Not simply more of the same: distinguishing between patient heterogeneity and parameter uncertainty.

PubMed

Vemer, Pepijn; Goossens, Lucas M A; Rutten-van Mölken, Maureen P M H

2014-11-01

In cost-effectiveness (CE) Markov models, heterogeneity in the patient population is not automatically taken into account. We aimed to compare methods of dealing with heterogeneity on estimates of CE, using a case study in chronic obstructive pulmonary disease (COPD). We first present a probabilistic sensitivity analysis (PSA) in which we sampled only from distributions representing parameter uncertainty. This ignores any heterogeneity. Next, we explored heterogeneity by presenting results for subgroups, using a method that samples parameter uncertainty simultaneously with heterogeneity in a single-loop PSA. Finally, we distinguished parameter uncertainty from heterogeneity in a double-loop PSA by performing a nested simulation within each PSA iteration. Point estimates and uncertainty differed substantially between methods. The incremental CE ratio (ICER) ranged from € 4900 to € 13,800. The single-loop PSA led to a substantially different shape of the CE plane and an overestimation of the uncertainty compared with the other 3 methods. The CE plane for the double-loop PSA showed substantially less uncertainty and a stronger negative correlation between the difference in costs and the difference in effects compared with the other methods. This came at the cost of higher calculation times. Not accounting for heterogeneity, subgroup analysis and the double-loop PSA can be viable options, depending on the decision makers' information needs. The single-loop PSA should not be used in CE research. It disregards the fundamental differences between heterogeneity and sampling uncertainty and overestimates uncertainty as a result. © The Author(s) 2014.

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.

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.

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.

Trajectory Dispersed Vehicle Process for Space Launch System

NASA Technical Reports Server (NTRS)

Statham, Tamara; Thompson, Seth

2017-01-01

The Space Launch System (SLS) vehicle is part of NASA's deep space exploration plans that includes manned missions to Mars. Manufacturing uncertainties in design parameters are key considerations throughout SLS development as they have significant effects on focus parameters such as lift-off-thrust-to-weight, vehicle payload, maximum dynamic pressure, and compression loads. This presentation discusses how the SLS program captures these uncertainties by utilizing a 3 degree of freedom (DOF) process called Trajectory Dispersed (TD) analysis. This analysis biases nominal trajectories to identify extremes in the design parameters for various potential SLS configurations and missions. This process utilizes a Design of Experiments (DOE) and response surface methodologies (RSM) to statistically sample uncertainties, and develop resulting vehicles using a Maximum Likelihood Estimate (MLE) process for targeting uncertainties bias. These vehicles represent various missions and configurations which are used as key inputs into a variety of analyses in the SLS design process, including 6 DOF dispersions, separation clearances, and engine out failure studies.

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.

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.

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.

A stochastic approach to uncertainty quantification in residual moveout analysis

NASA Astrophysics Data System (ADS)

Johng-Ay, T.; Landa, E.; Dossou-Gbété, S.; Bordes, L.

2015-06-01

Oil and gas exploration and production relies usually on the interpretation of a single seismic image, which is obtained from observed data. However, the statistical nature of seismic data and the various approximations and assumptions are sources of uncertainties which may corrupt the evaluation of parameters. The quantification of these uncertainties is a major issue which supposes to help in decisions that have important social and commercial implications. The residual moveout analysis, which is an important step in seismic data processing is usually performed by a deterministic approach. In this paper we discuss a Bayesian approach to the uncertainty analysis.

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

Accounting for uncertain fault geometry in earthquake source inversions - I: theory and simplified application

NASA Astrophysics Data System (ADS)

Ragon, Théa; Sladen, Anthony; Simons, Mark

2018-05-01

The ill-posed nature of earthquake source estimation derives from several factors including the quality and quantity of available observations and the fidelity of our forward theory. Observational errors are usually accounted for in the inversion process. Epistemic errors, which stem from our simplified description of the forward problem, are rarely dealt with despite their potential to bias the estimate of a source model. In this study, we explore the impact of uncertainties related to the choice of a fault geometry in source inversion problems. The geometry of a fault structure is generally reduced to a set of parameters, such as position, strike and dip, for one or a few planar fault segments. While some of these parameters can be solved for, more often they are fixed to an uncertain value. We propose a practical framework to address this limitation by following a previously implemented method exploring the impact of uncertainties on the elastic properties of our models. We develop a sensitivity analysis to small perturbations of fault dip and position. The uncertainties in fault geometry are included in the inverse problem under the formulation of the misfit covariance matrix that combines both prediction and observation uncertainties. We validate this approach with the simplified case of a fault that extends infinitely along strike, using both Bayesian and optimization formulations of a static inversion. If epistemic errors are ignored, predictions are overconfident in the data and source parameters are not reliably estimated. In contrast, inclusion of uncertainties in fault geometry allows us to infer a robust posterior source model. Epistemic uncertainties can be many orders of magnitude larger than observational errors for great earthquakes (Mw > 8). Not accounting for uncertainties in fault geometry may partly explain observed shallow slip deficits for continental earthquakes. Similarly, ignoring the impact of epistemic errors can also bias estimates of near surface slip and predictions of tsunamis induced by megathrust earthquakes. (Mw > 8)

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.

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.

Uncertainty in aerosol hygroscopicity resulting from semi-volatile organic compounds

NASA Astrophysics Data System (ADS)

Goulden, Olivia; Crooks, Matthew; Connolly, Paul

2018-01-01

We present a novel method of exploring the effect of uncertainties in aerosol properties on cloud droplet number using existing cloud droplet activation parameterisations. Aerosol properties of a single involatile particle mode are randomly sampled within an uncertainty range and resulting maximum supersaturations and critical diameters calculated using the cloud droplet activation scheme. Hygroscopicity parameters are subsequently derived and the values of the mean and uncertainty are found to be comparable to experimental observations. A recently proposed cloud droplet activation scheme that includes the effects of co-condensation of semi-volatile organic compounds (SVOCs) onto a single lognormal mode of involatile particles is also considered. In addition to the uncertainties associated with the involatile particles, concentrations, volatility distributions and chemical composition of the SVOCs are randomly sampled and hygroscopicity parameters are derived using the cloud droplet activation scheme. The inclusion of SVOCs is found to have a significant effect on the hygroscopicity and contributes a large uncertainty. For non-volatile particles that are effective cloud condensation nuclei, the co-condensation of SVOCs reduces their actual hygroscopicity by approximately 25 %. A new concept of an effective hygroscopicity parameter is introduced that can computationally efficiently simulate the effect of SVOCs on cloud droplet number concentration without direct modelling of the organic compounds. These effective hygroscopicities can be as much as a factor of 2 higher than those of the non-volatile particles onto which the volatile organic compounds condense.

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.

Uncertainty relation based on unbiased parameter estimations

NASA Astrophysics Data System (ADS)

Sun, Liang-Liang; Song, Yong-Shun; Qiao, Cong-Feng; Yu, Sixia; Chen, Zeng-Bing

2017-02-01

Heisenberg's uncertainty relation has been extensively studied in spirit of its well-known original form, in which the inaccuracy measures used exhibit some controversial properties and don't conform with quantum metrology, where the measurement precision is well defined in terms of estimation theory. In this paper, we treat the joint measurement of incompatible observables as a parameter estimation problem, i.e., estimating the parameters characterizing the statistics of the incompatible observables. Our crucial observation is that, in a sequential measurement scenario, the bias induced by the first unbiased measurement in the subsequent measurement can be eradicated by the information acquired, allowing one to extract unbiased information of the second measurement of an incompatible observable. In terms of Fisher information we propose a kind of information comparison measure and explore various types of trade-offs between the information gains and measurement precisions, which interpret the uncertainty relation as surplus variance trade-off over individual perfect measurements instead of a constraint on extracting complete information of incompatible observables.

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.

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

An Iterative Local Updating Ensemble Smoother for Estimation and Uncertainty Assessment of Hydrologic Model Parameters With Multimodal Distributions

NASA Astrophysics Data System (ADS)

Zhang, Jiangjiang; Lin, Guang; Li, Weixuan; Wu, Laosheng; Zeng, Lingzao

2018-03-01

Ensemble smoother (ES) has been widely used in inverse modeling of hydrologic systems. However, for problems where the distribution of model parameters is multimodal, using ES directly would be problematic. One popular solution is to use a clustering algorithm to identify each mode and update the clusters with ES separately. However, this strategy may not be very efficient when the dimension of parameter space is high or the number of modes is large. Alternatively, we propose in this paper a very simple and efficient algorithm, i.e., the iterative local updating ensemble smoother (ILUES), to explore multimodal distributions of model parameters in nonlinear hydrologic systems. The ILUES algorithm works by updating local ensembles of each sample with ES to explore possible multimodal distributions. To achieve satisfactory data matches in nonlinear problems, we adopt an iterative form of ES to assimilate the measurements multiple times. Numerical cases involving nonlinearity and multimodality are tested to illustrate the performance of the proposed method. It is shown that overall the ILUES algorithm can well quantify the parametric uncertainties of complex hydrologic models, no matter whether the multimodal distribution exists.

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.

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.

Impact of influent data frequency and model structure on the quality of WWTP model calibration and uncertainty.

PubMed

Cierkens, Katrijn; Plano, Salvatore; Benedetti, Lorenzo; Weijers, Stefan; de Jonge, Jarno; Nopens, Ingmar

2012-01-01

Application of activated sludge models (ASMs) to full-scale wastewater treatment plants (WWTPs) is still hampered by the problem of model calibration of these over-parameterised models. This either requires expert knowledge or global methods that explore a large parameter space. However, a better balance in structure between the submodels (ASM, hydraulic, aeration, etc.) and improved quality of influent data result in much smaller calibration efforts. In this contribution, a methodology is proposed that links data frequency and model structure to calibration quality and output uncertainty. It is composed of defining the model structure, the input data, an automated calibration, confidence interval computation and uncertainty propagation to the model output. Apart from the last step, the methodology is applied to an existing WWTP using three models differing only in the aeration submodel. A sensitivity analysis was performed on all models, allowing the ranking of the most important parameters to select in the subsequent calibration step. The aeration submodel proved very important to get good NH(4) predictions. Finally, the impact of data frequency was explored. Lowering the frequency resulted in larger deviations of parameter estimates from their default values and larger confidence intervals. Autocorrelation due to high frequency calibration data has an opposite effect on the confidence intervals. The proposed methodology opens doors to facilitate and improve calibration efforts and to design measurement campaigns.

Impact of signal scattering and parametric uncertainties on receiver operating characteristics

NASA Astrophysics Data System (ADS)

Wilson, D. Keith; Breton, Daniel J.; Hart, Carl R.; Pettit, Chris L.

2017-05-01

The receiver operating characteristic (ROC curve), which is a plot of the probability of detection as a function of the probability of false alarm, plays a key role in the classical analysis of detector performance. However, meaningful characterization of the ROC curve is challenging when practically important complications such as variations in source emissions, environmental impacts on the signal propagation, uncertainties in the sensor response, and multiple sources of interference are considered. In this paper, a relatively simple but realistic model for scattered signals is employed to explore how parametric uncertainties impact the ROC curve. In particular, we show that parametric uncertainties in the mean signal and noise power substantially raise the tails of the distributions; since receiver operation with a very low probability of false alarm and a high probability of detection is normally desired, these tails lead to severely degraded performance. Because full a priori knowledge of such parametric uncertainties is rarely available in practice, analyses must typically be based on a finite sample of environmental states, which only partially characterize the range of parameter variations. We show how this effect can lead to misleading assessments of system performance. For the cases considered, approximately 64 or more statistically independent samples of the uncertain parameters are needed to accurately predict the probabilities of detection and false alarm. A connection is also described between selection of suitable distributions for the uncertain parameters, and Bayesian adaptive methods for inferring the parameters.

Uncertainty analysis and robust trajectory linearization control of a flexible air-breathing hypersonic vehicle

NASA Astrophysics Data System (ADS)

Pu, Zhiqiang; Tan, Xiangmin; Fan, Guoliang; Yi, Jianqiang

2014-08-01

Flexible air-breathing hypersonic vehicles feature significant uncertainties which pose huge challenges to robust controller designs. In this paper, four major categories of uncertainties are analyzed, that is, uncertainties associated with flexible effects, aerodynamic parameter variations, external environmental disturbances, and control-oriented modeling errors. A uniform nonlinear uncertainty model is explored for the first three uncertainties which lumps all uncertainties together and consequently is beneficial for controller synthesis. The fourth uncertainty is additionally considered in stability analysis. Based on these analyses, the starting point of the control design is to decompose the vehicle dynamics into five functional subsystems. Then a robust trajectory linearization control (TLC) scheme consisting of five robust subsystem controllers is proposed. In each subsystem controller, TLC is combined with the extended state observer (ESO) technique for uncertainty compensation. The stability of the overall closed-loop system with the four aforementioned uncertainties and additional singular perturbations is analyzed. Particularly, the stability of nonlinear ESO is also discussed from a Liénard system perspective. At last, simulations demonstrate the great control performance and the uncertainty rejection ability of the robust scheme.

Equation of state for dense nucleonic matter from metamodeling. I. Foundational aspects

NASA Astrophysics Data System (ADS)

Margueron, Jérôme; Hoffmann Casali, Rudiney; Gulminelli, Francesca

2018-02-01

Metamodeling for the nucleonic equation of state (EOS), inspired from a Taylor expansion around the saturation density of symmetric nuclear matter, is proposed and parameterized in terms of the empirical parameters. The present knowledge of nuclear empirical parameters is first reviewed in order to estimate their average values and associated uncertainties, and thus defining the parameter space of the metamodeling. They are divided into isoscalar and isovector types, and ordered according to their power in the density expansion. The goodness of the metamodeling is analyzed against the predictions of the original models. In addition, since no correlation among the empirical parameters is assumed a priori, all arbitrary density dependences can be explored, which might not be accessible in existing functionals. Spurious correlations due to the assumed functional form are also removed. This meta-EOS allows direct relations between the uncertainties on the empirical parameters and the density dependence of the nuclear equation of state and its derivatives, and the mapping between the two can be done with standard Bayesian techniques. A sensitivity analysis shows that the more influential empirical parameters are the isovector parameters Lsym and Ksym, and that laboratory constraints at supersaturation densities are essential to reduce the present uncertainties. The present metamodeling for the EOS for nuclear matter is proposed for further applications in neutron stars and supernova matter.

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 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.

The relationship of parental overprotection, perceived child vulnerability, and parenting stress to uncertainty in youth with chronic illness.

PubMed

Mullins, Larry L; Wolfe-Christensen, Cortney; Pai, Ahna L Hoff; Carpentier, Melissa Y; Gillaspy, Stephen; Cheek, Jeff; Page, Melanie

2007-09-01

To examine the relationship of parent-reported overprotection (OP), perceived child vulnerability (PCV), and parenting stress (PS) to youth-reported illness uncertainty, and to explore potential developmental differences. Eighty-two children and 82 adolescents (n = 164) diagnosed with Type 1 diabetes mellitus (DM1) or asthma, completed a measure of illness uncertainty, while their parents completed measures of OP, PCV, and PS. After controlling for demographic and illness parameters, both PCV and PS significantly predicted youth illness uncertainty in the combined sample. Within the child group, only PS significantly predicted illness uncertainty, whereas only PCV significantly predicted uncertainty for adolescents. Specific parenting variables are associated with youth-reported illness uncertainty; however, their relationship varies according to developmental level. Although OP has been identified as a predictor of child psychological outcomes in other studies, it does not appear to be associated with illness uncertainty in youth with DM1 or asthma.

A Simple Model Framework to Explore the Deeply Uncertain, Local Sea Level Response to Climate Change. A Case Study on New Orleans, Louisiana

NASA Astrophysics Data System (ADS)

Bakker, Alexander; Louchard, Domitille; Keller, Klaus

2016-04-01

Sea-level rise threatens many coastal areas around the world. The integrated assessment of potential adaptation and mitigation strategies requires a sound understanding of the upper tails and the major drivers of the uncertainties. Global warming causes sea-level to rise, primarily due to thermal expansion of the oceans and mass loss of the major ice sheets, smaller ice caps and glaciers. These components show distinctly different responses to temperature changes with respect to response time, threshold behavior, and local fingerprints. Projections of these different components are deeply uncertain. Projected uncertainty ranges strongly depend on (necessary) pragmatic choices and assumptions; e.g. on the applied climate scenarios, which processes to include and how to parameterize them, and on error structure of the observations. Competing assumptions are very hard to objectively weigh. Hence, uncertainties of sea-level response are hard to grasp in a single distribution function. The deep uncertainty can be better understood by making clear the key assumptions. Here we demonstrate this approach using a relatively simple model framework. We present a mechanistically motivated, but simple model framework that is intended to efficiently explore the deeply uncertain sea-level response to anthropogenic climate change. The model consists of 'building blocks' that represent the major components of sea-level response and its uncertainties, including threshold behavior. The framework's simplicity enables the simulation of large ensembles allowing for an efficient exploration of parameter uncertainty and for the simulation of multiple combined adaptation and mitigation strategies. The model framework can skilfully reproduce earlier major sea level assessments, but due to the modular setup it can also be easily utilized to explore high-end scenarios and the effect of competing assumptions and parameterizations.

Fragmentation uncertainties in hadronic observables for top-quark mass measurements

NASA Astrophysics Data System (ADS)

Corcella, Gennaro; Franceschini, Roberto; Kim, Doojin

2018-04-01

We study the Monte Carlo uncertainties due to modeling of hadronization and showering in the extraction of the top-quark mass from observables that use exclusive hadronic final states in top decays, such as t →anything + J / ψ or t →anything + (B →charged tracks), where B is a B-hadron. To this end, we investigate the sensitivity of the top-quark mass, determined by means of a few observables already proposed in the literature as well as some new proposals, to the relevant parameters of event generators, such as HERWIG 6 and PYTHIA 8. We find that constraining those parameters at O (1%- 10%) is required to avoid a Monte Carlo uncertainty on mt greater than 500 MeV. For the sake of achieving the needed accuracy on such parameters, we examine the sensitivity of the top-quark mass measured from spectral features, such as peaks, endpoints and distributions of EB, mBℓ, and some mT2-like variables. We find that restricting oneself to regions sufficiently close to the endpoints enables one to substantially decrease the dependence on the Monte Carlo parameters, but at the price of inflating significantly the statistical uncertainties. To ameliorate this situation we study how well the data on top-quark production and decay at the LHC can be utilized to constrain the showering and hadronization variables. We find that a global exploration of several calibration observables, sensitive to the Monte Carlo parameters but very mildly to mt, can offer useful constraints on the parameters, as long as such quantities are measured with a 1% precision.

Monte Carlo exploration of Mikheyev-Smirnov-Wolfenstein solutions to the solar neutrino problem

NASA Technical Reports Server (NTRS)

Shi, X.; Schramm, D. N.; Bahcall, J. N.

1992-01-01

The paper explores the impact of astrophysical uncertainties on the Mikheyev-Smirnov-Wolfenstein (MSW) solution by calculating the allowed MSW solutions for 1000 different solar models with a Monte Carlo selection of solar model input parameters, assuming a full three-family MSW mixing. Applications are made to the chlorine, gallium, Kamiokande, and Borexino experiments. The initial GALLEX result limits the mixing parameters to the upper diagonal and the vertical regions of the MSW triangle. The expected event rates in the Borexino experiment are also calculated, assuming the MSW solutions implied by GALLEX.

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.

A Bootstrap-Based Probabilistic Optimization Method to Explore and Efficiently Converge in Solution Spaces of Earthquake Source Parameter Estimation Problems: Application to Volcanic and Tectonic Earthquakes

NASA Astrophysics Data System (ADS)

Dahm, T.; Heimann, S.; Isken, M.; Vasyura-Bathke, H.; Kühn, D.; Sudhaus, H.; Kriegerowski, M.; Daout, S.; Steinberg, A.; Cesca, S.

2017-12-01

Seismic source and moment tensor waveform inversion is often ill-posed or non-unique if station coverage is poor or signals are weak. Therefore, the interpretation of moment tensors can become difficult, if not the full model space is explored, including all its trade-offs and uncertainties. This is especially true for non-double couple components of weak or shallow earthquakes, as for instance found in volcanic, geothermal or mining environments.We developed a bootstrap-based probabilistic optimization scheme (Grond), which is based on pre-calculated Greens function full waveform databases (e.g. fomosto tool, doi.org/10.5880/GFZ.2.1.2017.001). Grond is able to efficiently explore the full model space, the trade-offs and the uncertainties of source parameters. The program is highly flexible with respect to the adaption to specific problems, the design of objective functions, and the diversity of empirical datasets.It uses an integrated, robust waveform data processing based on a newly developed Python toolbox for seismology (Pyrocko, see Heimann et al., 2017, http://doi.org/10.5880/GFZ.2.1.2017.001), and allows for visual inspection of many aspects of the optimization problem. Grond has been applied to the CMT moment tensor inversion using W-phases, to nuclear explosions in Korea, to meteorite atmospheric explosions, to volcano-tectonic events during caldera collapse and to intra-plate volcanic and tectonic crustal events.Grond can be used to optimize simultaneously seismological waveforms, amplitude spectra and static displacements of geodetic data as InSAR and GPS (e.g. KITE, Isken et al., 2017, http://doi.org/10.5880/GFZ.2.1.2017.002). We present examples of Grond optimizations to demonstrate the advantage of a full exploration of source parameter uncertainties for interpretation.

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.

Optimal test selection for prediction uncertainty reduction

DOE PAGES

Mullins, Joshua; Mahadevan, Sankaran; Urbina, Angel

2016-12-02

Economic factors and experimental limitations often lead to sparse and/or imprecise data used for the calibration and validation of computational models. This paper addresses resource allocation for calibration and validation experiments, in order to maximize their effectiveness within given resource constraints. When observation data are used for model calibration, the quality of the inferred parameter descriptions is directly affected by the quality and quantity of the data. This paper characterizes parameter uncertainty within a probabilistic framework, which enables the uncertainty to be systematically reduced with additional data. The validation assessment is also uncertain in the presence of sparse and imprecisemore » data; therefore, this paper proposes an approach for quantifying the resulting validation uncertainty. Since calibration and validation uncertainty affect the prediction of interest, the proposed framework explores the decision of cost versus importance of data in terms of the impact on the prediction uncertainty. Often, calibration and validation tests may be performed for different input scenarios, and this paper shows how the calibration and validation results from different conditions may be integrated into the prediction. Then, a constrained discrete optimization formulation that selects the number of tests of each type (calibration or validation at given input conditions) is proposed. Furthermore, the proposed test selection methodology is demonstrated on a microelectromechanical system (MEMS) example.« less

Uncertainty analyses of CO2 plume expansion subsequent to wellbore CO2 leakage into aquifers

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

Hou, Zhangshuan; Bacon, Diana H.; Engel, David W.

2014-08-01

In this study, we apply an uncertainty quantification (UQ) framework to CO2 sequestration problems. In one scenario, we look at the risk of wellbore leakage of CO2 into a shallow unconfined aquifer in an urban area; in another scenario, we study the effects of reservoir heterogeneity on CO2 migration. We combine various sampling approaches (quasi-Monte Carlo, probabilistic collocation, and adaptive sampling) in order to reduce the number of forward calculations while trying to fully explore the input parameter space and quantify the input uncertainty. The CO2 migration is simulated using the PNNL-developed simulator STOMP-CO2e (the water-salt-CO2 module). For computationally demandingmore » simulations with 3D heterogeneity fields, we combined the framework with a scalable version module, eSTOMP, as the forward modeling simulator. We built response curves and response surfaces of model outputs with respect to input parameters, to look at the individual and combined effects, and identify and rank the significance of the input parameters.« less

A Framework to Determine New System Requirements Under Design Parameter and Demand Uncertainties

DTIC Science & Technology

2015-04-30

relegates quantitative complexities of decision-making to the method and designates trade-space exploration to the practitioner. We demonstrate the...quantitative complexities of decision-making to the method and designates trade-space exploration to the practitioner. We demonstrate the approach...play a critical role in determining new system requirements. Scope and Method of Approach The early stages of the design process have substantial

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.

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.

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.

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.

Characterizing Drought Events from a Hydrological Model Ensemble

NASA Astrophysics Data System (ADS)

Smith, Katie; Parry, Simon; Prudhomme, Christel; Hannaford, Jamie; Tanguy, Maliko; Barker, Lucy; Svensson, Cecilia

2017-04-01

Hydrological droughts are a slow onset natural hazard that can affect large areas. Within the United Kingdom there have been eight major drought events over the last 50 years, with several events acting at the continental scale, and covering the entire nation. Many of these events have lasted several years and had significant impacts on agriculture, the environment and the economy. Generally in the UK, due to a northwest-southeast gradient in rainfall and relief, as well as varying underlying geology, droughts tend to be most severe in the southeast, which can threaten water supplies to the capital in London. With the impacts of climate change likely to increase the severity and duration of drought events worldwide, it is crucial that we gain an understanding of the characteristics of some of the longer and more extreme droughts of the 19th and 20th centuries, so we may utilize this information in planning for the future. Hydrological models are essential both for reconstructing such events that predate streamflow records, and for use in drought forecasting. However, whilst the uncertainties involved in modelling hydrological extremes on the flooding end of the flow regime have been studied in depth over the past few decades, the uncertainties in simulating droughts and low flow events have not yet received such rigorous academic attention. The "Cascade of Uncertainty" approach has been applied to explore uncertainty and coherence across simulations of notable drought events from the past 50 years using the airGR family of daily lumped catchment models. Parameter uncertainty has been addressed using a Latin Hypercube sampled experiment of 500,000 parameter sets per model (GR4J, GR5J and GR6J), over more than 200 catchments across the UK. The best performing model parameterisations, determined using a multi-objective function approach, have then been taken forward for use in the assessment of the impact of model parameters and model structure on drought event detection and characterization. This ensemble approach allows for uncertainty estimates and confidence intervals to be explored in simulations of drought event characteristics, such as duration and severity, which would not otherwise be available from a deterministic approach. The acquired understanding of uncertainty in drought events may then be applied to historic drought reconstructions, supplying evidence which could prove vital in decision making scenarios.

