by National Science Centre of Poland (grant 2011/01/B/ST10/06866).

Variability and epistemic uncertainty in water ingestion rates and pharmacokinetic parameters, and impact on the association between perfluorooctanoate and preeclampsia in the C8 Health Project population.

PubMed

Avanasi, Raghavendhran; Shin, Hyeong-Moo; Vieira, Veronica M; Bartell, Scott M

2016-04-01

We recently utilized a suite of environmental fate and transport models and an integrated exposure and pharmacokinetic model to estimate individual perfluorooctanoate (PFOA) serum concentrations, and also assessed the association of those concentrations with preeclampsia for participants in the C8 Health Project (a cross-sectional study of over 69,000 people who were environmentally exposed to PFOA near a major U.S. fluoropolymer production facility located in West Virginia). However, the exposure estimates from this integrated model relied on default values for key independent exposure parameters including water ingestion rates, the serum PFOA half-life, and the volume of distribution for PFOA. The aim of the present study is to assess the impact of inter-individual variability and epistemic uncertainty in these parameters on the exposure estimates and subsequently, the epidemiological association between PFOA exposure and preeclampsia. We used Monte Carlo simulation to propagate inter-individual variability/epistemic uncertainty in the exposure assessment and reanalyzed the epidemiological association. Inter-individual variability in these parameters mildly impacted the serum PFOA concentration predictions (the lowest mean rank correlation between the estimated serum concentrations in our study and the original predicted serum concentrations was 0.95) and there was a negligible impact on the epidemiological association with preeclampsia (no change in the mean adjusted odds ratio (AOR) and the contribution of exposure uncertainty to the total uncertainty including sampling variability was 7%). However, when epistemic uncertainty was added along with the inter-individual variability, serum PFOA concentration predictions and their association with preeclampsia were moderately impacted (the mean AOR of preeclampsia occurrence was reduced from 1.12 to 1.09, and the contribution of exposure uncertainty to the total uncertainty was increased up to 33%). In conclusion, our study shows that the change of the rank exposure among the study participants due to variability and epistemic uncertainty in the independent exposure parameters was large enough to cause a 25% bias towards the null. This suggests that the true AOR of the association between PFOA and preeclampsia in this population might be higher than the originally reported AOR and has more uncertainty than indicated by the originally reported confidence interval. Copyright © 2016 Elsevier Inc. All rights reserved.

A Probabilistic Approach to Quantify the Impact of Uncertainty Propagation in Musculoskeletal Simulations

PubMed Central

Myers, Casey A.; Laz, Peter J.; Shelburne, Kevin B.; Davidson, Bradley S.

2015-01-01

Uncertainty that arises from measurement error and parameter estimation can significantly affect the interpretation of musculoskeletal simulations; however, these effects are rarely addressed. The objective of this study was to develop an open-source probabilistic musculoskeletal modeling framework to assess how measurement error and parameter uncertainty propagate through a gait simulation. A baseline gait simulation was performed for a male subject using OpenSim for three stages: inverse kinematics, inverse dynamics, and muscle force prediction. A series of Monte Carlo simulations were performed that considered intrarater variability in marker placement, movement artifacts in each phase of gait, variability in body segment parameters, and variability in muscle parameters calculated from cadaveric investigations. Propagation of uncertainty was performed by also using the output distributions from one stage as input distributions to subsequent stages. Confidence bounds (5–95%) and sensitivity of outputs to model input parameters were calculated throughout the gait cycle. The combined impact of uncertainty resulted in mean bounds that ranged from 2.7° to 6.4° in joint kinematics, 2.7 to 8.1 N m in joint moments, and 35.8 to 130.8 N in muscle forces. The impact of movement artifact was 1.8 times larger than any other propagated source. Sensitivity to specific body segment parameters and muscle parameters were linked to where in the gait cycle they were calculated. We anticipate that through the increased use of probabilistic tools, researchers will better understand the strengths and limitations of their musculoskeletal simulations and more effectively use simulations to evaluate hypotheses and inform clinical decisions. PMID:25404535

Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model

NASA Astrophysics Data System (ADS)

Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran

2016-09-01

In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7, but likelihood function L5 may result in biased and unreliable estimation of parameters due to violation of the residualerror assumptions. Thus, likelihood function L7 provides posterior distribution of model parameters credibly and therefore can be employed for further applications.

A Reliability Estimation in Modeling Watershed Runoff With Uncertainties

NASA Astrophysics Data System (ADS)

Melching, Charles S.; Yen, Ben Chie; Wenzel, Harry G., Jr.

1990-10-01

The reliability of simulation results produced by watershed runoff models is a function of uncertainties in nature, data, model parameters, and model structure. A framework is presented here for using a reliability analysis method (such as first-order second-moment techniques or Monte Carlo simulation) to evaluate the combined effect of the uncertainties on the reliability of output hydrographs from hydrologic models. For a given event the prediction reliability can be expressed in terms of the probability distribution of the estimated hydrologic variable. The peak discharge probability for a watershed in Illinois using the HEC-1 watershed model is given as an example. The study of the reliability of predictions from watershed models provides useful information on the stochastic nature of output from deterministic models subject to uncertainties and identifies the relative contribution of the various uncertainties to unreliability of model predictions.

A Bayesian Uncertainty Framework for Conceptual Snowmelt and Hydrologic Models Applied to the Tenderfoot Creek Experimental Forest

NASA Astrophysics Data System (ADS)

Smith, T.; Marshall, L.

2007-12-01

In many mountainous regions, the single most important parameter in forecasting the controls on regional water resources is snowpack (Williams et al., 1999). In an effort to bridge the gap between theoretical understanding and functional modeling of snow-driven watersheds, a flexible hydrologic modeling framework is being developed. The aim is to create a suite of models that move from parsimonious structures, concentrated on aggregated watershed response, to those focused on representing finer scale processes and distributed response. This framework will operate as a tool to investigate the link between hydrologic model predictive performance, uncertainty, model complexity, and observable hydrologic processes. Bayesian methods, and particularly Markov chain Monte Carlo (MCMC) techniques, are extremely useful in uncertainty assessment and parameter estimation of hydrologic models. However, these methods have some difficulties in implementation. In a traditional Bayesian setting, it can be difficult to reconcile multiple data types, particularly those offering different spatial and temporal coverage, depending on the model type. These difficulties are also exacerbated by sensitivity of MCMC algorithms to model initialization and complex parameter interdependencies. As a way of circumnavigating some of the computational complications, adaptive MCMC algorithms have been developed to take advantage of the information gained from each successive iteration. Two adaptive algorithms are compared is this study, the Adaptive Metropolis (AM) algorithm, developed by Haario et al (2001), and the Delayed Rejection Adaptive Metropolis (DRAM) algorithm, developed by Haario et al (2006). While neither algorithm is truly Markovian, it has been proven that each satisfies the desired ergodicity and stationarity properties of Markov chains. Both algorithms were implemented as the uncertainty and parameter estimation framework for a conceptual rainfall-runoff model based on the Probability Distributed Model (PDM), developed by Moore (1985). We implement the modeling framework in Stringer Creek watershed in the Tenderfoot Creek Experimental Forest (TCEF), Montana. The snowmelt-driven watershed offers that additional challenge of modeling snow accumulation and melt and current efforts are aimed at developing a temperature- and radiation-index snowmelt model. Auxiliary data available from within TCEF's watersheds are used to support in the understanding of information value as it relates to predictive performance. Because the model is based on lumped parameters, auxiliary data are hard to incorporate directly. However, these additional data offer benefits through the ability to inform prior distributions of the lumped, model parameters. By incorporating data offering different information into the uncertainty assessment process, a cross-validation technique is engaged to better ensure that modeled results reflect real process complexity.

Identifying and assessing critical uncertainty thresholds in a forest pest risk model

Treesearch

Frank H. Koch; Denys Yemshanov

2015-01-01

Pest risk maps can provide helpful decision support for invasive alien species management, but often fail to address adequately the uncertainty associated with their predicted risk values. Th is chapter explores how increased uncertainty in a risk model’s numeric assumptions (i.e. its principal parameters) might aff ect the resulting risk map. We used a spatial...

Fast integration-based prediction bands for ordinary differential equation models.

PubMed

Hass, Helge; Kreutz, Clemens; Timmer, Jens; Kaschek, Daniel

2016-04-15

To gain a deeper understanding of biological processes and their relevance in disease, mathematical models are built upon experimental data. Uncertainty in the data leads to uncertainties of the model's parameters and in turn to uncertainties of predictions. Mechanistic dynamic models of biochemical networks are frequently based on nonlinear differential equation systems and feature a large number of parameters, sparse observations of the model components and lack of information in the available data. Due to the curse of dimensionality, classical and sampling approaches propagating parameter uncertainties to predictions are hardly feasible and insufficient. However, for experimental design and to discriminate between competing models, prediction and confidence bands are essential. To circumvent the hurdles of the former methods, an approach to calculate a profile likelihood on arbitrary observations for a specific time point has been introduced, which provides accurate confidence and prediction intervals for nonlinear models and is computationally feasible for high-dimensional models. In this article, reliable and smooth point-wise prediction and confidence bands to assess the model's uncertainty on the whole time-course are achieved via explicit integration with elaborate correction mechanisms. The corresponding system of ordinary differential equations is derived and tested on three established models for cellular signalling. An efficiency analysis is performed to illustrate the computational benefit compared with repeated profile likelihood calculations at multiple time points. The integration framework and the examples used in this article are provided with the software package Data2Dynamics, which is based on MATLAB and freely available at http://www.data2dynamics.org helge.hass@fdm.uni-freiburg.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Global Sampling for Integrating Physics-Specific Subsystems and Quantifying Uncertainties of CO 2 Geological Sequestration

DOE PAGES

Sun, Y.; Tong, C.; Trainor-Guitten, W. J.; ...

2012-12-20

The risk of CO 2 leakage from a deep storage reservoir into a shallow aquifer through a fault is assessed and studied using physics-specific computer models. The hypothetical CO 2 geological sequestration system is composed of three subsystems: a deep storage reservoir, a fault in caprock, and a shallow aquifer, which are modeled respectively by considering sub-domain-specific physics. Supercritical CO 2 is injected into the reservoir subsystem with uncertain permeabilities of reservoir, caprock, and aquifer, uncertain fault location, and injection rate (as a decision variable). The simulated pressure and CO 2/brine saturation are connected to the fault-leakage model as amore » boundary condition. CO 2 and brine fluxes from the fault-leakage model at the fault outlet are then imposed in the aquifer model as a source term. Moreover, uncertainties are propagated from the deep reservoir model, to the fault-leakage model, and eventually to the geochemical model in the shallow aquifer, thus contributing to risk profiles. To quantify the uncertainties and assess leakage-relevant risk, we propose a global sampling-based method to allocate sub-dimensions of uncertain parameters to sub-models. The risk profiles are defined and related to CO 2 plume development for pH value and total dissolved solids (TDS) below the EPA's Maximum Contaminant Levels (MCL) for drinking water quality. A global sensitivity analysis is conducted to select the most sensitive parameters to the risk profiles. The resulting uncertainty of pH- and TDS-defined aquifer volume, which is impacted by CO 2 and brine leakage, mainly results from the uncertainty of fault permeability. Subsequently, high-resolution, reduced-order models of risk profiles are developed as functions of all the decision variables and uncertain parameters in all three subsystems.« less

A computationally inexpensive model for estimating dimensional measurement uncertainty due to x-ray computed tomography instrument misalignments

NASA Astrophysics Data System (ADS)

Ametova, Evelina; Ferrucci, Massimiliano; Chilingaryan, Suren; Dewulf, Wim

2018-06-01

The recent emergence of advanced manufacturing techniques such as additive manufacturing and an increased demand on the integrity of components have motivated research on the application of x-ray computed tomography (CT) for dimensional quality control. While CT has shown significant empirical potential for this purpose, there is a need for metrological research to accelerate the acceptance of CT as a measuring instrument. The accuracy in CT-based measurements is vulnerable to the instrument geometrical configuration during data acquisition, namely the relative position and orientation of x-ray source, rotation stage, and detector. Consistency between the actual instrument geometry and the corresponding parameters used in the reconstruction algorithm is critical. Currently available procedures provide users with only estimates of geometrical parameters. Quantification and propagation of uncertainty in the measured geometrical parameters must be considered to provide a complete uncertainty analysis and to establish confidence intervals for CT dimensional measurements. In this paper, we propose a computationally inexpensive model to approximate the influence of errors in CT geometrical parameters on dimensional measurement results. We use surface points extracted from a computer-aided design (CAD) model to model discrepancies in the radiographic image coordinates assigned to the projected edges between an aligned system and a system with misalignments. The efficacy of the proposed method was confirmed on simulated and experimental data in the presence of various geometrical uncertainty contributors.

Trans-dimensional inversion of microtremor array dispersion data with hierarchical autoregressive error models

NASA Astrophysics Data System (ADS)

Dettmer, Jan; Molnar, Sheri; Steininger, Gavin; Dosso, Stan E.; Cassidy, John F.

2012-02-01

This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing. In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.

6 DOF synchronized control for spacecraft formation flying with input constraint and parameter uncertainties.

PubMed

Lv, Yueyong; Hu, Qinglei; Ma, Guangfu; Zhou, Jiakang

2011-10-01

This paper treats the problem of synchronized control of spacecraft formation flying (SFF) in the presence of input constraint and parameter uncertainties. More specifically, backstepping based robust control is first developed for the total 6 DOF dynamic model of SFF with parameter uncertainties, in which the model consists of relative translation and attitude rotation. Then this controller is redesigned to deal with the input constraint problem by incorporating a command filter such that the generated control could be implementable even under physical or operating constraints on the control input. The convergence of the proposed control algorithms is proved by the Lyapunov stability theorem. Compared with conventional methods, illustrative simulations of spacecraft formation flying are conducted to verify the effectiveness of the proposed approach to achieve the spacecraft track the desired attitude and position trajectories in a synchronized fashion even in the presence of uncertainties, external disturbances and control saturation constraint. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Using dry and wet year hydroclimatic extremes to guide future hydrologic projections

NASA Astrophysics Data System (ADS)

Oni, Stephen; Futter, Martyn; Ledesma, Jose; Teutschbein, Claudia; Buttle, Jim; Laudon, Hjalmar

2016-07-01

There are growing numbers of studies on climate change impacts on forest hydrology, but limited attempts have been made to use current hydroclimatic variabilities to constrain projections of future climatic conditions. Here we used historical wet and dry years as a proxy for expected future extreme conditions in a boreal catchment. We showed that runoff could be underestimated by at least 35 % when dry year parameterizations were used for wet year conditions. Uncertainty analysis showed that behavioural parameter sets from wet and dry years separated mainly on precipitation-related parameters and to a lesser extent on parameters related to landscape processes, while uncertainties inherent in climate models (as opposed to differences in calibration or performance metrics) appeared to drive the overall uncertainty in runoff projections under dry and wet hydroclimatic conditions. Hydrologic model calibration for climate impact studies could be based on years that closely approximate anticipated conditions to better constrain uncertainty in projecting extreme conditions in boreal and temperate regions.

Significant uncertainty in global scale hydrological modeling from precipitation data errors

NASA Astrophysics Data System (ADS)

Sperna Weiland, Frederiek C.; Vrugt, Jasper A.; van Beek, Rens (L.) P. H.; Weerts, Albrecht H.; Bierkens, Marc F. P.

2015-10-01

In the past decades significant progress has been made in the fitting of hydrologic models to data. Most of this work has focused on simple, CPU-efficient, lumped hydrologic models using discharge, water table depth, soil moisture, or tracer data from relatively small river basins. In this paper, we focus on large-scale hydrologic modeling and analyze the effect of parameter and rainfall data uncertainty on simulated discharge dynamics with the global hydrologic model PCR-GLOBWB. We use three rainfall data products; the CFSR reanalysis, the ERA-Interim reanalysis, and a combined ERA-40 reanalysis and CRU dataset. Parameter uncertainty is derived from Latin Hypercube Sampling (LHS) using monthly discharge data from five of the largest river systems in the world. Our results demonstrate that the default parameterization of PCR-GLOBWB, derived from global datasets, can be improved by calibrating the model against monthly discharge observations. Yet, it is difficult to find a single parameterization of PCR-GLOBWB that works well for all of the five river basins considered herein and shows consistent performance during both the calibration and evaluation period. Still there may be possibilities for regionalization based on catchment similarities. Our simulations illustrate that parameter uncertainty constitutes only a minor part of predictive uncertainty. Thus, the apparent dichotomy between simulations of global-scale hydrologic behavior and actual data cannot be resolved by simply increasing the model complexity of PCR-GLOBWB and resolving sub-grid processes. Instead, it would be more productive to improve the characterization of global rainfall amounts at spatial resolutions of 0.5° and smaller.

Predicting the performance uncertainty of a 1-MW pilot-scale carbon capture system after hierarchical laboratory-scale calibration and validation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Zhijie; Lai, Canhai; Marcy, Peter William

2017-05-01

A challenging problem in designing pilot-scale carbon capture systems is to predict, with uncertainty, the adsorber performance and capture efficiency under various operating conditions where no direct experimental data exist. Motivated by this challenge, we previously proposed a hierarchical framework in which relevant parameters of physical models were sequentially calibrated from different laboratory-scale carbon capture unit (C2U) experiments. Specifically, three models of increasing complexity were identified based on the fundamental physical and chemical processes of the sorbent-based carbon capture technology. Results from the corresponding laboratory experiments were used to statistically calibrate the physical model parameters while quantifying some of theirmore » inherent uncertainty. The parameter distributions obtained from laboratory-scale C2U calibration runs are used in this study to facilitate prediction at a larger scale where no corresponding experimental results are available. In this paper, we first describe the multiphase reactive flow model for a sorbent-based 1-MW carbon capture system then analyze results from an ensemble of simulations with the upscaled model. The simulation results are used to quantify uncertainty regarding the design’s predicted efficiency in carbon capture. In particular, we determine the minimum gas flow rate necessary to achieve 90% capture efficiency with 95% confidence.« less

Uncertainty analysis of least-cost modeling for designing wildlife linkages.