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.

Biophysics of NASA radiation quality factors.

PubMed

Cucinotta, Francis A

2015-09-01

NASA has implemented new radiation quality factors (QFs) for projecting cancer risks from space radiation exposures to astronauts. The NASA QFs are based on particle track structure concepts with parameters derived from available radiobiology data, and NASA introduces distinct QFs for solid cancer and leukaemia risk estimates. The NASA model was reviewed by the US National Research Council and approved for use by NASA for risk assessment for International Space Station missions and trade studies of future exploration missions to Mars and other destinations. A key feature of the NASA QFs is to represent the uncertainty in the QF assessments and evaluate the importance of the QF uncertainty to overall uncertainties in cancer risk projections. In this article, the biophysical basis for the probability distribution functions representing QF uncertainties was reviewed, and approaches needed to reduce uncertainties were discussed. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Dynamics of entanglement and uncertainty relation in coupled harmonic oscillator system: exact results

NASA Astrophysics Data System (ADS)

Park, DaeKil

2018-06-01

The dynamics of entanglement and uncertainty relation is explored by solving the time-dependent Schrödinger equation for coupled harmonic oscillator system analytically when the angular frequencies and coupling constant are arbitrarily time dependent. We derive the spectral and Schmidt decompositions for vacuum solution. Using the decompositions, we derive the analytical expressions for von Neumann and Rényi entropies. Making use of Wigner distribution function defined in phase space, we derive the time dependence of position-momentum uncertainty relations. To show the dynamics of entanglement and uncertainty relation graphically, we introduce two toy models and one realistic quenched model. While the dynamics can be conjectured by simple consideration in the toy models, the dynamics in the realistic quenched model is somewhat different from that in the toy models. In particular, the dynamics of entanglement exhibits similar pattern to dynamics of uncertainty parameter in the realistic quenched model.

Amazon collapse in the next century: exploring the sensitivity to climate and model formulation uncertainties

NASA Astrophysics Data System (ADS)

Booth, B.; Collins, M.; Harris, G.; Chris, H.; Jones, C.

2007-12-01

A number of recent studies have highlighted the risk of abrupt dieback of the Amazon Rain Forest as the result of climate changes over the next century. The recent 2005 Amazon drought brought wider acceptance of the idea that that climate drivers will play a significant role in future rain forest stability, yet that stability is still subject to considerable degree of uncertainty. We present a study which seeks to explore some of the underlying uncertainties both in the climate drivers of dieback and in the terrestrial land surface formulation used in GCMs. We adopt a perturbed physics approach which forms part of a wider project which is covered in an accompanying abstract submitted to the multi-model ensembles session. We first couple the same interactive land surface model to a number of different versions of the Hadley Centre atmosphere-ocean model that exhibit a wide range of different physical climate responses in the future. The rainforest extent is shown to collapse in all model cases but the timing of the collapse is dependent on the magnitude of the climate drivers. In the second part, we explore uncertainties in the terrestrial land surface model using the perturbed physics ensemble approach, perturbing uncertain parameters which have an important role in the vegetation and soil response. Contrasting the two approaches enables a greater understanding of the relative importance of climatic and land surface model uncertainties in Amazon dieback.

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.

Quantifying model-structure- and parameter-driven uncertainties in spring wheat phenology prediction with Bayesian analysis

DOE PAGES

Alderman, Phillip D.; Stanfill, Bryan

2016-10-06

Recent international efforts have brought renewed emphasis on the comparison of different agricultural systems models. Thus far, analysis of model-ensemble simulated results has not clearly differentiated between ensemble prediction uncertainties due to model structural differences per se and those due to parameter value uncertainties. Additionally, despite increasing use of Bayesian parameter estimation approaches with field-scale crop models, inadequate attention has been given to the full posterior distributions for estimated parameters. The objectives of this study were to quantify the impact of parameter value uncertainty on prediction uncertainty for modeling spring wheat phenology using Bayesian analysis and to assess the relativemore » contributions of model-structure-driven and parameter-value-driven uncertainty to overall prediction uncertainty. This study used a random walk Metropolis algorithm to estimate parameters for 30 spring wheat genotypes using nine phenology models based on multi-location trial data for days to heading and days to maturity. Across all cases, parameter-driven uncertainty accounted for between 19 and 52% of predictive uncertainty, while model-structure-driven uncertainty accounted for between 12 and 64%. Here, this study demonstrated the importance of quantifying both model-structure- and parameter-value-driven uncertainty when assessing overall prediction uncertainty in modeling spring wheat phenology. More generally, Bayesian parameter estimation provided a useful framework for quantifying and analyzing sources of prediction uncertainty.« less

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 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.

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.

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.

Impact of Hydrogeological Uncertainty on Estimation of Environmental Risks Posed by Hydrocarbon Transportation Networks

NASA Astrophysics Data System (ADS)

Ciriello, V.; Lauriola, I.; Bonvicini, S.; Cozzani, V.; Di Federico, V.; Tartakovsky, Daniel M.

2017-11-01

Ubiquitous hydrogeological uncertainty undermines the veracity of quantitative predictions of soil and groundwater contamination due to accidental hydrocarbon spills from onshore pipelines. Such predictions, therefore, must be accompanied by quantification of predictive uncertainty, especially when they are used for environmental risk assessment. We quantify the impact of parametric uncertainty on quantitative forecasting of temporal evolution of two key risk indices, volumes of unsaturated and saturated soil contaminated by a surface spill of light nonaqueous-phase liquids. This is accomplished by treating the relevant uncertain parameters as random variables and deploying two alternative probabilistic models to estimate their effect on predictive uncertainty. A physics-based model is solved with a stochastic collocation method and is supplemented by a global sensitivity analysis. A second model represents the quantities of interest as polynomials of random inputs and has a virtually negligible computational cost, which enables one to explore any number of risk-related contamination scenarios. For a typical oil-spill scenario, our method can be used to identify key flow and transport parameters affecting the risk indices, to elucidate texture-dependent behavior of different soils, and to evaluate, with a degree of confidence specified by the decision-maker, the extent of contamination and the correspondent remediation costs.

Statistical emulation of landslide-induced tsunamis at the Rockall Bank, NE Atlantic

PubMed Central

Guillas, S.; Georgiopoulou, A.; Dias, F.

2017-01-01

Statistical methods constitute a useful approach to understand and quantify the uncertainty that governs complex tsunami mechanisms. Numerical experiments may often have a high computational cost. This forms a limiting factor for performing uncertainty and sensitivity analyses, where numerous simulations are required. Statistical emulators, as surrogates of these simulators, can provide predictions of the physical process in a much faster and computationally inexpensive way. They can form a prominent solution to explore thousands of scenarios that would be otherwise numerically expensive and difficult to achieve. In this work, we build a statistical emulator of the deterministic codes used to simulate submarine sliding and tsunami generation at the Rockall Bank, NE Atlantic Ocean, in two stages. First we calibrate, against observations of the landslide deposits, the parameters used in the landslide simulations. This calibration is performed under a Bayesian framework using Gaussian Process (GP) emulators to approximate the landslide model, and the discrepancy function between model and observations. Distributions of the calibrated input parameters are obtained as a result of the calibration. In a second step, a GP emulator is built to mimic the coupled landslide-tsunami numerical process. The emulator propagates the uncertainties in the distributions of the calibrated input parameters inferred from the first step to the outputs. As a result, a quantification of the uncertainty of the maximum free surface elevation at specified locations is obtained. PMID:28484339

Statistical emulation of landslide-induced tsunamis at the Rockall Bank, NE Atlantic.

PubMed

Salmanidou, D M; Guillas, S; Georgiopoulou, A; Dias, F

2017-04-01

Statistical methods constitute a useful approach to understand and quantify the uncertainty that governs complex tsunami mechanisms. Numerical experiments may often have a high computational cost. This forms a limiting factor for performing uncertainty and sensitivity analyses, where numerous simulations are required. Statistical emulators, as surrogates of these simulators, can provide predictions of the physical process in a much faster and computationally inexpensive way. They can form a prominent solution to explore thousands of scenarios that would be otherwise numerically expensive and difficult to achieve. In this work, we build a statistical emulator of the deterministic codes used to simulate submarine sliding and tsunami generation at the Rockall Bank, NE Atlantic Ocean, in two stages. First we calibrate, against observations of the landslide deposits, the parameters used in the landslide simulations. This calibration is performed under a Bayesian framework using Gaussian Process (GP) emulators to approximate the landslide model, and the discrepancy function between model and observations. Distributions of the calibrated input parameters are obtained as a result of the calibration. In a second step, a GP emulator is built to mimic the coupled landslide-tsunami numerical process. The emulator propagates the uncertainties in the distributions of the calibrated input parameters inferred from the first step to the outputs. As a result, a quantification of the uncertainty of the maximum free surface elevation at specified locations is obtained.

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.

Uncertainty analysis of scintillometers methods in measuring sensible heat fluxes of forest ecosystem

NASA Astrophysics Data System (ADS)

Zheng, N.

2017-12-01

Sensible heat flux (H) is one of the driving factors of surface turbulent motion and energy exchange. Therefore, it is particularly important to measure sensible heat flux accurately at the regional scale. However, due to the heterogeneity of the underlying surface, hydrothermal regime, and different weather conditions, it is difficult to estimate the represented flux at the kilometer scale. The scintillometer have been developed into an effective and universal equipment for deriving heat flux at the regional-scale which based on the turbulence effect of light in the atmosphere since the 1980s. The parameter directly obtained by the scintillometer is the structure parameter of the refractive index of air based on the changes of light intensity fluctuation. Combine with parameters such as temperature structure parameter, zero-plane displacement, surface roughness, wind velocity, air temperature and the other meteorological data heat fluxes can be derived. These additional parameters increase the uncertainties of flux because the difference between the actual feature of turbulent motion and the applicable conditions of turbulence theory. Most previous studies often focused on the constant flux layers that are above the rough sub-layers and homogeneous flat surfaces underlying surfaces with suitable weather conditions. Therefore, the criteria and modified forms of key parameters are invariable. In this study, we conduct investment over the hilly area of northern China with different plants, such as cork oak, cedar-black and locust. On the basis of key research on the threshold and modified forms of saturation with different turbulence intensity, modified forms of Bowen ratio with different drying-and-wetting conditions, universal function for the temperature structure parameter under different atmospheric stability, the dominant sources of uncertainty will be determined. The above study is significant to reveal influence mechanism of uncertainty and explore influence degree of uncertainty with quantitative analysis. The study can provide theoretical basis and technical support for accurately measuring sensible heat fluxes of forest ecosystem with scintillometer method, and can also provide work foundation for further study on role of forest ecosystem in energy balance and climate change.

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.

Validating an Air Traffic Management Concept of Operation Using Statistical Modeling

NASA Technical Reports Server (NTRS)

He, Yuning; Davies, Misty Dawn

2013-01-01

Validating a concept of operation for a complex, safety-critical system (like the National Airspace System) is challenging because of the high dimensionality of the controllable parameters and the infinite number of states of the system. In this paper, we use statistical modeling techniques to explore the behavior of a conflict detection and resolution algorithm designed for the terminal airspace. These techniques predict the robustness of the system simulation to both nominal and off-nominal behaviors within the overall airspace. They also can be used to evaluate the output of the simulation against recorded airspace data. Additionally, the techniques carry with them a mathematical value of the worth of each prediction-a statistical uncertainty for any robustness estimate. Uncertainty Quantification (UQ) is the process of quantitative characterization and ultimately a reduction of uncertainties in complex systems. UQ is important for understanding the influence of uncertainties on the behavior of a system and therefore is valuable for design, analysis, and verification and validation. In this paper, we apply advanced statistical modeling methodologies and techniques on an advanced air traffic management system, namely the Terminal Tactical Separation Assured Flight Environment (T-TSAFE). We show initial results for a parameter analysis and safety boundary (envelope) detection in the high-dimensional parameter space. For our boundary analysis, we developed a new sequential approach based upon the design of computer experiments, allowing us to incorporate knowledge from domain experts into our modeling and to determine the most likely boundary shapes and its parameters. We carried out the analysis on system parameters and describe an initial approach that will allow us to include time-series inputs, such as the radar track data, into the analysis

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.

ACCOUNTING FOR CALIBRATION UNCERTAINTIES IN X-RAY ANALYSIS: EFFECTIVE AREAS IN SPECTRAL FITTING

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

Lee, Hyunsook; Kashyap, Vinay L.; Drake, Jeremy J.

2011-04-20

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here, we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can bemore » applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.« less

Uncertainty Analysis in 3D Equilibrium Reconstruction

DOE PAGES

Cianciosa, Mark R.; Hanson, James D.; Maurer, David A.

2018-02-21

Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the resultsmore » of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.« less

Uncertainty Analysis in 3D Equilibrium Reconstruction

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

Cianciosa, Mark R.; Hanson, James D.; Maurer, David A.

Reconstruction is an inverse process where a parameter space is searched to locate a set of parameters with the highest probability of describing experimental observations. Due to systematic errors and uncertainty in experimental measurements, this optimal set of parameters will contain some associated uncertainty. This uncertainty in the optimal parameters leads to uncertainty in models derived using those parameters. V3FIT is a three-dimensional (3D) equilibrium reconstruction code that propagates uncertainty from the input signals, to the reconstructed parameters, and to the final model. Here in this paper, we describe the methods used to propagate uncertainty in V3FIT. Using the resultsmore » of whole shot 3D equilibrium reconstruction of the Compact Toroidal Hybrid, this propagated uncertainty is validated against the random variation in the resulting parameters. Two different model parameterizations demonstrate how the uncertainty propagation can indicate the quality of a reconstruction. As a proxy for random sampling, the whole shot reconstruction results in a time interval that will be used to validate the propagated uncertainty from a single time slice.« less

Global Nonlinear Optimization for the Interpretation of Magnetic Anomalies Over Idealized Geological Bodies for Ore Exploration - An Insight about Uncertainty

NASA Astrophysics Data System (ADS)

Biswas, A.

2016-12-01

A Very Fast Simulated Annealing (VFSA) global optimization code is produced for elucidation of magnetic data over various idealized bodies for mineral investigation. The way of uncertainty in the interpretation is additionally analyzed in the present study. This strategy fits the watched information exceptionally well by some straightforward geometrically body in the confined class of Sphere, horizontal cylinder, thin dyke and sheet type models. The consequences of VFSA improvement uncover that different parameters demonstrate various identical arrangements when state of the objective body is not known and shape factor "q" is additionally advanced together with other model parameters. The study uncovers that amplitude coefficient k is firmly subject to shape factor. This demonstrates there is multi-model sort vulnerability between these two model parameters. Be that as it may, the assessed estimations of shape factor from different VFSA runs without a doubt show whether the subsurface structure is sphere, horizontal cylinder, and dyke or sheet type structure. Thus, the precise shape element (2.5 for sphere, 2.0 for horizontal cylinder and 1.0 for dyke and sheet) is settled and improvement procedure is rehashed. Next, altering the shape factor and investigation of uncertainty as well as scatter-plots demonstrates a very much characterized uni-model characteristics. The mean model figured in the wake of settling the shape factor gives the highest dependable results. Inversion of noise-free and noisy synthetic data information and additionally field information shows the adequacy of the methodology. The procedure has been carefully and practically connected to five genuine field cases with the nearness of mineralized bodies covered at various profundities in the subsurface and complex geological settings. The method can be to a great degree appropriate for mineral investigation, where the attractive information is seen because of mineral body established in the shallow/deeper subsurface and the calculation time for the entire procedure are short. Keywords: Magnetic anomaly, idealized body, uncertainty, VFSA, multiple structure, ore exploration.

Joint analysis of epistemic and aleatory uncertainty in stability analysis for geo-hazard assessments

NASA Astrophysics Data System (ADS)

Rohmer, Jeremy; Verdel, Thierry

2017-04-01

Uncertainty analysis is an unavoidable task of stability analysis of any geotechnical systems. Such analysis usually relies on the safety factor SF (if SF is below some specified threshold), the failure is possible). The objective of the stability analysis is then to estimate the failure probability P for SF to be below the specified threshold. When dealing with uncertainties, two facets should be considered as outlined by several authors in the domain of geotechnics, namely "aleatoric uncertainty" (also named "randomness" or "intrinsic variability") and "epistemic uncertainty" (i.e. when facing "vague, incomplete or imprecise information" such as limited databases and observations or "imperfect" modelling). The benefits of separating both facets of uncertainty can be seen from a risk management perspective because: - Aleatoric uncertainty, being a property of the system under study, cannot be reduced. However, practical actions can be taken to circumvent the potentially dangerous effects of such variability; - Epistemic uncertainty, being due to the incomplete/imprecise nature of available information, can be reduced by e.g., increasing the number of tests (lab or in site survey), improving the measurement methods or evaluating calculation procedure with model tests, confronting more information sources (expert opinions, data from literature, etc.). Uncertainty treatment in stability analysis usually restricts to the probabilistic framework to represent both facets of uncertainty. Yet, in the domain of geo-hazard assessments (like landslides, mine pillar collapse, rockfalls, etc.), the validity of this approach can be debatable. In the present communication, we propose to review the major criticisms available in the literature against the systematic use of probability in situations of high degree of uncertainty. On this basis, the feasibility of using a more flexible uncertainty representation tool is then investigated, namely Possibility distributions (e.g., Baudrit et al., 2007) for geo-hazard assessments. A graphical tool is then developed to explore: 1. the contribution of both types of uncertainty, aleatoric and epistemic; 2. the regions of the imprecise or random parameters which contribute the most to the imprecision on the failure probability P. The method is applied on two case studies (a mine pillar and a steep slope stability analysis, Rohmer and Verdel, 2014) to investigate the necessity for extra data acquisition on parameters whose imprecision can hardly be modelled by probabilities due to the scarcity of the available information (respectively the extraction ratio and the cliff geometry). References Baudrit, C., Couso, I., & Dubois, D. (2007). Joint propagation of probability and possibility in risk analysis: Towards a formal framework. International Journal of Approximate Reasoning, 45(1), 82-105. Rohmer, J., & Verdel, T. (2014). Joint exploration of regional importance of possibilistic and probabilistic uncertainty in stability analysis. Computers and Geotechnics, 61, 308-315.

Exploring tropical forest vegetation dynamics using the FATES model

NASA Astrophysics Data System (ADS)

Koven, C. D.; Fisher, R.; Knox, R. G.; Chambers, J.; Kueppers, L. M.; Christoffersen, B. O.; Davies, S. J.; Dietze, M.; Holm, J.; Massoud, E. C.; Muller-Landau, H. C.; Powell, T.; Serbin, S.; Shuman, J. K.; Walker, A. P.; Wright, S. J.; Xu, C.

2017-12-01

Tropical forest vegetation dynamics represent a critical climate feedback in the Earth system, which is poorly represented in current global modeling approaches. We discuss recent progress on exploring these dynamics using the Functionally Assembled Terrestrial Ecosystem Simulator (FATES), a demographic vegetation model for the CESM and ACME ESMs. We will discuss benchmarks of FATES predictions for forest structure against inventory sites, sensitivity of FATES predictions of size and age structure to model parameter uncertainty, and experiments using the FATES model to explore PFT competitive dynamics and the dynamics of size and age distributions in responses to changing climate and CO2.

Quantitative body DW-MRI biomarkers uncertainty estimation using unscented wild-bootstrap.

PubMed

Freiman, M; Voss, S D; Mulkern, R V; Perez-Rossello, J M; Warfield, S K

2011-01-01

We present a new method for the uncertainty estimation of diffusion parameters for quantitative body DW-MRI assessment. Diffusion parameters uncertainty estimation from DW-MRI is necessary for clinical applications that use these parameters to assess pathology. However, uncertainty estimation using traditional techniques requires repeated acquisitions, which is undesirable in routine clinical use. Model-based bootstrap techniques, for example, assume an underlying linear model for residuals rescaling and cannot be utilized directly for body diffusion parameters uncertainty estimation due to the non-linearity of the body diffusion model. To offset this limitation, our method uses the Unscented transform to compute the residuals rescaling parameters from the non-linear body diffusion model, and then applies the wild-bootstrap method to infer the body diffusion parameters uncertainty. Validation through phantom and human subject experiments shows that our method identify the regions with higher uncertainty in body DWI-MRI model parameters correctly with realtive error of -36% in the uncertainty values.

Shining Light into Cosmic Dark Ages

NASA Astrophysics Data System (ADS)

Fialkov, Anastasia

2018-06-01

Exploration of the early Universe is ongoing. One of the most interesting probes of the epoch is the redshifted 21-cm line of neutral hydrogen. Modeling of this signal is difficult due to large uncertainties in both astrophysical and cosmological parameters that describe the high redshift Universe. In my talk I will discuss current theoretical understanding and the status of modeling.

A Sensitivity Study on Modeling Black Carbon in Snow and its Radiative Forcing over the Arctic and Northern China

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

Qian, Yun; Wang, Hailong; Zhang, Rudong

2014-06-02

Black carbon in snow (BCS) simulated in the Community Atmosphere Model (CAM5) is evaluated against measurements over Northern China and the Arctic, and its sensitivity to atmospheric deposition and two parameters that affect post-depositional enrichment is explored. The BCS concentration is overestimated (underestimated) by a factor of two in Northern China (Arctic) in the default model, but agreement with observations is good over both regions in the simulation with improvements in BC transport and deposition. Sensitivity studies indicate that uncertainty in the melt-water scavenging efficiency (MSE) parameter substantially affects BCS and its radiative forcing (by a factor of 2-7) inmore » the Arctic through post-depositional enrichment. The MSE parameter has a relatively small effect on the magnitude of BCS seasonal cycle but can alter its phase in Northern China. The impact of the snow aging scaling factor (SAF) on BCS, partly through the post-depositional enrichment effect, shows more complex latitudinal and seasonal dependence. Similar to MSE, SAF affects more significantly the magnitude (phase) of BCS season cycle over the Arctic (Northern China). While uncertainty associated with the representation of BC transport and deposition processes in CAM5 is more important than that associated with the two snow model parameters in Northern China, the two uncertainties have comparable effect in the Arctic.« less

Bayesian inference for OPC modeling

NASA Astrophysics Data System (ADS)

Burbine, Andrew; Sturtevant, John; Fryer, David; Smith, Bruce W.

2016-03-01

The use of optical proximity correction (OPC) demands increasingly accurate models of the photolithographic process. Model building and inference techniques in the data science community have seen great strides in the past two decades which make better use of available information. This paper aims to demonstrate the predictive power of Bayesian inference as a method for parameter selection in lithographic models by quantifying the uncertainty associated with model inputs and wafer data. Specifically, the method combines the model builder's prior information about each modelling assumption with the maximization of each observation's likelihood as a Student's t-distributed random variable. Through the use of a Markov chain Monte Carlo (MCMC) algorithm, a model's parameter space is explored to find the most credible parameter values. During parameter exploration, the parameters' posterior distributions are generated by applying Bayes' rule, using a likelihood function and the a priori knowledge supplied. The MCMC algorithm used, an affine invariant ensemble sampler (AIES), is implemented by initializing many walkers which semiindependently explore the space. The convergence of these walkers to global maxima of the likelihood volume determine the parameter values' highest density intervals (HDI) to reveal champion models. We show that this method of parameter selection provides insights into the data that traditional methods do not and outline continued experiments to vet the method.

Medial prefrontal cortex and the adaptive regulation of reinforcement learning parameters.

PubMed

Khamassi, Mehdi; Enel, Pierre; Dominey, Peter Ford; Procyk, Emmanuel

2013-01-01

Converging evidence suggest that the medial prefrontal cortex (MPFC) is involved in feedback categorization, performance monitoring, and task monitoring, and may contribute to the online regulation of reinforcement learning (RL) parameters that would affect decision-making processes in the lateral prefrontal cortex (LPFC). Previous neurophysiological experiments have shown MPFC activities encoding error likelihood, uncertainty, reward volatility, as well as neural responses categorizing different types of feedback, for instance, distinguishing between choice errors and execution errors. Rushworth and colleagues have proposed that the involvement of MPFC in tracking the volatility of the task could contribute to the regulation of one of RL parameters called the learning rate. We extend this hypothesis by proposing that MPFC could contribute to the regulation of other RL parameters such as the exploration rate and default action values in case of task shifts. Here, we analyze the sensitivity to RL parameters of behavioral performance in two monkey decision-making tasks, one with a deterministic reward schedule and the other with a stochastic one. We show that there exist optimal parameter values specific to each of these tasks, that need to be found for optimal performance and that are usually hand-tuned in computational models. In contrast, automatic online regulation of these parameters using some heuristics can help producing a good, although non-optimal, behavioral performance in each task. We finally describe our computational model of MPFC-LPFC interaction used for online regulation of the exploration rate and its application to a human-robot interaction scenario. There, unexpected uncertainties are produced by the human introducing cued task changes or by cheating. The model enables the robot to autonomously learn to reset exploration in response to such uncertain cues and events. The combined results provide concrete evidence specifying how prefrontal cortical subregions may cooperate to regulate RL parameters. It also shows how such neurophysiologically inspired mechanisms can control advanced robots in the real world. Finally, the model's learning mechanisms that were challenged in the last robotic scenario provide testable predictions on the way monkeys may learn the structure of the task during the pretraining phase of the previous laboratory experiments. Copyright © 2013 Elsevier B.V. All rights reserved.

Empirical Bolometric Fluxes and Angular Diameters of 1.6 Million Tycho-2 Stars and Radii of 350,000 Stars with Gaia DR1 Parallaxes

NASA Astrophysics Data System (ADS)

Stevens, Daniel J.; Stassun, Keivan G.; Gaudi, B. Scott

2017-12-01

We present bolometric fluxes and angular diameters for over 1.6 million stars in the Tycho-2 catalog, determined using previously determined empirical color-temperature and color-flux relations. We vet these relations via full fits to the full broadband spectral energy distributions for a subset of benchmark stars and perform quality checks against the large set of stars for which spectroscopically determined parameters are available from LAMOST, RAVE, and/or APOGEE. We then estimate radii for the 355,502 Tycho-2 stars in our sample whose Gaia DR1 parallaxes are precise to ≲ 10 % . For these stars, we achieve effective temperature, bolometric flux, and angular diameter uncertainties of the order of 1%-2% and radius uncertainties of order 8%, and we explore the effect that imposing spectroscopic effective temperature priors has on these uncertainties. These stellar parameters are shown to be reliable for stars with {T}{eff} ≲ 7000 K. The over half a million bolometric fluxes and angular diameters presented here will serve as an immediate trove of empirical stellar radii with the Gaia second data release, at which point effective temperature uncertainties will dominate the radius uncertainties. Already, dwarf, subgiant, and giant populations are readily identifiable in our purely empirical luminosity-effective temperature (theoretical) Hertzsprung-Russell diagrams.

Reducing Design Risk Using Robust Design Methods: A Dual Response Surface Approach

NASA Technical Reports Server (NTRS)

Unal, Resit; Yeniay, Ozgur; Lepsch, Roger A. (Technical Monitor)

2003-01-01

Space transportation system conceptual design is a multidisciplinary process containing considerable element of risk. Risk here is defined as the variability in the estimated (output) performance characteristic of interest resulting from the uncertainties in the values of several disciplinary design and/or operational parameters. Uncertainties from one discipline (and/or subsystem) may propagate to another, through linking parameters and the final system output may have a significant accumulation of risk. This variability can result in significant deviations from the expected performance. Therefore, an estimate of variability (which is called design risk in this study) together with the expected performance characteristic value (e.g. mean empty weight) is necessary for multidisciplinary optimization for a robust design. Robust design in this study is defined as a solution that minimizes variability subject to a constraint on mean performance characteristics. Even though multidisciplinary design optimization has gained wide attention and applications, the treatment of uncertainties to quantify and analyze design risk has received little attention. This research effort explores the dual response surface approach to quantify variability (risk) in critical performance characteristics (such as weight) during conceptual design.

Exploring Land Use and Land Cover Change and Feedbacks in the Global Change Assessment Model

NASA Astrophysics Data System (ADS)

Chen, M.; Vernon, C. R.; Huang, M.; Calvin, K. V.; Le Page, Y.; Kraucunas, I.

2017-12-01

Land Use and Land Cover Change (LULCC) is a major driver of global and regional environmental change. Projections of land use change are thus an essential component in Integrated Assessment Models (IAMs) to study feedbacks between transformation of energy systems and land productivity under the context of climate change. However, the spatial scale of IAMs, e.g., the Global Change Assessment Model (GCAM), is typically larger than the scale of terrestrial processes in the human-Earth system, LULCC downscaling therefore becomes a critical linkage among these multi-scale and multi-sector processes. Parametric uncertainties in LULCC downscaling algorithms, however, have been under explored, especially in the context of how such uncertainties could propagate to affect energy systems in a changing climate. In this study, we use a LULCC downscaling model, Demeter, to downscale GCAM-based future land use scenarios into fine spatial scales, and explore the sensitivity of downscaled land allocations to key parameters. Land productivity estimates (e.g., biomass production and crop yield) based on the downscaled LULCC scenarios are then fed to GCAM to evaluate how energy systems might change due to altered water and carbon cycle dynamics and their interactions with the human system, , which would in turn affect future land use projections. We demonstrate that uncertainties in LULCC downscaling can result in significant differences in simulated scenarios, indicating the importance of quantifying parametric uncertainties in LULCC downscaling models for integrated assessment studies.

Karhunen-Loeve Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early Sloan Digital Sky Survey Data

NASA Technical Reports Server (NTRS)

Szalay, Alexander S.; Jain, Bhuvnesh; Matsubara, Takahiko; Scranton, Ryan; Vogeley, Michael S.; Connolly, Andrew; Dodelson, Scott; Eisenstein, Daniel; Frieman, Joshua A.; Gunn, James E.

2003-01-01

We present measurements of parameters of the three-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey (SDSS). The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve (KL) eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the three-dimensional power spectrum of galaxies in the SDSS magnitude-limited sample with r* less than 21. Our best estimates are gamma = 0.188 +/- 0.04 and sigma(sub 8L) = 0.915 +/- 0.06 (statistical errors only), for a flat universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the three-dimensional power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size, and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2 sigma uncertainties of our fiducial result.

Global Sensitivity Analysis for Identifying Important Parameters of Nitrogen Nitrification and Denitrification under Model and Scenario Uncertainties

NASA Astrophysics Data System (ADS)

Ye, M.; Chen, Z.; Shi, L.; Zhu, Y.; Yang, J.

2017-12-01

Nitrogen reactive transport modeling is subject to uncertainty in model parameters, structures, and scenarios. While global sensitivity analysis is a vital tool for identifying the parameters important to nitrogen reactive transport, conventional global sensitivity analysis only considers parametric uncertainty. This may result in inaccurate selection of important parameters, because parameter importance may vary under different models and modeling scenarios. By using a recently developed variance-based global sensitivity analysis method, this paper identifies important parameters with simultaneous consideration of parametric uncertainty, model uncertainty, and scenario uncertainty. In a numerical example of nitrogen reactive transport modeling, a combination of three scenarios of soil temperature and two scenarios of soil moisture leads to a total of six scenarios. Four alternative models are used to evaluate reduction functions used for calculating actual rates of nitrification and denitrification. The model uncertainty is tangled with scenario uncertainty, as the reduction functions depend on soil temperature and moisture content. The results of sensitivity analysis show that parameter importance varies substantially between different models and modeling scenarios, which may lead to inaccurate selection of important parameters if model and scenario uncertainties are not considered. This problem is avoided by using the new method of sensitivity analysis in the context of model averaging and scenario averaging. The new method of sensitivity analysis can be applied to other problems of contaminant transport modeling when model uncertainty and/or scenario uncertainty are present.

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.

Optimization Under Uncertainty for Electronics Cooling Design

NASA Astrophysics Data System (ADS)

Bodla, Karthik K.; Murthy, Jayathi Y.; Garimella, Suresh V.

Optimization under uncertainty is a powerful methodology used in design and optimization to produce robust, reliable designs. Such an optimization methodology, employed when the input quantities of interest are uncertain, produces output uncertainties, helping the designer choose input parameters that would result in satisfactory thermal solutions. Apart from providing basic statistical information such as mean and standard deviation in the output quantities, auxiliary data from an uncertainty based optimization, such as local and global sensitivities, help the designer decide the input parameter(s) to which the output quantity of interest is most sensitive. This helps the design of experiments based on the most sensitive input parameter(s). A further crucial output of such a methodology is the solution to the inverse problem - finding the allowable uncertainty range in the input parameter(s), given an acceptable uncertainty range in the output quantity of interest...

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

Uncertainty quantification for optical model parameters

DOE PAGES

Lovell, A. E.; Nunes, F. M.; Sarich, J.; ...

2017-02-21

Although uncertainty quantification has been making its way into nuclear theory, these methods have yet to be explored in the context of reaction theory. For example, it is well known that different parameterizations of the optical potential can result in different cross sections, but these differences have not been systematically studied and quantified. The purpose of our work is to investigate the uncertainties in nuclear reactions that result from fitting a given model to elastic-scattering data, as well as to study how these uncertainties propagate to the inelastic and transfer channels. We use statistical methods to determine a best fitmore » and create corresponding 95% confidence bands. A simple model of the process is fit to elastic-scattering data and used to predict either inelastic or transfer cross sections. In this initial work, we assume that our model is correct, and the only uncertainties come from the variation of the fit parameters. Here, we study a number of reactions involving neutron and deuteron projectiles with energies in the range of 5–25 MeV/u, on targets with mass A=12–208. We investigate the correlations between the parameters in the fit. The case of deuterons on 12C is discussed in detail: the elastic-scattering fit and the prediction of 12C(d,p) 13C transfer angular distributions, using both uncorrelated and correlated χ 2 minimization functions. The general features for all cases are compiled in a systematic manner to identify trends. This work shows that, in many cases, the correlated χ 2 functions (in comparison to the uncorrelated χ 2 functions) provide a more natural parameterization of the process. These correlated functions do, however, produce broader confidence bands. Further optimization may require improvement in the models themselves and/or more information included in the fit.« less

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.

Efficient Optimization of Stimuli for Model-Based Design of Experiments to Resolve Dynamical Uncertainty.

PubMed

Mdluli, Thembi; Buzzard, Gregery T; Rundell, Ann E

2015-09-01

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm's scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.

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.

Efficient Optimization of Stimuli for Model-Based Design of Experiments to Resolve Dynamical Uncertainty

PubMed Central

Mdluli, Thembi; Buzzard, Gregery T.; Rundell, Ann E.

2015-01-01

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements. PMID:26379275

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.

Uncertainty Determination for Aeroheating in Uranus and Saturn Probe Entries by the Monte Carlo Method

NASA Technical Reports Server (NTRS)

Palmer, Grant; Prabhu, Dinesh; Cruden, Brett A.

2013-01-01

The 2013-2022 Decaedal survey for planetary exploration has identified probe missions to Uranus and Saturn as high priorities. This work endeavors to examine the uncertainty for determining aeroheating in such entry environments. Representative entry trajectories are constructed using the TRAJ software. Flowfields at selected points on the trajectories are then computed using the Data Parallel Line Relaxation (DPLR) Computational Fluid Dynamics Code. A Monte Carlo study is performed on the DPLR input parameters to determine the uncertainty in the predicted aeroheating, and correlation coefficients are examined to identify which input parameters show the most influence on the uncertainty. A review of the present best practices for input parameters (e.g. transport coefficient and vibrational relaxation time) is also conducted. It is found that the 2(sigma) - uncertainty for heating on Uranus entry is no more than 2.1%, assuming an equilibrium catalytic wall, with the uncertainty being determined primarily by diffusion and H(sub 2) recombination rate within the boundary layer. However, if the wall is assumed to be partially or non-catalytic, this uncertainty may increase to as large as 18%. The catalytic wall model can contribute over 3x change in heat flux and a 20% variation in film coefficient. Therefore, coupled material response/fluid dynamic models are recommended for this problem. It was also found that much of this variability is artificially suppressed when a constant Schmidt number approach is implemented. Because the boundary layer is reacting, it is necessary to employ self-consistent effective binary diffusion to obtain a correct thermal transport solution. For Saturn entries, the 2(sigma) - uncertainty for convective heating was less than 3.7%. The major uncertainty driver was dependent on shock temperature/velocity, changing from boundary layer thermal conductivity to diffusivity and then to shock layer ionization rate as velocity increases. While radiative heating for Uranus entry was negligible, the nominal solution for Saturn computed up to 20% radiative heating at the highest velocity examined. The radiative heating followed a non-normal distribution, with up to a 3x variation in magnitude. This uncertainty is driven by the H(sub 2) dissociation rate, as H(sub 2) that persists in the hot non-equilibrium zone contributes significantly to radiation.

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.

Accounting for parameter uncertainty in the definition of parametric distributions used to describe individual patient variation in health economic models.

PubMed

Degeling, Koen; IJzerman, Maarten J; Koopman, Miriam; Koffijberg, Hendrik

2017-12-15

Parametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty. Although general guidance is available on how parameter uncertainty should be accounted for in probabilistic sensitivity analysis, there is no comprehensive guidance on reflecting parameter uncertainty in the (correlated) parameters of distributions used to represent stochastic uncertainty in patient-level models. This study aims to provide this guidance by proposing appropriate methods and illustrating the impact of this uncertainty on modeling outcomes. Two approaches, 1) using non-parametric bootstrapping and 2) using multivariate Normal distributions, were applied in a simulation and case study. The approaches were compared based on point-estimates and distributions of time-to-event and health economic outcomes. To assess sample size impact on the uncertainty in these outcomes, sample size was varied in the simulation study and subgroup analyses were performed for the case-study. Accounting for parameter uncertainty in distributions that reflect stochastic uncertainty substantially increased the uncertainty surrounding health economic outcomes, illustrated by larger confidence ellipses surrounding the cost-effectiveness point-estimates and different cost-effectiveness acceptability curves. Although both approaches performed similar for larger sample sizes (i.e. n = 500), the second approach was more sensitive to extreme values for small sample sizes (i.e. n = 25), yielding infeasible modeling outcomes. Modelers should be aware that parameter uncertainty in distributions used to describe stochastic uncertainty needs to be reflected in probabilistic sensitivity analysis, as it could substantially impact the total amount of uncertainty surrounding health economic outcomes. If feasible, the bootstrap approach is recommended to account for this uncertainty.

Identification of gene regulation models from single-cell data

NASA Astrophysics Data System (ADS)

Weber, Lisa; Raymond, William; Munsky, Brian

2018-09-01

In quantitative analyses of biological processes, one may use many different scales of models (e.g. spatial or non-spatial, deterministic or stochastic, time-varying or at steady-state) or many different approaches to match models to experimental data (e.g. model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ MATLAB and PYTHON software to consider a time-dependent input signal (e.g. a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g. deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast (Neuert et al 2013 Science 339 584–7) and human cells (Senecal et al 2014 Cell Rep. 8 75–83)5.

Quantifying Key Climate Parameter Uncertainties Using an Earth System Model with a Dynamic 3D Ocean

NASA Astrophysics Data System (ADS)

Olson, R.; Sriver, R. L.; Goes, M. P.; Urban, N.; Matthews, D.; Haran, M.; Keller, K.

2011-12-01

Climate projections hinge critically on uncertain climate model parameters such as climate sensitivity, vertical ocean diffusivity and anthropogenic sulfate aerosol forcings. Climate sensitivity is defined as the equilibrium global mean temperature response to a doubling of atmospheric CO2 concentrations. Vertical ocean diffusivity parameterizes sub-grid scale ocean vertical mixing processes. These parameters are typically estimated using Intermediate Complexity Earth System Models (EMICs) that lack a full 3D representation of the oceans, thereby neglecting the effects of mixing on ocean dynamics and meridional overturning. We improve on these studies by employing an EMIC with a dynamic 3D ocean model to estimate these parameters. We carry out historical climate simulations with the University of Victoria Earth System Climate Model (UVic ESCM) varying parameters that affect climate sensitivity, vertical ocean mixing, and effects of anthropogenic sulfate aerosols. We use a Bayesian approach whereby the likelihood of each parameter combination depends on how well the model simulates surface air temperature and upper ocean heat content. We use a Gaussian process emulator to interpolate the model output to an arbitrary parameter setting. We use Markov Chain Monte Carlo method to estimate the posterior probability distribution function (pdf) of these parameters. We explore the sensitivity of the results to prior assumptions about the parameters. In addition, we estimate the relative skill of different observations to constrain the parameters. We quantify the uncertainty in parameter estimates stemming from climate variability, model and observational errors. We explore the sensitivity of key decision-relevant climate projections to these parameters. We find that climate sensitivity and vertical ocean diffusivity estimates are consistent with previously published results. The climate sensitivity pdf is strongly affected by the prior assumptions, and by the scaling parameter for the aerosols. The estimation method is computationally fast and can be used with more complex models where climate sensitivity is diagnosed rather than prescribed. The parameter estimates can be used to create probabilistic climate projections using the UVic ESCM model in future studies.

Estimating Model Prediction Error: Should You Treat Predictions as Fixed or Random?

NASA Technical Reports Server (NTRS)

Wallach, Daniel; Thorburn, Peter; Asseng, Senthold; Challinor, Andrew J.; Ewert, Frank; Jones, James W.; Rotter, Reimund; Ruane, Alexander

2016-01-01

Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEP fixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEP uncertain( X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEP uncertain (X) can be estimated using a random effects ANOVA. It is argued that MSEP uncertain (X) is the more informative uncertainty criterion, because it is specific to each prediction situation.

Framework for Uncertainty Assessment - Hanford Site-Wide Groundwater Flow and Transport Modeling

NASA Astrophysics Data System (ADS)

Bergeron, M. P.; Cole, C. R.; Murray, C. J.; Thorne, P. D.; Wurstner, S. K.

2002-05-01

Pacific Northwest National Laboratory is in the process of development and implementation of an uncertainty estimation methodology for use in future site assessments that addresses parameter uncertainty as well as uncertainties related to the groundwater conceptual model. The long-term goals of the effort are development and implementation of an uncertainty estimation methodology for use in future assessments and analyses being made with the Hanford site-wide groundwater model. The basic approach in the framework developed for uncertainty assessment consists of: 1) Alternate conceptual model (ACM) identification to identify and document the major features and assumptions of each conceptual model. The process must also include a periodic review of the existing and proposed new conceptual models as data or understanding become available. 2) ACM development of each identified conceptual model through inverse modeling with historical site data. 3) ACM evaluation to identify which of conceptual models are plausible and should be included in any subsequent uncertainty assessments. 4) ACM uncertainty assessments will only be carried out for those ACMs determined to be plausible through comparison with historical observations and model structure identification measures. The parameter uncertainty assessment process generally involves: a) Model Complexity Optimization - to identify the important or relevant parameters for the uncertainty analysis; b) Characterization of Parameter Uncertainty - to develop the pdfs for the important uncertain parameters including identification of any correlations among parameters; c) Propagation of Uncertainty - to propagate parameter uncertainties (e.g., by first order second moment methods if applicable or by a Monte Carlo approach) through the model to determine the uncertainty in the model predictions of interest. 5)Estimation of combined ACM and scenario uncertainty by a double sum with each component of the inner sum (an individual CCDF) representing parameter uncertainty associated with a particular scenario and ACM and the outer sum enumerating the various plausible ACM and scenario combinations in order to represent the combined estimate of uncertainty (a family of CCDFs). A final important part of the framework includes identification, enumeration, and documentation of all the assumptions, which include those made during conceptual model development, required by the mathematical model, required by the numerical model, made during the spatial and temporal descretization process, needed to assign the statistical model and associated parameters that describe the uncertainty in the relevant input parameters, and finally those assumptions required by the propagation method. Pacific Northwest National Laboratory is operated for the U.S. Department of Energy under Contract DE-AC06-76RL01830.

Weak vector boson production with many jets at the LHC √{s }=13 TeV

NASA Astrophysics Data System (ADS)

Anger, F. R.; Febres Cordero, F.; Höche, S.; Maître, D.

2018-05-01

Signatures with an electroweak vector boson and many jets play a crucial role at the Large Hadron Collider, both in the measurement of Standard-Model parameters and in searches for new physics. Precise predictions for these multiscale processes are therefore indispensable. We present next-to-leading order QCD predictions for W±/Z +jets at √{s }=13 TeV , including up to five/four jets in the final state. All production channels are included, and leptonic decays of the vector bosons are considered at the amplitude level. We assess theoretical uncertainties arising from renormalization- and factorization-scale dependence by considering fixed-order dynamical scales based on the HT variable as well as on the MiNLO procedure. We also explore uncertainties associated with different choices of parton-distribution functions. We provide event samples that can be explored through publicly available n -tuple sets, generated with BlackHat in combination with Sherpa.

DOE-EPSCOR SPONSORED PROJECT FINAL REPORT

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

Zhu, Jianting

Concern over the quality of environmental management and restoration has motivated the model development for predicting water and solute transport in the vadose zone. Soil hydraulic properties are required inputs to subsurface models of water flow and contaminant transport in the vadose zone. Computer models are now routinely used in research and management to predict the movement of water and solutes into and through the vadose zone of soils. Such models can be used successfully only if reliable estimates of the soil hydraulic parameters are available. The hydraulic parameters considered in this project consist of the saturated hydraulic conductivity andmore » four parameters of the water retention curves. To quantify hydraulic parameters for heterogeneous soils is both difficult and time consuming. The overall objective of this project was to better quantify soil hydraulic parameters which are critical in predicting water flows and contaminant transport in the vadose zone through a comprehensive and quantitative study to predict heterogeneous soil hydraulic properties and the associated uncertainties. Systematic and quantitative consideration of the parametric heterogeneity and uncertainty can properly address and further reduce predictive uncertainty for contamination characterization and environmental restoration at DOE-managed sites. We conducted a comprehensive study to assess soil hydraulic parameter heterogeneity and uncertainty. We have addressed a number of important issues related to the soil hydraulic property characterizations. The main focus centered on new methods to characterize anisotropy of unsaturated hydraulic property typical of layered soil formations, uncertainty updating method, and artificial neural network base pedo-transfer functions to predict hydraulic parameters from easily available data. The work also involved upscaling of hydraulic properties applicable to large scale flow and contaminant transport modeling in the vadose zone and geostatistical characterization of hydraulic parameter heterogeneity. The project also examined the validity of the some simple average schemes for unsaturated hydraulic properties widely used in previous studies. A new suite of pedo-transfer functions were developed to improve the predictability of hydraulic parameters. We also explored the concept of tension-dependent hydraulic conductivity anisotropy of unsaturated layered soils. This project strengthens collaboration between researchers at the Desert Research Institute in the EPSCoR State of Nevada and their colleagues at the Pacific Northwest National Laboratory. The results of numerical simulations of a field injection experiment at Hanford site in this project could be used to provide insights to the DOE mission of appropriate contamination characterization and environmental remediation.« less

A probabilistic approach to emissions from transportation sector in the coming decades

NASA Astrophysics Data System (ADS)

Yan, F.; Winijkul, E.; Bond, T. C.; Streets, D. G.

2010-12-01

Future emission estimates are necessary for understanding climate change, designing national and international strategies for air quality control and evaluating mitigation policies. Emission inventories are uncertain and future projections even more so. Most current emission projection models are deterministic; in other words, there is only single answer for each scenario. As a result, uncertainties have not been included in the estimation of climate forcing or other environmental effects, but it is important to quantify the uncertainty inherent in emission projections. We explore uncertainties of emission projections from transportation sector in the coming decades by sensitivity analysis and Monte Carlo simulations. These projections are based on a technology driven model: the Speciated Pollutants Emission Wizard (SPEW)-Trend, which responds to socioeconomic conditions in different economic and mitigation scenarios. The model contains detail about technology stock, including consumption growth rates, retirement rates, timing of emission standards, deterioration rates and transition rates from normal vehicles to vehicles with extremely high emission factors (termed “superemitters”). However, understanding of these parameters, as well as relationships with socioeconomic conditions, is uncertain. We project emissions from transportation sectors under four different IPCC scenarios (A1B, A2, B1, and B2). Due to the later implementation of advanced emission standards, Africa has the highest annual growth rate (1.2-3.1%) from 2010 to 2050. Superemitters begin producing more than 50% of global emissions around year 2020. We estimate uncertainties from the relationships between technological change and socioeconomic conditions and examine their impact on future emissions. Sensitivities to parameters governing retirement rates are highest, causing changes in global emissions from-26% to +55% on average from 2010 to 2050. We perform Monte Carlo simulations to examine how these uncertainties will affect total emissions if any input parameter that has inherent the uncertainties is substituted by a range of values-probability distribution and varies at the same time; the 95% confidence interval of global emission annual growth rate is -1.9% to +0.2% per year.

Interstellar Flow and Temperature Determination with IBEX: Robustness and Sensitivity to Systematic Effects

NASA Astrophysics Data System (ADS)

Möbius, E.; Bzowski, M.; Frisch, P. C.; Fuselier, S. A.; Heirtzler, D.; Kubiak, M. A.; Kucharek, H.; Lee, M. A.; Leonard, T.; McComas, D. J.; Schwadron, N. A.; Sokół, J. M.; Swaczyna, P.; Wurz, P.