PubMed

Beier, Paul; Majka, Daniel R; Newell, Shawn L

2009-12-01

Least-cost models for focal species are widely used to design wildlife corridors. To evaluate the least-cost modeling approach used to develop 15 linkage designs in southern California, USA, we assessed robustness of the largest and least constrained linkage. Species experts parameterized models for eight species with weights for four habitat factors (land cover, topographic position, elevation, road density) and resistance values for each class within a factor (e.g., each class of land cover). Each model produced a proposed corridor for that species. We examined the extent to which uncertainty in factor weights and class resistance values affected two key conservation-relevant outputs, namely, the location and modeled resistance to movement of each proposed corridor. To do so, we compared the proposed corridor to 13 alternative corridors created with parameter sets that spanned the plausible ranges of biological uncertainty in these parameters. Models for five species were highly robust (mean overlap 88%, little or no increase in resistance). Although the proposed corridors for the other three focal species overlapped as little as 0% (mean 58%) of the alternative corridors, resistance in the proposed corridors for these three species was rarely higher than resistance in the alternative corridors (mean difference was 0.025 on a scale of 1 10; worst difference was 0.39). As long as the model had the correct rank order of resistance values and factor weights, our results suggest that the predicted corridor is robust to uncertainty. The three carnivore focal species, alone or in combination, were not effective umbrellas for the other focal species. The carnivore corridors failed to overlap the predicted corridors of most other focal species and provided relatively high resistance for the other focal species (mean increase of 2.7 resistance units). Least-cost modelers should conduct uncertainty analysis so that decision-makers can appreciate the potential impact of model uncertainty on conservation decisions. Our approach to uncertainty analysis (which can be called a worst-case scenario approach) is appropriate for complex models in which distribution of the input parameters cannot be specified.

Evaluating the impacts of agricultural land management practices on water resources: A probabilistic hydrologic modeling approach.

PubMed

Prada, A F; Chu, M L; Guzman, J A; Moriasi, D N

2017-05-15

Evaluating the effectiveness of agricultural land management practices in minimizing environmental impacts using models is challenged by the presence of inherent uncertainties during the model development stage. One issue faced during the model development stage is the uncertainty involved in model parameterization. Using a single optimized set of parameters (one snapshot) to represent baseline conditions of the system limits the applicability and robustness of the model to properly represent future or alternative scenarios. The objective of this study was to develop a framework that facilitates model parameter selection while evaluating uncertainty to assess the impacts of land management practices at the watershed scale. The model framework was applied to the Lake Creek watershed located in southwestern Oklahoma, USA. A two-step probabilistic approach was implemented to parameterize the Agricultural Policy/Environmental eXtender (APEX) model using global uncertainty and sensitivity analysis to estimate the full spectrum of total monthly water yield (WYLD) and total monthly Nitrogen loads (N) in the watershed under different land management practices. Twenty-seven models were found to represent the baseline scenario in which uncertainty of up to 29% and 400% in WYLD and N, respectively, is plausible. Changing the land cover to pasture manifested the highest decrease in N to up to 30% for a full pasture coverage while changing to full winter wheat cover can increase the N up to 11%. The methodology developed in this study was able to quantify the full spectrum of system responses, the uncertainty associated with them, and the most important parameters that drive their variability. Results from this study can be used to develop strategic decisions on the risks and tradeoffs associated with different management alternatives that aim to increase productivity while also minimizing their environmental impacts. Copyright © 2017 Elsevier Ltd. All rights reserved.

A New Approach for Obtaining Cosmological Constraints from Type Ia Supernovae using Approximate Bayesian Computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jennings, Elise; Wolf, Rachel; Sako, Masao

2016-11-09

Cosmological parameter estimation techniques that robustly account for systematic measurement uncertainties will be crucial for the next generation of cosmological surveys. We present a new analysis method, superABC, for obtaining cosmological constraints from Type Ia supernova (SN Ia) light curves using Approximate Bayesian Computation (ABC) without any likelihood assumptions. The ABC method works by using a forward model simulation of the data where systematic uncertainties can be simulated and marginalized over. A key feature of the method presented here is the use of two distinct metrics, the `Tripp' and `Light Curve' metrics, which allow us to compare the simulated data to the observed data set. The Tripp metric takes as input the parameters of models fit to each light curve with the SALT-II method, whereas the Light Curve metric uses the measured fluxes directly without model fitting. We apply the superABC sampler to a simulated data set ofmore » $$\\sim$$1000 SNe corresponding to the first season of the Dark Energy Survey Supernova Program. Varying $$\\Omega_m, w_0, \\alpha$$ and $$\\beta$$ and a magnitude offset parameter, with no systematics we obtain $$\\Delta(w_0) = w_0^{\\rm true} - w_0^{\\rm best \\, fit} = -0.036\\pm0.109$$ (a $$\\sim11$$% 1$$\\sigma$$ uncertainty) using the Tripp metric and $$\\Delta(w_0) = -0.055\\pm0.068$$ (a $$\\sim7$$% 1$$\\sigma$$ uncertainty) using the Light Curve metric. Including 1% calibration uncertainties in four passbands, adding 4 more parameters, we obtain $$\\Delta(w_0) = -0.062\\pm0.132$$ (a $$\\sim14$$% 1$$\\sigma$$ uncertainty) using the Tripp metric. Overall we find a $17$% increase in the uncertainty on $$w_0$$ with systematics compared to without. We contrast this with a MCMC approach where systematic effects are approximately included. We find that the MCMC method slightly underestimates the impact of calibration uncertainties for this simulated data set.« less

Effect of soil property uncertainties on permafrost thaw projections: A calibration-constrained analysis

DOE PAGES

Harp, Dylan R.; Atchley, Adam L.; Painter, Scott L.; ...

2016-02-11

Here, the effect of soil property uncertainties on permafrost thaw projections are studied using a three-phase subsurface thermal hydrology model and calibration-constrained uncertainty analysis. The Null-Space Monte Carlo method is used to identify soil hydrothermal parameter combinations that are consistent with borehole temperature measurements at the study site, the Barrow Environmental Observatory. Each parameter combination is then used in a forward projection of permafrost conditions for the 21more » $$^{st}$$ century (from calendar year 2006 to 2100) using atmospheric forcings from the Community Earth System Model (CESM) in the Representative Concentration Pathway (RCP) 8.5 greenhouse gas concentration trajectory. A 100-year projection allows for the evaluation of intra-annual uncertainty due to soil properties and the inter-annual variability due to year to year differences in CESM climate forcings. After calibrating to borehole temperature data at this well-characterized site, soil property uncertainties are still significant and result in significant intra-annual uncertainties in projected active layer thickness and annual thaw depth-duration even with a specified future climate. Intra-annual uncertainties in projected soil moisture content and Stefan number are small. A volume and time integrated Stefan number decreases significantly in the future climate, indicating that latent heat of phase change becomes more important than heat conduction in future climates. Out of 10 soil parameters, ALT, annual thaw depth-duration, and Stefan number are highly dependent on mineral soil porosity, while annual mean liquid saturation of the active layer is highly dependent on the mineral soil residual saturation and moderately dependent on peat residual saturation. By comparing the ensemble statistics to the spread of projected permafrost metrics using different climate models, we show that the effect of calibration-constrained uncertainty in soil properties, although significant, is less than that produced by structural climate model uncertainty for this location.« less

Effect of soil property uncertainties on permafrost thaw projections: A calibration-constrained analysis

DOE PAGES

Harp, D. R.; Atchley, A. L.; Painter, S. L.; ...

2015-06-29

The effect of soil property uncertainties on permafrost thaw projections are studied using a three-phase subsurface thermal hydrology model and calibration-constrained uncertainty analysis. The Null-Space Monte Carlo method is used to identify soil hydrothermal parameter combinations that are consistent with borehole temperature measurements at the study site, the Barrow Environmental Observatory. Each parameter combination is then used in a forward projection of permafrost conditions for the 21st century (from calendar year 2006 to 2100) using atmospheric forcings from the Community Earth System Model (CESM) in the Representative Concentration Pathway (RCP) 8.5 greenhouse gas concentration trajectory. A 100-year projection allows formore » the evaluation of intra-annual uncertainty due to soil properties and the inter-annual variability due to year to year differences in CESM climate forcings. After calibrating to borehole temperature data at this well-characterized site, soil property uncertainties are still significant and result in significant intra-annual uncertainties in projected active layer thickness and annual thaw depth-duration even with a specified future climate. Intra-annual uncertainties in projected soil moisture content and Stefan number are small. A volume and time integrated Stefan number decreases significantly in the future climate, indicating that latent heat of phase change becomes more important than heat conduction in future climates. Out of 10 soil parameters, ALT, annual thaw depth-duration, and Stefan number are highly dependent on mineral soil porosity, while annual mean liquid saturation of the active layer is highly dependent on the mineral soil residual saturation and moderately dependent on peat residual saturation. As a result, by comparing the ensemble statistics to the spread of projected permafrost metrics using different climate models, we show that the effect of calibration-constrained uncertainty in soil properties, although significant, is less than that produced by structural climate model uncertainty for this location.« less

Effect of soil property uncertainties on permafrost thaw projections: a calibration-constrained analysis

NASA Astrophysics Data System (ADS)

Harp, D. R.; Atchley, A. L.; Painter, S. L.; Coon, E. T.; Wilson, C. J.; Romanovsky, V. E.; Rowland, J. C.

2015-06-01

The effect of soil property uncertainties on permafrost thaw projections are studied using a three-phase subsurface thermal hydrology model and calibration-constrained uncertainty analysis. The Null-Space Monte Carlo method is used to identify soil hydrothermal parameter combinations that are consistent with borehole temperature measurements at the study site, the Barrow Environmental Observatory. Each parameter combination is then used in a forward projection of permafrost conditions for the 21st century (from calendar year 2006 to 2100) using atmospheric forcings from the Community Earth System Model (CESM) in the Representative Concentration Pathway (RCP) 8.5 greenhouse gas concentration trajectory. A 100-year projection allows for the evaluation of intra-annual uncertainty due to soil properties and the inter-annual variability due to year to year differences in CESM climate forcings. After calibrating to borehole temperature data at this well-characterized site, soil property uncertainties are still significant and result in significant intra-annual uncertainties in projected active layer thickness and annual thaw depth-duration even with a specified future climate. Intra-annual uncertainties in projected soil moisture content and Stefan number are small. A volume and time integrated Stefan number decreases significantly in the future climate, indicating that latent heat of phase change becomes more important than heat conduction in future climates. Out of 10 soil parameters, ALT, annual thaw depth-duration, and Stefan number are highly dependent on mineral soil porosity, while annual mean liquid saturation of the active layer is highly dependent on the mineral soil residual saturation and moderately dependent on peat residual saturation. By comparing the ensemble statistics to the spread of projected permafrost metrics using different climate models, we show that the effect of calibration-constrained uncertainty in soil properties, although significant, is less than that produced by structural climate model uncertainty for this location.

Assessment of input uncertainty by seasonally categorized latent variables using SWAT

USDA-ARS?s Scientific Manuscript database

Watershed processes have been explored with sophisticated simulation models for the past few decades. It has been stated that uncertainty attributed to alternative sources such as model parameters, forcing inputs, and measured data should be incorporated during the simulation process. Among varyin...

Quantifying the uncertainty in discharge data using hydraulic knowledge and uncertain gaugings: a Bayesian method named BaRatin

NASA Astrophysics Data System (ADS)

Le Coz, Jérôme; Renard, Benjamin; Bonnifait, Laurent; Branger, Flora; Le Boursicaud, Raphaël; Horner, Ivan; Mansanarez, Valentin; Lang, Michel; Vigneau, Sylvain

2015-04-01

River discharge is a crucial variable for Hydrology: as the output variable of most hydrologic models, it is used for sensitivity analyses, model structure identification, parameter estimation, data assimilation, prediction, etc. A major difficulty stems from the fact that river discharge is not measured continuously. Instead, discharge time series used by hydrologists are usually based on simple stage-discharge relations (rating curves) calibrated using a set of direct stage-discharge measurements (gaugings). In this presentation, we present a Bayesian approach (cf. Le Coz et al., 2014) to build such hydrometric rating curves, to estimate the associated uncertainty and to propagate this uncertainty to discharge time series. The three main steps of this approach are described: (1) Hydraulic analysis: identification of the hydraulic controls that govern the stage-discharge relation, identification of the rating curve equation and specification of prior distributions for the rating curve parameters; (2) Rating curve estimation: Bayesian inference of the rating curve parameters, accounting for the individual uncertainties of available gaugings, which often differ according to the discharge measurement procedure and the flow conditions; (3) Uncertainty propagation: quantification of the uncertainty in discharge time series, accounting for both the rating curve uncertainties and the uncertainty of recorded stage values. The rating curve uncertainties combine the parametric uncertainties and the remnant uncertainties that reflect the limited accuracy of the mathematical model used to simulate the physical stage-discharge relation. In addition, we also discuss current research activities, including the treatment of non-univocal stage-discharge relationships (e.g. due to hydraulic hysteresis, vegetation growth, sudden change of the geometry of the section, etc.). An operational version of the BaRatin software and its graphical interface are made available free of charge on request to the authors. J. Le Coz, B. Renard, L. Bonnifait, F. Branger, R. Le Boursicaud (2014). Combining hydraulic knowledge and uncertain gaugings in the estimation of hydrometric rating curves: a Bayesian approach, Journal of Hydrology, 509, 573-587.

PEBBED Uncertainty and Sensitivity Analysis of the CRP-5 PBMR DLOFC Transient Benchmark with the SUSA Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerhard Strydom

2011-01-01

The need for a defendable and systematic uncertainty and sensitivity approach that conforms to the Code Scaling, Applicability, and Uncertainty (CSAU) process, and that could be used for a wide variety of software codes, was defined in 2008. The GRS (Gesellschaft für Anlagen und Reaktorsicherheit) company of Germany has developed one type of CSAU approach that is particularly well suited for legacy coupled core analysis codes, and a trial version of their commercial software product SUSA (Software for Uncertainty and Sensitivity Analyses) was acquired on May 12, 2010. This report summarized the results of the initial investigations performed with SUSA,more » utilizing a typical High Temperature Reactor benchmark (the IAEA CRP-5 PBMR 400MW Exercise 2) and the PEBBED-THERMIX suite of codes. The following steps were performed as part of the uncertainty and sensitivity analysis: 1. Eight PEBBED-THERMIX model input parameters were selected for inclusion in the uncertainty study: the total reactor power, inlet gas temperature, decay heat, and the specific heat capability and thermal conductivity of the fuel, pebble bed and reflector graphite. 2. The input parameters variations and probability density functions were specified, and a total of 800 PEBBED-THERMIX model calculations were performed, divided into 4 sets of 100 and 2 sets of 200 Steady State and Depressurized Loss of Forced Cooling (DLOFC) transient calculations each. 3. The steady state and DLOFC maximum fuel temperature, as well as the daily pebble fuel load rate data, were supplied to SUSA as model output parameters of interest. The 6 data sets were statistically analyzed to determine the 5% and 95% percentile values for each of the 3 output parameters with a 95% confidence level, and typical statistical indictors were also generated (e.g. Kendall, Pearson and Spearman coefficients). 4. A SUSA sensitivity study was performed to obtain correlation data between the input and output parameters, and to identify the primary contributors to the output data uncertainties. It was found that the uncertainties in the decay heat, pebble bed and reflector thermal conductivities were responsible for the bulk of the propagated uncertainty in the DLOFC maximum fuel temperature. It was also determined that the two standard deviation (2s) uncertainty on the maximum fuel temperature was between ±58oC (3.6%) and ±76oC (4.7%) on a mean value of 1604 oC. These values mostly depended on the selection of the distributions types, and not on the number of model calculations above the required Wilks criteria (a (95%,95%) statement would usually require 93 model runs).« less

Reconstructing solar magnetic fields from historical observations. II. Testing the surface flux transport model

NASA Astrophysics Data System (ADS)

Virtanen, I. O. I.; Virtanen, I. I.; Pevtsov, A. A.; Yeates, A.; Mursula, K.

2017-07-01

Aims: We aim to use the surface flux transport model to simulate the long-term evolution of the photospheric magnetic field from historical observations. In this work we study the accuracy of the model and its sensitivity to uncertainties in its main parameters and the input data. Methods: We tested the model by running simulations with different values of meridional circulation and supergranular diffusion parameters, and studied how the flux distribution inside active regions and the initial magnetic field affected the simulation. We compared the results to assess how sensitive the simulation is to uncertainties in meridional circulation speed, supergranular diffusion, and input data. We also compared the simulated magnetic field with observations. Results: We find that there is generally good agreement between simulations and observations. Although the model is not capable of replicating fine details of the magnetic field, the long-term evolution of the polar field is very similar in simulations and observations. Simulations typically yield a smoother evolution of polar fields than observations, which often include artificial variations due to observational limitations. We also find that the simulated field is fairly insensitive to uncertainties in model parameters or the input data. Due to the decay term included in the model the effects of the uncertainties are somewhat minor or temporary, lasting typically one solar cycle.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms.

PubMed

Biehler, J; Wall, W A

2018-02-01

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model. Copyright © 2017 John Wiley & Sons, Ltd.

Addressing the impact of environmental uncertainty in plankton model calibration with a dedicated software system: the Marine Model Optimization Testbed (MarMOT 1.1 alpha)

NASA Astrophysics Data System (ADS)

Hemmings, J. C. P.; Challenor, P. G.

2012-04-01

A wide variety of different plankton system models have been coupled with ocean circulation models, with the aim of understanding and predicting aspects of environmental change. However, an ability to make reliable inferences about real-world processes from the model behaviour demands a quantitative understanding of model error that remains elusive. Assessment of coupled model output is inhibited by relatively limited observing system coverage of biogeochemical components. Any direct assessment of the plankton model is further inhibited by uncertainty in the physical state. Furthermore, comparative evaluation of plankton models on the basis of their design is inhibited by the sensitivity of their dynamics to many adjustable parameters. Parameter uncertainty has been widely addressed by calibrating models at data-rich ocean sites. However, relatively little attention has been given to quantifying uncertainty in the physical fields required by the plankton models at these sites, and tendencies in the biogeochemical properties due to the effects of horizontal processes are often neglected. Here we use model twin experiments, in which synthetic data are assimilated to estimate a system's known "true" parameters, to investigate the impact of error in a plankton model's environmental input data. The experiments are supported by a new software tool, the Marine Model Optimization Testbed, designed for rigorous analysis of plankton models in a multi-site 1-D framework. Simulated errors are derived from statistical characterizations of the mixed layer depth, the horizontal flux divergence tendencies of the biogeochemical tracers and the initial state. Plausible patterns of uncertainty in these data are shown to produce strong temporal and spatial variability in the expected simulation error variance over an annual cycle, indicating variation in the significance attributable to individual model-data differences. An inverse scheme using ensemble-based estimates of the simulation error variance to allow for this environment error performs well compared with weighting schemes used in previous calibration studies, giving improved estimates of the known parameters. The efficacy of the new scheme in real-world applications will depend on the quality of statistical characterizations of the input data. Practical approaches towards developing reliable characterizations are discussed.

Predictions of space radiation fatality risk for exploration missions

NASA Astrophysics Data System (ADS)

Cucinotta, Francis A.; To, Khiet; Cacao, Eliedonna

2017-05-01

In this paper we describe revisions to the NASA Space Cancer Risk (NSCR) model focusing on updates to probability distribution functions (PDF) representing the uncertainties in the radiation quality factor (QF) model parameters and the dose and dose-rate reduction effectiveness factor (DDREF). We integrate recent heavy ion data on liver, colorectal, intestinal, lung, and Harderian gland tumors with other data from fission neutron experiments into the model analysis. In an earlier work we introduced distinct QFs for leukemia and solid cancer risk predictions, and here we consider liver cancer risks separately because of the higher RBE's reported in mouse experiments compared to other tumors types, and distinct risk factors for liver cancer for astronauts compared to the U.S. population. The revised model is used to make predictions of fatal cancer and circulatory disease risks for 1-year deep space and International Space Station (ISS) missions, and a 940 day Mars mission. We analyzed the contribution of the various model parameter uncertainties to the overall uncertainty, which shows that the uncertainties in relative biological effectiveness (RBE) factors at high LET due to statistical uncertainties and differences across tissue types and mouse strains are the dominant uncertainty. NASA's exposure limits are approached or exceeded for each mission scenario considered. Two main conclusions are made: 1) Reducing the current estimate of about a 3-fold uncertainty to a 2-fold or lower uncertainty will require much more expansive animal carcinogenesis studies in order to reduce statistical uncertainties and understand tissue, sex and genetic variations. 2) Alternative model assumptions such as non-targeted effects, increased tumor lethality and decreased latency at high LET, and non-cancer mortality risks from circulatory diseases could significantly increase risk estimates to several times higher than the NASA limits.

Multiple Damage Progression Paths in Model-Based Prognostics

NASA Technical Reports Server (NTRS)

Daigle, Matthew; Goebel, Kai Frank

2011-01-01

Model-based prognostics approaches employ domain knowledge about a system, its components, and how they fail through the use of physics-based models. Component wear is driven by several different degradation phenomena, each resulting in their own damage progression path, overlapping to contribute to the overall degradation of the component. We develop a model-based prognostics methodology using particle filters, in which the problem of characterizing multiple damage progression paths is cast as a joint state-parameter estimation problem. The estimate is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control mechanism that maintains an uncertainty bound around the hidden parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump, to which we apply our model-based prognostics algorithms. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the chosen approach when multiple damage mechanisms are active

Data Assimilation and Propagation of Uncertainty in Multiscale Cardiovascular Simulation

NASA Astrophysics Data System (ADS)

Schiavazzi, Daniele; Marsden, Alison

2015-11-01

Cardiovascular modeling is the application of computational tools to predict hemodynamics. State-of-the-art techniques couple a 3D incompressible Navier-Stokes solver with a boundary circulation model and can predict local and peripheral hemodynamics, analyze the post-operative performance of surgical designs and complement clinical data collection minimizing invasive and risky measurement practices. The ability of these tools to make useful predictions is directly related to their accuracy in representing measured physiologies. Tuning of model parameters is therefore a topic of paramount importance and should include clinical data uncertainty, revealing how this uncertainty will affect the predictions. We propose a fully Bayesian, multi-level approach to data assimilation of uncertain clinical data in multiscale circulation models. To reduce the computational cost, we use a stable, condensed approximation of the 3D model build by linear sparse regression of the pressure/flow rate relationship at the outlets. Finally, we consider the problem of non-invasively propagating the uncertainty in model parameters to the resulting hemodynamics and compare Monte Carlo simulation with Stochastic Collocation approaches based on Polynomial or Multi-resolution Chaos expansions.

Supporting Fisheries Management by Means of Complex Models: Can We Point out Isles of Robustness in a Sea of Uncertainty?

PubMed Central

Gasche, Loïc; Mahévas, Stéphanie; Marchal, Paul

2013-01-01

Ecosystems are usually complex, nonlinear and strongly influenced by poorly known environmental variables. Among these systems, marine ecosystems have high uncertainties: marine populations in general are known to exhibit large levels of natural variability and the intensity of fishing efforts can change rapidly. These uncertainties are a source of risks that threaten the sustainability of both fish populations and fishing fleets targeting them. Appropriate management measures have to be found in order to reduce these risks and decrease sensitivity to uncertainties. Methods have been developed within decision theory that aim at allowing decision making under severe uncertainty. One of these methods is the information-gap decision theory. The info-gap method has started to permeate ecological modelling, with recent applications to conservation. However, these practical applications have so far been restricted to simple models with analytical solutions. Here we implement a deterministic approach based on decision theory in a complex model of the Eastern English Channel. Using the ISIS-Fish modelling platform, we model populations of sole and plaice in this area. We test a wide range of values for ecosystem, fleet and management parameters. From these simulations, we identify management rules controlling fish harvesting that allow reaching management goals recommended by ICES (International Council for the Exploration of the Sea) working groups while providing the highest robustness to uncertainties on ecosystem parameters. PMID:24204873

Supporting fisheries management by means of complex models: can we point out isles of robustness in a sea of uncertainty?

PubMed

Gasche, Loïc; Mahévas, Stéphanie; Marchal, Paul

2013-01-01

Ecosystems are usually complex, nonlinear and strongly influenced by poorly known environmental variables. Among these systems, marine ecosystems have high uncertainties: marine populations in general are known to exhibit large levels of natural variability and the intensity of fishing efforts can change rapidly. These uncertainties are a source of risks that threaten the sustainability of both fish populations and fishing fleets targeting them. Appropriate management measures have to be found in order to reduce these risks and decrease sensitivity to uncertainties. Methods have been developed within decision theory that aim at allowing decision making under severe uncertainty. One of these methods is the information-gap decision theory. The info-gap method has started to permeate ecological modelling, with recent applications to conservation. However, these practical applications have so far been restricted to simple models with analytical solutions. Here we implement a deterministic approach based on decision theory in a complex model of the Eastern English Channel. Using the ISIS-Fish modelling platform, we model populations of sole and plaice in this area. We test a wide range of values for ecosystem, fleet and management parameters. From these simulations, we identify management rules controlling fish harvesting that allow reaching management goals recommended by ICES (International Council for the Exploration of the Sea) working groups while providing the highest robustness to uncertainties on ecosystem parameters.

Good Models Gone Bad: Quantifying and Predicting Parameter-Induced Climate Model Simulation Failures

NASA Astrophysics Data System (ADS)

Lucas, D. D.; Klein, R.; Tannahill, J.; Brandon, S.; Covey, C. C.; Domyancic, D.; Ivanova, D. P.

2012-12-01

Simulations using IPCC-class climate models are subject to fail or crash for a variety of reasons. Statistical analysis of the failures can yield useful insights to better understand and improve the models. During the course of uncertainty quantification (UQ) ensemble simulations to assess the effects of ocean model parameter uncertainties on climate simulations, we experienced a series of simulation failures of the Parallel Ocean Program (POP2). About 8.5% of our POP2 runs failed for numerical reasons at certain combinations of parameter values. We apply support vector machine (SVM) classification from the fields of pattern recognition and machine learning to quantify and predict the probability of failure as a function of the values of 18 POP2 parameters. The SVM classifiers readily predict POP2 failures in an independent validation ensemble, and are subsequently used to determine the causes of the failures via a global sensitivity analysis. Four parameters related to ocean mixing and viscosity are identified as the major sources of POP2 failures. Our method can be used to improve the robustness of complex scientific models to parameter perturbations and to better steer UQ ensembles. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and was funded by the Uncertainty Quantification Strategic Initiative Laboratory Directed Research and Development Project at LLNL under project tracking code 10-SI-013 (UCRL LLNL-ABS-569112).

Modelling ecological and human exposure to POPs in Venice lagoon - Part II: Quantitative uncertainty and sensitivity analysis in coupled exposure models.

PubMed

Radomyski, Artur; Giubilato, Elisa; Ciffroy, Philippe; Critto, Andrea; Brochot, Céline; Marcomini, Antonio

2016-11-01

The study is focused on applying uncertainty and sensitivity analysis to support the application and evaluation of large exposure models where a significant number of parameters and complex exposure scenarios might be involved. The recently developed MERLIN-Expo exposure modelling tool was applied to probabilistically assess the ecological and human exposure to PCB 126 and 2,3,7,8-TCDD in the Venice lagoon (Italy). The 'Phytoplankton', 'Aquatic Invertebrate', 'Fish', 'Human intake' and PBPK models available in MERLIN-Expo library were integrated to create a specific food web to dynamically simulate bioaccumulation in various aquatic species and in the human body over individual lifetimes from 1932 until 1998. MERLIN-Expo is a high tier exposure modelling tool allowing propagation of uncertainty on the model predictions through Monte Carlo simulation. Uncertainty in model output can be further apportioned between parameters by applying built-in sensitivity analysis tools. In this study, uncertainty has been extensively addressed in the distribution functions to describe the data input and the effect on model results by applying sensitivity analysis techniques (screening Morris method, regression analysis, and variance-based method EFAST). In the exposure scenario developed for the Lagoon of Venice, the concentrations of 2,3,7,8-TCDD and PCB 126 in human blood turned out to be mainly influenced by a combination of parameters (half-lives of the chemicals, body weight variability, lipid fraction, food assimilation efficiency), physiological processes (uptake/elimination rates), environmental exposure concentrations (sediment, water, food) and eating behaviours (amount of food eaten). In conclusion, this case study demonstrated feasibility of MERLIN-Expo to be successfully employed in integrated, high tier exposure assessment. Copyright © 2016 Elsevier B.V. All rights reserved.

Assessment of parameter uncertainty in hydrological model using a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis method

NASA Astrophysics Data System (ADS)

Zhang, Junlong; Li, Yongping; Huang, Guohe; Chen, Xi; Bao, Anming

2016-07-01

Without a realistic assessment of parameter uncertainty, decision makers may encounter difficulties in accurately describing hydrologic processes and assessing relationships between model parameters and watershed characteristics. In this study, a Markov-Chain-Monte-Carlo-based multilevel-factorial-analysis (MCMC-MFA) method is developed, which can not only generate samples of parameters from a well constructed Markov chain and assess parameter uncertainties with straightforward Bayesian inference, but also investigate the individual and interactive effects of multiple parameters on model output through measuring the specific variations of hydrological responses. A case study is conducted for addressing parameter uncertainties in the Kaidu watershed of northwest China. Effects of multiple parameters and their interactions are quantitatively investigated using the MCMC-MFA with a three-level factorial experiment (totally 81 runs). A variance-based sensitivity analysis method is used to validate the results of parameters' effects. Results disclose that (i) soil conservation service runoff curve number for moisture condition II (CN2) and fraction of snow volume corresponding to 50% snow cover (SNO50COV) are the most significant factors to hydrological responses, implying that infiltration-excess overland flow and snow water equivalent represent important water input to the hydrological system of the Kaidu watershed; (ii) saturate hydraulic conductivity (SOL_K) and soil evaporation compensation factor (ESCO) have obvious effects on hydrological responses; this implies that the processes of percolation and evaporation would impact hydrological process in this watershed; (iii) the interactions of ESCO and SNO50COV as well as CN2 and SNO50COV have an obvious effect, implying that snow cover can impact the generation of runoff on land surface and the extraction of soil evaporative demand in lower soil layers. These findings can help enhance the hydrological model's capability for simulating/predicting water resources.

Incorporating uncertainty of management costs in sensitivity analyses of matrix population models.

PubMed

Salomon, Yacov; McCarthy, Michael A; Taylor, Peter; Wintle, Brendan A

2013-02-01

The importance of accounting for economic costs when making environmental-management decisions subject to resource constraints has been increasingly recognized in recent years. In contrast, uncertainty associated with such costs has often been ignored. We developed a method, on the basis of economic theory, that accounts for the uncertainty in population-management decisions. We considered the case where, rather than taking fixed values, model parameters are random variables that represent the situation when parameters are not precisely known. Hence, the outcome is not precisely known either. Instead of maximizing the expected outcome, we maximized the probability of obtaining an outcome above a threshold of acceptability. We derived explicit analytical expressions for the optimal allocation and its associated probability, as a function of the threshold of acceptability, where the model parameters were distributed according to normal and uniform distributions. To illustrate our approach we revisited a previous study that incorporated cost-efficiency analyses in management decisions that were based on perturbation analyses of matrix population models. Incorporating derivations from this study into our framework, we extended the model to address potential uncertainties. We then applied these results to 2 case studies: management of a Koala (Phascolarctos cinereus) population and conservation of an olive ridley sea turtle (Lepidochelys olivacea) population. For low aspirations, that is, when the threshold of acceptability is relatively low, the optimal strategy was obtained by diversifying the allocation of funds. Conversely, for high aspirations, the budget was directed toward management actions with the highest potential effect on the population. The exact optimal allocation was sensitive to the choice of uncertainty model. Our results highlight the importance of accounting for uncertainty when making decisions and suggest that more effort should be placed on understanding the distributional characteristics of such uncertainty. Our approach provides a tool to improve decision making. © 2013 Society for Conservation Biology.

Physical Uncertainty Bounds (PUB)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vaughan, Diane Elizabeth; Preston, Dean L.

2015-03-19

This paper introduces and motivates the need for a new methodology for determining upper bounds on the uncertainties in simulations of engineered systems due to limited fidelity in the composite continuum-level physics models needed to simulate the systems. We show that traditional uncertainty quantification methods provide, at best, a lower bound on this uncertainty. We propose to obtain bounds on the simulation uncertainties by first determining bounds on the physical quantities or processes relevant to system performance. By bounding these physics processes, as opposed to carrying out statistical analyses of the parameter sets of specific physics models or simply switchingmore » out the available physics models, one can obtain upper bounds on the uncertainties in simulated quantities of interest.« less

Pinatubo Emulation in Multiple Models (POEMs): co-ordinated experiments in the ISA-MIP model intercomparison activity component of the SPARC Stratospheric Sulphur and it's Role in Climate initiative (SSiRC)

NASA Astrophysics Data System (ADS)

Lee, Lindsay; Mann, Graham; Carslaw, Ken; Toohey, Matthew; Aquila, Valentina

2016-04-01

The World Climate Research Program's SPARC initiative has a new international activity "Stratospheric Sulphur and its Role in Climate" (SSiRC) to better understand changes in stratospheric aerosol and precursor gaseous sulphur species. One component of SSiRC involves an intercomparison "ISA-MIP" of composition-climate models that simulate the stratospheric aerosol layer interactively. Within PoEMS each modelling group will run a "perturbed physics ensemble" (PPE) of interactive stratospheric aerosol (ISA) simulations of the Pinatubo eruption, varying several uncertain parameters associated with the eruption's SO2 emissions and model processes. A powerful new technique to quantify and attribute sources of uncertainty in complex global models is described by Lee et al. (2011, ACP). The analysis uses Gaussian emulation to derive a probability density function (pdf) of predicted quantities, essentially interpolating the PPE results in multi-dimensional parameter space. Once trained on the ensemble, a Monte Carlo simulation with the fast Gaussian emulator enabling a full variance-based sensitivity analysis. The approach has already been used effectively by Carslaw et al., (2013, Nature) to quantify the uncertainty in the cloud albedo effect forcing from a 3D global aerosol-microphysics model allowing to compare the sensitivy of different predicted quantities to uncertainties in natural and anthropogenic emissions types, and structural parameters in the models. Within ISA-MIP, each group will carry out a PPE of runs, with the subsequent analysis with the emulator assessing the uncertainty in the volcanic forcings predicted by each model. In this poster presentation we will give an outline of the "PoEMS" analysis, describing the uncertain parameters to be varied and the relevance to further understanding differences identified in previous international stratospheric aerosol assessments.

Usage of ensemble geothermal models to consider geological uncertainties

NASA Astrophysics Data System (ADS)

Rühaak, Wolfram; Steiner, Sarah; Welsch, Bastian; Sass, Ingo

2015-04-01

The usage of geothermal energy for instance by borehole heat exchangers (BHE) is a promising concept for a sustainable supply of heat for buildings. BHE are closed pipe systems, in which a fluid is circulating. Heat from the surrounding rocks is transferred to the fluid purely by conduction. The fluid carries the heat to the surface, where it can be utilized. Larger arrays of BHE require typically previous numerical models. Motivations are the design of the system (number and depth of the required BHE) but also regulatory reasons. Especially such regulatory operating permissions often require maximum realistic models. Although such realistic models are possible in many cases with today's codes and computer resources, they are often expensive in terms of time and effort. A particular problem is the knowledge about the accuracy of the achieved results. An issue, which is often neglected while dealing with highly complex models, is the quantification of parameter uncertainties as a consequence of the natural heterogeneity of the geological subsurface. Experience has shown, that these heterogeneities can lead to wrong forecasts. But also variations in the technical realization and especially of the operational parameters (which are mainly a consequence of the regional climate) can lead to strong variations in the simulation results. Instead of one very detailed single forecast model, it should be considered, to model numerous more simple models. By varying parameters, the presumed subsurface uncertainties, but also the uncertainties in the presumed operational parameters can be reflected. Finally not only one single result should be reported, but instead the range of possible solutions and their respective probabilities. In meteorology such an approach is well known as ensemble-modeling. The concept is demonstrated at a real world data set and discussed.