2015-10-01

The Interstellar Boundary Explorer (IBEX) samples the interstellar neutral (ISN) gas flow of several species every year from December through late March when the Earth moves into the incoming flow. The first quantitative analyses of these data resulted in a narrow tube in four-dimensional interstellar parameter space, which couples speed, flow latitude, flow longitude, and temperature, and center values with approximately 3° larger longitude and 3 km s-1 lower speed, but with temperatures similar to those obtained from observations by the Ulysses spacecraft. IBEX has now recorded six years of ISN flow observations, providing a large database over increasing solar activity and using varying viewing strategies. In this paper, we evaluate systematic effects that are important for the ISN flow vector and temperature determination. We find that all models in use return ISN parameters well within the observational uncertainties and that the derived ISN flow direction is resilient against uncertainties in the ionization rate. We establish observationally an effective IBEX-Lo pointing uncertainty of ±0.°18 in spin angle and confirm an uncertainty of ±0.°1 in longitude. We also show that the IBEX viewing strategy with different spin-axis orientations minimizes the impact of several systematic uncertainties, and thus improves the robustness of the measurement. The Helium Warm Breeze has likely contributed substantially to the somewhat different center values of the ISN flow vector. By separating the flow vector and temperature determination, we can mitigate these effects on the analysis, which returns an ISN flow vector very close to the Ulysses results, but with a substantially higher temperature. Due to coupling with the ISN flow speed along the ISN parameter tube, we provide the temperature {T}{VISN∞ }=8710+440/-680 K for {V}{ISN∞ }=26 {km} {{{s}}}-1 for comparison, where most of the uncertainty is systematic and likely due to the presence of the Warm Breeze.

Exploring uncertainty of Amazon dieback in a perturbed parameter Earth system ensemble.

PubMed

Boulton, Chris A; Booth, Ben B B; Good, Peter

2017-12-01

The future of the Amazon rainforest is unknown due to uncertainties in projected climate change and the response of the forest to this change (forest resiliency). Here, we explore the effect of some uncertainties in climate and land surface processes on the future of the forest, using a perturbed physics ensemble of HadCM3C. This is the first time Amazon forest changes are presented using an ensemble exploring both land vegetation processes and physical climate feedbacks in a fully coupled modelling framework. Under three different emissions scenarios, we measure the change in the forest coverage by the end of the 21st century (the transient response) and make a novel adaptation to a previously used method known as "dry-season resilience" to predict the long-term committed response of the forest, should the state of the climate remain constant past 2100. Our analysis of this ensemble suggests that there will be a high chance of greater forest loss on longer timescales than is realized by 2100, especially for mid-range and low emissions scenarios. In both the transient and predicted committed responses, there is an increasing uncertainty in the outcome of the forest as the strength of the emissions scenarios increases. It is important to note however, that very few of the simulations produce future forest loss of the magnitude previously shown under the standard model configuration. We find that low optimum temperatures for photosynthesis and a high minimum leaf area index needed for the forest to compete for space appear to be precursors for dieback. We then decompose the uncertainty into that associated with future climate change and that associated with forest resiliency, finding that it is important to reduce the uncertainty in both of these if we are to better determine the Amazon's outcome. © 2017 John Wiley & Sons Ltd.

Towards quantifying uncertainty in predictions of Amazon 'dieback'.

PubMed

Huntingford, Chris; Fisher, Rosie A; Mercado, Lina; Booth, Ben B B; Sitch, Stephen; Harris, Phil P; Cox, Peter M; Jones, Chris D; Betts, Richard A; Malhi, Yadvinder; Harris, Glen R; Collins, Mat; Moorcroft, Paul

2008-05-27

Simulations with the Hadley Centre general circulation model (HadCM3), including carbon cycle model and forced by a 'business-as-usual' emissions scenario, predict a rapid loss of Amazonian rainforest from the middle of this century onwards. The robustness of this projection to both uncertainty in physical climate drivers and the formulation of the land surface scheme is investigated. We analyse how the modelled vegetation cover in Amazonia responds to (i) uncertainty in the parameters specified in the atmosphere component of HadCM3 and their associated influence on predicted surface climate. We then enhance the land surface description and (ii) implement a multilayer canopy light interception model and compare with the simple 'big-leaf' approach used in the original simulations. Finally, (iii) we investigate the effect of changing the method of simulating vegetation dynamics from an area-based model (TRIFFID) to a more complex size- and age-structured approximation of an individual-based model (ecosystem demography). We find that the loss of Amazonian rainforest is robust across the climate uncertainty explored by perturbed physics simulations covering a wide range of global climate sensitivity. The introduction of the refined light interception model leads to an increase in simulated gross plant carbon uptake for the present day, but, with altered respiration, the net effect is a decrease in net primary productivity. However, this does not significantly affect the carbon loss from vegetation and soil as a consequence of future simulated depletion in soil moisture; the Amazon forest is still lost. The introduction of the more sophisticated dynamic vegetation model reduces but does not halt the rate of forest dieback. The potential for human-induced climate change to trigger the loss of Amazon rainforest appears robust within the context of the uncertainties explored in this paper. Some further uncertainties should be explored, particularly with respect to the representation of rooting depth.

Predictions of space radiation fatality risk for exploration missions.

PubMed

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. 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. Copyright © 2017 The Committee on Space Research (COSPAR). Published by Elsevier Ltd. All rights reserved.

Management of uncertainties on parameters elicited by experts - Applications to sea-level rise and to CO2 storage operations risk assessment

NASA Astrophysics Data System (ADS)

Manceau, Jean-Charles; Loschetter, Annick; Rohmer, Jérémy; Le Cozannet, Gonéri; Lary Louis, de; Guénan Thomas, Le; Ken, Hnottavange-Telleen

2017-04-01

In a context of high degree of uncertainty, when very few data are available, experts are commonly requested to provide their opinions on input parameters of risk assessment models. Not only might each expert express a certain degree of uncertainty on his/her own statements, but the set of information collected from the pool of experts introduces an additional level of uncertainty. It is indeed very unlikely that all experts agree on exactly the same data, especially regarding parameters needed for natural risk assessments. In some cases, their opinions may differ only slightly (e.g. the most plausible value for a parameter is similar for different experts, and they only disagree on the level of uncertainties that taint the said value) while on other cases they may express incompatible opinions for a same parameter. Dealing with these different kinds of uncertainties remains a challenge for assessing geological hazards or/and risks. Extra-probabilistic approaches (such as the Dempster-Shafer theory or the possibility theory) have shown to offer promising solutions for representing parameters on which the knowledge is limited. It is the case for instance when the available information prevents an expert from identifying a unique probability law to picture the total uncertainty. Moreover, such approaches are known to be particularly flexible when it comes to aggregating several and potentially conflicting opinions. We therefore propose to discuss the opportunity of applying these new theories for managing the uncertainties on parameters elicited by experts, by a comparison with the application of more classical probability approaches. The discussion is based on two different examples. The first example deals with the estimation of the injected CO2 plume extent in a reservoir in the context of CO2 geological storage. This estimation requires information on the effective porosity of the reservoir, which has been estimated by 14 different experts. The Dempster-Shafer theory has been used to represent and aggregate these pieces of information. The results of different aggregation rules as well as those of a classical probabilistic approach are compared with the purpose of highlighting the elements each of them could provide to the decision-maker (Manceau et al., 2016). The second example focuses on projections of future sea-level rise. Based on IPCC's constraints on the projection quantiles, and on the scientific community consensus level on the physical limits to future sea-level rise, a possibility distribution of the projections by 2100 under the RCP 8.5 scenario has been established. This possibility distribution has been confronted with a set of previously published probabilistic sea-level projections, with a focus on their ability to explore high ranges of sea-level rise (Le Cozannet et al., 2016). These two examples are complementary in the sense that they allow to address various aspects of the problem (e.g. representation of different types of information, conflict among experts, sources dependence). Moreover, we believe that the issues faced during these two experiences can be generalized to many risks/hazards assessment situations. References Manceau, JC., Loschetter, A., Rohmer, J., de Lary, L., Le Guénan, T., Hnottavange-Telleen, K. (2016). Dealing with uncertainty on parameters elicited from a pool of experts for CCS risk assessment. Congrès λμ 20 (St-Malo, France). Le Cozannet G., Manceau JC., Rohmer, J. (2016). Bounding probabilistic sea-level rise projections within the framework of the possibility theory. Accepted in Environmental Research Letters.

Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods

DOE PAGES

Perfetti, Christopher M.; Rearden, Bradley T.

2016-03-01

The sensitivity and uncertainty analysis tools of the ORNL SCALE nuclear modeling and simulation code system that have been developed over the last decade have proven indispensable for numerous application and design studies for nuclear criticality safety and reactor physics. SCALE contains tools for analyzing the uncertainty in the eigenvalue of critical systems, but cannot quantify uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with realistic three-dimensional Monte Carlo simulations. A more complete understanding of the sources of uncertainty in these design-limiting parameters could lead to improvements in processmore » optimization, reactor safety, and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was recently explored as academic research and has been found to accurately and rapidly calculate sensitivity coefficients in criticality safety applications. The work presented here describes a new method, known as the GEAR-MC method, which extends the CLUTCH theory for calculating eigenvalue sensitivity coefficients to enable sensitivity coefficient calculations and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Here, several criticality safety systems were examined to demonstrate proof of principle for the GEAR-MC method, and GEAR-MC was seen to produce response sensitivity coefficients that agreed well with reference direct perturbation sensitivity coefficients.« less

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.

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

Knudsen, J.K.; Smith, C.L.

The steps involved to incorporate parameter uncertainty into the Nuclear Regulatory Commission (NRC) accident sequence precursor (ASP) models is covered in this paper. Three different uncertainty distributions (i.e., lognormal, beta, gamma) were evaluated to Determine the most appropriate distribution. From the evaluation, it was Determined that the lognormal distribution will be used for the ASP models uncertainty parameters. Selection of the uncertainty parameters for the basic events is also discussed. This paper covers the process of determining uncertainty parameters for the supercomponent basic events (i.e., basic events that are comprised of more than one component which can have more thanmore » one failure mode) that are utilized in the ASP models. Once this is completed, the ASP model is ready to be utilized to propagate parameter uncertainty for event assessments.« less

Approaches to highly parameterized inversion: A guide to using PEST for model-parameter and predictive-uncertainty analysis

USGS Publications Warehouse

Doherty, John E.; Hunt, Randall J.; Tonkin, Matthew J.

2010-01-01

Analysis of the uncertainty associated with parameters used by a numerical model, and with predictions that depend on those parameters, is fundamental to the use of modeling in support of decisionmaking. Unfortunately, predictive uncertainty analysis with regard to models can be very computationally demanding, due in part to complex constraints on parameters that arise from expert knowledge of system properties on the one hand (knowledge constraints) and from the necessity for the model parameters to assume values that allow the model to reproduce historical system behavior on the other hand (calibration constraints). Enforcement of knowledge and calibration constraints on parameters used by a model does not eliminate the uncertainty in those parameters. In fact, in many cases, enforcement of calibration constraints simply reduces the uncertainties associated with a number of broad-scale combinations of model parameters that collectively describe spatially averaged system properties. The uncertainties associated with other combinations of parameters, especially those that pertain to small-scale parameter heterogeneity, may not be reduced through the calibration process. To the extent that a prediction depends on system-property detail, its postcalibration variability may be reduced very little, if at all, by applying calibration constraints; knowledge constraints remain the only limits on the variability of predictions that depend on such detail. Regrettably, in many common modeling applications, these constraints are weak. Though the PEST software suite was initially developed as a tool for model calibration, recent developments have focused on the evaluation of model-parameter and predictive uncertainty. As a complement to functionality that it provides for highly parameterized inversion (calibration) by means of formal mathematical regularization techniques, the PEST suite provides utilities for linear and nonlinear error-variance and uncertainty analysis in these highly parameterized modeling contexts. Availability of these utilities is particularly important because, in many cases, a significant proportion of the uncertainty associated with model parameters-and the predictions that depend on them-arises from differences between the complex properties of the real world and the simplified representation of those properties that is expressed by the calibrated model. This report is intended to guide intermediate to advanced modelers in the use of capabilities available with the PEST suite of programs for evaluating model predictive error and uncertainty. A brief theoretical background is presented on sources of parameter and predictive uncertainty and on the means for evaluating this uncertainty. Applications of PEST tools are then discussed for overdetermined and underdetermined problems, both linear and nonlinear. PEST tools for calculating contributions to model predictive uncertainty, as well as optimization of data acquisition for reducing parameter and predictive uncertainty, are presented. The appendixes list the relevant PEST variables, files, and utilities required for the analyses described in the document.

MODFLOW 2000 Head Uncertainty, a First-Order Second Moment Method

USGS Publications Warehouse

Glasgow, H.S.; Fortney, M.D.; Lee, J.; Graettinger, A.J.; Reeves, H.W.

2003-01-01

A computationally efficient method to estimate the variance and covariance in piezometric head results computed through MODFLOW 2000 using a first-order second moment (FOSM) approach is presented. This methodology employs a first-order Taylor series expansion to combine model sensitivity with uncertainty in geologic data. MODFLOW 2000 is used to calculate both the ground water head and the sensitivity of head to changes in input data. From a limited number of samples, geologic data are extrapolated and their associated uncertainties are computed through a conditional probability calculation. Combining the spatially related sensitivity and input uncertainty produces the variance-covariance matrix, the diagonal of which is used to yield the standard deviation in MODFLOW 2000 head. The variance in piezometric head can be used for calibrating the model, estimating confidence intervals, directing exploration, and evaluating the reliability of a design. A case study illustrates the approach, where aquifer transmissivity is the spatially related uncertain geologic input data. The FOSM methodology is shown to be applicable for calculating output uncertainty for (1) spatially related input and output data, and (2) multiple input parameters (transmissivity and recharge).

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.

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.

Stellar Parameters in an Instant with Machine Learning. Application to Kepler LEGACY Targets

NASA Astrophysics Data System (ADS)

Bellinger, Earl P.; Angelou, George C.; Hekker, Saskia; Basu, Sarbani; Ball, Warrick H.; Guggenberger, Elisabet

2017-10-01

With the advent of dedicated photometric space missions, the ability to rapidly process huge catalogues of stars has become paramount. Bellinger and Angelou et al. [1] recently introduced a new method based on machine learning for inferring the stellar parameters of main-sequence stars exhibiting solar-like oscillations. The method makes precise predictions that are consistent with other methods, but with the advantages of being able to explore many more parameters while costing practically no time. Here we apply the method to 52 so-called "LEGACY" main-sequence stars observed by the Kepler space mission. For each star, we present estimates and uncertainties of mass, age, radius, luminosity, core hydrogen abundance, surface helium abundance, surface gravity, initial helium abundance, and initial metallicity as well as estimates of their evolutionary model parameters of mixing length, overshooting coeffcient, and diffusion multiplication factor. We obtain median uncertainties in stellar age, mass, and radius of 14.8%, 3.6%, and 1.7%, respectively. The source code for all analyses and for all figures appearing in this manuscript can be found electronically at https://github.com/earlbellinger/asteroseismology

Estimation and impact assessment of input and parameter uncertainty in predicting groundwater flow with a fully distributed model

NASA Astrophysics Data System (ADS)

Touhidul Mustafa, Syed Md.; Nossent, Jiri; Ghysels, Gert; Huysmans, Marijke

2017-04-01

Transient numerical groundwater flow models have been used to understand and forecast groundwater flow systems under anthropogenic and climatic effects, but the reliability of the predictions is strongly influenced by different sources of uncertainty. Hence, researchers in hydrological sciences are developing and applying methods for uncertainty quantification. Nevertheless, spatially distributed flow models pose significant challenges for parameter and spatially distributed input estimation and uncertainty quantification. In this study, we present a general and flexible approach for input and parameter estimation and uncertainty analysis of groundwater models. The proposed approach combines a fully distributed groundwater flow model (MODFLOW) with the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm. To avoid over-parameterization, the uncertainty of the spatially distributed model input has been represented by multipliers. The posterior distributions of these multipliers and the regular model parameters were estimated using DREAM. The proposed methodology has been applied in an overexploited aquifer in Bangladesh where groundwater pumping and recharge data are highly uncertain. The results confirm that input uncertainty does have a considerable effect on the model predictions and parameter distributions. Additionally, our approach also provides a new way to optimize the spatially distributed recharge and pumping data along with the parameter values under uncertain input conditions. It can be concluded from our approach that considering model input uncertainty along with parameter uncertainty is important for obtaining realistic model predictions and a correct estimation of the uncertainty bounds.

CASL L1 Milestone report : CASL.P4.01, sensitivity and uncertainty analysis for CIPS with VIPRE-W and BOA.

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

Sung, Yixing; Adams, Brian M.; Secker, Jeffrey R.

2011-12-01

The CASL Level 1 Milestone CASL.P4.01, successfully completed in December 2011, aimed to 'conduct, using methodologies integrated into VERA, a detailed sensitivity analysis and uncertainty quantification of a crud-relevant problem with baseline VERA capabilities (ANC/VIPRE-W/BOA).' The VUQ focus area led this effort, in partnership with AMA, and with support from VRI. DAKOTA was coupled to existing VIPRE-W thermal-hydraulics and BOA crud/boron deposit simulations representing a pressurized water reactor (PWR) that previously experienced crud-induced power shift (CIPS). This work supports understanding of CIPS by exploring the sensitivity and uncertainty in BOA outputs with respect to uncertain operating and model parameters. Thismore » report summarizes work coupling the software tools, characterizing uncertainties, and analyzing the results of iterative sensitivity and uncertainty studies. These studies focused on sensitivity and uncertainty of CIPS indicators calculated by the current version of the BOA code used in the industry. Challenges with this kind of analysis are identified to inform follow-on research goals and VERA development targeting crud-related challenge problems.« less

Issues and recent advances in optimal experimental design for site investigation (Invited)

NASA Astrophysics Data System (ADS)

Nowak, W.

2013-12-01

This presentation provides an overview over issues and recent advances in model-based experimental design for site exploration. The addressed issues and advances are (1) how to provide an adequate envelope to prior uncertainty, (2) how to define the information needs in a task-oriented manner, (3) how to measure the expected impact of a data set that it not yet available but only planned to be collected, and (4) how to perform best the optimization of the data collection plan. Among other shortcomings of the state-of-the-art, it is identified that there is a lack of demonstrator studies where exploration schemes based on expert judgment are compared to exploration schemes obtained by optimal experimental design. Such studies will be necessary do address the often voiced concern that experimental design is an academic exercise with little improvement potential over the well- trained gut feeling of field experts. When addressing this concern, a specific focus has to be given to uncertainty in model structure, parameterizations and parameter values, and to related surprises that data often bring about in field studies, but never in synthetic-data based studies. The background of this concern is that, initially, conceptual uncertainty may be so large that surprises are the rule rather than the exception. In such situations, field experts have a large body of experience in handling the surprises, and expert judgment may be good enough compared to meticulous optimization based on a model that is about to be falsified by the incoming data. In order to meet surprises accordingly and adapt to them, there needs to be a sufficient representation of conceptual uncertainty within the models used. Also, it is useless to optimize an entire design under this initial range of uncertainty. Thus, the goal setting of the optimization should include the objective to reduce conceptual uncertainty. A possible way out is to upgrade experimental design theory towards real-time interaction with the ongoing site investigation, such that surprises in the data are immediately accounted for to restrict the conceptual uncertainty and update the optimization of the plan.

Are quantitative sensitivity analysis methods always reliable?

NASA Astrophysics Data System (ADS)

Huang, X.

2016-12-01

Physical parameterizations developed to represent subgrid-scale physical processes include various uncertain parameters, leading to large uncertainties in today's Earth System Models (ESMs). Sensitivity Analysis (SA) is an efficient approach to quantitatively determine how the uncertainty of the evaluation metric can be apportioned to each parameter. Also, SA can identify the most influential parameters, as a result to reduce the high dimensional parametric space. In previous studies, some SA-based approaches, such as Sobol' and Fourier amplitude sensitivity testing (FAST), divide the parameters into sensitive and insensitive groups respectively. The first one is reserved but the other is eliminated for certain scientific study. However, these approaches ignore the disappearance of the interactive effects between the reserved parameters and the eliminated ones, which are also part of the total sensitive indices. Therefore, the wrong sensitive parameters might be identified by these traditional SA approaches and tools. In this study, we propose a dynamic global sensitivity analysis method (DGSAM), which iteratively removes the least important parameter until there are only two parameters left. We use the CLM-CASA, a global terrestrial model, as an example to verify our findings with different sample sizes ranging from 7000 to 280000. The result shows DGSAM has abilities to identify more influential parameters, which is confirmed by parameter calibration experiments using four popular optimization methods. For example, optimization using Top3 parameters filtered by DGSAM could achieve substantial improvement against Sobol' by 10%. Furthermore, the current computational cost for calibration has been reduced to 1/6 of the original one. In future, it is necessary to explore alternative SA methods emphasizing parameter interactions.

Assessing the relative importance of parameter and forcing uncertainty and their interactions in conceptual hydrological model simulations

NASA Astrophysics Data System (ADS)

Mockler, E. M.; Chun, K. P.; Sapriza-Azuri, G.; Bruen, M.; Wheater, H. S.

2016-11-01

Predictions of river flow dynamics provide vital information for many aspects of water management including water resource planning, climate adaptation, and flood and drought assessments. Many of the subjective choices that modellers make including model and criteria selection can have a significant impact on the magnitude and distribution of the output uncertainty. Hydrological modellers are tasked with understanding and minimising the uncertainty surrounding streamflow predictions before communicating the overall uncertainty to decision makers. Parameter uncertainty in conceptual rainfall-runoff models has been widely investigated, and model structural uncertainty and forcing data have been receiving increasing attention. This study aimed to assess uncertainties in streamflow predictions due to forcing data and the identification of behavioural parameter sets in 31 Irish catchments. By combining stochastic rainfall ensembles and multiple parameter sets for three conceptual rainfall-runoff models, an analysis of variance model was used to decompose the total uncertainty in streamflow simulations into contributions from (i) forcing data, (ii) identification of model parameters and (iii) interactions between the two. The analysis illustrates that, for our subjective choices, hydrological model selection had a greater contribution to overall uncertainty, while performance criteria selection influenced the relative intra-annual uncertainties in streamflow predictions. Uncertainties in streamflow predictions due to the method of determining parameters were relatively lower for wetter catchments, and more evenly distributed throughout the year when the Nash-Sutcliffe Efficiency of logarithmic values of flow (lnNSE) was the evaluation criterion.

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

Uncertainty in the Modeling of Tsunami Sediment Transport

NASA Astrophysics Data System (ADS)

Jaffe, B. E.; Sugawara, D.; Goto, K.; Gelfenbaum, G. R.; La Selle, S.

2016-12-01

Erosion and deposition from tsunamis record information about tsunami hydrodynamics and size that can be interpreted to improve tsunami hazard assessment. A recent study (Jaffe et al., 2016) explores sources and methods for quantifying uncertainty in tsunami sediment transport modeling. Uncertainty varies with tsunami properties, study site characteristics, available input data, sediment grain size, and the model used. Although uncertainty has the potential to be large, case studies for both forward and inverse models have shown that sediment transport modeling provides useful information on tsunami inundation and hydrodynamics that can be used to improve tsunami hazard assessment. 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 the development of hybrid modeling approaches to exploit the strengths of forward and inverse models. As uncertainty in tsunami sediment transport modeling is reduced, and with increased ability to quantify uncertainty, the geologic record of tsunamis will become more valuable in the assessment of tsunami hazard. Jaffe, B., Goto, K., Sugawara, D., Gelfenbaum, G., and La Selle, S., "Uncertainty in Tsunami Sediment Transport Modeling", Journal of Disaster Research Vol. 11 No. 4, pp. 647-661, 2016, doi: 10.20965/jdr.2016.p0647 https://www.fujipress.jp/jdr/dr/dsstr001100040647/

Evaluating uncertainty in environmental life-cycle assessment. A case study comparing two insulation options for a Dutch one-family dwelling.

PubMed

Huijbregts, Mark A J; Gilijamse, Wim; Ragas, Ad M J; Reijnders, Lucas

2003-06-01

The evaluation of uncertainty is relatively new in environmental life-cycle assessment (LCA). It provides useful information to assess the reliability of LCA-based decisions and to guide future research toward reducing uncertainty. Most uncertainty studies in LCA quantify only one type of uncertainty, i.e., uncertainty due to input data (parameter uncertainty). However, LCA outcomes can also be uncertain due to normative choices (scenario uncertainty) and the mathematical models involved (model uncertainty). The present paper outlines a new methodology that quantifies parameter, scenario, and model uncertainty simultaneously in environmental life-cycle assessment. The procedure is illustrated in a case study that compares two insulation options for a Dutch one-family dwelling. Parameter uncertainty was quantified by means of Monte Carlo simulation. Scenario and model uncertainty were quantified by resampling different decision scenarios and model formulations, respectively. Although scenario and model uncertainty were not quantified comprehensively, the results indicate that both types of uncertainty influence the case study outcomes. This stresses the importance of quantifying parameter, scenario, and model uncertainty simultaneously. The two insulation options studied were found to have significantly different impact scores for global warming, stratospheric ozone depletion, and eutrophication. The thickest insulation option has the lowest impact on global warming and eutrophication, and the highest impact on stratospheric ozone depletion.

MeProRisk - a Joint Venture for Minimizing Risk in Geothermal Reservoir Development

NASA Astrophysics Data System (ADS)

Clauser, C.; Marquart, G.

2009-12-01

Exploration and development of geothermal reservoirs for the generation of electric energy involves high engineering and economic risks due to the need for 3-D geophysical surface surveys and deep boreholes. The MeProRisk project provides a strategy guideline for reducing these risks by combining cross-disciplinary information from different specialists: Scientists from three German universities and two private companies contribute with new methods in seismic modeling and interpretation, numerical reservoir simulation, estimation of petrophysical parameters, and 3-D visualization. The approach chosen in MeProRisk consists in considering prospecting and developing of geothermal reservoirs as an iterative process. A first conceptual model for fluid flow and heat transport simulation can be developed based on limited available initial information on geology and rock properties. In the next step, additional data is incorporated which is based on (a) new seismic interpretation methods designed for delineating fracture systems, (b) statistical studies on large numbers of rock samples for estimating reliable rock parameters, (c) in situ estimates of the hydraulic conductivity tensor. This results in a continuous refinement of the reservoir model where inverse modelling of fluid flow and heat transport allows infering the uncertainty and resolution of the model at each iteration step. This finally yields a calibrated reservoir model which may be used to direct further exploration by optimizing additional borehole locations, estimate the uncertainty of key operational and economic parameters, and optimize the long-term operation of a geothermal resrvoir.