Inverse modeling of geochemical and mechanical compaction in sedimentary basins

NASA Astrophysics Data System (ADS)

Colombo, Ivo; Porta, Giovanni Michele; Guadagnini, Alberto

2015-04-01

We study key phenomena driving the feedback between sediment compaction processes and fluid flow in stratified sedimentary basins formed through lithification of sand and clay sediments after deposition. Processes we consider are mechanic compaction of the host rock and the geochemical compaction due to quartz cementation in sandstones. Key objectives of our study include (i) the quantification of the influence of the uncertainty of the model input parameters on the model output and (ii) the application of an inverse modeling technique to field scale data. Proper accounting of the feedback between sediment compaction processes and fluid flow in the subsurface is key to quantify a wide set of environmentally and industrially relevant phenomena. These include, e.g., compaction-driven brine and/or saltwater flow at deep locations and its influence on (a) tracer concentrations observed in shallow sediments, (b) build up of fluid overpressure, (c) hydrocarbon generation and migration, (d) subsidence due to groundwater and/or hydrocarbons withdrawal, and (e) formation of ore deposits. Main processes driving the diagenesis of sediments after deposition are mechanical compaction due to overburden and precipitation/dissolution associated with reactive transport. The natural evolution of sedimentary basins is characterized by geological time scales, thus preventing direct and exhaustive measurement of the system dynamical changes. The outputs of compaction models are plagued by uncertainty because of the incomplete knowledge of the models and parameters governing diagenesis. Development of robust methodologies for inverse modeling and parameter estimation under uncertainty is therefore crucial to the quantification of natural compaction phenomena. We employ a numerical methodology based on three building blocks: (i) space-time discretization of the compaction process; (ii) representation of target output variables through a Polynomial Chaos Expansion (PCE); and (iii) model inversion (parameter estimation) within a maximum likelihood framework. In this context, the PCE-based surrogate model enables one to (i) minimize the computational cost associated with the (forward and inverse) modeling procedures leading to uncertainty quantification and parameter estimation, and (ii) compute the full set of Sobol indices quantifying the contribution of each uncertain parameter to the variability of target state variables. Results are illustrated through the simulation of one-dimensional test cases. The analyses focuses on the calibration of model parameters through literature field cases. The quality of parameter estimates is then analyzed as a function of number, type and location of data.

Predicting Ice Sheet and Climate Evolution at Extreme Scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heimbach, Patrick

2016-02-06

A main research objectives of PISCEES is the development of formal methods for quantifying uncertainties in ice sheet modeling. Uncertainties in simulating and projecting mass loss from the polar ice sheets arise primarily from initial conditions, surface and basal boundary conditions, and model parameters. In general terms, two main chains of uncertainty propagation may be identified: 1. inverse propagation of observation and/or prior onto posterior control variable uncertainties; 2. forward propagation of prior or posterior control variable uncertainties onto those of target output quantities of interest (e.g., climate indices or ice sheet mass loss). A related goal is the developmentmore » of computationally efficient methods for producing initial conditions for an ice sheet that are close to available present-day observations and essentially free of artificial model drift, which is required in order to be useful for model projections (“initialization problem”). To be of maximum value, such optimal initial states should be accompanied by “useful” uncertainty estimates that account for the different sources of uncerainties, as well as the degree to which the optimum state is constrained by available observations. The PISCEES proposal outlined two approaches for quantifying uncertainties. The first targets the full exploration of the uncertainty in model projections with sampling-based methods and a workflow managed by DAKOTA (the main delivery vehicle for software developed under QUEST). This is feasible for low-dimensional problems, e.g., those with a handful of global parameters to be inferred. This approach can benefit from derivative/adjoint information, but it is not necessary, which is why it often referred to as “non-intrusive”. The second approach makes heavy use of derivative information from model adjoints to address quantifying uncertainty in high-dimensions (e.g., basal boundary conditions in ice sheet models). The use of local gradient, or Hessian information (i.e., second derivatives of the cost function), requires additional code development and implementation, and is thus often referred to as an “intrusive” approach. Within PISCEES, MIT has been tasked to develop methods for derivative-based UQ, the ”intrusive” approach discussed above. These methods rely on the availability of first (adjoint) and second (Hessian) derivative code, developed through intrusive methods such as algorithmic differentiation (AD). While representing a significant burden in terms of code development, derivative-baesd UQ is able to cope with very high-dimensional uncertainty spaces. That is, unlike sampling methods (all variations of Monte Carlo), calculational burden is independent of the dimension of the uncertainty space. This is a significant advantage for spatially distributed uncertainty fields, such as threedimensional initial conditions, three-dimensional parameter fields, or two-dimensional surface and basal boundary conditions. Importantly, uncertainty fields for ice sheet models generally fall into this category.« less

Development of an automated procedure for estimation of the spatial variation of runoff in large river basins

USDA-ARS?s Scientific Manuscript database

The use of distributed parameter models to address water resource management problems has increased in recent years. Calibration is necessary to reduce the uncertainties associated with model input parameters. Manual calibration of a distributed parameter model is a very time consuming effort. There...

On the uncertainty of phenological responses to climate change and its implication for terrestrial biosphere models

NASA Astrophysics Data System (ADS)

Migliavacca, M.; Sonnentag, O.; Keenan, T. F.; Cescatti, A.; O'Keefe, J.; Richardson, A. D.

2012-01-01

Phenology, the timing of recurring life cycle events, controls numerous land surface feedbacks to the climate systems through the regulation of exchanges of carbon, water and energy between the biosphere and atmosphere. Land surface models, however, are known to have systematic errors in the simulation of spring phenology, which potentially could propagate to uncertainty in modeled responses to future climate change. Here, we analyzed the Harvard Forest phenology record to investigate and characterize the sources of uncertainty in phenological forecasts and the subsequent impacts on model forecasts of carbon and water cycling in the future. Using a model-data fusion approach, we combined information from 20 yr of phenological observations of 11 North American woody species with 12 phenological models of different complexity to predict leaf bud-burst. The evaluation of different phenological models indicated support for spring warming models with photoperiod limitations and, though to a lesser extent, to chilling models based on the alternating model structure. We assessed three different sources of uncertainty in phenological forecasts: parameter uncertainty, model uncertainty, and driver uncertainty. The latter was characterized running the models to 2099 using 2 different IPCC climate scenarios (A1fi vs. B1, i.e. high CO2 emissions vs. low CO2 emissions scenario). Parameter uncertainty was the smallest (average 95% CI: 2.4 day century-1 for scenario B1 and 4.5 day century-1 for A1fi), whereas driver uncertainty was the largest (up to 8.4 day century-1 in the simulated trends). The uncertainty related to model structure is also large and the predicted bud-burst trends as well as the shape of the smoothed projections varied somewhat among models (±7.7 day century-1 for A1fi, ±3.6 day century-1 for B1). The forecast sensitivity of bud-burst to temperature (i.e. days bud-burst advanced per degree of warming) varied between 2.2 day °C-1 and 5.2 day °C-1 depending on model structure. We quantified the impact of uncertainties in bud-burst forecasts on simulated carbon and water fluxes using a process-based terrestrial biosphere model. Uncertainty in phenology model structure led to uncertainty in the description of the seasonality of processes, which accumulated to uncertainty in annual model estimates of gross primary productivity (GPP) and evapotranspiration (ET) of 9.6% and 2.9% respectively. A sensitivity analysis shows that a variation of ±10 days in bud-burst dates led to a variation of ±5.0% for annual GPP and about ±2.0% for ET. For phenology models, differences among future climate scenarios represent the largest source of uncertainty, followed by uncertainties related to model structure, and finally, uncertainties related to model parameterization. The uncertainties we have quantified will affect the description of the seasonality of processes and in particular the simulation of carbon uptake by forest ecosystems, with a larger impact of uncertainties related to phenology model structure, followed by uncertainties related to phenological model parameterization.

Estimation of ice activation parameters within a particle tracking Lagrangian cloud model using the ensemble Kalman filter to match ISCDAC golden case observations

NASA Astrophysics Data System (ADS)

Reisner, J. M.; Dubey, M. K.

2010-12-01

To both quantify and reduce uncertainty in ice activation parameterizations for stratus clouds occurring in the temperature range between -5 to -10 C ensemble simulations of an ISDAC golden case have been conducted. To formulate the ensemble, three parameters found within an ice activation model have been sampled using a Latin hypercube technique over a parameter range that induces large variability in both number and mass of ice. The ice activation model is contained within a Lagrangian cloud model that simulates particle number as a function of radius for cloud ice, snow, graupel, cloud, and rain particles. A unique aspect of this model is that it produces very low levels of numerical diffusion that enable the model to accurately resolve the sharp cloud edges associated with the ISDAC stratus deck. Another important aspect of the model is that near the cloud edges the number of particles can be significantly increased to reduce sampling errors and accurately resolve physical processes such as collision-coalescence that occur in this region. Thus, given these relatively low numerical errors, as compared to traditional bin models, the sensitivity of a stratus deck to changes in parameters found within the activation model can be examined without fear of numerical contamination. Likewise, once the ensemble has been completed, ISDAC observations can be incorporated into a Kalman filter to optimally estimate the ice activation parameters and reduce overall model uncertainty. Hence, this work will highlight the ability of an ensemble Kalman filter system coupled to a highly accurate numerical model to estimate important parameters found within microphysical parameterizations containing high uncertainty.

Visual Basic, Excel-based fish population modeling tool - The pallid sturgeon example

USGS Publications Warehouse

Moran, Edward H.; Wildhaber, Mark L.; Green, Nicholas S.; Albers, Janice L.

2016-02-10

The model presented in this report is a spreadsheet-based model using Visual Basic for Applications within Microsoft Excel (http://dx.doi.org/10.5066/F7057D0Z) prepared in cooperation with the U.S. Army Corps of Engineers and U.S. Fish and Wildlife Service. It uses the same model structure and, initially, parameters as used by Wildhaber and others (2015) for pallid sturgeon. The difference between the model structure used for this report and that used by Wildhaber and others (2015) is that variance is not partitioned. For the model of this report, all variance is applied at the iteration and time-step levels of the model. Wildhaber and others (2015) partition variance into parameter variance (uncertainty about the value of a parameter itself) applied at the iteration level and temporal variance (uncertainty caused by random environmental fluctuations with time) applied at the time-step level. They included implicit individual variance (uncertainty caused by differences between individuals) within the time-step level.The interface developed for the model of this report is designed to allow the user the flexibility to change population model structure and parameter values and uncertainty separately for every component of the model. This flexibility makes the modeling tool potentially applicable to any fish species; however, the flexibility inherent in this modeling tool makes it possible for the user to obtain spurious outputs. The value and reliability of the model outputs are only as good as the model inputs. Using this modeling tool with improper or inaccurate parameter values, or for species for which the structure of the model is inappropriate, could lead to untenable management decisions. By facilitating fish population modeling, this modeling tool allows the user to evaluate a range of management options and implications. The goal of this modeling tool is to be a user-friendly modeling tool for developing fish population models useful to natural resource managers to inform their decision-making processes; however, as with all population models, caution is needed, and a full understanding of the limitations of a model and the veracity of user-supplied parameters should always be considered when using such model output in the management of any species.

A fully Bayesian method for jointly fitting instrumental calibration and X-ray spectral models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, Jin; Yu, Yaming; Van Dyk, David A.

2014-10-20

Owing to a lack of robust principled methods, systematic instrumental uncertainties have generally been ignored in astrophysical data analysis despite wide recognition of the importance of including them. Ignoring calibration uncertainty can cause bias in the estimation of source model parameters and can lead to underestimation of the variance of these estimates. We previously introduced a pragmatic Bayesian method to address this problem. The method is 'pragmatic' in that it introduced an ad hoc technique that simplified computation by neglecting the potential information in the data for narrowing the uncertainty for the calibration product. Following that work, we use amore » principal component analysis to efficiently represent the uncertainty of the effective area of an X-ray (or γ-ray) telescope. Here, however, we leverage this representation to enable a principled, fully Bayesian method that coherently accounts for the calibration uncertainty in high-energy spectral analysis. In this setting, the method is compared with standard analysis techniques and the pragmatic Bayesian method. The advantage of the fully Bayesian method is that it allows the data to provide information not only for estimation of the source parameters but also for the calibration product—here the effective area, conditional on the adopted spectral model. In this way, it can yield more accurate and efficient estimates of the source parameters along with valid estimates of their uncertainty. Provided that the source spectrum can be accurately described by a parameterized model, this method allows rigorous inference about the effective area by quantifying which possible curves are most consistent with the data.« less

Ice particle mass-dimensional parameter retrieval and uncertainty analysis using an Optimal Estimation framework applied to in situ data

NASA Astrophysics Data System (ADS)

Xu, Zhuocan; Mace, Jay; Avalone, Linnea; Wang, Zhien

2015-04-01

The extreme variability of ice particle habits in precipitating clouds affects our understanding of these cloud systems in every aspect (i.e. radiation transfer, dynamics, precipitation rate, etc) and largely contributes to the uncertainties in the model representation of related processes. Ice particle mass-dimensional power law relationships, M=a*(D ^ b), are commonly assumed in models and retrieval algorithms, while very little knowledge exists regarding the uncertainties of these M-D parameters in real-world situations. In this study, we apply Optimal Estimation (OE) methodology to infer ice particle mass-dimensional relationship from ice particle size distributions and bulk water contents independently measured on board the University of Wyoming King Air during the Colorado Airborne Multi-Phase Cloud Study (CAMPS). We also utilize W-band radar reflectivity obtained on the same platform (King Air) offering a further constraint to this ill-posed problem (Heymsfield et al. 2010). In addition to the values of retrieved M-D parameters, the associated uncertainties are conveniently acquired in the OE framework, within the limitations of assumed Gaussian statistics. We find, given the constraints provided by the bulk water measurement and in situ radar reflectivity, that the relative uncertainty of mass-dimensional power law prefactor (a) is approximately 80% and the relative uncertainty of exponent (b) is 10-15%. With this level of uncertainty, the forward model uncertainty in radar reflectivity would be on the order of 4 dB or a factor of approximately 2.5 in ice water content. The implications of this finding are that inferences of bulk water from either remote or in situ measurements of particle spectra cannot be more certain than this when the mass-dimensional relationships are not known a priori which is almost never the case.

Uncertainty-enabled design of electromagnetic reflectors with integrated shape control

NASA Astrophysics Data System (ADS)

Haque, Samiul; Kindrat, Laszlo P.; Zhang, Li; Mikheev, Vikenty; Kim, Daewa; Liu, Sijing; Chung, Jooyeon; Kuian, Mykhailo; Massad, Jordan E.; Smith, Ralph C.

2018-03-01

We implemented a computationally efficient model for a corner-supported, thin, rectangular, orthotropic polyvinylidene fluoride (PVDF) laminate membrane, actuated by a two-dimensional array of segmented electrodes. The laminate can be used as shape-controlled electromagnetic reflector and the model estimates the reflector's shape given an array of control voltages. In this paper, we describe a model to determine the shape of the laminate for a given distribution of control voltages. Then, we investigate the surface shape error and its sensitivity to the model parameters. Subsequently, we analyze the simulated deflection of the actuated bimorph using a Zernike polynomial decomposition. Finally, we provide a probabilistic description of reflector performance using statistical methods to quantify uncertainty. We make design recommendations for nominal parameter values and their tolerances based on optimization under uncertainty using multiple methods.

Optimized production planning model for a multi-plant cultivation system under uncertainty

NASA Astrophysics Data System (ADS)

Ke, Shunkui; Guo, Doudou; Niu, Qingliang; Huang, Danfeng

2015-02-01

An inexact multi-constraint programming model under uncertainty was developed by incorporating a production plan algorithm into the crop production optimization framework under the multi-plant collaborative cultivation system. In the production plan, orders from the customers are assigned to a suitable plant under the constraints of plant capabilities and uncertainty parameters to maximize profit and achieve customer satisfaction. The developed model and solution method were applied to a case study of a multi-plant collaborative cultivation system to verify its applicability. As determined in the case analysis involving different orders from customers, the period of plant production planning and the interval between orders can significantly affect system benefits. Through the analysis of uncertain parameters, reliable and practical decisions can be generated using the suggested model of a multi-plant collaborative cultivation system.

Assessing the impact of model and climate uncertainty in malaria simulations for the Kenyan Highlands.

NASA Astrophysics Data System (ADS)

Tompkins, A. M.; Thomson, M. C.

2017-12-01

Simulations of the impact of climate variations on a vector-bornedisease such as malaria are subject to a number of sources ofuncertainty. These include the model structure and parameter settingsin addition to errors in the climate data and the neglect of theirspatial heterogeneity, especially over complex terrain. We use aconstrained genetic algorithm to confront these two sources ofuncertainty for malaria transmission in the highlands of Kenya. Thetechnique calibrates the parameter settings of a process-based,mathematical model of malaria transmission to vary within theirassessed level of uncertainty and also allows the calibration of thedriving climate data. The simulations show that in highland settingsclose to the threshold for sustained transmission, the uncertainty inclimate is more important to address than the malaria modeluncertainty. Applications of the coupled climate-malaria modelling system are briefly presented.

Sliding mode fault tolerant control dealing with modeling uncertainties and actuator faults.

PubMed

Wang, Tao; Xie, Wenfang; Zhang, Youmin

2012-05-01

In this paper, two sliding mode control algorithms are developed for nonlinear systems with both modeling uncertainties and actuator faults. The first algorithm is developed under an assumption that the uncertainty bounds are known. Different design parameters are utilized to deal with modeling uncertainties and actuator faults, respectively. The second algorithm is an adaptive version of the first one, which is developed to accommodate uncertainties and faults without utilizing exact bounds information. The stability of the overall control systems is proved by using a Lyapunov function. The effectiveness of the developed algorithms have been verified on a nonlinear longitudinal model of Boeing 747-100/200. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Coupled semivariogram uncertainty of hydrogeological and geophysical data on capture zone uncertainty analysis

USGS Publications Warehouse

Rahman, A.; Tsai, F.T.-C.; White, C.D.; Willson, C.S.

2008-01-01

This study investigates capture zone uncertainty that relates to the coupled semivariogram uncertainty of hydrogeological and geophysical data. Semivariogram uncertainty is represented by the uncertainty in structural parameters (range, sill, and nugget). We used the beta distribution function to derive the prior distributions of structural parameters. The probability distributions of structural parameters were further updated through the Bayesian approach with the Gaussian likelihood functions. Cokriging of noncollocated pumping test data and electrical resistivity data was conducted to better estimate hydraulic conductivity through autosemivariograms and pseudo-cross-semivariogram. Sensitivities of capture zone variability with respect to the spatial variability of hydraulic conductivity, porosity and aquifer thickness were analyzed using ANOVA. The proposed methodology was applied to the analysis of capture zone uncertainty at the Chicot aquifer in Southwestern Louisiana, where a regional groundwater flow model was developed. MODFLOW-MODPATH was adopted to delineate the capture zone. The ANOVA results showed that both capture zone area and compactness were sensitive to hydraulic conductivity variation. We concluded that the capture zone uncertainty due to the semivariogram uncertainty is much higher than that due to the kriging uncertainty for given semivariograms. In other words, the sole use of conditional variances of kriging may greatly underestimate the flow response uncertainty. Semivariogram uncertainty should also be taken into account in the uncertainty analysis. ?? 2008 ASCE.

A systematic uncertainty analysis of an evaluative fate and exposure model.

PubMed

Hertwich, E G; McKone, T E; Pease, W S

2000-08-01

Multimedia fate and exposure models are widely used to regulate the release of toxic chemicals, to set cleanup standards for contaminated sites, and to evaluate emissions in life-cycle assessment. CalTOX, one of these models, is used to calculate the potential dose, an outcome that is combined with the toxicity of the chemical to determine the Human Toxicity Potential (HTP), used to aggregate and compare emissions. The comprehensive assessment of the uncertainty in the potential dose calculation in this article serves to provide the information necessary to evaluate the reliability of decisions based on the HTP A framework for uncertainty analysis in multimedia risk assessment is proposed and evaluated with four types of uncertainty. Parameter uncertainty is assessed through Monte Carlo analysis. The variability in landscape parameters is assessed through a comparison of potential dose calculations for different regions in the United States. Decision rule uncertainty is explored through a comparison of the HTP values under open and closed system boundaries. Model uncertainty is evaluated through two case studies, one using alternative formulations for calculating the plant concentration and the other testing the steady state assumption for wet deposition. This investigation shows that steady state conditions for the removal of chemicals from the atmosphere are not appropriate and result in an underestimate of the potential dose for 25% of the 336 chemicals evaluated.

Microbial models with data-driven parameters predict stronger soil carbon responses to climate change.

PubMed

Hararuk, Oleksandra; Smith, Matthew J; Luo, Yiqi

2015-06-01

Long-term carbon (C) cycle feedbacks to climate depend on the future dynamics of soil organic carbon (SOC). Current models show low predictive accuracy at simulating contemporary SOC pools, which can be improved through parameter estimation. However, major uncertainty remains in global soil responses to climate change, particularly uncertainty in how the activity of soil microbial communities will respond. To date, the role of microbes in SOC dynamics has been implicitly described by decay rate constants in most conventional global carbon cycle models. Explicitly including microbial biomass dynamics into C cycle model formulations has shown potential to improve model predictive performance when assessed against global SOC databases. This study aimed to data-constrained parameters of two soil microbial models, evaluate the improvements in performance of those calibrated models in predicting contemporary carbon stocks, and compare the SOC responses to climate change and their uncertainties between microbial and conventional models. Microbial models with calibrated parameters explained 51% of variability in the observed total SOC, whereas a calibrated conventional model explained 41%. The microbial models, when forced with climate and soil carbon input predictions from the 5th Coupled Model Intercomparison Project (CMIP5), produced stronger soil C responses to 95 years of climate change than any of the 11 CMIP5 models. The calibrated microbial models predicted between 8% (2-pool model) and 11% (4-pool model) soil C losses compared with CMIP5 model projections which ranged from a 7% loss to a 22.6% gain. Lastly, we observed unrealistic oscillatory SOC dynamics in the 2-pool microbial model. The 4-pool model also produced oscillations, but they were less prominent and could be avoided, depending on the parameter values. © 2014 John Wiley & Sons Ltd.

Uncertainty in simulating wheat yields under climate change

NASA Astrophysics Data System (ADS)

Asseng, S.; Ewert, F.; Rosenzweig, C.; Jones, J. W.; Hatfield, J. L.; Ruane, A. C.; Boote, K. J.; Thorburn, P. J.; Rötter, R. P.; Cammarano, D.; Brisson, N.; Basso, B.; Martre, P.; Aggarwal, P. K.; Angulo, C.; Bertuzzi, P.; Biernath, C.; Challinor, A. J.; Doltra, J.; Gayler, S.; Goldberg, R.; Grant, R.; Heng, L.; Hooker, J.; Hunt, L. A.; Ingwersen, J.; Izaurralde, R. C.; Kersebaum, K. C.; Müller, C.; Naresh Kumar, S.; Nendel, C.; O'Leary, G.; Olesen, J. E.; Osborne, T. M.; Palosuo, T.; Priesack, E.; Ripoche, D.; Semenov, M. A.; Shcherbak, I.; Steduto, P.; Stöckle, C.; Stratonovitch, P.; Streck, T.; Supit, I.; Tao, F.; Travasso, M.; Waha, K.; Wallach, D.; White, J. W.; Williams, J. R.; Wolf, J.

2013-09-01

Projections of climate change impacts on crop yields are inherently uncertain. Uncertainty is often quantified when projecting future greenhouse gas emissions and their influence on climate. However, multi-model uncertainty analysis of crop responses to climate change is rare because systematic and objective comparisons among process-based crop simulation models are difficult. Here we present the largest standardized model intercomparison for climate change impacts so far. We found that individual crop models are able to simulate measured wheat grain yields accurately under a range of environments, particularly if the input information is sufficient. However, simulated climate change impacts vary across models owing to differences in model structures and parameter values. A greater proportion of the uncertainty in climate change impact projections was due to variations among crop models than to variations among downscaled general circulation models. Uncertainties in simulated impacts increased with CO2 concentrations and associated warming. These impact uncertainties can be reduced by improving temperature and CO2 relationships in models and better quantified through use of multi-model ensembles. Less uncertainty in describing how climate change may affect agricultural productivity will aid adaptation strategy development andpolicymaking.

A facility location model for municipal solid waste management system under uncertain environment.

PubMed

Yadav, Vinay; Bhurjee, A K; Karmakar, Subhankar; Dikshit, A K

2017-12-15

In municipal solid waste management system, decision makers have to develop an insight into the processes namely, waste generation, collection, transportation, processing, and disposal methods. Many parameters (e.g., waste generation rate, functioning costs of facilities, transportation cost, and revenues) in this system are associated with uncertainties. Often, these uncertainties of parameters need to be modeled under a situation of data scarcity for generating probability distribution function or membership function for stochastic mathematical programming or fuzzy mathematical programming respectively, with only information of extreme variations. Moreover, if uncertainties are ignored, then the problems like insufficient capacities of waste management facilities or improper utilization of available funds may be raised. To tackle uncertainties of these parameters in a more efficient manner an algorithm, based on interval analysis, has been developed. This algorithm is applied to find optimal solutions for a facility location model, which is formulated to select economically best locations of transfer stations in a hypothetical urban center. Transfer stations are an integral part of contemporary municipal solid waste management systems, and economic siting of transfer stations ensures financial sustainability of this system. The model is written in a mathematical programming language AMPL with KNITRO as a solver. The developed model selects five economically best locations out of ten potential locations with an optimum overall cost of [394,836, 757,440] Rs. 1 /day ([5906, 11,331] USD/day) approximately. Further, the requirement of uncertainty modeling is explained based on the results of sensitivity analysis. Copyright © 2017 Elsevier B.V. All rights reserved.

An Integrated Uncertainty Analysis and Ensemble-based Data Assimilation Framework for Operational Snow Predictions

NASA Astrophysics Data System (ADS)

He, M.; Hogue, T. S.; Franz, K.; Margulis, S. A.; Vrugt, J. A.

2009-12-01

The National Weather Service (NWS), the agency responsible for short- and long-term streamflow predictions across the nation, primarily applies the SNOW17 model for operational forecasting of snow accumulation and melt. The SNOW17-forecasted snowmelt serves as an input to a rainfall-runoff model for streamflow forecasts in snow-dominated areas. The accuracy of streamflow predictions in these areas largely relies on the accuracy of snowmelt. However, no direct snowmelt measurements are available to validate the SNOW17 predictions. Instead, indirect measurements such as snow water equivalent (SWE) measurements or discharge are typically used to calibrate SNOW17 parameters. In addition, the forecast practice is inherently deterministic, lacking tools to systematically address forecasting uncertainties (e.g., uncertainties in parameters, forcing, SWE and discharge observations, etc.). The current research presents an Integrated Uncertainty analysis and Ensemble-based data Assimilation (IUEA) framework to improve predictions of snowmelt and discharge while simultaneously providing meaningful estimates of the associated uncertainty. The IUEA approach uses the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) to simultaneously estimate uncertainties in model parameters, forcing, and observations. The robustness and usefulness of the IUEA-SNOW17 framework is evaluated for snow-dominated watersheds in the northern Sierra Mountains, using the coupled IUEA-SNOW17 and an operational soil moisture accounting model (SAC-SMA). Preliminary results are promising and indicate successful performance of the coupled IUEA-SNOW17 framework. Implementation of the SNOW17 with the IUEA is straightforward and requires no major modification to the SNOW17 model structure. The IUEA-SNOW17 framework is intended to be modular and transferable and should assist the NWS in advancing the current forecasting system and reinforcing current operational forecasting skill.

Data worth and prediction uncertainty for pesticide transport and fate models in Nebraska and Maryland, United States

USGS Publications Warehouse

Nolan, Bernard T.; Malone, Robert W.; Doherty, John E.; Barbash, Jack E.; Ma, Liwang; Shaner, Dale L.

2015-01-01

CONCLUSIONS: Although the observed data were sparse, they substantially reduced prediction uncertainty in unsampled regions of pesticide breakthrough curves. Nitrate evidently functioned as a surrogate for soil hydraulic data in well-drained loam soils conducive to conservative transport of nitrogen. Pesticide properties and macropore parameters could most benefit from improved characterization further to reduce model misfit and prediction uncertainty.

Multiobjective design of aquifer monitoring networks for optimal spatial prediction and geostatistical parameter estimation

NASA Astrophysics Data System (ADS)

Alzraiee, Ayman H.; Bau, Domenico A.; Garcia, Luis A.

2013-06-01

Effective sampling of hydrogeological systems is essential in guiding groundwater management practices. Optimal sampling of groundwater systems has previously been formulated based on the assumption that heterogeneous subsurface properties can be modeled using a geostatistical approach. Therefore, the monitoring schemes have been developed to concurrently minimize the uncertainty in the spatial distribution of systems' states and parameters, such as the hydraulic conductivity K and the hydraulic head H, and the uncertainty in the geostatistical model of system parameters using a single objective function that aggregates all objectives. However, it has been shown that the aggregation of possibly conflicting objective functions is sensitive to the adopted aggregation scheme and may lead to distorted results. In addition, the uncertainties in geostatistical parameters affect the uncertainty in the spatial prediction of K and H according to a complex nonlinear relationship, which has often been ineffectively evaluated using a first-order approximation. In this study, we propose a multiobjective optimization framework to assist the design of monitoring networks of K and H with the goal of optimizing their spatial predictions and estimating the geostatistical parameters of the K field. The framework stems from the combination of a data assimilation (DA) algorithm and a multiobjective evolutionary algorithm (MOEA). The DA algorithm is based on the ensemble Kalman filter, a Monte-Carlo-based Bayesian update scheme for nonlinear systems, which is employed to approximate the posterior uncertainty in K, H, and the geostatistical parameters of K obtained by collecting new measurements. Multiple MOEA experiments are used to investigate the trade-off among design objectives and identify the corresponding monitoring schemes. The methodology is applied to design a sampling network for a shallow unconfined groundwater system located in Rocky Ford, Colorado. Results indicate that the effect of uncertainties associated with the geostatistical parameters on the spatial prediction might be significantly alleviated (by up to 80% of the prior uncertainty in K and by 90% of the prior uncertainty in H) by sampling evenly distributed measurements with a spatial measurement density of more than 1 observation per 60 m × 60 m grid block. In addition, exploration of the interaction of objective functions indicates that the ability of head measurements to reduce the uncertainty associated with the correlation scale is comparable to the effect of hydraulic conductivity measurements.

Structural and parameteric uncertainty quantification in cloud microphysics parameterization schemes

NASA Astrophysics Data System (ADS)

van Lier-Walqui, M.; Morrison, H.; Kumjian, M. R.; Prat, O. P.; Martinkus, C.

2017-12-01

Atmospheric model parameterization schemes employ approximations to represent the effects of unresolved processes. These approximations are a source of error in forecasts, caused in part by considerable uncertainty about the optimal value of parameters within each scheme -- parameteric uncertainty. Furthermore, there is uncertainty regarding the best choice of the overarching structure of the parameterization scheme -- structrual uncertainty. Parameter estimation can constrain the first, but may struggle with the second because structural choices are typically discrete. We address this problem in the context of cloud microphysics parameterization schemes by creating a flexible framework wherein structural and parametric uncertainties can be simultaneously constrained. Our scheme makes no assuptions about drop size distribution shape or the functional form of parametrized process rate terms. Instead, these uncertainties are constrained by observations using a Markov Chain Monte Carlo sampler within a Bayesian inference framework. Our scheme, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS), has flexibility to predict various sets of prognostic drop size distribution moments as well as varying complexity of process rate formulations. We compare idealized probabilistic forecasts from versions of BOSS with varying levels of structural complexity. This work has applications in ensemble forecasts with model physics uncertainty, data assimilation, and cloud microphysics process studies.

Stream Discharge and Evapotranspiration Responses to Climate Change and Their Associated Uncertainties in a Large Semi-Arid Basin

NASA Astrophysics Data System (ADS)

Bassam, S.; Ren, J.

2017-12-01

Predicting future water availability in watersheds is very important for proper water resources management, especially in semi-arid regions with scarce water resources. Hydrological models have been considered as powerful tools in predicting future hydrological conditions in watershed systems in the past two decades. Streamflow and evapotranspiration are the two important components in watershed water balance estimation as the former is the most commonly-used indicator of the overall water budget estimation, and the latter is the second biggest component of water budget (biggest outflow from the system). One of the main concerns in watershed scale hydrological modeling is the uncertainties associated with model prediction, which could arise from errors in model parameters and input meteorological data, or errors in model representation of the physics of hydrological processes. Understanding and quantifying these uncertainties are vital to water resources managers for proper decision making based on model predictions. In this study, we evaluated the impacts of different climate change scenarios on the future stream discharge and evapotranspiration, and their associated uncertainties, throughout a large semi-arid basin using a stochastically-calibrated, physically-based, semi-distributed hydrological model. The results of this study could provide valuable insights in applying hydrological models in large scale watersheds, understanding the associated sensitivity and uncertainties in model parameters, and estimating the corresponding impacts on interested hydrological process variables under different climate change scenarios.

The significance of parameter uncertainties for the prediction of offshore pile driving noise.

PubMed

Lippert, Tristan; von Estorff, Otto

2014-11-01

Due to the construction of offshore wind farms and its potential effect on marine wildlife, the numerical prediction of pile driving noise over long ranges has recently gained importance. In this contribution, a coupled finite element/wavenumber integration model for noise prediction is presented and validated by measurements. The ocean environment, especially the sea bottom, can only be characterized with limited accuracy in terms of input parameters for the numerical model at hand. Therefore the effect of these parameter uncertainties on the prediction of sound pressure levels (SPLs) in the water column is investigated by a probabilistic approach. In fact, a variation of the bottom material parameters by means of Monte-Carlo simulations shows significant effects on the predicted SPLs. A sensitivity analysis of the model with respect to the single quantities is performed, as well as a global variation. Based on the latter, the probability distribution of the SPLs at an exemplary receiver position is evaluated and compared to measurements. The aim of this procedure is to develop a model to reliably predict an interval for the SPLs, by quantifying the degree of uncertainty of the SPLs with the MC simulations.

Assimilating solar-induced chlorophyll fluorescence into the terrestrial biosphere model BETHY-SCOPE v1.0: model description and information content

NASA Astrophysics Data System (ADS)

Norton, Alexander J.; Rayner, Peter J.; Koffi, Ernest N.; Scholze, Marko

2018-04-01

The synthesis of model and observational information using data assimilation can improve our understanding of the terrestrial carbon cycle, a key component of the Earth's climate-carbon system. Here we provide a data assimilation framework for combining observations of solar-induced chlorophyll fluorescence (SIF) and a process-based model to improve estimates of terrestrial carbon uptake or gross primary production (GPP). We then quantify and assess the constraint SIF provides on the uncertainty in global GPP through model process parameters in an error propagation study. By incorporating 1 year of SIF observations from the GOSAT satellite, we find that the parametric uncertainty in global annual GPP is reduced by 73 % from ±19.0 to ±5.2 Pg C yr-1. This improvement is achieved through strong constraint of leaf growth processes and weak to moderate constraint of physiological parameters. We also find that the inclusion of uncertainty in shortwave down-radiation forcing has a net-zero effect on uncertainty in GPP when incorporated into the SIF assimilation framework. This study demonstrates the powerful capacity of SIF to reduce uncertainties in process-based model estimates of GPP and the potential for improving our predictive capability of this uncertain carbon flux.

Using prediction uncertainty analysis to design hydrologic monitoring networks: Example applications from the Great Lakes water availability pilot project

USGS Publications Warehouse

Fienen, Michael N.; Doherty, John E.; Hunt, Randall J.; Reeves, Howard W.

2010-01-01

The importance of monitoring networks for resource-management decisions is becoming more recognized, in both theory and application. Quantitative computer models provide a science-based framework to evaluate the efficacy and efficiency of existing and possible future monitoring networks. In the study described herein, two suites of tools were used to evaluate the worth of new data for specific predictions, which in turn can support efficient use of resources needed to construct a monitoring network. The approach evaluates the uncertainty of a model prediction and, by using linear propagation of uncertainty, estimates how much uncertainty could be reduced if the model were calibrated with addition information (increased a priori knowledge of parameter values or new observations). The theoretical underpinnings of the two suites of tools addressing this technique are compared, and their application to a hypothetical model based on a local model inset into the Great Lakes Water Availability Pilot model are described. Results show that meaningful guidance for monitoring network design can be obtained by using the methods explored. The validity of this guidance depends substantially on the parameterization as well; hence, parameterization must be considered not only when designing the parameter-estimation paradigm but also-importantly-when designing the prediction-uncertainty paradigm.