Parameter-induced uncertainty quantification of crop yields, soil N2O and CO2 emission for 8 arable sites across Europe using the LandscapeDNDC model

NASA Astrophysics Data System (ADS)

Santabarbara, Ignacio; Haas, Edwin; Kraus, David; Herrera, Saul; Klatt, Steffen; Kiese, Ralf

2014-05-01

When using biogeochemical models to estimate greenhouse gas emissions at site to regional/national levels, the assessment and quantification of the uncertainties of simulation results are of significant importance. The uncertainties in simulation results of process-based ecosystem models may result from uncertainties of the process parameters that describe the processes of the model, model structure inadequacy as well as uncertainties in the observations. Data for development and testing of uncertainty analisys were corp yield observations, measurements of soil fluxes of nitrous oxide (N2O) and carbon dioxide (CO2) from 8 arable sites across Europe. Using the process-based biogeochemical model LandscapeDNDC for simulating crop yields, N2O and CO2 emissions, our aim is to assess the simulation uncertainty by setting up a Bayesian framework based on Metropolis-Hastings algorithm. Using Gelman statistics convergence criteria and parallel computing techniques, enable multi Markov Chains to run independently in parallel and create a random walk to estimate the joint model parameter distribution. Through means distribution we limit the parameter space, get probabilities of parameter values and find the complex dependencies among them. With this parameter distribution that determines soil-atmosphere C and N exchange, we are able to obtain the parameter-induced uncertainty of simulation results and compare them with the measurements data.

Fukushima Daiichi Unit 1 Uncertainty Analysis-Exploration of Core Melt Progression Uncertain Parameters-Volume II.

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

Denman, Matthew R.; Brooks, Dusty Marie

Sandia National Laboratories (SNL) has conducted an uncertainty analysi s (UA) on the Fukushima Daiichi unit (1F1) accident progression wit h the MELCOR code. Volume I of the 1F1 UA discusses the physical modeling details and time history results of the UA. Volume II of the 1F1 UA discusses the statistical viewpoint. The model used was developed for a previous accident reconstruction investigation jointly sponsored by the US Department of Energy (DOE) and Nuclear Regulatory Commission (NRC). The goal of this work was to perform a focused evaluation of uncertainty in core damage progression behavior and its effect on keymore » figures - of - merit (e.g., hydrogen production, fraction of intact fuel, vessel lower head failure) and in doing so assess the applicability of traditional sensitivity analysis techniques .« less

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.

A design methodology for nonlinear systems containing parameter uncertainty

NASA Technical Reports Server (NTRS)

Young, G. E.; Auslander, D. M.

1983-01-01

In the present design methodology for nonlinear systems containing parameter uncertainty, a generalized sensitivity analysis is incorporated which employs parameter space sampling and statistical inference. For the case of a system with j adjustable and k nonadjustable parameters, this methodology (which includes an adaptive random search strategy) is used to determine the combination of j adjustable parameter values which maximize the probability of those performance indices which simultaneously satisfy design criteria in spite of the uncertainty due to k nonadjustable parameters.

Advanced Stochastic Collocation Methods for Polynomial Chaos in RAVEN

NASA Astrophysics Data System (ADS)

Talbot, Paul W.

As experiment complexity in fields such as nuclear engineering continually increases, so does the demand for robust computational methods to simulate them. In many simulations, input design parameters and intrinsic experiment properties are sources of uncertainty. Often small perturbations in uncertain parameters have significant impact on the experiment outcome. For instance, in nuclear fuel performance, small changes in fuel thermal conductivity can greatly affect maximum stress on the surrounding cladding. The difficulty quantifying input uncertainty impact in such systems has grown with the complexity of numerical models. Traditionally, uncertainty quantification has been approached using random sampling methods like Monte Carlo. For some models, the input parametric space and corresponding response output space is sufficiently explored with few low-cost calculations. For other models, it is computationally costly to obtain good understanding of the output space. To combat the expense of random sampling, this research explores the possibilities of using advanced methods in Stochastic Collocation for generalized Polynomial Chaos (SCgPC) as an alternative to traditional uncertainty quantification techniques such as Monte Carlo (MC) and Latin Hypercube Sampling (LHS) methods for applications in nuclear engineering. We consider traditional SCgPC construction strategies as well as truncated polynomial spaces using Total Degree and Hyperbolic Cross constructions. We also consider applying anisotropy (unequal treatment of different dimensions) to the polynomial space, and offer methods whereby optimal levels of anisotropy can be approximated. We contribute development to existing adaptive polynomial construction strategies. Finally, we consider High-Dimensional Model Reduction (HDMR) expansions, using SCgPC representations for the subspace terms, and contribute new adaptive methods to construct them. We apply these methods on a series of models of increasing complexity. We use analytic models of various levels of complexity, then demonstrate performance on two engineering-scale problems: a single-physics nuclear reactor neutronics problem, and a multiphysics fuel cell problem coupling fuels performance and neutronics. Lastly, we demonstrate sensitivity analysis for a time-dependent fuels performance problem. We demonstrate the application of all the algorithms in RAVEN, a production-level uncertainty quantification framework.

Computational Evaluation of Cochlear Implant Surgery Outcomes Accounting for Uncertainty and Parameter Variability.

PubMed

Mangado, Nerea; Pons-Prats, Jordi; Coma, Martí; Mistrík, Pavel; Piella, Gemma; Ceresa, Mario; González Ballester, Miguel Á

2018-01-01

Cochlear implantation (CI) is a complex surgical procedure that restores hearing in patients with severe deafness. The successful outcome of the implanted device relies on a group of factors, some of them unpredictable or difficult to control. Uncertainties on the electrode array position and the electrical properties of the bone make it difficult to accurately compute the current propagation delivered by the implant and the resulting neural activation. In this context, we use uncertainty quantification methods to explore how these uncertainties propagate through all the stages of CI computational simulations. To this end, we employ an automatic framework, encompassing from the finite element generation of CI models to the assessment of the neural response induced by the implant stimulation. To estimate the confidence intervals of the simulated neural response, we propose two approaches. First, we encode the variability of the cochlear morphology among the population through a statistical shape model. This allows us to generate a population of virtual patients using Monte Carlo sampling and to assign to each of them a set of parameter values according to a statistical distribution. The framework is implemented and parallelized in a High Throughput Computing environment that enables to maximize the available computing resources. Secondly, we perform a patient-specific study to evaluate the computed neural response to seek the optimal post-implantation stimulus levels. Considering a single cochlear morphology, the uncertainty in tissue electrical resistivity and surgical insertion parameters is propagated using the Probabilistic Collocation method, which reduces the number of samples to evaluate. Results show that bone resistivity has the highest influence on CI outcomes. In conjunction with the variability of the cochlear length, worst outcomes are obtained for small cochleae with high resistivity values. However, the effect of the surgical insertion length on the CI outcomes could not be clearly observed, since its impact may be concealed by the other considered parameters. Whereas the Monte Carlo approach implies a high computational cost, Probabilistic Collocation presents a suitable trade-off between precision and computational time. Results suggest that the proposed framework has a great potential to help in both surgical planning decisions and in the audiological setting process.

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.

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.

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.

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.

Stochastic inversion of time-lapse geophysical data to characterize the vadose zone at the Arrenaes field site (Denmark)

NASA Astrophysics Data System (ADS)

Marie, S.; Irving, J. D.; Looms, M. C.; Nielsen, L.; Holliger, K.

2011-12-01

Geophysical methods such as ground-penetrating radar (GPR) can provide valuable information on the hydrological properties of the vadose zone. In particular, there is evidence to suggest that the stochastic inversion of such data may allow for significant reductions in uncertainty regarding subsurface van-Genuchten-Mualem (VGM) parameters, which characterize unsaturated hydrodynamic behaviour as defined by the combination of the water retention and hydraulic conductivity functions. A significant challenge associated with the use of geophysical methods in a hydrological context is that they generally exhibit an indirect and/or weak sensitivity to the hydraulic parameters of interest. A novel and increasingly popular means of addressing this issue involves the acquisition of geophysical data in a time-lapse fashion while changes occur in the hydrological condition of the probed subsurface region. Another significant challenge when attempting to use geophysical data for the estimation of subsurface hydrological properties is the inherent non-linearity and non-uniqueness of the corresponding inverse problems. Stochastic inversion approaches have the advantage of providing a comprehensive exploration of the model space, which makes them ideally suited for addressing such issues. In this work, we present the stochastic inversion of time-lapse zero-offset-profile (ZOP) crosshole GPR traveltime data, collected during a forced infiltration experiment at the Arreneas field site in Denmark, in order to estimate subsurface VGM parameters and their corresponding uncertainties. We do this using a Bayesian Markov-chain-Monte-Carlo (MCMC) inversion approach. We find that the Bayesian-MCMC methodology indeed allows for a substantial refinement in the inferred posterior parameter distributions of the VGM parameters as compared to the corresponding priors. To further understand the potential impact on capturing the underlying hydrological behaviour, we also explore how the posterior VGM parameter distributions affect the hydrodynamic characteristics. In doing so, we find clear evidence that the approach pursued in this study allows for effective characterization of the hydrological behaviour of the probed subsurface region.

Linking 1D coastal ocean modelling to environmental management: an ensemble approach

NASA Astrophysics Data System (ADS)

Mussap, Giulia; Zavatarelli, Marco; Pinardi, Nadia

2017-12-01

The use of a one-dimensional interdisciplinary numerical model of the coastal ocean as a tool contributing to the formulation of ecosystem-based management (EBM) is explored. The focus is on the definition of an experimental design based on ensemble simulations, integrating variability linked to scenarios (characterised by changes in the system forcing) and to the concurrent variation of selected, and poorly constrained, model parameters. The modelling system used was previously specifically designed for the use in "data-rich" areas, so that horizontal dynamics can be resolved by a diagnostic approach and external inputs can be parameterised by nudging schemes properly calibrated. Ensembles determined by changes in the simulated environmental (physical and biogeochemical) dynamics, under joint forcing and parameterisation variations, highlight the uncertainties associated to the application of specific scenarios that are relevant to EBM, providing an assessment of the reliability of the predicted changes. The work has been carried out by implementing the coupled modelling system BFM-POM1D in an area of Gulf of Trieste (northern Adriatic Sea), considered homogeneous from the point of view of hydrological properties, and forcing it by changing climatic (warming) and anthropogenic (reduction of the land-based nutrient input) pressure. Model parameters affected by considerable uncertainties (due to the lack of relevant observations) were varied jointly with the scenarios of change. The resulting large set of ensemble simulations provided a general estimation of the model uncertainties related to the joint variation of pressures and model parameters. The information of the model result variability aimed at conveying efficiently and comprehensibly the information on the uncertainties/reliability of the model results to non-technical EBM planners and stakeholders, in order to have the model-based information effectively contributing to EBM.

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.

Parameter and prediction uncertainty in an optimized terrestrial carbon cycle model: Effects of constraining variables and data record length

NASA Astrophysics Data System (ADS)

Ricciuto, Daniel M.; King, Anthony W.; Dragoni, D.; Post, Wilfred M.

2011-03-01

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 are 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.

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

Global emission projections of particulate matter (PM): II. Uncertainty analyses of on-road vehicle exhaust emissions

NASA Astrophysics Data System (ADS)

Yan, Fang; Winijkul, Ekbordin; Bond, Tami C.; Streets, David G.

2014-04-01

Estimates of future emissions are necessary for understanding the future health of the atmosphere, designing national and international strategies for air quality control, and evaluating mitigation policies. Emission inventories are uncertain and future projections even more so, thus it is important to quantify the uncertainty inherent in emission projections. This paper is the second in a series that seeks to establish a more mechanistic understanding of future air pollutant emissions based on changes in technology. The first paper in this series (Yan et al., 2011) described a model that projects emissions based on dynamic changes of vehicle fleet, Speciated Pollutant Emission Wizard-Trend, or SPEW-Trend. In this paper, we explore the underlying uncertainties of global and regional exhaust PM emission projections from on-road vehicles in the coming decades using sensitivity analysis and Monte Carlo simulation. This work examines the emission sensitivities due to uncertainties in retirement rate, timing of emission standards, transition rate of high-emitting vehicles called “superemitters”, and emission factor degradation rate. It is concluded that global emissions are most sensitive to parameters in the retirement rate function. Monte Carlo simulations show that emission uncertainty caused by lack of knowledge about technology composition is comparable to the uncertainty demonstrated by alternative economic scenarios, especially during the period 2010-2030.

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

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

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.

Measurement uncertainty of liquid chromatographic analyses visualized by Ishikawa diagrams.

PubMed

Meyer, Veronika R

2003-09-01

Ishikawa, or cause-and-effect diagrams, help to visualize the parameters that influence a chromatographic analysis. Therefore, they facilitate the set up of the uncertainty budget of the analysis, which can then be expressed in mathematical form. If the uncertainty is calculated as the Gaussian sum of all uncertainty parameters, it is necessary to quantitate them all, a task that is usually not practical. The other possible approach is to use the intermediate precision as a base for the uncertainty calculation. In this case, it is at least necessary to consider the uncertainty of the purity of the reference material in addition to the precision data. The Ishikawa diagram is then very simple, and so is the uncertainty calculation. This advantage is given by the loss of information about the parameters that influence the measurement uncertainty.

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.

Can climate variability information constrain a hydrological model for an ungauged Costa Rican catchment?

NASA Astrophysics Data System (ADS)

Quesada-Montano, Beatriz; Westerberg, Ida K.; Fuentes-Andino, Diana; Hidalgo-Leon, Hugo; Halldin, Sven

2017-04-01

Long-term hydrological data are key to understanding catchment behaviour and for decision making within water management and planning. Given the lack of observed data in many regions worldwide, hydrological models are an alternative for reproducing historical streamflow series. Additional types of information - to locally observed discharge - can be used to constrain model parameter uncertainty for ungauged catchments. Climate variability exerts a strong influence on streamflow variability on long and short time scales, in particular in the Central-American region. We therefore explored the use of climate variability knowledge to constrain the simulated discharge uncertainty of a conceptual hydrological model applied to a Costa Rican catchment, assumed to be ungauged. To reduce model uncertainty we first rejected parameter relationships that disagreed with our understanding of the system. We then assessed how well climate-based constraints applied at long-term, inter-annual and intra-annual time scales could constrain model uncertainty. Finally, we compared the climate-based constraints to a constraint on low-flow statistics based on information obtained from global maps. We evaluated our method in terms of the ability of the model to reproduce the observed hydrograph and the active catchment processes in terms of two efficiency measures, a statistical consistency measure, a spread measure and 17 hydrological signatures. We found that climate variability knowledge was useful for reducing model uncertainty, in particular, unrealistic representation of deep groundwater processes. The constraints based on global maps of low-flow statistics provided more constraining information than those based on climate variability, but the latter rejected slow rainfall-runoff representations that the low flow statistics did not reject. The use of such knowledge, together with information on low-flow statistics and constraints on parameter relationships showed to be useful to constrain model uncertainty for an - assumed to be - ungauged basin. This shows that our method is promising for reconstructing long-term flow data for ungauged catchments on the Pacific side of Central America, and that similar methods can be developed for ungauged basins in other regions where climate variability exerts a strong control on streamflow variability.

Frontal Theta Reflects Uncertainty and Unexpectedness during Exploration and Exploitation

PubMed Central

Figueroa, Christina M.; Cohen, Michael X; Frank, Michael J.

2012-01-01

In order to understand the exploitation/exploration trade-off in reinforcement learning, previous theoretical and empirical accounts have suggested that increased uncertainty may precede the decision to explore an alternative option. To date, the neural mechanisms that support the strategic application of uncertainty-driven exploration remain underspecified. In this study, electroencephalography (EEG) was used to assess trial-to-trial dynamics relevant to exploration and exploitation. Theta-band activities over middle and lateral frontal areas have previously been implicated in EEG studies of reinforcement learning and strategic control. It was hypothesized that these areas may interact during top-down strategic behavioral control involved in exploratory choices. Here, we used a dynamic reward–learning task and an associated mathematical model that predicted individual response times. This reinforcement-learning model generated value-based prediction errors and trial-by-trial estimates of exploration as a function of uncertainty. Mid-frontal theta power correlated with unsigned prediction error, although negative prediction errors had greater power overall. Trial-to-trial variations in response-locked frontal theta were linearly related to relative uncertainty and were larger in individuals who used uncertainty to guide exploration. This finding suggests that theta-band activities reflect prefrontal-directed strategic control during exploratory choices. PMID:22120491

Next-Generation Tools For Next-Generation Surveys

NASA Astrophysics Data System (ADS)

Murray, S. G.

2017-04-01

The next generation of large-scale galaxy surveys, across the electromagnetic spectrum, loom on the horizon as explosively game-changing datasets, in terms of our understanding of cosmology and structure formation. We are on the brink of a torrent of data that is set to both confirm and constrain current theories to an unprecedented level, and potentially overturn many of our conceptions. One of the great challenges of this forthcoming deluge is to extract maximal scientific content from the vast array of raw data. This challenge requires not only well-understood and robust physical models, but a commensurate network of software implementations with which to efficiently apply them. The halo model, a semi-analytic treatment of cosmological spatial statistics down to nonlinear scales, provides an excellent mathematical framework for exploring the nature of dark matter. This thesis presents a next-generation toolkit based on the halo model formalism, intended to fulfil the requirements of next-generation surveys. Our toolkit comprises three tools: (i) hmf, a comprehensive and flexible calculator for halo mass functions (HMFs) within extended Press-Schechter theory, (ii) the MRP distribution for extremely efficient analytic characterisation of HMFs, and (iii) halomod, an extension of hmf which provides support for the full range of halo model components. In addition to the development and technical presentation of these tools, we apply each to the task of physical modelling. With hmf, we determine the precision of our knowledge of the HMF, due to uncertainty in our knowledge of the cosmological parameters, over the past decade of cosmic microwave background (CMB) experiments. We place rule-of-thumb uncertainties on the predicted HMF for the Planck cosmology, and find that current limits on the precision are driven by modeling uncertainties rather than those from cosmological parameters. With the MRP, we create and test a method for robustly fitting the HMF to observed masses with arbitrary measurement uncertainties on a per-object basis. We find that our method reduces estimation uncertainty on parameters by over 50%, and correctly accounts for Eddington bias even in extremely poorly measured data. Additionally, we use the analytical properties of the MRP to obtain asymptotically correct forms for the stellar-mass halo-mass relation, in the subhalo abundance matching scheme. Finally, with halomod, we explore the viability of the halo model as a test of warm dark matter (WDM) via galaxy clustering. Examining three distinct scale regimes, we find that the clustering of galaxies at the smallest resolvable scales may provide a valuable independent probe in the coming era.

Incorporating uncertainty in RADTRAN 6.0 input files.

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

Dennis, Matthew L.; Weiner, Ruth F.; Heames, Terence John

Uncertainty may be introduced into RADTRAN analyses by distributing input parameters. The MELCOR Uncertainty Engine (Gauntt and Erickson, 2004) has been adapted for use in RADTRAN to determine the parameter shape and minimum and maximum of the distribution, to sample on the distribution, and to create an appropriate RADTRAN batch file. Coupling input parameters is not possible in this initial application. It is recommended that the analyst be very familiar with RADTRAN and able to edit or create a RADTRAN input file using a text editor before implementing the RADTRAN Uncertainty Analysis Module. Installation of the MELCOR Uncertainty Engine ismore » required for incorporation of uncertainty into RADTRAN. Gauntt and Erickson (2004) provides installation instructions as well as a description and user guide for the uncertainty engine.« less

A stochastic optimization model under modeling uncertainty and parameter certainty for groundwater remediation design--part I. Model development.

PubMed

He, L; Huang, G H; Lu, H W

2010-04-15

Solving groundwater remediation optimization problems based on proxy simulators can usually yield optimal solutions differing from the "true" ones of the problem. This study presents a new stochastic optimization model under modeling uncertainty and parameter certainty (SOMUM) and the associated solution method for simultaneously addressing modeling uncertainty associated with simulator residuals and optimizing groundwater remediation processes. This is a new attempt different from the previous modeling efforts. The previous ones focused on addressing uncertainty in physical parameters (i.e. soil porosity) while this one aims to deal with uncertainty in mathematical simulator (arising from model residuals). Compared to the existing modeling approaches (i.e. only parameter uncertainty is considered), the model has the advantages of providing mean-variance analysis for contaminant concentrations, mitigating the effects of modeling uncertainties on optimal remediation strategies, offering confidence level of optimal remediation strategies to system designers, and reducing computational cost in optimization processes. 2009 Elsevier B.V. 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.

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.

Diel trend in plant sensitivity to ozone: Implications for exposure- and flux-based ozone metrics

NASA Astrophysics Data System (ADS)

Grantz, David A.

2014-12-01

Plant sensitivity to ozone (O3) is critical to modeling impacts of air pollution on vegetation. A diel timecourse of sensitivity (S) was recently determined in Pima cotton (Grantz et al., 2013). The sensitivity parameter serves as a weighting factor for stomatal uptake (ozone flux, F), or cumulative F (dose, D). Previous approaches used various weighting schemes to modify ozone concentration ([O3]) or cumulative [O3] (exposure, E). Use of the S parameter allows calculation of effective flux (Feff) and effective dose (Deff). Though theoretically sound, the practical significance of S has not been evaluated due to the previous lack of available data. Here, the newly available S parameter is used to explore the relationships between exposure- and flux-based O3 metrics in response to scenarios of contrasting stomatal conductance (gs) and ambient [O3]. The O3 scenarios were similar but differed in timing of peak [O3]. E varied by up to 13.7%, D by up to 15.4%, and Deff, which factors in sensitivity, by up to 19.0%. The gs scenarios differed in midday magnitude and nocturnal closure. Cumulative gs varied by 65.2%, which was attenuated in D to 49.2% and in Deff to 51.1%. A simulation of hourly [O3], F, and Feff was run using Monte Carlo techniques with a full month of ambient [O3] data. Resulting diel timecourses of [O3], F, and Feff were realistic, with the principal sources of uncertainty in the physiological parameters, gs and S. Analysis of hourly values from the scenarios and the simulation output demonstrated significant correlation among the O3 metrics. However, the uncertainty in both F and Feff predicted from [O3] was large and proportional to [O3], yielding greatest uncertainty under conditions of high [O3] and potential phytotoxicity. In contrast, Feff was significantly correlated with F, with low variability that was not proportional to F. As a result, uncertainty was low and prediction potentially useful under conditions of likely injury. These results suggest that F, which incorporates gs, represents a substantial improvement over ambient [O3], which does not. Feff, which incorporates S, was closely related to F, which does not use S. The substantial effort required to measure or model S and Feff may not be justified under some conditions. Further research to obtain additional timecourses of S and to explore additional [O3] and gs scenarios is urgently required.

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

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.

Uncertainty analysis of hydrological modeling in a tropical area using different algorithms

NASA Astrophysics Data System (ADS)

Rafiei Emam, Ammar; Kappas, Martin; Fassnacht, Steven; Linh, Nguyen Hoang Khanh

2018-01-01

Hydrological modeling outputs are subject to uncertainty resulting from different sources of errors (e.g., error in input data, model structure, and model parameters), making quantification of uncertainty in hydrological modeling imperative and meant to improve reliability of modeling results. The uncertainty analysis must solve difficulties in calibration of hydrological models, which further increase in areas with data scarcity. The purpose of this study is to apply four uncertainty analysis algorithms to a semi-distributed hydrological model, quantifying different source of uncertainties (especially parameter uncertainty) and evaluate their performance. In this study, the Soil and Water Assessment Tools (SWAT) eco-hydrological model was implemented for the watershed in the center of Vietnam. The sensitivity of parameters was analyzed, and the model was calibrated. The uncertainty analysis for the hydrological model was conducted based on four algorithms: Generalized Likelihood Uncertainty Estimation (GLUE), Sequential Uncertainty Fitting (SUFI), Parameter Solution method (ParaSol) and Particle Swarm Optimization (PSO). The performance of the algorithms was compared using P-factor and Rfactor, coefficient of determination (R 2), the Nash Sutcliffe coefficient of efficiency (NSE) and Percent Bias (PBIAS). The results showed the high performance of SUFI and PSO with P-factor>0.83, R-factor <0.56 and R 2>0.91, NSE>0.89, and 0.18

Uncertainty quantification and propagation of errors of the Lennard-Jones 12-6 parameters for n-alkanes

PubMed Central

Knotts, Thomas A.