Multivariate Probabilistic Analysis of an Hydrological Model

NASA Astrophysics Data System (ADS)

Franceschini, Samuela; Marani, Marco

2010-05-01

Model predictions derived based on rainfall measurements and hydrological model results are often limited by the systematic error of measuring instruments, by the intrinsic variability of the natural processes and by the uncertainty of the mathematical representation. We propose a means to identify such sources of uncertainty and to quantify their effects based on point-estimate approaches, as a valid alternative to cumbersome Montecarlo methods. We present uncertainty analyses on the hydrologic response to selected meteorological events, in the mountain streamflow-generating portion of the Brenta basin at Bassano del Grappa, Italy. The Brenta river catchment has a relatively uniform morphology and quite a heterogeneous rainfall-pattern. In the present work, we evaluate two sources of uncertainty: data uncertainty (the uncertainty due to data handling and analysis) and model uncertainty (the uncertainty related to the formulation of the model). We thus evaluate the effects of the measurement error of tipping-bucket rain gauges, the uncertainty in estimating spatially-distributed rainfall through block kriging, and the uncertainty associated with estimated model parameters. To this end, we coupled a deterministic model based on the geomorphological theory of the hydrologic response to probabilistic methods. In particular we compare the results of Monte Carlo Simulations (MCS) to the results obtained, in the same conditions, using Li's Point Estimate Method (LiM). The LiM is a probabilistic technique that approximates the continuous probability distribution function of the considered stochastic variables by means of discrete points and associated weights. This allows to satisfactorily reproduce results with only few evaluations of the model function. The comparison between the LiM and MCS results highlights the pros and cons of using an approximating method. LiM is less computationally demanding than MCS, but has limited applicability especially when the model response is highly nonlinear. Higher-order approximations can provide more accurate estimations, but reduce the numerical advantage of the LiM. The results of the uncertainty analysis identify the main sources of uncertainty in the computation of river discharge. In this particular case the spatial variability of rainfall and the model parameters uncertainty are shown to have the greatest impact on discharge evaluation. This, in turn, highlights the need to support any estimated hydrological response with probability information and risk analysis results in order to provide a robust, systematic framework for decision making.

Uncertainty quantification in Rothermel's Model using an efficient sampling method

Treesearch

Edwin Jimenez; M. Yousuff Hussaini; Scott L. Goodrick

2007-01-01

The purpose of the present work is to quantify parametric uncertainty in Rothermel’s wildland fire spread model (implemented in software such as BehavePlus3 and FARSITE), which is undoubtedly among the most widely used fire spread models in the United States. This model consists of a nonlinear system of equations that relates environmental variables (input parameter...

Identification of sensitive parameters in the modeling of SVOC reemission processes from soil to atmosphere.

PubMed

Loizeau, Vincent; Ciffroy, Philippe; Roustan, Yelva; Musson-Genon, Luc

2014-09-15

Semi-volatile organic compounds (SVOCs) are subject to Long-Range Atmospheric Transport because of transport-deposition-reemission successive processes. Several experimental data available in the literature suggest that soil is a non-negligible contributor of SVOCs to atmosphere. Then coupling soil and atmosphere in integrated coupled models and simulating reemission processes can be essential for estimating atmospheric concentration of several pollutants. However, the sources of uncertainty and variability are multiple (soil properties, meteorological conditions, chemical-specific parameters) and can significantly influence the determination of reemissions. In order to identify the key parameters in reemission modeling and their effect on global modeling uncertainty, we conducted a sensitivity analysis targeted on the 'reemission' output variable. Different parameters were tested, including soil properties, partition coefficients and meteorological conditions. We performed EFAST sensitivity analysis for four chemicals (benzo-a-pyrene, hexachlorobenzene, PCB-28 and lindane) and different spatial scenari (regional and continental scales). Partition coefficients between air, solid and water phases are influent, depending on the precision of data and global behavior of the chemical. Reemissions showed a lower variability to soil parameters (soil organic matter and water contents at field capacity and wilting point). A mapping of these parameters at a regional scale is sufficient to correctly estimate reemissions when compared to other sources of uncertainty. Copyright © 2014 Elsevier B.V. All rights reserved.

A polynomial chaos ensemble hydrologic prediction system for efficient parameter inference and robust uncertainty assessment

NASA Astrophysics Data System (ADS)

Wang, S.; Huang, G. H.; Baetz, B. W.; Huang, W.

2015-11-01

This paper presents a polynomial chaos ensemble hydrologic prediction system (PCEHPS) for an efficient and robust uncertainty assessment of model parameters and predictions, in which possibilistic reasoning is infused into probabilistic parameter inference with simultaneous consideration of randomness and fuzziness. The PCEHPS is developed through a two-stage factorial polynomial chaos expansion (PCE) framework, which consists of an ensemble of PCEs to approximate the behavior of the hydrologic model, significantly speeding up the exhaustive sampling of the parameter space. Multiple hypothesis testing is then conducted to construct an ensemble of reduced-dimensionality PCEs with only the most influential terms, which is meaningful for achieving uncertainty reduction and further acceleration of parameter inference. The PCEHPS is applied to the Xiangxi River watershed in China to demonstrate its validity and applicability. A detailed comparison between the HYMOD hydrologic model, the ensemble of PCEs, and the ensemble of reduced PCEs is performed in terms of accuracy and efficiency. Results reveal temporal and spatial variations in parameter sensitivities due to the dynamic behavior of hydrologic systems, and the effects (magnitude and direction) of parametric interactions depending on different hydrological metrics. The case study demonstrates that the PCEHPS is capable not only of capturing both expert knowledge and probabilistic information in the calibration process, but also of implementing an acceleration of more than 10 times faster than the hydrologic model without compromising the predictive accuracy.

Probabilistic projections of 21st century climate change over Northern Eurasia

NASA Astrophysics Data System (ADS)

Monier, E.; Sokolov, A. P.; Schlosser, C. A.; Scott, J. R.; Gao, X.

2013-12-01

We present probabilistic projections of 21st century climate change over Northern Eurasia using the Massachusetts Institute of Technology (MIT) Integrated Global System Model (IGSM), an integrated assessment model that couples an earth system model of intermediate complexity, with a two-dimensional zonal-mean atmosphere, to a human activity model. Regional climate change is obtained by two downscaling methods: a dynamical downscaling, where the IGSM is linked to a three dimensional atmospheric model; and a statistical downscaling, where a pattern scaling algorithm uses climate-change patterns from 17 climate models. This framework allows for key sources of uncertainty in future projections of regional climate change to be accounted for: emissions projections; climate system parameters (climate sensitivity, strength of aerosol forcing and ocean heat uptake rate); natural variability; and structural uncertainty. Results show that the choice of climate policy and the climate parameters are the largest drivers of uncertainty. We also nd that dierent initial conditions lead to dierences in patterns of change as large as when using different climate models. Finally, this analysis reveals the wide range of possible climate change over Northern Eurasia, emphasizing the need to consider all sources of uncertainty when modeling climate impacts over Northern Eurasia.

Probabilistic projections of 21st century climate change over Northern Eurasia

NASA Astrophysics Data System (ADS)

Monier, Erwan; Sokolov, Andrei; Schlosser, Adam; Scott, Jeffery; Gao, Xiang

2013-12-01

We present probabilistic projections of 21st century climate change over Northern Eurasia using the Massachusetts Institute of Technology (MIT) Integrated Global System Model (IGSM), an integrated assessment model that couples an Earth system model of intermediate complexity with a two-dimensional zonal-mean atmosphere to a human activity model. Regional climate change is obtained by two downscaling methods: a dynamical downscaling, where the IGSM is linked to a three-dimensional atmospheric model, and a statistical downscaling, where a pattern scaling algorithm uses climate change patterns from 17 climate models. This framework allows for four major sources of uncertainty in future projections of regional climate change to be accounted for: emissions projections, climate system parameters (climate sensitivity, strength of aerosol forcing and ocean heat uptake rate), natural variability, and structural uncertainty. The results show that the choice of climate policy and the climate parameters are the largest drivers of uncertainty. We also find that different initial conditions lead to differences in patterns of change as large as when using different climate models. Finally, this analysis reveals the wide range of possible climate change over Northern Eurasia, emphasizing the need to consider these sources of uncertainty when modeling climate impacts over Northern Eurasia.

Uncertainty quantification for constitutive model calibration of brain tissue.

PubMed

Brewick, Patrick T; Teferra, Kirubel

2018-05-31

The results of a study comparing model calibration techniques for Ogden's constitutive model that describes the hyperelastic behavior of brain tissue are presented. One and two-term Ogden models are fit to two different sets of stress-strain experimental data for brain tissue using both least squares optimization and Bayesian estimation. For the Bayesian estimation, the joint posterior distribution of the constitutive parameters is calculated by employing Hamiltonian Monte Carlo (HMC) sampling, a type of Markov Chain Monte Carlo method. The HMC method is enriched in this work to intrinsically enforce the Drucker stability criterion by formulating a nonlinear parameter constraint function, which ensures the constitutive model produces physically meaningful results. Through application of the nested sampling technique, 95% confidence bounds on the constitutive model parameters are identified, and these bounds are then propagated through the constitutive model to produce the resultant bounds on the stress-strain response. The behavior of the model calibration procedures and the effect of the characteristics of the experimental data are extensively evaluated. It is demonstrated that increasing model complexity (i.e., adding an additional term in the Ogden model) improves the accuracy of the best-fit set of parameters while also increasing the uncertainty via the widening of the confidence bounds of the calibrated parameters. Despite some similarity between the two data sets, the resulting distributions are noticeably different, highlighting the sensitivity of the calibration procedures to the characteristics of the data. For example, the amount of uncertainty reported on the experimental data plays an essential role in how data points are weighted during the calibration, and this significantly affects how the parameters are calibrated when combining experimental data sets from disparate sources. Published by Elsevier Ltd.

Handling Uncertainty in Palaeo-Climate Models and Data

NASA Astrophysics Data System (ADS)

Voss, J.; Haywood, A. M.; Dolan, A. M.; Domingo, D.

2017-12-01

The study of palaeoclimates can provide data on the behaviour of the Earth system with boundary conditions different from the ones we observe in the present. One of the main challenges in this approach is that data on past climates comes with large uncertainties, since quantities of interest cannot be observed directly, but must be derived from proxies instead. We consider proxy-derived data from the Pliocene (around 3 millions years ago; the last interval in Earth history when CO2 was at modern or near future levels) and contrast this data to the output of complex climate models. In order to perform a meaningful data-model comparison, uncertainties must be taken into account. In this context, we discuss two examples of complex data-model comparison problems. Both examples have in common that they involve fitting a statistical model to describe how the output of the climate simulations depends on various model parameters, including atmospheric CO2 concentration and orbital parameters (obliquity, excentricity, and precession). This introduces additional uncertainties, but allows to explore a much larger range of model parameters than would be feasible by only relying on simulation runs. The first example shows how Gaussian process emulators can be used to perform data-model comparison when simulation runs only differ in the choice of orbital parameters, but temperature data is given in the (somewhat inconvenient) form of "warm peak averages". The second example shows how a simpler approach, based on linear regression, can be used to analyse a more complex problem where we use a larger and more varied ensemble of climate simulations with the aim to estimate Earth System Sensitivity.

Exploiting Surface Albedos Products to Bridge the Gap Between Remote Sensing Information and Climate Models

NASA Astrophysics Data System (ADS)

Pinty, Bernard; Andredakis, Ioannis; Clerici, Marco; Kaminski, Thomas; Taberner, Malcolm; Stephen, Plummer

2011-01-01

We present results from the application of an inversion method conducted using MODIS derived broadband visible and near-infrared surface albedo products. This contribution is an extension of earlier efforts to optimally retrieve land surface fluxes and associated two- stream model parameters based on the Joint Research Centre Two-stream Inversion Package (JRC-TIP). The discussion focuses on products (based on the mean and one-sigma values of the Probability Distribution Functions (PDFs)) obtained during the summer and winter and highlight specific issues related to snowy conditions. This paper discusses the retrieved model parameters including the effective Leaf Area Index (LAI), the background brightness and the scattering efficiency of the vegetation elements. The spatial and seasonal changes exhibited by these parameters agree with common knowledge and underscore the richness of the high quality surface albedo data sets. At the same time, the opportunity to generate global maps of new products, such as the background albedo, underscores the advantages of using state of the art algorithmic approaches capable of fully exploiting accurate satellite remote sensing datasets. The detailed analyses of the retrieval uncertainties highlight the central role and contribution of the LAI, the main process parameter to interpret radiation transfer observations over vegetated surfaces. The posterior covariance matrix of the uncertainties is further exploited to quantify the knowledge gain from the ingestion of MODIS surface albedo products. The estimation of the radiation fluxes that are absorbed, transmitted and scattered by the vegetation layer and its background is achieved on the basis of the retrieved PDFs of the model parameters. The propagation of uncertainties from the observations to the model parameters is achieved via the Hessian of the cost function and yields a covariance matrix of posterior parameter uncertainties. This matrix is propagated to the radiation fluxes via the model’s Jacobian matrix of first derivatives. A definite asset of the JRC-TIP lies in its capability to control and ultimately relax a number of assumptions that are often implicit in traditional approaches. These features greatly help understand the discrepancies between the different data sets of land surface properties and fluxes that are currently available. Through a series of selected examples, the inverse procedure implemented in the JRC-TIP is shown to be robust, reliable and compliant with large scale processing requirements. Furthermore, this package ensures the physical consistency between the set of observations, the two-stream model parameters and radiation fluxes. It also documents the retrieval of associated uncertainties. The knowledge gained from the availability of remote sensing surface albedo products can be expressed in quantitative terms using a simple metric. This metric helps identify the geographical locations and periods of the year where the remote sensing products fail in reducing the uncertainty on the process model parameters as can be specified from current knowledge.

Uncertainty quantification for environmental models

USGS Publications Warehouse

Hill, Mary C.; Lu, Dan; Kavetski, Dmitri; Clark, Martyn P.; Ye, Ming

2012-01-01

Environmental models are used to evaluate the fate of fertilizers in agricultural settings (including soil denitrification), the degradation of hydrocarbons at spill sites, and water supply for people and ecosystems in small to large basins and cities—to mention but a few applications of these models. They also play a role in understanding and diagnosing potential environmental impacts of global climate change. The models are typically mildly to extremely nonlinear. The persistent demand for enhanced dynamics and resolution to improve model realism [17] means that lengthy individual model execution times will remain common, notwithstanding continued enhancements in computer power. In addition, high-dimensional parameter spaces are often defined, which increases the number of model runs required to quantify uncertainty [2]. Some environmental modeling projects have access to extensive funding and computational resources; many do not. The many recent studies of uncertainty quantification in environmental model predictions have focused on uncertainties related to data error and sparsity of data, expert judgment expressed mathematically through prior information, poorly known parameter values, and model structure (see, for example, [1,7,9,10,13,18]). Approaches for quantifying uncertainty include frequentist (potentially with prior information [7,9]), Bayesian [13,18,19], and likelihood-based. A few of the numerous methods, including some sensitivity and inverse methods with consequences for understanding and quantifying uncertainty, are as follows: Bayesian hierarchical modeling and Bayesian model averaging; single-objective optimization with error-based weighting [7] and multi-objective optimization [3]; methods based on local derivatives [2,7,10]; screening methods like OAT (one at a time) and the method of Morris [14]; FAST (Fourier amplitude sensitivity testing) [14]; the Sobol' method [14]; randomized maximum likelihood [10]; Markov chain Monte Carlo (MCMC) [10]. There are also bootstrapping and cross-validation approaches.Sometimes analyses are conducted using surrogate models [12]. The availability of so many options can be confusing. Categorizing methods based on fundamental questions assists in communicating the essential results of uncertainty analyses to stakeholders. Such questions can focus on model adequacy (e.g., How well does the model reproduce observed system characteristics and dynamics?) and sensitivity analysis (e.g., What parameters can be estimated with available data? What observations are important to parameters and predictions? What parameters are important to predictions?), as well as on the uncertainty quantification (e.g., How accurate and precise are the predictions?). The methods can also be classified by the number of model runs required: few (10s to 1000s) or many (10,000s to 1,000,000s). Of the methods listed above, the most computationally frugal are generally those based on local derivatives; MCMC methods tend to be among the most computationally demanding. Surrogate models (emulators)do not necessarily produce computational frugality because many runs of the full model are generally needed to create a meaningful surrogate model. With this categorization, we can, in general, address all the fundamental questions mentioned above using either computationally frugal or demanding methods. Model development and analysis can thus be conducted consistently using either computation-ally frugal or demanding methods; alternatively, different fundamental questions can be addressed using methods that require different levels of effort. Based on this perspective, we pose the question: Can computationally frugal methods be useful companions to computationally demanding meth-ods? The reliability of computationally frugal methods generally depends on the model being reasonably linear, which usually means smooth nonlin-earities and the assumption of Gaussian errors; both tend to be more valid with more linear

A trans-dimensional Bayesian Markov chain Monte Carlo algorithm for model assessment using frequency-domain electromagnetic data

USGS Publications Warehouse

Minsley, Burke J.

2011-01-01

A meaningful interpretation of geophysical measurements requires an assessment of the space of models that are consistent with the data, rather than just a single, ‘best’ model which does not convey information about parameter uncertainty. For this purpose, a trans-dimensional Bayesian Markov chain Monte Carlo (MCMC) algorithm is developed for assessing frequencydomain electromagnetic (FDEM) data acquired from airborne or ground-based systems. By sampling the distribution of models that are consistent with measured data and any prior knowledge, valuable inferences can be made about parameter values such as the likely depth to an interface, the distribution of possible resistivity values as a function of depth and non-unique relationships between parameters. The trans-dimensional aspect of the algorithm allows the number of layers to be a free parameter that is controlled by the data, where models with fewer layers are inherently favoured, which provides a natural measure of parsimony and a significant degree of flexibility in parametrization. The MCMC algorithm is used with synthetic examples to illustrate how the distribution of acceptable models is affected by the choice of prior information, the system geometry and configuration and the uncertainty in the measured system elevation. An airborne FDEM data set that was acquired for the purpose of hydrogeological characterization is also studied. The results compare favorably with traditional least-squares analysis, borehole resistivity and lithology logs from the site, and also provide new information about parameter uncertainty necessary for model assessment.

Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations

NASA Technical Reports Server (NTRS)

DeLannoy, Gabrielle J. M.; Reichle, Rolf H.; Vrugt, Jasper A.

2013-01-01

Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).

Two-Stage Modeling of Formaldehyde-Induced Tumor Incidence in the Rat—analysis of Uncertainties

EPA Science Inventory

This works extends the 2-stage cancer modeling of tumor incidence in formaldehyde-exposed rats carried out at the CIIT Centers for Health Research. We modify key assumptions, evaluate the effect of selected uncertainties, and develop confidence bounds on parameter estimates. Th...

UNCERTAINTY AND SENSITIVITY ANALYSES FOR INTEGRATED HUMAN HEALTH AND ECOLOGICAL RISK ASSESSMENT OF HAZARDOUS WASTE DISPOSAL

EPA Science Inventory

While there is a high potential for exposure of humans and ecosystems to chemicals released from hazardous waste sites, the degree to which this potential is realized is often uncertain. Conceptually divided among parameter, model, and modeler uncertainties imparted during simula...

A methodology for global-sensitivity analysis of time-dependent outputs in systems biology modelling.

PubMed

Sumner, T; Shephard, E; Bogle, I D L

2012-09-07

One of the main challenges in the development of mathematical and computational models of biological systems is the precise estimation of parameter values. Understanding the effects of uncertainties in parameter values on model behaviour is crucial to the successful use of these models. Global sensitivity analysis (SA) can be used to quantify the variability in model predictions resulting from the uncertainty in multiple parameters and to shed light on the biological mechanisms driving system behaviour. We present a new methodology for global SA in systems biology which is computationally efficient and can be used to identify the key parameters and their interactions which drive the dynamic behaviour of a complex biological model. The approach combines functional principal component analysis with established global SA techniques. The methodology is applied to a model of the insulin signalling pathway, defects of which are a major cause of type 2 diabetes and a number of key features of the system are identified.

SU-F-T-316: A Model to Deal with Dosimetric and Delivery Uncertainties in Radiotherapy Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haering, P; Lang, C; Splinter, M

2016-06-15

Purpose The conventional way of dealing with uncertainties resulting from dose calculation or beam delivery in IMRT, is to do verification measurements for the plan in question. Here we present an alternative based on recommendations given in the AAPM 142 report and treatment specific parameters that model the uncertainties for the plan delivery. Methods Basis of the model is the assignment of uncertainty parameters to all segment fields or control point sequences of a plan. The given field shape is analyzed for complexity, dose rate, number of MU, field size related output as well as factors for in/out field positionmore » and penumbra regions. Together with depth related uncertainties, a 3D matrix is generated by a projection algorithm. Patient anatomy is included as uncertainty CT data set as well. Therefore, object density is classified in 4 categories close to water, lung, bone and gradient regions with additional uncertainties. The result is then exported as a DICOM dose file by the software tool (written in IDL, Exelis), having the given resolution and target point. Results Uncertainty matrixes for several patient cases have been calculated and compared side by side in the planning system. The result is not quite always intuitive but it clearly indicates high and low uncertainties related to OARs and target volumes as well as to measured gamma distributions.ConclusionThe imported uncertainty datasets may help the treatment planner to understand the complexity of the treatment plan. He then might decide to change the plan to produce a more suited uncertainty distribution, e.g. by changing the beam angles the high uncertainty spots can be influenced or try to use another treatment setup, resulting in a plan with lower uncertainties. A next step could be to include such a model into the optimization algorithm to add a new dose uncertainty constraint.« less

Translating landfill methane generation parameters among first-order decay models.

PubMed

Krause, Max J; Chickering, Giles W; Townsend, Timothy G

2016-11-01

Landfill gas (LFG) generation is predicted by a first-order decay (FOD) equation that incorporates two parameters: a methane generation potential (L 0 ) and a methane generation rate (k). Because non-hazardous waste landfills may accept many types of waste streams, multiphase models have been developed in an attempt to more accurately predict methane generation from heterogeneous waste streams. The ability of a single-phase FOD model to predict methane generation using weighted-average methane generation parameters and tonnages translated from multiphase models was assessed in two exercises. In the first exercise, waste composition from four Danish landfills represented by low-biodegradable waste streams was modeled in the Afvalzorg Multiphase Model and methane generation was compared to the single-phase Intergovernmental Panel on Climate Change (IPCC) Waste Model and LandGEM. In the second exercise, waste composition represented by IPCC waste components was modeled in the multiphase IPCC and compared to single-phase LandGEM and Australia's Solid Waste Calculator (SWC). In both cases, weight-averaging of methane generation parameters from waste composition data in single-phase models was effective in predicting cumulative methane generation from -7% to +6% of the multiphase models. The results underscore the understanding that multiphase models will not necessarily improve LFG generation prediction because the uncertainty of the method rests largely within the input parameters. A unique method of calculating the methane generation rate constant by mass of anaerobically degradable carbon was presented (k c ) and compared to existing methods, providing a better fit in 3 of 8 scenarios. Generally, single phase models with weighted-average inputs can accurately predict methane generation from multiple waste streams with varied characteristics; weighted averages should therefore be used instead of regional default values when comparing models. Translating multiphase first-order decay model input parameters by weighted average shows that single-phase models can predict cumulative methane generation within the level of uncertainty of many of the input parameters as defined by the Intergovernmental Panel on Climate Change (IPCC), which indicates that decreasing the uncertainty of the input parameters will make the model more accurate rather than adding multiple phases or input parameters.

Evaluation of the information content of long-term wastewater characteristics data in relation to activated sludge model parameters.

PubMed

Alikhani, Jamal; Takacs, Imre; Al-Omari, Ahmed; Murthy, Sudhir; Massoudieh, Arash

2017-03-01

A parameter estimation framework was used to evaluate the ability of observed data from a full-scale nitrification-denitrification bioreactor to reduce the uncertainty associated with the bio-kinetic and stoichiometric parameters of an activated sludge model (ASM). Samples collected over a period of 150 days from the effluent as well as from the reactor tanks were used. A hybrid genetic algorithm and Bayesian inference were used to perform deterministic and parameter estimations, respectively. The main goal was to assess the ability of the data to obtain reliable parameter estimates for a modified version of the ASM. The modified ASM model includes methylotrophic processes which play the main role in methanol-fed denitrification. Sensitivity analysis was also used to explain the ability of the data to provide information about each of the parameters. The results showed that the uncertainty in the estimates of the most sensitive parameters (including growth rate, decay rate, and yield coefficients) decreased with respect to the prior information.

Quantifying radar-rainfall uncertainties in urban drainage flow modelling

NASA Astrophysics Data System (ADS)

Rico-Ramirez, M. A.; Liguori, S.; Schellart, A. N. A.

2015-09-01

This work presents the results of the implementation of a probabilistic system to model the uncertainty associated to radar rainfall (RR) estimates and the way this uncertainty propagates through the sewer system of an urban area located in the North of England. The spatial and temporal correlations of the RR errors as well as the error covariance matrix were computed to build a RR error model able to generate RR ensembles that reproduce the uncertainty associated with the measured rainfall. The results showed that the RR ensembles provide important information about the uncertainty in the rainfall measurement that can be propagated in the urban sewer system. The results showed that the measured flow peaks and flow volumes are often bounded within the uncertainty area produced by the RR ensembles. In 55% of the simulated events, the uncertainties in RR measurements can explain the uncertainties observed in the simulated flow volumes. However, there are also some events where the RR uncertainty cannot explain the whole uncertainty observed in the simulated flow volumes indicating that there are additional sources of uncertainty that must be considered such as the uncertainty in the urban drainage model structure, the uncertainty in the urban drainage model calibrated parameters, and the uncertainty in the measured sewer flows.

Quantification of downscaled precipitation uncertainties via Bayesian inference

NASA Astrophysics Data System (ADS)

Nury, A. H.; Sharma, A.; Marshall, L. A.

2017-12-01

Prediction of precipitation from global climate model (GCM) outputs remains critical to decision-making in water-stressed regions. In this regard, downscaling of GCM output has been a useful tool for analysing future hydro-climatological states. Several downscaling approaches have been developed for precipitation downscaling, including those using dynamical or statistical downscaling methods. Frequently, outputs from dynamical downscaling are not readily transferable across regions for significant methodical and computational difficulties. Statistical downscaling approaches provide a flexible and efficient alternative, providing hydro-climatological outputs across multiple temporal and spatial scales in many locations. However these approaches are subject to significant uncertainty, arising due to uncertainty in the downscaled model parameters and in the use of different reanalysis products for inferring appropriate model parameters. Consequently, these will affect the performance of simulation in catchment scale. This study develops a Bayesian framework for modelling downscaled daily precipitation from GCM outputs. This study aims to introduce uncertainties in downscaling evaluating reanalysis datasets against observational rainfall data over Australia. In this research a consistent technique for quantifying downscaling uncertainties by means of Bayesian downscaling frame work has been proposed. The results suggest that there are differences in downscaled precipitation occurrences and extremes.

A new Bayesian Earthquake Analysis Tool (BEAT)

NASA Astrophysics Data System (ADS)

Vasyura-Bathke, Hannes; Dutta, Rishabh; Jónsson, Sigurjón; Mai, Martin

2017-04-01

Modern earthquake source estimation studies increasingly use non-linear optimization strategies to estimate kinematic rupture parameters, often considering geodetic and seismic data jointly. However, the optimization process is complex and consists of several steps that need to be followed in the earthquake parameter estimation procedure. These include pre-describing or modeling the fault geometry, calculating the Green's Functions (often assuming a layered elastic half-space), and estimating the distributed final slip and possibly other kinematic source parameters. Recently, Bayesian inference has become popular for estimating posterior distributions of earthquake source model parameters given measured/estimated/assumed data and model uncertainties. For instance, some research groups consider uncertainties of the layered medium and propagate these to the source parameter uncertainties. Other groups make use of informative priors to reduce the model parameter space. In addition, innovative sampling algorithms have been developed that efficiently explore the often high-dimensional parameter spaces. Compared to earlier studies, these improvements have resulted in overall more robust source model parameter estimates that include uncertainties. However, the computational demands of these methods are high and estimation codes are rarely distributed along with the published results. Even if codes are made available, it is often difficult to assemble them into a single optimization framework as they are typically coded in different programing languages. Therefore, further progress and future applications of these methods/codes are hampered, while reproducibility and validation of results has become essentially impossible. In the spirit of providing open-access and modular codes to facilitate progress and reproducible research in earthquake source estimations, we undertook the effort of producing BEAT, a python package that comprises all the above-mentioned features in one single programing environment. The package is build on top of the pyrocko seismological toolbox (www.pyrocko.org) and makes use of the pymc3 module for Bayesian statistical model fitting. BEAT is an open-source package (https://github.com/hvasbath/beat) and we encourage and solicit contributions to the project. In this contribution, we present our strategy for developing BEAT, show application examples, and discuss future developments.

A general Bayesian framework for calibrating and evaluating stochastic models of annual multi-site hydrological data

NASA Astrophysics Data System (ADS)

Frost, Andrew J.; Thyer, Mark A.; Srikanthan, R.; Kuczera, George

2007-07-01

SummaryMulti-site simulation of hydrological data are required for drought risk assessment of large multi-reservoir water supply systems. In this paper, a general Bayesian framework is presented for the calibration and evaluation of multi-site hydrological data at annual timescales. Models included within this framework are the hidden Markov model (HMM) and the widely used lag-1 autoregressive (AR(1)) model. These models are extended by the inclusion of a Box-Cox transformation and a spatial correlation function in a multi-site setting. Parameter uncertainty is evaluated using Markov chain Monte Carlo techniques. Models are evaluated by their ability to reproduce a range of important extreme statistics and compared using Bayesian model selection techniques which evaluate model probabilities. The case study, using multi-site annual rainfall data situated within catchments which contribute to Sydney's main water supply, provided the following results: Firstly, in terms of model probabilities and diagnostics, the inclusion of the Box-Cox transformation was preferred. Secondly the AR(1) and HMM performed similarly, while some other proposed AR(1)/HMM models with regionally pooled parameters had greater posterior probability than these two models. The practical significance of parameter and model uncertainty was illustrated using a case study involving drought security analysis for urban water supply. It was shown that ignoring parameter uncertainty resulted in a significant overestimate of reservoir yield and an underestimation of system vulnerability to severe drought.

On the uncertainty of phenological responses to climate change, and implications for a terrestrial biosphere model

NASA Astrophysics Data System (ADS)

Migliavacca, M.; Sonnentag, O.; Keenan, T. F.; Cescatti, A.; O'Keefe, J.; Richardson, A. D.

2012-06-01

Phenology, the timing of recurring life cycle events, controls numerous land surface feedbacks to the climate system through the regulation of exchanges of carbon, water and energy between the biosphere and atmosphere. Terrestrial biosphere models, however, are known to have systematic errors in the simulation of spring phenology, which potentially could propagate to uncertainty in modeled responses to future climate change. Here, we used the Harvard Forest phenology record to investigate and characterize sources of uncertainty in predicting phenology, and the subsequent impacts on model forecasts of carbon and water cycling. Using a model-data fusion approach, we combined information from 20 yr of phenological observations of 11 North American woody species, with 12 leaf bud-burst models that varied in complexity. Akaike's Information Criterion indicated support for spring warming models with photoperiod limitations and, to a lesser extent, models that included chilling requirements. We assessed three different sources of uncertainty in phenological forecasts: parameter uncertainty, model uncertainty, and driver uncertainty. The latter was characterized running the models to 2099 using 2 different IPCC climate scenarios (A1fi vs. B1, i.e. high CO2 emissions vs. low CO2 emissions scenario). Parameter uncertainty was the smallest (average 95% Confidence Interval - CI: 2.4 days century-1 for scenario B1 and 4.5 days century-1 for A1fi), whereas driver uncertainty was the largest (up to 8.4 days century-1 in the simulated trends). The uncertainty related to model structure is also large and the predicted bud-burst trends as well as the shape of the smoothed projections varied among models (±7.7 days century-1 for A1fi, ±3.6 days century-1 for B1). The forecast sensitivity of bud-burst to temperature (i.e. days bud-burst advanced per degree of warming) varied between 2.2 days °C-1 and 5.2 days °C-1 depending on model structure. We quantified the impact of uncertainties in bud-burst forecasts on simulated photosynthetic CO2 uptake and evapotranspiration (ET) using a process-based terrestrial biosphere model. Uncertainty in phenology model structure led to uncertainty in the description of forest seasonality, which accumulated to uncertainty in annual model estimates of gross primary productivity (GPP) and ET of 9.6% and 2.9%, respectively. A sensitivity analysis shows that a variation of ±10 days in bud-burst dates led to a variation of ±5.0% for annual GPP and about ±2.0% for ET. For phenology models, differences among future climate scenarios (i.e. driver) represent the largest source of uncertainty, followed by uncertainties related to model structure, and finally, related to model parameterization. The uncertainties we have quantified will affect the description of the seasonality of ecosystem processes and in particular the simulation of carbon uptake by forest ecosystems, with a larger impact of uncertainties related to phenology model structure, followed by uncertainties related to phenological model parameterization.

Robustness Analysis and Reliable Flight Regime Estimation of an Integrated Resilent Control System for a Transport Aircraft

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Belcastro, Christine

2008-01-01

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. As a part of the validation process, this paper describes an analysis method for determining a reliable flight regime in the flight envelope within which an integrated resilent control system can achieve the desired performance of tracking command signals and detecting additive faults in the presence of parameter uncertainty and unmodeled dynamics. To calculate a reliable flight regime, a structured singular value analysis method is applied to analyze the closed-loop system over the entire flight envelope. To use the structured singular value analysis method, a linear fractional transform (LFT) model of a transport aircraft longitudinal dynamics is developed over the flight envelope by using a preliminary LFT modeling software tool developed at the NASA Langley Research Center, which utilizes a matrix-based computational approach. The developed LFT model can capture original nonlinear dynamics over the flight envelope with the ! block which contains key varying parameters: angle of attack and velocity, and real parameter uncertainty: aerodynamic coefficient uncertainty and moment of inertia uncertainty. Using the developed LFT model and a formal robustness analysis method, a reliable flight regime is calculated for a transport aircraft closed-loop system.

On the use of published radiobiological parameters and the evaluation of NTCP models regarding lung pneumonitis in clinical breast radiotherapy.

PubMed

Svolos, Patricia; Tsougos, Ioannis; Kyrgias, Georgios; Kappas, Constantine; Theodorou, Kiki

2011-04-01

In this study we sought to evaluate and accent the importance of radiobiological parameter selection and implementation to the normal tissue complication probability (NTCP) models. The relative seriality (RS) and the Lyman-Kutcher-Burman (LKB) models were studied. For each model, a minimum and maximum set of radiobiological parameter sets was selected from the overall published sets applied in literature and a theoretical mean parameter set was computed. In order to investigate the potential model weaknesses in NTCP estimation and to point out the correct use of model parameters, these sets were used as input to the RS and the LKB model, estimating radiation induced complications for a group of 36 breast cancer patients treated with radiotherapy. The clinical endpoint examined was Radiation Pneumonitis. Each model was represented by a certain dose-response range when the selected parameter sets were applied. Comparing the models with their ranges, a large area of coincidence was revealed. If the parameter uncertainties (standard deviation) are included in the models, their area of coincidence might be enlarged, constraining even greater their predictive ability. The selection of the proper radiobiological parameter set for a given clinical endpoint is crucial. Published parameter values are not definite but should be accompanied by uncertainties, and one should be very careful when applying them to the NTCP models. Correct selection and proper implementation of published parameters provides a quite accurate fit of the NTCP models to the considered endpoint.

iSCHRUNK--In Silico Approach to Characterization and Reduction of Uncertainty in the Kinetic Models of Genome-scale Metabolic Networks.

PubMed

Andreozzi, Stefano; Miskovic, Ljubisa; Hatzimanikatis, Vassily

2016-01-01

Accurate determination of physiological states of cellular metabolism requires detailed information about metabolic fluxes, metabolite concentrations and distribution of enzyme states. Integration of fluxomics and metabolomics data, and thermodynamics-based metabolic flux analysis contribute to improved understanding of steady-state properties of metabolism. However, knowledge about kinetics and enzyme activities though essential for quantitative understanding of metabolic dynamics remains scarce and involves uncertainty. Here, we present a computational methodology that allow us to determine and quantify the kinetic parameters that correspond to a certain physiology as it is described by a given metabolic flux profile and a given metabolite concentration vector. Though we initially determine kinetic parameters that involve a high degree of uncertainty, through the use of kinetic modeling and machine learning principles we are able to obtain more accurate ranges of kinetic parameters, and hence we are able to reduce the uncertainty in the model analysis. We computed the distribution of kinetic parameters for glucose-fed E. coli producing 1,4-butanediol and we discovered that the observed physiological state corresponds to a narrow range of kinetic parameters of only a few enzymes, whereas the kinetic parameters of other enzymes can vary widely. Furthermore, this analysis suggests which are the enzymes that should be manipulated in order to engineer the reference state of the cell in a desired way. The proposed approach also sets up the foundations of a novel type of approaches for efficient, non-asymptotic, uniform sampling of solution spaces. Copyright © 2015 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.