2017-01-01

Molecular simulation has the ability to predict various physical properties that are difficult to obtain experimentally. For example, we implement molecular simulation to predict the critical constants (i.e., critical temperature, critical density, critical pressure, and critical compressibility factor) for large n-alkanes that thermally decompose experimentally (as large as C48). Historically, molecular simulation has been viewed as a tool that is limited to providing qualitative insight. One key reason for this perceived weakness in molecular simulation is the difficulty to quantify the uncertainty in the results. This is because molecular simulations have many sources of uncertainty that propagate and are difficult to quantify. We investigate one of the most important sources of uncertainty, namely, the intermolecular force field parameters. Specifically, we quantify the uncertainty in the Lennard-Jones (LJ) 12-6 parameters for the CH4, CH3, and CH2 united-atom interaction sites. We then demonstrate how the uncertainties in the parameters lead to uncertainties in the saturated liquid density and critical constant values obtained from Gibbs Ensemble Monte Carlo simulation. Our results suggest that the uncertainties attributed to the LJ 12-6 parameters are small enough that quantitatively useful estimates of the saturated liquid density and the critical constants can be obtained from molecular simulation. PMID:28527455

Exploring the impact of forcing error characteristics on physically based snow simulations within a global sensitivity analysis framework

NASA Astrophysics Data System (ADS)

Raleigh, M. S.; Lundquist, J. D.; Clark, M. P.

2015-07-01

Physically based models provide insights into key hydrologic processes but are associated with uncertainties due to deficiencies in forcing data, model parameters, and model structure. Forcing uncertainty is enhanced in snow-affected catchments, where weather stations are scarce and prone to measurement errors, and meteorological variables exhibit high variability. Hence, there is limited understanding of how forcing error characteristics affect simulations of cold region hydrology and which error characteristics are most important. Here we employ global sensitivity analysis to explore how (1) different error types (i.e., bias, random errors), (2) different error probability distributions, and (3) different error magnitudes influence physically based simulations of four snow variables (snow water equivalent, ablation rates, snow disappearance, and sublimation). We use the Sobol' global sensitivity analysis, which is typically used for model parameters but adapted here for testing model sensitivity to coexisting errors in all forcings. We quantify the Utah Energy Balance model's sensitivity to forcing errors with 1 840 000 Monte Carlo simulations across four sites and five different scenarios. Model outputs were (1) consistently more sensitive to forcing biases than random errors, (2) generally less sensitive to forcing error distributions, and (3) critically sensitive to different forcings depending on the relative magnitude of errors. For typical error magnitudes found in areas with drifting snow, precipitation bias was the most important factor for snow water equivalent, ablation rates, and snow disappearance timing, but other forcings had a more dominant impact when precipitation uncertainty was due solely to gauge undercatch. Additionally, the relative importance of forcing errors depended on the model output of interest. Sensitivity analysis can reveal which forcing error characteristics matter most for hydrologic modeling.

Using internal discharge data in a distributed conceptual model to reduce uncertainty in streamflow simulations

NASA Astrophysics Data System (ADS)

Guerrero, J.; Halldin, S.; Xu, C.; Lundin, L.

2011-12-01

Distributed hydrological models are important tools in water management as they account for the spatial variability of the hydrological data, as well as being able to produce spatially distributed outputs. They can directly incorporate and assess potential changes in the characteristics of our basins. A recognized problem for models in general is equifinality, which is only exacerbated for distributed models who tend to have a large number of parameters. We need to deal with the fundamentally ill-posed nature of the problem that such models force us to face, i.e. a large number of parameters and very few variables that can be used to constrain them, often only the catchment discharge. There is a growing but yet limited literature showing how the internal states of a distributed model can be used to calibrate/validate its predictions. In this paper, a distributed version of WASMOD, a conceptual rainfall runoff model with only three parameters, combined with a routing algorithm based on the high-resolution HydroSHEDS data was used to simulate the discharge in the Paso La Ceiba basin in Honduras. The parameter space was explored using Monte-Carlo simulations and the region of space containing the parameter-sets that were considered behavioral according to two different criteria was delimited using the geometric concept of alpha-shapes. The discharge data from five internal sub-basins was used to aid in the calibration of the model and to answer the following questions: Can this information improve the simulations at the outlet of the catchment, or decrease their uncertainty? Also, after reducing the number of model parameters needing calibration through sensitivity analysis: Is it possible to relate them to basin characteristics? The analysis revealed that in most cases the internal discharge data can be used to reduce the uncertainty in the discharge at the outlet, albeit with little improvement in the overall simulation results.

The Impact of Model and Rainfall Forcing Errors on Characterizing Soil Moisture Uncertainty in Land Surface Modeling

NASA Technical Reports Server (NTRS)

Maggioni, V.; Anagnostou, E. N.; Reichle, R. H.

2013-01-01

The contribution of rainfall forcing errors relative to model (structural and parameter) uncertainty in the prediction of soil moisture is investigated by integrating the NASA Catchment Land Surface Model (CLSM), forced with hydro-meteorological data, in the Oklahoma region. Rainfall-forcing uncertainty is introduced using a stochastic error model that generates ensemble rainfall fields from satellite rainfall products. The ensemble satellite rain fields are propagated through CLSM to produce soil moisture ensembles. Errors in CLSM are modeled with two different approaches: either by perturbing model parameters (representing model parameter uncertainty) or by adding randomly generated noise (representing model structure and parameter uncertainty) to the model prognostic variables. Our findings highlight that the method currently used in the NASA GEOS-5 Land Data Assimilation System to perturb CLSM variables poorly describes the uncertainty in the predicted soil moisture, even when combined with rainfall model perturbations. On the other hand, by adding model parameter perturbations to rainfall forcing perturbations, a better characterization of uncertainty in soil moisture simulations is observed. Specifically, an analysis of the rank histograms shows that the most consistent ensemble of soil moisture is obtained by combining rainfall and model parameter perturbations. When rainfall forcing and model prognostic perturbations are added, the rank histogram shows a U-shape at the domain average scale, which corresponds to a lack of variability in the forecast ensemble. The more accurate estimation of the soil moisture prediction uncertainty obtained by combining rainfall and parameter perturbations is encouraging for the application of this approach in ensemble data assimilation systems.

Theoretical study of the hyperfine-interaction constants and the isotope-shift factors for the 3 s21S0-3 s 3 p 3,1P1o transitions in Al+

NASA Astrophysics Data System (ADS)

Zhang, Tingxian; Xie, Luyou; Li, Jiguang; Lu, Zehuang

2017-07-01

We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of 3 s 3 p 3,1P1o states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state 3 s 2 1S0 in Al+ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the core-core and the higher order correlations are considerable for evaluating the uncertainties of the atomic parameters concerned. The uncertainties of the hyperfine interaction constants in this work are less than 1.6%. Although the isotope shift factors are highly sensitive to the electron correlations, reasonable uncertainties were obtained by exploring the effects of the electron correlations. Moreover, we found that the relativistic nuclear recoil corrections to the mass shift factors are very small and insensitive to the electron correlations for Al+. These atomic parameters present in this work are valuable for extracting the nuclear electric quadrupole moments and the mean-square charge radii of Al isotopes.

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...

A probabilistic approach towards understanding how planet composition affects plate tectonics - through time and space.

NASA Astrophysics Data System (ADS)

Stamenkovic, V.

2017-12-01

We focus on the connections between plate tectonics and planet composition — by studying how plate yielding is affected by surface and mantle water, and by variable amounts of Fe, SiC, or radiogenic heat sources within the planet interior. We especially explore whether we can make any robust conclusions if we account for variable initial conditions, current uncertainties in model parameters and the pressure dependence of the viscosity, as well as uncertainties on how a variable composition affects mantle rheology, melting temperatures, and thermal conductivities. We use a 1D thermal evolution model to explore with more than 200,000 simulations the robustness of our results and use our previous results from 3D calculations to help determine the most likely scenario within the uncertainties we still face today. The results that are robust in spite of all uncertainties are that iron-rich mantle rock seems to reduce the efficiency of plate yielding occurring on silicate planets like the Earth if those planets formed along or above mantle solidus and that carbon planets do not seem to be ideal candidates for plate tectonics because of slower creep rates and generally higher thermal conductivities for SiC. All other conclusions depend on not yet sufficiently constrained parameters. For the most likely case based on our current understanding, we find that, within our range of varied planet conditions (1-10 Earth masses), planets with the greatest efficiency of plate yielding are silicate rocky planets of 1 Earth mass with large metallic cores (average density 5500-7000 kg m-3) with minimal mantle concentrations of iron (as little as 0% is preferred) and radiogenic isotopes at formation (up to 10 times less than Earth's initial abundance; less heat sources do not mean no heat sources). Based on current planet formation scenarios and observations of stellar abundances across the Galaxy as well as models of the evolution of the interstellar medium, such planets are suggested to be statistically more common around young stars in the outer disk of the Milky Way. Rocky super-Earths, undifferentiated planets, and still hypothetical carbon planets have the lowest plate yielding efficiencies found in our study. This work aids exoplanet characterization and helps explore the fundamental drivers of plate tectonics.

Estimating the Properties of Hard X-Ray Solar Flares by Constraining Model Parameters

NASA Technical Reports Server (NTRS)

Ireland, J.; Tolbert, A. K.; Schwartz, R. A.; Holman, G. D.; Dennis, B. R.

2013-01-01

We wish to better constrain the properties of solar flares by exploring how parameterized models of solar flares interact with uncertainty estimation methods. We compare four different methods of calculating uncertainty estimates in fitting parameterized models to Ramaty High Energy Solar Spectroscopic Imager X-ray spectra, considering only statistical sources of error. Three of the four methods are based on estimating the scale-size of the minimum in a hypersurface formed by the weighted sum of the squares of the differences between the model fit and the data as a function of the fit parameters, and are implemented as commonly practiced. The fourth method is also based on the difference between the data and the model, but instead uses Bayesian data analysis and Markov chain Monte Carlo (MCMC) techniques to calculate an uncertainty estimate. Two flare spectra are modeled: one from the Geostationary Operational Environmental Satellite X1.3 class flare of 2005 January 19, and the other from the X4.8 flare of 2002 July 23.We find that the four methods give approximately the same uncertainty estimates for the 2005 January 19 spectral fit parameters, but lead to very different uncertainty estimates for the 2002 July 23 spectral fit. This is because each method implements different analyses of the hypersurface, yielding method-dependent results that can differ greatly depending on the shape of the hypersurface. The hypersurface arising from the 2005 January 19 analysis is consistent with a normal distribution; therefore, the assumptions behind the three non- Bayesian uncertainty estimation methods are satisfied and similar estimates are found. The 2002 July 23 analysis shows that the hypersurface is not consistent with a normal distribution, indicating that the assumptions behind the three non-Bayesian uncertainty estimation methods are not satisfied, leading to differing estimates of the uncertainty. We find that the shape of the hypersurface is crucial in understanding the output from each uncertainty estimation technique, and that a crucial factor determining the shape of hypersurface is the location of the low-energy cutoff relative to energies where the thermal emission dominates. The Bayesian/MCMC approach also allows us to provide detailed information on probable values of the low-energy cutoff, Ec, a crucial parameter in defining the energy content of the flare-accelerated electrons. We show that for the 2002 July 23 flare data, there is a 95% probability that Ec lies below approximately 40 keV, and a 68% probability that it lies in the range 7-36 keV. Further, the low-energy cutoff is more likely to be in the range 25-35 keV than in any other 10 keV wide energy range. The low-energy cutoff for the 2005 January 19 flare is more tightly constrained to 107 +/- 4 keV with 68% probability.

NEUTRON STAR MASS–RADIUS CONSTRAINTS USING EVOLUTIONARY OPTIMIZATION

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

Stevens, A. L.; Morsink, S. M.; Fiege, J. D.

The equation of state of cold supra-nuclear-density matter, such as in neutron stars, is an open question in astrophysics. A promising method for constraining the neutron star equation of state is modeling pulse profiles of thermonuclear X-ray burst oscillations from hot spots on accreting neutron stars. The pulse profiles, constructed using spherical and oblate neutron star models, are comparable to what would be observed by a next-generation X-ray timing instrument like ASTROSAT , NICER , or a mission similar to LOFT . In this paper, we showcase the use of an evolutionary optimization algorithm to fit pulse profiles to determinemore » the best-fit masses and radii. By fitting synthetic data, we assess how well the optimization algorithm can recover the input parameters. Multiple Poisson realizations of the synthetic pulse profiles, constructed with 1.6 million counts and no background, were fitted with the Ferret algorithm to analyze both statistical and degeneracy-related uncertainty and to explore how the goodness of fit depends on the input parameters. For the regions of parameter space sampled by our tests, the best-determined parameter is the projected velocity of the spot along the observer’s line of sight, with an accuracy of ≤3% compared to the true value and with ≤5% statistical uncertainty. The next best determined are the mass and radius; for a neutron star with a spin frequency of 600 Hz, the best-fit mass and radius are accurate to ≤5%, with respective uncertainties of ≤7% and ≤10%. The accuracy and precision depend on the observer inclination and spot colatitude, with values of ∼1% achievable in mass and radius if both the inclination and colatitude are ≳60°.« less

Data-Constrained Projections of Methane Fluxes in a Northern Minnesota Peatland in Response to Elevated CO 2 and Warming

DOE PAGES

Ma, Shuang; Jiang, Jiang; Huang, Yuanyuan; ...

2017-10-20

Large uncertainties exist in predicting responses of wetland methane (CH 4) fluxes to future climate change. However, sources of the uncertainty have not been clearly identified despite the fact that methane production and emission processes have been extensively explored. In this study, we took advantage of manual CH 4 flux measurements under ambient environment from 2011 to 2014 at the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experimental site and developed a data-informed process-based methane module. The module was incorporated into the Terrestrial ECOsystem (TECO) model before its parameters were constrained with multiple years of methane flux data formore » forecasting CH 4 emission under five warming and two elevated CO 2 treatments at SPRUCE. We found that 9°C warming treatments significantly increased methane emission by approximately 400%, and elevated CO 2 treatments stimulated methane emission by 10.4%–23.6% in comparison with ambient conditions. The relative contribution of plant-mediated transport to methane emission decreased from 96% at the control to 92% at the 9°C warming, largely to compensate for an increase in ebullition. The uncertainty in plant-mediated transportation and ebullition increased with warming and contributed to the overall changes of emissions uncertainties. At the same time, our modeling results indicated a significant increase in the emitted CH 4:CO 2 ratio. This result, together with the larger warming potential of CH 4, will lead to a strong positive feedback from terrestrial ecosystems to climate warming. In conclusion, the model-data fusion approach used in this study enabled parameter estimation and uncertainty quantification for forecasting methane fluxes.« less

Data-Constrained Projections of Methane Fluxes in a Northern Minnesota Peatland in Response to Elevated CO2 and Warming

NASA Astrophysics Data System (ADS)

Ma, Shuang; Jiang, Jiang; Huang, Yuanyuan; Shi, Zheng; Wilson, Rachel M.; Ricciuto, Daniel; Sebestyen, Stephen D.; Hanson, Paul J.; Luo, Yiqi

2017-11-01

Large uncertainties exist in predicting responses of wetland methane (CH4) fluxes to future climate change. However, sources of the uncertainty have not been clearly identified despite the fact that methane production and emission processes have been extensively explored. In this study, we took advantage of manual CH4 flux measurements under ambient environment from 2011 to 2014 at the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experimental site and developed a data-informed process-based methane module. The module was incorporated into the Terrestrial ECOsystem (TECO) model before its parameters were constrained with multiple years of methane flux data for forecasting CH4 emission under five warming and two elevated CO2 treatments at SPRUCE. We found that 9°C warming treatments significantly increased methane emission by approximately 400%, and elevated CO2 treatments stimulated methane emission by 10.4%-23.6% in comparison with ambient conditions. The relative contribution of plant-mediated transport to methane emission decreased from 96% at the control to 92% at the 9°C warming, largely to compensate for an increase in ebullition. The uncertainty in plant-mediated transportation and ebullition increased with warming and contributed to the overall changes of emissions uncertainties. At the same time, our modeling results indicated a significant increase in the emitted CH4:CO2 ratio. This result, together with the larger warming potential of CH4, will lead to a strong positive feedback from terrestrial ecosystems to climate warming. The model-data fusion approach used in this study enabled parameter estimation and uncertainty quantification for forecasting methane fluxes.

Data-Constrained Projections of Methane Fluxes in a Northern Minnesota Peatland in Response to Elevated CO 2 and Warming

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

Ma, Shuang; Jiang, Jiang; Huang, Yuanyuan

Large uncertainties exist in predicting responses of wetland methane (CH 4) fluxes to future climate change. However, sources of the uncertainty have not been clearly identified despite the fact that methane production and emission processes have been extensively explored. In this study, we took advantage of manual CH 4 flux measurements under ambient environment from 2011 to 2014 at the Spruce and Peatland Responses Under Changing Environments (SPRUCE) experimental site and developed a data-informed process-based methane module. The module was incorporated into the Terrestrial ECOsystem (TECO) model before its parameters were constrained with multiple years of methane flux data formore » forecasting CH 4 emission under five warming and two elevated CO 2 treatments at SPRUCE. We found that 9°C warming treatments significantly increased methane emission by approximately 400%, and elevated CO 2 treatments stimulated methane emission by 10.4%–23.6% in comparison with ambient conditions. The relative contribution of plant-mediated transport to methane emission decreased from 96% at the control to 92% at the 9°C warming, largely to compensate for an increase in ebullition. The uncertainty in plant-mediated transportation and ebullition increased with warming and contributed to the overall changes of emissions uncertainties. At the same time, our modeling results indicated a significant increase in the emitted CH 4:CO 2 ratio. This result, together with the larger warming potential of CH 4, will lead to a strong positive feedback from terrestrial ecosystems to climate warming. In conclusion, the model-data fusion approach used in this study enabled parameter estimation and uncertainty quantification for forecasting methane fluxes.« less

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

Uncertainty analysis of an inflow forecasting model: extension of the UNEEC machine learning-based method

NASA Astrophysics Data System (ADS)

Pianosi, Francesca; Lal Shrestha, Durga; Solomatine, Dimitri

2010-05-01

This research presents an extension of UNEEC (Uncertainty Estimation based on Local Errors and Clustering, Shrestha and Solomatine, 2006, 2008 & Solomatine and Shrestha, 2009) method in the direction of explicit inclusion of parameter uncertainty. UNEEC method assumes that there is an optimal model and the residuals of the model can be used to assess the uncertainty of the model prediction. It is assumed that all sources of uncertainty including input, parameter and model structure uncertainty are explicitly manifested in the model residuals. In this research, theses assumptions are relaxed, and the UNEEC method is extended to consider parameter uncertainty as well (abbreviated as UNEEC-P). In UNEEC-P, first we use Monte Carlo (MC) sampling in parameter space to generate N model realizations (each of which is a time series), estimate the prediction quantiles based on the empirical distribution functions of the model residuals considering all the residual realizations, and only then apply the standard UNEEC method that encapsulates the uncertainty of a hydrologic model (expressed by quantiles of the error distribution) in a machine learning model (e.g., ANN). UNEEC-P is applied first to a linear regression model of synthetic data, and then to a real case study of forecasting inflow to lake Lugano in northern Italy. The inflow forecasting model is a stochastic heteroscedastic model (Pianosi and Soncini-Sessa, 2009). The preliminary results show that the UNEEC-P method produces wider uncertainty bounds, which is consistent with the fact that the method considers also parameter uncertainty of the optimal model. In the future UNEEC method will be further extended to consider input and structure uncertainty which will provide more realistic estimation of model predictions.

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

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

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.

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...

Evaluating the Impact of Contaminant Dilution and Biodegradation in Uncertainty Quantification of Human Health Risk

NASA Astrophysics Data System (ADS)

Zarlenga, Antonio; de Barros, Felipe; Fiori, Aldo

2016-04-01

We present a probabilistic framework for assessing human health risk due to groundwater contamination. Our goal is to quantify how physical hydrogeological and biochemical parameters control the magnitude and uncertainty of human health risk. Our methodology captures the whole risk chain from the aquifer contamination to the tap water assumption by human population. The contaminant concentration, the key parameter for the risk estimation, is governed by the interplay between the large-scale advection, caused by heterogeneity and the degradation processes strictly related to the local scale dispersion processes. The core of the hazard identification and of the methodology is the reactive transport model: erratic displacement of contaminant in groundwater, due to the spatial variability of hydraulic conductivity (K), is characterized by a first-order Lagrangian stochastic model; different dynamics are considered as possible ways of biodegradation in aerobic and anaerobic conditions. With the goal of quantifying uncertainty, the Beta distribution is assumed for the concentration probability density function (pdf) model, while different levels of approximation are explored for the estimation of the one-point concentration moments. The information pertaining the flow and transport is connected with a proper dose response assessment which generally involves the estimation of physiological parameters of the exposed population. Human health response depends on the exposed individual metabolism (e.g. variability) and is subject to uncertainty. Therefore, the health parameters are intrinsically a stochastic. As a consequence, we provide an integrated in a global probabilistic human health risk framework which allows the propagation of the uncertainty from multiple sources. The final result, the health risk pdf, is expressed as function of a few relevant, physically-based parameters such as the size of the injection area, the Péclet number, the K structure metrics and covariance shape, reaction parameters pertaining to aerobic and anaerobic degradation processes respectively as well as the dose response parameters. Even though the final result assumes a relatively simple form, few numerical quadratures are required in order to evaluate the trajectory moments of the solute plume. In order to perform a sensitivity analysis we apply the methodology to a hypothetical case study. The scenario investigated is made by an aquifer which constitutes a water supply for a population where a continuous source of NAPL contaminant feeds a steady plume. The risk analysis is limited to carcinogenic compounds for which the well-known linear relation for human risk is assumed. Analysis performed shows few interesting findings: the risk distribution is strictly dependent on the pore scale dynamics that trigger dilution and mixing; biodegradation may involve a significant reduction of the risk.

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.

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.

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

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.

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.

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.

Robust Control Design for Systems With Probabilistic Uncertainty

NASA Technical Reports Server (NTRS)

Crespo, Luis G.; Kenny, Sean P.

2005-01-01

This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.

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.

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.

Seismic velocity uncertainties and their effect on geothermal predictions: A case study

NASA Astrophysics Data System (ADS)

Rabbel, Wolfgang; Köhn, Daniel; Bahadur Motra, Hem; Niederau, Jan; Thorwart, Martin; Wuttke, Frank; Descramble Working Group

2017-04-01

Geothermal exploration relies in large parts on geophysical subsurface models derived from seismic reflection profiling. These models are the framework of hydro-geothermal modeling, which further requires estimating thermal and hydraulic parameters to be attributed to the seismic strata. All petrophysical and structural properties involved in this process can be determined only with limited accuracy and thus impose uncertainties onto the resulting model predictions of temperature-depth profiles and hydraulic flow, too. In the present study we analyze sources and effects of uncertainties of the seismic velocity field, which translate directly into depth uncertainties of the hydraulically and thermally relevant horizons. Geological sources of these uncertainties are subsurface heterogeneity and seismic anisotropy, methodical sources are limitations in spread length and physical resolution. We demonstrate these effects using data of the EU-Horizon 2020 project DESCRAMBLE investigating a shallow super-critical geothermal reservoir in the Larderello area. The study is based on 2D- and 3D seismic reflection data and laboratory measurements on representative rock samples under simulated in-situ conditions. The rock samples consistently show P-wave anisotropy values of 10-20% order of magnitude. However, the uncertainty of layer depths induced by anisotropy is likely to be lower depending on the accuracy, with which the spatial orientation of bedding planes can be determined from the seismic reflection images.

Lessons from Climate Modeling on the Design and Use of Ensembles for Crop Modeling

NASA Technical Reports Server (NTRS)

Wallach, Daniel; Mearns, Linda O.; Ruane, Alexander C.; Roetter, Reimund P.; Asseng, Senthold

2016-01-01

Working with ensembles of crop models is a recent but important development in crop modeling which promises to lead to better uncertainty estimates for model projections and predictions, better predictions using the ensemble mean or median, and closer collaboration within the modeling community. There are numerous open questions about the best way to create and analyze such ensembles. Much can be learned from the field of climate modeling, given its much longer experience with ensembles. We draw on that experience to identify questions and make propositions that should help make ensemble modeling with crop models more rigorous and informative. The propositions include defining criteria for acceptance of models in a crop MME, exploring criteria for evaluating the degree of relatedness of models in a MME, studying the effect of number of models in the ensemble, development of a statistical model of model sampling, creation of a repository for MME results, studies of possible differential weighting of models in an ensemble, creation of single model ensembles based on sampling from the uncertainty distribution of parameter values or inputs specifically oriented toward uncertainty estimation, the creation of super ensembles that sample more than one source of uncertainty, the analysis of super ensemble results to obtain information on total uncertainty and the separate contributions of different sources of uncertainty and finally further investigation of the use of the multi-model mean or median as a predictor.

Uncertainty in modeled upper ocean heat content change

NASA Astrophysics Data System (ADS)

Tokmakian, Robin; Challenor, Peter

2014-02-01

This paper examines the uncertainty in the change in the heat content in the ocean component of a general circulation model. We describe the design and implementation of our statistical methodology. Using an ensemble of model runs and an emulator, we produce an estimate of the full probability distribution function (PDF) for the change in upper ocean heat in an Atmosphere/Ocean General Circulation Model, the Community Climate System Model v. 3, across a multi-dimensional input space. We show how the emulator of the GCM's heat content change and hence, the PDF, can be validated and how implausible outcomes from the emulator can be identified when compared to observational estimates of the metric. In addition, the paper describes how the emulator outcomes and related uncertainty information might inform estimates of the same metric from a multi-model Coupled Model Intercomparison Project phase 3 ensemble. We illustrate how to (1) construct an ensemble based on experiment design methods, (2) construct and evaluate an emulator for a particular metric of a complex model, (3) validate the emulator using observational estimates and explore the input space with respect to implausible outcomes and (4) contribute to the understanding of uncertainties within a multi-model ensemble. Finally, we estimate the most likely value for heat content change and its uncertainty for the model, with respect to both observations and the uncertainty in the value for the input parameters.