Assessment of source-specific health effects associated with an unknown number of major sources of multiple air pollutants: a unified Bayesian approach.

PubMed

Park, Eun Sug; Hopke, Philip K; Oh, Man-Suk; Symanski, Elaine; Han, Daikwon; Spiegelman, Clifford H

2014-07-01

There has been increasing interest in assessing health effects associated with multiple air pollutants emitted by specific sources. A major difficulty with achieving this goal is that the pollution source profiles are unknown and source-specific exposures cannot be measured directly; rather, they need to be estimated by decomposing ambient measurements of multiple air pollutants. This estimation process, called multivariate receptor modeling, is challenging because of the unknown number of sources and unknown identifiability conditions (model uncertainty). The uncertainty in source-specific exposures (source contributions) as well as uncertainty in the number of major pollution sources and identifiability conditions have been largely ignored in previous studies. A multipollutant approach that can deal with model uncertainty in multivariate receptor models while simultaneously accounting for parameter uncertainty in estimated source-specific exposures in assessment of source-specific health effects is presented in this paper. The methods are applied to daily ambient air measurements of the chemical composition of fine particulate matter ([Formula: see text]), weather data, and counts of cardiovascular deaths from 1995 to 1997 for Phoenix, AZ, USA. Our approach for evaluating source-specific health effects yields not only estimates of source contributions along with their uncertainties and associated health effects estimates but also estimates of model uncertainty (posterior model probabilities) that have been ignored in previous studies. The results from our methods agreed in general with those from the previously conducted workshop/studies on the source apportionment of PM health effects in terms of number of major contributing sources, estimated source profiles, and contributions. However, some of the adverse source-specific health effects identified in the previous studies were not statistically significant in our analysis, which probably resulted because we incorporated parameter uncertainty in estimated source contributions that has been ignored in the previous studies into the estimation of health effects parameters. © The Author 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Robust guaranteed-cost adaptive quantum phase estimation

NASA Astrophysics Data System (ADS)

Roy, Shibdas; Berry, Dominic W.; Petersen, Ian R.; Huntington, Elanor H.

2017-05-01

Quantum parameter estimation plays a key role in many fields like quantum computation, communication, and metrology. Optimal estimation allows one to achieve the most precise parameter estimates, but requires accurate knowledge of the model. Any inevitable uncertainty in the model parameters may heavily degrade the quality of the estimate. It is therefore desired to make the estimation process robust to such uncertainties. Robust estimation was previously studied for a varying phase, where the goal was to estimate the phase at some time in the past, using the measurement results from both before and after that time within a fixed time interval up to current time. Here, we consider a robust guaranteed-cost filter yielding robust estimates of a varying phase in real time, where the current phase is estimated using only past measurements. Our filter minimizes the largest (worst-case) variance in the allowable range of the uncertain model parameter(s) and this determines its guaranteed cost. It outperforms in the worst case the optimal Kalman filter designed for the model with no uncertainty, which corresponds to the center of the possible range of the uncertain parameter(s). Moreover, unlike the Kalman filter, our filter in the worst case always performs better than the best achievable variance for heterodyne measurements, which we consider as the tolerable threshold for our system. Furthermore, we consider effective quantum efficiency and effective noise power, and show that our filter provides the best results by these measures in the worst case.

Uncertainties in the 2004 Sumatra–Andaman source through nonlinear stochastic inversion of tsunami waves

PubMed Central

Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.

2017-01-01

Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311

Uncertainties in the 2004 Sumatra-Andaman source through nonlinear stochastic inversion of tsunami waves.

PubMed

Gopinathan, D; Venugopal, M; Roy, D; Rajendran, K; Guillas, S; Dias, F

2017-09-01

Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra-Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems.

When to Make Mountains out of Molehills: The Pros and Cons of Simple and Complex Model Calibration Procedures

NASA Astrophysics Data System (ADS)

Smith, K. A.; Barker, L. J.; Harrigan, S.; Prudhomme, C.; Hannaford, J.; Tanguy, M.; Parry, S.

2017-12-01

Earth and environmental models are relied upon to investigate system responses that cannot otherwise be examined. In simulating physical processes, models have adjustable parameters which may, or may not, have a physical meaning. Determining the values to assign to these model parameters is an enduring challenge for earth and environmental modellers. Selecting different error metrics by which the models results are compared to observations will lead to different sets of calibrated model parameters, and thus different model results. Furthermore, models may exhibit `equifinal' behaviour, where multiple combinations of model parameters lead to equally acceptable model performance against observations. These decisions in model calibration introduce uncertainty that must be considered when model results are used to inform environmental decision-making. This presentation focusses on the uncertainties that derive from the calibration of a four parameter lumped catchment hydrological model (GR4J). The GR models contain an inbuilt automatic calibration algorithm that can satisfactorily calibrate against four error metrics in only a few seconds. However, a single, deterministic model result does not provide information on parameter uncertainty. Furthermore, a modeller interested in extreme events, such as droughts, may wish to calibrate against more low flows specific error metrics. In a comprehensive assessment, the GR4J model has been run with 500,000 Latin Hypercube Sampled parameter sets across 303 catchments in the United Kingdom. These parameter sets have been assessed against six error metrics, including two drought specific metrics. This presentation compares the two approaches, and demonstrates that the inbuilt automatic calibration can outperform the Latin Hypercube experiment approach in single metric assessed performance. However, it is also shown that there are many merits of the more comprehensive assessment, which allows for probabilistic model results, multi-objective optimisation, and better tailoring to calibrate the model for specific applications such as drought event characterisation. Modellers and decision-makers may be constrained in their choice of calibration method, so it is important that they recognise the strengths and limitations of their chosen approach.

Uncertainty assessment and implications for data acquisition in support of integrated hydrologic models

NASA Astrophysics Data System (ADS)

Brunner, Philip; Doherty, J.; Simmons, Craig T.

2012-07-01

The data set used for calibration of regional numerical models which simulate groundwater flow and vadose zone processes is often dominated by head observations. It is to be expected therefore, that parameters describing vadose zone processes are poorly constrained. A number of studies on small spatial scales explored how additional data types used in calibration constrain vadose zone parameters or reduce predictive uncertainty. However, available studies focused on subsets of observation types and did not jointly account for different measurement accuracies or different hydrologic conditions. In this study, parameter identifiability and predictive uncertainty are quantified in simulation of a 1-D vadose zone soil system driven by infiltration, evaporation and transpiration. The worth of different types of observation data (employed individually, in combination, and with different measurement accuracies) is evaluated by using a linear methodology and a nonlinear Pareto-based methodology under different hydrological conditions. Our main conclusions are (1) Linear analysis provides valuable information on comparative parameter and predictive uncertainty reduction accrued through acquisition of different data types. Its use can be supplemented by nonlinear methods. (2) Measurements of water table elevation can support future water table predictions, even if such measurements inform the individual parameters of vadose zone models to only a small degree. (3) The benefits of including ET and soil moisture observations in the calibration data set are heavily dependent on depth to groundwater. (4) Measurements of groundwater levels, measurements of vadose ET or soil moisture poorly constrain regional groundwater system forcing functions.

Uncertainty analysis in 3D global models: Aerosol representation in MOZART-4

NASA Astrophysics Data System (ADS)

Gasore, J.; Prinn, R. G.

2012-12-01

The Probabilistic Collocation Method (PCM) has been proven to be an efficient general method of uncertainty analysis in atmospheric models (Tatang et al 1997, Cohen&Prinn 2011). However, its application has been mainly limited to urban- and regional-scale models and chemical source-sink models, because of the drastic increase in computational cost when the dimension of uncertain parameters increases. Moreover, the high-dimensional output of global models has to be reduced to allow a computationally reasonable number of polynomials to be generated. This dimensional reduction has been mainly achieved by grouping the model grids into a few regions based on prior knowledge and expectations; urban versus rural for instance. As the model output is used to estimate the coefficients of the polynomial chaos expansion (PCE), the arbitrariness in the regional aggregation can generate problems in estimating uncertainties. To address these issues in a complex model, we apply the probabilistic collocation method of uncertainty analysis to the aerosol representation in MOZART-4, which is a 3D global chemical transport model (Emmons et al., 2010). Thereafter, we deterministically delineate the model output surface into regions of homogeneous response using the method of Principal Component Analysis. This allows the quantification of the uncertainty associated with the dimensional reduction. Because only a bulk mass is calculated online in Mozart-4, a lognormal number distribution is assumed with a priori fixed scale and location parameters, to calculate the surface area for heterogeneous reactions involving tropospheric oxidants. We have applied the PCM to the six parameters of the lognormal number distributions of Black Carbon, Organic Carbon and Sulfate. We have carried out a Monte-Carlo sampling from the probability density functions of the six uncertain parameters, using the reduced PCE model. The global mean concentration of major tropospheric oxidants did not show a significant variation in response to the variation in input parameters. However, a substantial variation at regional and temporal scale has been found. Tatang M. A., Pan W., Prinn R G., McRae G. J., An efficient method for parametric uncertainty analysis of numerical geophysical models, J. Gephys. Res., 102, 21925-21932, 1997. Cohen, J.B., and R.G. Prinn, Development of a fast, urban chemistry metamodel for inclusion in global models,Atmos. Chem. Phys., 11, 7629-7656, doi:10.5194/acp-11-7629-2011, 2011. Emmons L. K., Walters S., Hess P. G., Lamarque J. -F., P_ster G. G., Fillmore D., Granier C., Guenther A., Kinnison D., Laepple T., Orlando J., Tie X., Tyndall G., Wiedinmyer C., Baughcum S. L., Kloster J. S., Description and evaluation of the Model for Ozone and Related chemical Tracers, version 4 (MOZART-4). Geosci. Model Dev., 3, 4367, 2010.

Treatment of uncertainties in atmospheric chemical systems: A combined modeling and experimental approach

NASA Astrophysics Data System (ADS)

Pun, Betty Kong-Ling

1998-12-01

Uncertainty is endemic in modeling. This thesis is a two- phase program to understand the uncertainties in urban air pollution model predictions and in field data used to validate them. Part I demonstrates how to improve atmospheric models by analyzing the uncertainties in these models and using the results to guide new experimentation endeavors. Part II presents an experiment designed to characterize atmospheric fluctuations, which have significant implications towards the model validation process. A systematic study was undertaken to investigate the effects of uncertainties in the SAPRC mechanism for gas- phase chemistry in polluted atmospheres. The uncertainties of more than 500 parameters were compiled, including reaction rate constants, product coefficients, organic composition, and initial conditions. Uncertainty propagation using the Deterministic Equivalent Modeling Method (DEMM) revealed that the uncertainties in ozone predictions can be up to 45% based on these parametric uncertainties. The key parameters found to dominate the uncertainties of the predictions include photolysis rates of NO2, O3, and formaldehyde; the rate constant for nitric acid formation; and initial amounts of NOx and VOC. Similar uncertainty analysis procedures applied to two other mechanisms used in regional air quality models led to the conclusion that in the presence of parametric uncertainties, the mechanisms cannot be discriminated. Research efforts should focus on reducing parametric uncertainties in photolysis rates, reaction rate constants, and source terms. A new tunable diode laser (TDL) infrared spectrometer was designed and constructed to measure multiple pollutants simultaneously in the same ambient air parcels. The sensitivities of the one hertz measurements were 2 ppb for ozone, 1 ppb for NO, and 0.5 ppb for NO2. Meteorological data were also collected for wind, temperature, and UV intensity. The field data showed clear correlations between ozone, NO, and NO2 in the one-second time scale. Fluctuations in pollutant concentrations were found to be extremely dependent on meteorological conditions. Deposition fluxes calculated using the Eddy Correlation technique were found to be small on concrete surfaces. These high time-resolution measurements were used to develop an understanding of the variability in atmospheric measurements, which would be useful in determining the acceptable discrepancy of model and observations. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Sensitivity analysis of a sediment dynamics model applied in a Mediterranean river basin: global change and management implications.

PubMed

Sánchez-Canales, M; López-Benito, A; Acuña, V; Ziv, G; Hamel, P; Chaplin-Kramer, R; Elorza, F J

2015-01-01

Climate change and land-use change are major factors influencing sediment dynamics. Models can be used to better understand sediment production and retention by the landscape, although their interpretation is limited by large uncertainties, including model parameter uncertainties. The uncertainties related to parameter selection may be significant and need to be quantified to improve model interpretation for watershed management. In this study, we performed a sensitivity analysis of the InVEST (Integrated Valuation of Environmental Services and Tradeoffs) sediment retention model in order to determine which model parameters had the greatest influence on model outputs, and therefore require special attention during calibration. The estimation of the sediment loads in this model is based on the Universal Soil Loss Equation (USLE). The sensitivity analysis was performed in the Llobregat basin (NE Iberian Peninsula) for exported and retained sediment, which support two different ecosystem service benefits (avoided reservoir sedimentation and improved water quality). Our analysis identified the model parameters related to the natural environment as the most influential for sediment export and retention. Accordingly, small changes in variables such as the magnitude and frequency of extreme rainfall events could cause major changes in sediment dynamics, demonstrating the sensitivity of these dynamics to climate change in Mediterranean basins. Parameters directly related to human activities and decisions (such as cover management factor, C) were also influential, especially for sediment exported. The importance of these human-related parameters in the sediment export process suggests that mitigation measures have the potential to at least partially ameliorate climate-change driven changes in sediment exportation. Copyright © 2014 Elsevier B.V. All rights reserved.

Reliability of a new biokinetic model of zirconium in internal dosimetry: part II, parameter sensitivity analysis.

PubMed

Li, Wei Bo; Greiter, Matthias; Oeh, Uwe; Hoeschen, Christoph

2011-12-01

The reliability of biokinetic models is essential for the assessment of internal doses and a radiation risk analysis for the public and occupational workers exposed to radionuclides. In the present study, a method for assessing the reliability of biokinetic models by means of uncertainty and sensitivity analysis was developed. In the first part of the paper, the parameter uncertainty was analyzed for two biokinetic models of zirconium (Zr); one was reported by the International Commission on Radiological Protection (ICRP), and one was developed at the Helmholtz Zentrum München-German Research Center for Environmental Health (HMGU). In the second part of the paper, the parameter uncertainties and distributions of the Zr biokinetic models evaluated in Part I are used as the model inputs for identifying the most influential parameters in the models. Furthermore, the most influential model parameter on the integral of the radioactivity of Zr over 50 y in source organs after ingestion was identified. The results of the systemic HMGU Zr model showed that over the first 10 d, the parameters of transfer rates between blood and other soft tissues have the largest influence on the content of Zr in the blood and the daily urinary excretion; however, after day 1,000, the transfer rate from bone to blood becomes dominant. For the retention in bone, the transfer rate from blood to bone surfaces has the most influence out to the endpoint of the simulation; the transfer rate from blood to the upper larger intestine contributes a lot in the later days; i.e., after day 300. The alimentary tract absorption factor (fA) influences mostly the integral of radioactivity of Zr in most source organs after ingestion.

Uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model at multiple flux tower sites

USGS Publications Warehouse

Chen, Mingshi; Senay, Gabriel B.; Singh, Ramesh K.; Verdin, James P.

2016-01-01

Evapotranspiration (ET) is an important component of the water cycle – ET from the land surface returns approximately 60% of the global precipitation back to the atmosphere. ET also plays an important role in energy transport among the biosphere, atmosphere, and hydrosphere. Current regional to global and daily to annual ET estimation relies mainly on surface energy balance (SEB) ET models or statistical and empirical methods driven by remote sensing data and various climatological databases. These models have uncertainties due to inevitable input errors, poorly defined parameters, and inadequate model structures. The eddy covariance measurements on water, energy, and carbon fluxes at the AmeriFlux tower sites provide an opportunity to assess the ET modeling uncertainties. In this study, we focused on uncertainty analysis of the Operational Simplified Surface Energy Balance (SSEBop) model for ET estimation at multiple AmeriFlux tower sites with diverse land cover characteristics and climatic conditions. The 8-day composite 1-km MODerate resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) was used as input land surface temperature for the SSEBop algorithms. The other input data were taken from the AmeriFlux database. Results of statistical analysis indicated that the SSEBop model performed well in estimating ET with an R2 of 0.86 between estimated ET and eddy covariance measurements at 42 AmeriFlux tower sites during 2001–2007. It was encouraging to see that the best performance was observed for croplands, where R2 was 0.92 with a root mean square error of 13 mm/month. The uncertainties or random errors from input variables and parameters of the SSEBop model led to monthly ET estimates with relative errors less than 20% across multiple flux tower sites distributed across different biomes. This uncertainty of the SSEBop model lies within the error range of other SEB models, suggesting systematic error or bias of the SSEBop model is within the normal range. This finding implies that the simplified parameterization of the SSEBop model did not significantly affect the accuracy of the ET estimate while increasing the ease of model setup for operational applications. The sensitivity analysis indicated that the SSEBop model is most sensitive to input variables, land surface temperature (LST) and reference ET (ETo); and parameters, differential temperature (dT), and maximum ET scalar (Kmax), particularly during the non-growing season and in dry areas. In summary, the uncertainty assessment verifies that the SSEBop model is a reliable and robust method for large-area ET estimation. The SSEBop model estimates can be further improved by reducing errors in two input variables (ETo and LST) and two key parameters (Kmax and dT).

Impact of parametric uncertainty on estimation of the energy deposition into an irradiated brain tumor

NASA Astrophysics Data System (ADS)

Taverniers, Søren; Tartakovsky, Daniel M.

2017-11-01

Predictions of the total energy deposited into a brain tumor through X-ray irradiation are notoriously error-prone. We investigate how this predictive uncertainty is affected by uncertainty in both the location of the region occupied by a dose-enhancing iodinated contrast agent and the agent's concentration. This is done within the probabilistic framework in which these uncertain parameters are modeled as random variables. We employ the stochastic collocation (SC) method to estimate statistical moments of the deposited energy in terms of statistical moments of the random inputs, and the global sensitivity analysis (GSA) to quantify the relative importance of uncertainty in these parameters on the overall predictive uncertainty. A nonlinear radiation-diffusion equation dramatically magnifies the coefficient of variation of the uncertain parameters, yielding a large coefficient of variation for the predicted energy deposition. This demonstrates that accurate prediction of the energy deposition requires a proper treatment of even small parametric uncertainty. Our analysis also reveals that SC outperforms standard Monte Carlo, but its relative efficiency decreases as the number of uncertain parameters increases from one to three. A robust GSA ameliorates this problem by reducing this number.