Development Optimization and Uncertainty Analysis Methods for Oil and Gas Reservoirs

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

Ettehadtavakkol, Amin, E-mail: amin.ettehadtavakkol@ttu.edu; Jablonowski, Christopher; Lake, Larry

Uncertainty complicates the development optimization of oil and gas exploration and production projects, but methods have been devised to analyze uncertainty and its impact on optimal decision-making. This paper compares two methods for development optimization and uncertainty analysis: Monte Carlo (MC) simulation and stochastic programming. Two example problems for a gas field development and an oilfield development are solved and discussed to elaborate the advantages and disadvantages of each method. Development optimization involves decisions regarding the configuration of initial capital investment and subsequent operational decisions. Uncertainty analysis involves the quantification of the impact of uncertain parameters on the optimum designmore » concept. The gas field development problem is designed to highlight the differences in the implementation of the two methods and to show that both methods yield the exact same optimum design. The results show that both MC optimization and stochastic programming provide unique benefits, and that the choice of method depends on the goal of the analysis. While the MC method generates more useful information, along with the optimum design configuration, the stochastic programming method is more computationally efficient in determining the optimal solution. Reservoirs comprise multiple compartments and layers with multiphase flow of oil, water, and gas. We present a workflow for development optimization under uncertainty for these reservoirs, and solve an example on the design optimization of a multicompartment, multilayer oilfield development.« less

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.

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.

Improving the Fitness of High-Dimensional Biomechanical Models via Data-Driven Stochastic Exploration

PubMed Central

Bustamante, Carlos D.; Valero-Cuevas, Francisco J.

2010-01-01

The field of complex biomechanical modeling has begun to rely on Monte Carlo techniques to investigate the effects of parameter variability and measurement uncertainty on model outputs, search for optimal parameter combinations, and define model limitations. However, advanced stochastic methods to perform data-driven explorations, such as Markov chain Monte Carlo (MCMC), become necessary as the number of model parameters increases. Here, we demonstrate the feasibility and, what to our knowledge is, the first use of an MCMC approach to improve the fitness of realistically large biomechanical models. We used a Metropolis–Hastings algorithm to search increasingly complex parameter landscapes (3, 8, 24, and 36 dimensions) to uncover underlying distributions of anatomical parameters of a “truth model” of the human thumb on the basis of simulated kinematic data (thumbnail location, orientation, and linear and angular velocities) polluted by zero-mean, uncorrelated multivariate Gaussian “measurement noise.” Driven by these data, ten Markov chains searched each model parameter space for the subspace that best fit the data (posterior distribution). As expected, the convergence time increased, more local minima were found, and marginal distributions broadened as the parameter space complexity increased. In the 36-D scenario, some chains found local minima but the majority of chains converged to the true posterior distribution (confirmed using a cross-validation dataset), thus demonstrating the feasibility and utility of these methods for realistically large biomechanical problems. PMID:19272906

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.

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.

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

Uncertainty in Early Occupational Aspirations: Role Exploration or Aimlessness?

ERIC Educational Resources Information Center

Staff, Jeremy; Harris, Angel; Sabates, Ricardo; Briddell, Laine

2010-01-01

Many youth in the United States lack clear occupational aspirations. This uncertainty in achievement ambitions may benefit socio-economic attainment if it signifies "role exploration," characterized by career development, continued education and enduring partnerships. By contrast, uncertainty may diminish attainment if it instead leads…

FITPOP, a heuristic simulation model of population dynamics and genetics with special reference to fisheries

USGS Publications Warehouse

McKenna, James E.

2000-01-01

Although, perceiving genetic differences and their effects on fish population dynamics is difficult, simulation models offer a means to explore and illustrate these effects. I partitioned the intrinsic rate of increase parameter of a simple logistic-competition model into three components, allowing specification of effects of relative differences in fitness and mortality, as well as finite rate of increase. This model was placed into an interactive, stochastic environment to allow easy manipulation of model parameters (FITPOP). Simulation results illustrated the effects of subtle differences in genetic and population parameters on total population size, overall fitness, and sensitivity of the system to variability. Several consequences of mixing genetically distinct populations were illustrated. For example, behaviors such as depression of population size after initial introgression and extirpation of native stocks due to continuous stocking of genetically inferior fish were reproduced. It also was shown that carrying capacity relative to the amount of stocking had an important influence on population dynamics. Uncertainty associated with parameter estimates reduced confidence in model projections. The FITPOP model provided a simple tool to explore population dynamics, which may assist in formulating management strategies and identifying research needs.

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.

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.

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.

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.

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.

DBH Prediction Using Allometry Described by Bivariate Copula Distribution

NASA Astrophysics Data System (ADS)

Xu, Q.; Hou, Z.; Li, B.; Greenberg, J. A.

2017-12-01

Forest biomass mapping based on single tree detection from the airborne laser scanning (ALS) usually depends on an allometric equation that relates diameter at breast height (DBH) with per-tree aboveground biomass. The incapability of the ALS technology in directly measuring DBH leads to the need to predict DBH with other ALS-measured tree-level structural parameters. A copula-based method is proposed in the study to predict DBH with the ALS-measured tree height and crown diameter using a dataset measured in the Lassen National Forest in California. Instead of exploring an explicit mathematical equation that explains the underlying relationship between DBH and other structural parameters, the copula-based prediction method utilizes the dependency between cumulative distributions of these variables, and solves the DBH based on an assumption that for a single tree, the cumulative probability of each structural parameter is identical. Results show that compared with the bench-marking least-square linear regression and the k-MSN imputation, the copula-based method obtains better accuracy in the DBH for the Lassen National Forest. To assess the generalization of the proposed method, prediction uncertainty is quantified using bootstrapping techniques that examine the variability of the RMSE of the predicted DBH. We find that the copula distribution is reliable in describing the allometric relationship between tree-level structural parameters, and it contributes to the reduction of prediction uncertainty.

A Methodology for Robust Comparative Life Cycle Assessments Incorporating Uncertainty.

PubMed

Gregory, Jeremy R; Noshadravan, Arash; Olivetti, Elsa A; Kirchain, Randolph E

2016-06-21

We propose a methodology for conducting robust comparative life cycle assessments (LCA) by leveraging uncertainty. The method evaluates a broad range of the possible scenario space in a probabilistic fashion while simultaneously considering uncertainty in input data. The method is intended to ascertain which scenarios have a definitive environmentally preferable choice among the alternatives being compared and the significance of the differences given uncertainty in the parameters, which parameters have the most influence on this difference, and how we can identify the resolvable scenarios (where one alternative in the comparison has a clearly lower environmental impact). This is accomplished via an aggregated probabilistic scenario-aware analysis, followed by an assessment of which scenarios have resolvable alternatives. Decision-tree partitioning algorithms are used to isolate meaningful scenario groups. In instances where the alternatives cannot be resolved for scenarios of interest, influential parameters are identified using sensitivity analysis. If those parameters can be refined, the process can be iterated using the refined parameters. We also present definitions of uncertainty quantities that have not been applied in the field of LCA and approaches for characterizing uncertainty in those quantities. We then demonstrate the methodology through a case study of pavements.

THE DYNAMICS OF MERGING CLUSTERS: A MONTE CARLO SOLUTION APPLIED TO THE BULLET AND MUSKET BALL CLUSTERS

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

Dawson, William A., E-mail: wadawson@ucdavis.edu

2013-08-01

Merging galaxy clusters have become one of the most important probes of dark matter, providing evidence for dark matter over modified gravity and even constraints on the dark matter self-interaction cross-section. To properly constrain the dark matter cross-section it is necessary to understand the dynamics of the merger, as the inferred cross-section is a function of both the velocity of the collision and the observed time since collision. While the best understanding of merging system dynamics comes from N-body simulations, these are computationally intensive and often explore only a limited volume of the merger phase space allowed by observed parametermore » uncertainty. Simple analytic models exist but the assumptions of these methods invalidate their results near the collision time, plus error propagation of the highly correlated merger parameters is unfeasible. To address these weaknesses I develop a Monte Carlo method to discern the properties of dissociative mergers and propagate the uncertainty of the measured cluster parameters in an accurate and Bayesian manner. I introduce this method, verify it against an existing hydrodynamic N-body simulation, and apply it to two known dissociative mergers: 1ES 0657-558 (Bullet Cluster) and DLSCL J0916.2+2951 (Musket Ball Cluster). I find that this method surpasses existing analytic models-providing accurate (10% level) dynamic parameter and uncertainty estimates throughout the merger history. This, coupled with minimal required a priori information (subcluster mass, redshift, and projected separation) and relatively fast computation ({approx}6 CPU hours), makes this method ideal for large samples of dissociative merging clusters.« less

I had a dream… Continuous InSAR measurement and transparent earth, the beauty of analogue modeling to assess direct model uncertainties

NASA Astrophysics Data System (ADS)

Taisne, B.; Pansino, S.; Manta, F.; Tay Wen Jing, C.

2017-12-01

Have you ever dreamed about continuous, high resolution InSAR data? Have you ever dreamed about a transparent earth allowing you to see what is actually going on under a volcano? Well, you likely dreamed about an analogue facility that allows you to scale down the natural system to fit into a room, with a controlled environment and complex visualisation system. Analogue modeling has been widely used to understand magmatic processes and thanks to a transparent analogue for the elastic Earth's crust, we can see, as it evolves with time, the migration of a dyke, the volume change of a chamber or the rise of a bubble in a conduit. All those phenomena are modeled theoretically or numerically, with their own simplifications. Therefore, how well are we really constraining the physical parameters describing the evolution of a dyke or a chamber? Getting access to those parameters, in real time and with high level of confidence is of paramount importance while dealing with unrest at volcanoes. The aim of this research is to estimate the uncertainties of the widely used Okada and Mogi models. To do so, we design a set of analogue experiments allowing us to explore different elastic properties of the medium, the characteristic of the fluid injected into the medium as well as the depth, size and volume change of a reservoir. The associated surface deformation is extracted using an array of synchronised cameras and using digital image correlation and structure from motion for horizontal and vertical deformation respectively. The surface deformation are then inverted to retrieve the controlling parameters (e.g. location and volume change of a chamber, or orientation, position, length, breadth and opening of a dyke). By comparing those results with the known parameters, that we can see and measure independently, we estimate the uncertainties of the models themself, and the associated level of confidence for each of the inverted parameters.

Uncertainty quantification and risk analyses of CO2 leakage in heterogeneous geological formations

NASA Astrophysics Data System (ADS)

Hou, Z.; Murray, C. J.; Rockhold, M. L.

2012-12-01

A stochastic sensitivity analysis framework is adopted to evaluate the impact of spatial heterogeneity in permeability on CO2 leakage risk. The leakage is defined as the total mass of CO2 moving into the overburden through the caprock-overburden interface, in both gaseous and liquid (dissolved) phases. The entropy-based framework has the ability to quantify the uncertainty associated with the input parameters in the form of prior pdfs (probability density functions). Effective sampling of the prior pdfs enables us to fully explore the parameter space and systematically evaluate the individual and combined effects of the parameters of interest on CO2 leakage risk. The parameters that are considered in the study include: mean, variance, and horizontal to vertical spatial anisotropy ratio for caprock permeability, and those same parameters for reservoir permeability. Given the sampled spatial variogram parameters, multiple realizations of permeability fields were generated using GSLIB subroutines. For each permeability field, a numerical simulator, STOMP, (in the water-salt-CO2-energy operational mode) is used to simulate the CO2 migration within the reservoir and caprock up to 50 years after injection. Due to intensive computational demand, we run both a scalable version simulator eSTOMP and serial STOMP on various supercomputers. We then perform statistical analyses and summarize the relationships between the parameters of interest (mean/variance/anisotropy ratio of caprock and reservoir permeability) and CO2 leakage ratio. We also present the effects of those parameters on CO2 plume radius and reservoir injectivity. The statistical analysis provides a reduced order model that can be used to estimate the impact of heterogeneity on caprock leakage.

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.

AN OVERVIEW OF THE UNCERTAINTY ANALYSIS, SENSITIVITY ANALYSIS, AND PARAMETER ESTIMATION (UA/SA/PE) API AND HOW TO IMPLEMENT IT

EPA Science Inventory

The Application Programming Interface (API) for Uncertainty Analysis, Sensitivity Analysis, and
Parameter Estimation (UA/SA/PE API) (also known as Calibration, Optimization and Sensitivity and Uncertainty (CUSO)) was developed in a joint effort between several members of both ...

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 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.

Risk management for the Space Exploration Initiative

NASA Technical Reports Server (NTRS)

Buchbinder, Ben

1993-01-01

Probabilistic Risk Assessment (PRA) is a quantitative engineering process that provides the analytic structure and decision-making framework for total programmatic risk management. Ideally, it is initiated in the conceptual design phase and used throughout the program life cycle. Although PRA was developed for assessment of safety, reliability, and availability risk, it has far greater application. Throughout the design phase, PRA can guide trade-off studies among system performance, safety, reliability, cost, and schedule. These studies are based on the assessment of the risk of meeting each parameter goal, with full consideration of the uncertainties. Quantitative trade-off studies are essential, but without full identification, propagation, and display of uncertainties, poor decisions may result. PRA also can focus attention on risk drivers in situations where risk is too high. For example, if safety risk is unacceptable, the PRA prioritizes the risk contributors to guide the use of resources for risk mitigation. PRA is used in the Space Exploration Initiative (SEI) Program. To meet the stringent requirements of the SEI mission, within strict budgetary constraints, the PRA structure supports informed and traceable decision-making. This paper briefly describes the SEI PRA process.

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

A method for determining the joint parameter density of Arrhenius rate expressions through the inference of missing experimental data is presented. This approach proposes noisy hypothetical data sets from target experiments and accepts those which agree with the reported statistics, in the form of nominal parameter values and their associated uncertainties. The data exploration procedure is formalized using Bayesian inference, employing maximum entropy and approximate Bayesian computation methods to arrive at a joint density on data and parameters. The method is demonstrated in the context of reactions in the H2-O2 system for predictive modeling of combustion systems of interest. Work supported by the US DOE BES CSGB. Sandia National Labs is a multimission lab managed and operated by Nat. Technology and Eng'g Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell Intl, for the US DOE NCSA under contract DE-NA-0003525.

Ensemble-based simultaneous state and parameter estimation for treatment of mesoscale model error: A real-data study

NASA Astrophysics Data System (ADS)

Hu, Xiao-Ming; Zhang, Fuqing; Nielsen-Gammon, John W.

2010-04-01

This study explores the treatment of model error and uncertainties through simultaneous state and parameter estimation (SSPE) with an ensemble Kalman filter (EnKF) in the simulation of a 2006 air pollution event over the greater Houston area during the Second Texas Air Quality Study (TexAQS-II). Two parameters in the atmospheric boundary layer parameterization associated with large model sensitivities are combined with standard prognostic variables in an augmented state vector to be continuously updated through assimilation of wind profiler observations. It is found that forecasts of the atmosphere with EnKF/SSPE are markedly improved over experiments with no state and/or parameter estimation. More specifically, the EnKF/SSPE is shown to help alleviate a near-surface cold bias and to alter the momentum mixing in the boundary layer to produce more realistic wind profiles.

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.

Error correction in multi-fidelity molecular dynamics simulations using functional uncertainty quantification

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

Reeve, Samuel Temple; Strachan, Alejandro, E-mail: strachan@purdue.edu

We use functional, Fréchet, derivatives to quantify how thermodynamic outputs of a molecular dynamics (MD) simulation depend on the potential used to compute atomic interactions. Our approach quantifies the sensitivity of the quantities of interest with respect to the input functions as opposed to its parameters as is done in typical uncertainty quantification methods. We show that the functional sensitivity of the average potential energy and pressure in isothermal, isochoric MD simulations using Lennard–Jones two-body interactions can be used to accurately predict those properties for other interatomic potentials (with different functional forms) without re-running the simulations. This is demonstrated undermore » three different thermodynamic conditions, namely a crystal at room temperature, a liquid at ambient pressure, and a high pressure liquid. The method provides accurate predictions as long as the change in potential can be reasonably described to first order and does not significantly affect the region in phase space explored by the simulation. The functional uncertainty quantification approach can be used to estimate the uncertainties associated with constitutive models used in the simulation and to correct predictions if a more accurate representation becomes available.« less

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.

Updating Parameters for Volcanic Hazard Assessment Using Multi-parameter Monitoring Data Streams And Bayesian Belief Networks

NASA Astrophysics Data System (ADS)

Odbert, Henry; Aspinall, Willy

2014-05-01

Evidence-based hazard assessment at volcanoes assimilates knowledge about the physical processes of hazardous phenomena and observations that indicate the current state of a volcano. Incorporating both these lines of evidence can inform our belief about the likelihood (probability) and consequences (impact) of possible hazardous scenarios, forming a basis for formal quantitative hazard assessment. However, such evidence is often uncertain, indirect or incomplete. Approaches to volcano monitoring have advanced substantially in recent decades, increasing the variety and resolution of multi-parameter timeseries data recorded at volcanoes. Interpreting these multiple strands of parallel, partial evidence thus becomes increasingly complex. In practice, interpreting many timeseries requires an individual to be familiar with the idiosyncrasies of the volcano, monitoring techniques, configuration of recording instruments, observations from other datasets, and so on. In making such interpretations, an individual must consider how different volcanic processes may manifest as measureable observations, and then infer from the available data what can or cannot be deduced about those processes. We examine how parts of this process may be synthesised algorithmically using Bayesian inference. Bayesian Belief Networks (BBNs) use probability theory to treat and evaluate uncertainties in a rational and auditable scientific manner, but only to the extent warranted by the strength of the available evidence. The concept is a suitable framework for marshalling multiple strands of evidence (e.g. observations, model results and interpretations) and their associated uncertainties in a methodical manner. BBNs are usually implemented in graphical form and could be developed as a tool for near real-time, ongoing use in a volcano observatory, for example. We explore the application of BBNs in analysing volcanic data from the long-lived eruption at Soufriere Hills Volcano, Montserrat. We discuss the uncertainty of inferences, and how our method provides a route to formal propagation of uncertainties in hazard models. Such approaches provide an attractive route to developing an interface between volcano monitoring analyses and probabilistic hazard scenario analysis. We discuss the use of BBNs in hazard analysis as a tractable and traceable tool for fast, rational assimilation of complex, multi-parameter data sets in the context of timely volcanic crisis decision support.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

PubMed

Nishiura, Hiroshi

2011-02-16

Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Lateral Viscosity Variations in the Both Local and Global and Viscoelastic Load Response and it's Uncertainty

NASA Astrophysics Data System (ADS)

Ivins, E. R.; Caron, L.; Adhikari, S.; Larour, E. Y.; Seroussi, H. L.; Wiens, D.; Lloyd, A. J.; Dietrich, R. O. R.; Richter, A.

2017-12-01

One aspect of GIA modeling that has been a source of contention for many years is the exploration, or lack thereof, of the parameters representing growth and collapse of ice loading while additionally allowing mantle structure to vary. These problems are today being approached with advanced coupled solid earth and ice sheet continuum mechanics. An additional source of non-uniqueness lies in the potential for large (4 orders of magnitude) variability in mantle creep strength. A main question that remains is how to seek some simplification of the set of problems that this implies and to shed from consideration those questions that lack relevance to properly interpreting geodetic data sets. Answering this question therefore entails defining what science questions are to be addressed and to define what parameters produce the highest sensitivities. Where mantle viscosity and lithospheric thickness have affinity with an active dynamic mantle that brings rejuvenation by upwelling of volatiles and heat, the time scales for ice and water loading shorten. Here we show how seismic images map with constitutive flow laws into effective laterally varying viscosity maps. As important, we map the uncertainties. In turn, these uncertainties also inform the time scales that are sensitive to load reconstruction for computing present-day deformation and gravity. We employ the wavelength-dependent viscoelastic response decay spectra derived from analytic solutions in order to quantitatively map these sensitivities.

The role of price and enforcement in water allocation: insights from Game Theory

NASA Astrophysics Data System (ADS)

Souza Filho, F.; Lall, U.; Porto, R.

2007-12-01

As many countries are moving towards water sector reforms, practical issues of how water management institutions can better effect allocation, regulation and enforcement of water rights have emerged. The uncertainty associated with water that is available at a particular diversion point becomes a parameter that is likely to influence the behavior of water users as to their application for water licenses, as well as their willingness to pay for licensed use. The ability of a water agency to reduce this uncertainty through effective water rights enforcement is related to the fiscal ability of the agency to sustain the enforcement effort. In this paper, this interplay across the users and the agency is explored, considering the hydraulic structure or sequence of water use, and parameters that define the users and the agency's economics. The potential for free rider behavior by the users, as well as their proposals for licensed use are derived conditional on this setting. The analyses presented are developed in the framework of the theory of "Law and Economics", with user interactions modeled as a game theoretic enterprise. The state of Ceara, Brazil is used loosely as an example setting, with parameter values for the experiments indexed to be approximately those relevant for current decisions. The potential for using the ideas in participatory decision making is discussed.

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.

Performance of two predictive uncertainty estimation approaches for conceptual Rainfall-Runoff Model: Bayesian Joint Inference and Hydrologic Uncertainty Post-processing

NASA Astrophysics Data System (ADS)

Hernández-López, Mario R.; Romero-Cuéllar, Jonathan; Camilo Múnera-Estrada, Juan; Coccia, Gabriele; Francés, Félix

2017-04-01

It is noticeably important to emphasize the role of uncertainty particularly when the model forecasts are used to support decision-making and water management. This research compares two approaches for the evaluation of the predictive uncertainty in hydrological modeling. First approach is the Bayesian Joint Inference of hydrological and error models. Second approach is carried out through the Model Conditional Processor using the Truncated Normal Distribution in the transformed space. This comparison is focused on the predictive distribution reliability. The case study is applied to two basins included in the Model Parameter Estimation Experiment (MOPEX). These two basins, which have different hydrological complexity, are the French Broad River (North Carolina) and the Guadalupe River (Texas). The results indicate that generally, both approaches are able to provide similar predictive performances. However, the differences between them can arise in basins with complex hydrology (e.g. ephemeral basins). This is because obtained results with Bayesian Joint Inference are strongly dependent on the suitability of the hypothesized error model. Similarly, the results in the case of the Model Conditional Processor are mainly influenced by the selected model of tails or even by the selected full probability distribution model of the data in the real space, and by the definition of the Truncated Normal Distribution in the transformed space. In summary, the different hypotheses that the modeler choose on each of the two approaches are the main cause of the different results. This research also explores a proper combination of both methodologies which could be useful to achieve less biased hydrological parameter estimation. For this approach, firstly the predictive distribution is obtained through the Model Conditional Processor. Secondly, this predictive distribution is used to derive the corresponding additive error model which is employed for the hydrological parameter estimation with the Bayesian Joint Inference methodology.

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.

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.

Escape of Hydrogen from the Exosphere of Mars

NASA Astrophysics Data System (ADS)

Bhattacharyya, Dolon; Clarke, John T.; Bertaux, Jean-Loup; Chaufray, Jean-Yves; Mayyasi-Matta, Majd A.

2016-10-01

After decades of exploration, the martian neutral hydrogen exosphere has remained largely uncharacterized even today. In my dissertation I have attempted to constrain the characteristics of the martian hydrogen exosphere using Hubble Space Telescope observations obtained during October-November 2007 and 2014. These observations reveal short-term seasonal changes exhibited by the martian hydrogen exosphere that are inconsistent with the diffusion-limited escape scenario. This seasonal behavior adds a new element towards backtracking the history of water loss from Mars. Modeling of the data also indicates the likely presence of a superthermal population of hydrogen created by non-thermal processes at Mars, another key element to understand the present-day escape. Exploration of the latitudinal symmetry of the martian exosphere indicates that it is symmetric above 2.5 martian radii and asymmetric below this altitude, which could be due to temperature differences between the day and night sides. Finally, the large uncertainties in determining the characteristics of the martian exosphere after decades of exploration is due to various assumptions about the intrinsic characteristics of the martian exosphere in the modeling process, degeneracy in the two modeling parameters temperature and density of the hydrogen atoms, unaccounted seasonal effects, and uncertainties introduced from spacecraft instrumentation as well as their viewing geometry.

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.

A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: Report of AAPM Task Group No. 138 and GEC-ESTRO

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

DeWerd, Larry A.; Ibbott, Geoffrey S.; Meigooni, Ali S.

2011-02-15

This report addresses uncertainties pertaining to brachytherapy single-source dosimetry preceding clinical use. The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) and the National Institute of Standards and Technology (NIST) Technical Note 1297 are taken as reference standards for uncertainty formalism. Uncertainties in using detectors to measure or utilizing Monte Carlo methods to estimate brachytherapy dose distributions are provided with discussion of the components intrinsic to the overall dosimetric assessment. Uncertainties provided are based on published observations and cited when available. The uncertainty propagation from the primary calibration standard through transfer to the clinicmore » for air-kerma strength is covered first. Uncertainties in each of the brachytherapy dosimetry parameters of the TG-43 formalism are then explored, ending with transfer to the clinic and recommended approaches. Dosimetric uncertainties during treatment delivery are considered briefly but are not included in the detailed analysis. For low- and high-energy brachytherapy sources of low dose rate and high dose rate, a combined dosimetric uncertainty <5% (k=1) is estimated, which is consistent with prior literature estimates. Recommendations are provided for clinical medical physicists, dosimetry investigators, and source and treatment planning system manufacturers. These recommendations include the use of the GUM and NIST reports, a requirement of constancy of manufacturer source design, dosimetry investigator guidelines, provision of the lowest uncertainty for patient treatment dosimetry, and the establishment of an action level based on dosimetric uncertainty. These recommendations reflect the guidance of the American Association of Physicists in Medicine (AAPM) and the Groupe Europeen de Curietherapie-European Society for Therapeutic Radiology and Oncology (GEC-ESTRO) for their members and may also be used as guidance to manufacturers and regulatory agencies in developing good manufacturing practices for sources used in routine clinical treatments.« less

A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: Report of AAPM Task Group No. 138 and GEC-ESTRO

PubMed Central

DeWerd, Larry A.; Ibbott, Geoffrey S.; Meigooni, Ali S.; Mitch, Michael G.; Rivard, Mark J.; Stump, Kurt E.; Thomadsen, Bruce R.; Venselaar, Jack L. M.

2011-01-01

This report addresses uncertainties pertaining to brachytherapy single-source dosimetry preceding clinical use. The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) and the National Institute of Standards and Technology (NIST) Technical Note 1297 are taken as reference standards for uncertainty formalism. Uncertainties in using detectors to measure or utilizing Monte Carlo methods to estimate brachytherapy dose distributions are provided with discussion of the components intrinsic to the overall dosimetric assessment. Uncertainties provided are based on published observations and cited when available. The uncertainty propagation from the primary calibration standard through transfer to the clinic for air-kerma strength is covered first. Uncertainties in each of the brachytherapy dosimetry parameters of the TG-43 formalism are then explored, ending with transfer to the clinic and recommended approaches. Dosimetric uncertainties during treatment delivery are considered briefly but are not included in the detailed analysis. For low- and high-energy brachytherapy sources of low dose rate and high dose rate, a combined dosimetric uncertainty <5% (k=1) is estimated, which is consistent with prior literature estimates. Recommendations are provided for clinical medical physicists, dosimetry investigators, and source and treatment planning system manufacturers. These recommendations include the use of the GUM and NIST reports, a requirement of constancy of manufacturer source design, dosimetry investigator guidelines, provision of the lowest uncertainty for patient treatment dosimetry, and the establishment of an action level based on dosimetric uncertainty. These recommendations reflect the guidance of the American Association of Physicists in Medicine (AAPM) and the Groupe Européen de Curiethérapie–European Society for Therapeutic Radiology and Oncology (GEC-ESTRO) for their members and may also be used as guidance to manufacturers and regulatory agencies in developing good manufacturing practices for sources used in routine clinical treatments. PMID:21452716

A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: report of AAPM Task Group No. 138 and GEC-ESTRO.

PubMed

DeWerd, Larry A; Ibbott, Geoffrey S; Meigooni, Ali S; Mitch, Michael G; Rivard, Mark J; Stump, Kurt E; Thomadsen, Bruce R; Venselaar, Jack L M

2011-02-01

This report addresses uncertainties pertaining to brachytherapy single-source dosimetry preceding clinical use. The International Organization for Standardization (ISO) Guide to the Expression of Uncertainty in Measurement (GUM) and the National Institute of Standards and Technology (NIST) Technical Note 1297 are taken as reference standards for uncertainty formalism. Uncertainties in using detectors to measure or utilizing Monte Carlo methods to estimate brachytherapy dose distributions are provided with discussion of the components intrinsic to the overall dosimetric assessment. Uncertainties provided are based on published observations and cited when available. The uncertainty propagation from the primary calibration standard through transfer to the clinic for air-kerma strength is covered first. Uncertainties in each of the brachytherapy dosimetry parameters of the TG-43 formalism are then explored, ending with transfer to the clinic and recommended approaches. Dosimetric uncertainties during treatment delivery are considered briefly but are not included in the detailed analysis. For low- and high-energy brachytherapy sources of low dose rate and high dose rate, a combined dosimetric uncertainty <5% (k=1) is estimated, which is consistent with prior literature estimates. Recommendations are provided for clinical medical physicists, dosimetry investigators, and source and treatment planning system manufacturers. These recommendations include the use of the GUM and NIST reports, a requirement of constancy of manufacturer source design, dosimetry investigator guidelines, provision of the lowest uncertainty for patient treatment dosimetry, and the establishment of an action level based on dosimetric uncertainty. These recommendations reflect the guidance of the American Association of Physicists in Medicine (AAPM) and the Groupe Européen de Curiethérapie-European Society for Therapeutic Radiology and Oncology (GEC-ESTRO) for their members and may also be used as guidance to manufacturers and regulatory agencies in developing good manufacturing practices for sources used in routine clinical treatments.

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.

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.

Ignoring correlation in uncertainty and sensitivity analysis in life cycle assessment: what is the risk?

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

Groen, E.A., E-mail: Evelyne.Groen@gmail.com; Heijungs, R.; Leiden University, Einsteinweg 2, Leiden 2333 CC

Life cycle assessment (LCA) is an established tool to quantify the environmental impact of a product. A good assessment of uncertainty is important for making well-informed decisions in comparative LCA, as well as for correctly prioritising data collection efforts. Under- or overestimation of output uncertainty (e.g. output variance) will lead to incorrect decisions in such matters. The presence of correlations between input parameters during uncertainty propagation, can increase or decrease the the output variance. However, most LCA studies that include uncertainty analysis, ignore correlations between input parameters during uncertainty propagation, which may lead to incorrect conclusions. Two approaches to include correlationsmore » between input parameters during uncertainty propagation and global sensitivity analysis were studied: an analytical approach and a sampling approach. The use of both approaches is illustrated for an artificial case study of electricity production. Results demonstrate that both approaches yield approximately the same output variance and sensitivity indices for this specific case study. Furthermore, we demonstrate that the analytical approach can be used to quantify the risk of ignoring correlations between input parameters during uncertainty propagation in LCA. We demonstrate that: (1) we can predict if including correlations among input parameters in uncertainty propagation will increase or decrease output variance; (2) we can quantify the risk of ignoring correlations on the output variance and the global sensitivity indices. Moreover, this procedure requires only little data. - Highlights: • Ignoring correlation leads to under- or overestimation of the output variance. • We demonstrated that the risk of ignoring correlation can be quantified. • The procedure proposed is generally applicable in life cycle assessment. • In some cases, ignoring correlation has a minimal effect on decision-making tools.« less

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.

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...

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.

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.

Uncertainties in the Item Parameter Estimates and Robust Automated Test Assembly

ERIC Educational Resources Information Center

Veldkamp, Bernard P.; Matteucci, Mariagiulia; de Jong, Martijn G.

2013-01-01

Item response theory parameters have to be estimated, and because of the estimation process, they do have uncertainty in them. In most large-scale testing programs, the parameters are stored in item banks, and automated test assembly algorithms are applied to assemble operational test forms. These algorithms treat item parameters as fixed values,…

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.

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...

Calculating High Speed Centrifugal Compressor Performance from Averaged Measurements

NASA Astrophysics Data System (ADS)

Lou, Fangyuan; Fleming, Ryan; Key, Nicole L.

2012-12-01

To improve the understanding of high performance centrifugal compressors found in modern aircraft engines, the aerodynamics through these machines must be experimentally studied. To accurately capture the complex flow phenomena through these devices, research facilities that can accurately simulate these flows are necessary. One such facility has been recently developed, and it is used in this paper to explore the effects of averaging total pressure and total temperature measurements to calculate compressor performance. Different averaging techniques (including area averaging, mass averaging, and work averaging) have been applied to the data. Results show that there is a negligible difference in both the calculated total pressure ratio and efficiency for the different techniques employed. However, the uncertainty in the performance parameters calculated with the different averaging techniques is significantly different, with area averaging providing the least uncertainty.

Living with uncertainty and hope: A qualitative study exploring parents' experiences of living with childhood multiple sclerosis.

PubMed

Hinton, Denise; Kirk, Susan

2017-06-01

Background There is growing recognition that multiple sclerosis is a possible, albeit uncommon, diagnosis in childhood. However, very little is known about the experiences of families living with childhood multiple sclerosis and this is the first study to explore this in depth. Objective Our objective was to explore the experiences of parents of children with multiple sclerosis. Methods Qualitative in-depth interviews with 31 parents using a grounded theory approach were conducted. Parents were sampled and recruited via health service and voluntary sector organisations in the United Kingdom. Results Parents' accounts of life with childhood multiple sclerosis were dominated by feelings of uncertainty associated with four sources; diagnostic uncertainty, daily uncertainty, interaction uncertainty and future uncertainty. Parents attempted to manage these uncertainties using specific strategies, which could in turn create further uncertainties about their child's illness. However, over time, ongoing uncertainty appeared to give parents hope for their child's future with multiple sclerosis. Conclusion Illness-related uncertainties appear to play a role in generating hope among parents of a child with multiple sclerosis. However, this may lead parents to avoid sources of information and support that threatens their fragile optimism. Professionals need to be sensitive to the role hope plays in supporting parental coping with childhood multiple sclerosis.

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.

Underwater passive acoustic localization of Pacific walruses in the northeastern Chukchi Sea.

PubMed

Rideout, Brendan P; Dosso, Stan E; Hannay, David E

2013-09-01

This paper develops and applies a linearized Bayesian localization algorithm based on acoustic arrival times of marine mammal vocalizations at spatially-separated receivers which provides three-dimensional (3D) location estimates with rigorous uncertainty analysis. To properly account for uncertainty in receiver parameters (3D hydrophone locations and synchronization times) and environmental parameters (water depth and sound-speed correction), these quantities are treated as unknowns constrained by prior estimates and prior uncertainties. Unknown scaling factors on both the prior and arrival-time uncertainties are estimated by minimizing Akaike's Bayesian information criterion (a maximum entropy condition). Maximum a posteriori estimates for sound source locations and times, receiver parameters, and environmental parameters are calculated simultaneously using measurements of arrival times for direct and interface-reflected acoustic paths. Posterior uncertainties for all unknowns incorporate both arrival time and prior uncertainties. Monte Carlo simulation results demonstrate that, for the cases considered here, linearization errors are small and the lack of an accurate sound-speed profile does not cause significant biases in the estimated locations. A sequence of Pacific walrus vocalizations, recorded in the Chukchi Sea northwest of Alaska, is localized using this technique, yielding a track estimate and uncertainties with an estimated speed comparable to normal walrus swim speeds.

Multi-Objective Reinforcement Learning-based Deep Neural Networks for Cognitive Space Communications

NASA Technical Reports Server (NTRS)

Ferreria, Paulo; Paffenroth, Randy; Wyglinski, Alexander M.; Hackett, Timothy; Bilen, Sven; Reinhart, Richard; Mortensen, Dale

2017-01-01

Future communication subsystems of space exploration missions can potentially benefit from software-defined radios (SDRs) controlled by machine learning algorithms. In this paper, we propose a novel hybrid radio resource allocation management control algorithm that integrates multi-objective reinforcement learning and deep artificial neural networks. The objective is to efficiently manage communications system resources by monitoring performance functions with common dependent variables that result in conflicting goals. The uncertainty in the performance of thousands of different possible combinations of radio parameters makes the trade-off between exploration and exploitation in reinforcement learning (RL) much more challenging for future critical space-based missions. Thus, the system should spend as little time as possible on exploring actions, and whenever it explores an action, it should perform at acceptable levels most of the time. The proposed approach enables on-line learning by interactions with the environment and restricts poor resource allocation performance through virtual environment exploration. Improvements in the multiobjective performance can be achieved via transmitter parameter adaptation on a packet-basis, with poorly predicted performance promptly resulting in rejected decisions. Simulations presented in this work considered the DVB-S2 standard adaptive transmitter parameters and additional ones expected to be present in future adaptive radio systems. Performance results are provided by analysis of the proposed hybrid algorithm when operating across a satellite communication channel from Earth to GEO orbit during clear sky conditions. The proposed approach constitutes part of the core cognitive engine proof-of-concept to be delivered to the NASA Glenn Research Center SCaN Testbed located onboard the International Space Station.

Multi-Objective Reinforcement Learning-Based Deep Neural Networks for Cognitive Space Communications

NASA Technical Reports Server (NTRS)

Ferreria, Paulo Victor R.; Paffenroth, Randy; Wyglinski, Alexander M.; Hackett, Timothy M.; Bilen, Sven G.; Reinhart, Richard C.; Mortensen, Dale J.

2017-01-01

Future communication subsystems of space exploration missions can potentially benefit from software-defined radios (SDRs) controlled by machine learning algorithms. In this paper, we propose a novel hybrid radio resource allocation management control algorithm that integrates multi-objective reinforcement learning and deep artificial neural networks. The objective is to efficiently manage communications system resources by monitoring performance functions with common dependent variables that result in conflicting goals. The uncertainty in the performance of thousands of different possible combinations of radio parameters makes the trade-off between exploration and exploitation in reinforcement learning (RL) much more challenging for future critical space-based missions. Thus, the system should spend as little time as possible on exploring actions, and whenever it explores an action, it should perform at acceptable levels most of the time. The proposed approach enables on-line learning by interactions with the environment and restricts poor resource allocation performance through virtual environment exploration. Improvements in the multiobjective performance can be achieved via transmitter parameter adaptation on a packet-basis, with poorly predicted performance promptly resulting in rejected decisions. Simulations presented in this work considered the DVB-S2 standard adaptive transmitter parameters and additional ones expected to be present in future adaptive radio systems. Performance results are provided by analysis of the proposed hybrid algorithm when operating across a satellite communication channel from Earth to GEO orbit during clear sky conditions. The proposed approach constitutes part of the core cognitive engine proof-of-concept to be delivered to the NASA Glenn Research Center SCaN Testbed located onboard the International Space Station.

Info-gap management of public health Policy for TB with HIV-prevalence and epidemiological uncertainty

PubMed Central

2012-01-01

Background Formulation and evaluation of public health policy commonly employs science-based mathematical models. For instance, epidemiological dynamics of TB is dominated, in general, by flow between actively and latently infected populations. Thus modelling is central in planning public health intervention. However, models are highly uncertain because they are based on observations that are geographically and temporally distinct from the population to which they are applied. Aims We aim to demonstrate the advantages of info-gap theory, a non-probabilistic approach to severe uncertainty when worst cases cannot be reliably identified and probability distributions are unreliable or unavailable. Info-gap is applied here to mathematical modelling of epidemics and analysis of public health decision-making. Methods Applying info-gap robustness analysis to tuberculosis/HIV (TB/HIV) epidemics, we illustrate the critical role of incorporating uncertainty in formulating recommendations for interventions. Robustness is assessed as the magnitude of uncertainty that can be tolerated by a given intervention. We illustrate the methodology by exploring interventions that alter the rates of diagnosis, cure, relapse and HIV infection. Results We demonstrate several policy implications. Equivalence among alternative rates of diagnosis and relapse are identified. The impact of initial TB and HIV prevalence on the robustness to uncertainty is quantified. In some configurations, increased aggressiveness of intervention improves the predicted outcome but also reduces the robustness to uncertainty. Similarly, predicted outcomes may be better at larger target times, but may also be more vulnerable to model error. Conclusions The info-gap framework is useful for managing model uncertainty and is attractive when uncertainties on model parameters are extreme. When a public health model underlies guidelines, info-gap decision theory provides valuable insight into the confidence of achieving agreed-upon goals. PMID:23249291

Info-gap management of public health Policy for TB with HIV-prevalence and epidemiological uncertainty.

PubMed

Ben-Haim, Yakov; Dacso, Clifford C; Zetola, Nicola M

2012-12-19

Formulation and evaluation of public health policy commonly employs science-based mathematical models. For instance, epidemiological dynamics of TB is dominated, in general, by flow between actively and latently infected populations. Thus modelling is central in planning public health intervention. However, models are highly uncertain because they are based on observations that are geographically and temporally distinct from the population to which they are applied. We aim to demonstrate the advantages of info-gap theory, a non-probabilistic approach to severe uncertainty when worst cases cannot be reliably identified and probability distributions are unreliable or unavailable. Info-gap is applied here to mathematical modelling of epidemics and analysis of public health decision-making. Applying info-gap robustness analysis to tuberculosis/HIV (TB/HIV) epidemics, we illustrate the critical role of incorporating uncertainty in formulating recommendations for interventions. Robustness is assessed as the magnitude of uncertainty that can be tolerated by a given intervention. We illustrate the methodology by exploring interventions that alter the rates of diagnosis, cure, relapse and HIV infection. We demonstrate several policy implications. Equivalence among alternative rates of diagnosis and relapse are identified. The impact of initial TB and HIV prevalence on the robustness to uncertainty is quantified. In some configurations, increased aggressiveness of intervention improves the predicted outcome but also reduces the robustness to uncertainty. Similarly, predicted outcomes may be better at larger target times, but may also be more vulnerable to model error. The info-gap framework is useful for managing model uncertainty and is attractive when uncertainties on model parameters are extreme. When a public health model underlies guidelines, info-gap decision theory provides valuable insight into the confidence of achieving agreed-upon goals.

Final Report: Optimal Model Complexity in Geological Carbon Sequestration: A Response Surface Uncertainty Analysis

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

Zhang, Ye

The critical component of a risk assessment study in evaluating GCS is an analysis of uncertainty in CO2 modeling. In such analyses, direct numerical simulation of CO2 flow and leakage requires many time-consuming model runs. Alternatively, analytical methods have been developed which allow fast and efficient estimation of CO2 storage and leakage, although restrictive assumptions on formation rock and fluid properties are employed. In this study, an intermediate approach is proposed based on the Design of Experiment and Response Surface methodology, which consists of using a limited number of numerical simulations to estimate a prediction outcome as a combination ofmore » the most influential uncertain site properties. The methodology can be implemented within a Monte Carlo framework to efficiently assess parameter and prediction uncertainty while honoring the accuracy of numerical simulations. The choice of the uncertain properties is flexible and can include geologic parameters that influence reservoir heterogeneity, engineering parameters that influence gas trapping and migration, and reactive parameters that influence the extent of fluid/rock reactions. The method was tested and verified on modeling long-term CO2 flow, non-isothermal heat transport, and CO2 dissolution storage by coupling two-phase flow with explicit miscibility calculation using an accurate equation of state that gives rise to convective mixing of formation brine variably saturated with CO2. All simulations were performed using three-dimensional high-resolution models including a target deep saline aquifer, overlying caprock, and a shallow aquifer. To evaluate the uncertainty in representing reservoir permeability, sediment hierarchy of a heterogeneous digital stratigraphy was mapped to create multiple irregularly shape stratigraphic models of decreasing geologic resolutions: heterogeneous (reference), lithofacies, depositional environment, and a (homogeneous) geologic formation. To ensure model equivalency, all the stratigraphic models were successfully upscaled from the reference heterogeneous model for bulk flow and transport predictions (Zhang & Zhang, 2015). GCS simulation was then simulated with all models, yielding insights into the level of parameterization complexity that is needed for the accurate simulation of reservoir pore pressure, CO2 storage, leakage, footprint, and dissolution over both short (i.e., injection) and longer (monitoring) time scales. Important uncertainty parameters that impact these key performance metrics were identified for the stratigraphic models as well as for the heterogeneous model, leading to the development of reduced/simplified models at lower characterization cost that can be used for the reservoir uncertainty analysis. All the CO2 modeling was conducted using PFLOTRAN – a massively parallel, multiphase, multi-component, and reactive transport simulator developed by a multi-laboratory DOE/SciDAC (Scientific Discovery through Advanced Computing) project (Zhang et al., 2017, in review). Within the uncertainty analysis framework, increasing reservoir depth were investigated to explore its effect on the uncertainty outcomes and the potential for developing gravity-stable injection with increased storage security (Dai et al., 20126; Dai et al., 2017, in review). Finally, to accurately model CO2 fluid-rock reactions and resulting long-term storage as secondary carbonate minerals, a modified kinetic rate law for general mineral dissolution and precipitation was proposed and verified that is invariant to a scale transformation of the mineral formula weight. This new formulation will lead to more accurate assessment of mineral storage over geologic time scales (Lichtner, 2016).« less

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.

Estimation of the ARNO model baseflow parameters using daily streamflow data

NASA Astrophysics Data System (ADS)

Abdulla, F. A.; Lettenmaier, D. P.; Liang, Xu

1999-09-01

An approach is described for estimation of baseflow parameters of the ARNO model, using historical baseflow recession sequences extracted from daily streamflow records. This approach allows four of the model parameters to be estimated without rainfall data, and effectively facilitates partitioning of the parameter estimation procedure so that parsimonious search procedures can be used to estimate the remaining storm response parameters separately. Three methods of optimization are evaluated for estimation of four baseflow parameters. These methods are the downhill Simplex (S), Simulated Annealing combined with the Simplex method (SA) and Shuffled Complex Evolution (SCE). These estimation procedures are explored in conjunction with four objective functions: (1) ordinary least squares; (2) ordinary least squares with Box-Cox transformation; (3) ordinary least squares on prewhitened residuals; (4) ordinary least squares applied to prewhitened with Box-Cox transformation of residuals. The effects of changing the seed random generator for both SA and SCE methods are also explored, as are the effects of the bounds of the parameters. Although all schemes converge to the same values of the objective function, SCE method was found to be less sensitive to these issues than both the SA and the Simplex schemes. Parameter uncertainty and interactions are investigated through estimation of the variance-covariance matrix and confidence intervals. As expected the parameters were found to be correlated and the covariance matrix was found to be not diagonal. Furthermore, the linearized confidence interval theory failed for about one-fourth of the catchments while the maximum likelihood theory did not fail for any of the catchments.

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.

Uncertainty in Climate Change Research: An Integrated Approach

NASA Astrophysics Data System (ADS)

Mearns, L.

2017-12-01

Uncertainty has been a major theme in research regarding climate change from virtually the very beginning. And appropriately characterizing and quantifying uncertainty has been an important aspect of this work. Initially, uncertainties were explored regarding the climate system and how it would react to future forcing. A concomitant area of concern was viewed in the future emissions and concentrations of important forcing agents such as greenhouse gases and aerosols. But, of course we know there are important uncertainties in all aspects of climate change research, not just that of the climate system and emissions. And as climate change research has become more important and of pragmatic concern as possible solutions to the climate change problem are addressed, exploring all the relevant uncertainties has become more relevant and urgent. More recently, over the past five years or so, uncertainties in impacts models, such as agricultural and hydrological models, have received much more attention, through programs such as AgMIP, and some research in this arena has indicated that the uncertainty in the impacts models can be as great or greater than that in the climate system. Still there remains other areas of uncertainty that remain underexplored and/or undervalued. This includes uncertainty in vulnerability and governance. Without more thoroughly exploring these last uncertainties, we likely will underestimate important uncertainties particularly regarding how different systems can successfully adapt to climate change . In this talk I will discuss these different uncertainties and how to combine them to give a complete picture of the total uncertainty individual systems are facing. And as part of this, I will discuss how the uncertainty can be successfully managed even if it is fairly large and deep. Part of my argument will be that large uncertainty is not the enemy, but rather false certainty is the true danger.

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.

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.

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

Estimating Convection Parameters in the GFDL CM2.1 Model Using Ensemble Data Assimilation

NASA Astrophysics Data System (ADS)

Li, Shan; Zhang, Shaoqing; Liu, Zhengyu; Lu, Lv; Zhu, Jiang; Zhang, Xuefeng; Wu, Xinrong; Zhao, Ming; Vecchi, Gabriel A.; Zhang, Rong-Hua; Lin, Xiaopei

2018-04-01

Parametric uncertainty in convection parameterization is one major source of model errors that cause model climate drift. Convection parameter tuning has been widely studied in atmospheric models to help mitigate the problem. However, in a fully coupled general circulation model (CGCM), convection parameters which impact the ocean as well as the climate simulation may have different optimal values. This study explores the possibility of estimating convection parameters with an ensemble coupled data assimilation method in a CGCM. Impacts of the convection parameter estimation on climate analysis and forecast are analyzed. In a twin experiment framework, five convection parameters in the GFDL coupled model CM2.1 are estimated individually and simultaneously under both perfect and imperfect model regimes. Results show that the ensemble data assimilation method can help reduce the bias in convection parameters. With estimated convection parameters, the analyses and forecasts for both the atmosphere and the ocean are generally improved. It is also found that information in low latitudes is relatively more important for estimating convection parameters. This study further suggests that when important parameters in appropriate physical parameterizations are identified, incorporating their estimation into traditional ensemble data assimilation procedure could improve the final analysis and climate prediction.

Comparing Planck and WMAP: Maps, Spectra, and Parameters

NASA Astrophysics Data System (ADS)

Larson, D.; Weiland, J. L.; Hinshaw, G.; Bennett, C. L.

2015-03-01

We examine the consistency of the 9 yr WMAP data and the first-release Planck data. We specifically compare sky maps, power spectra, and the inferred Λ cold dark matter (ΛCDM) cosmological parameters. Residual dipoles are seen in the WMAP and Planck sky map differences, but their amplitudes are consistent within the quoted uncertainties, and they are not large enough to explain the widely noted differences in angular power spectra at higher l. We remove the residual dipoles and use templates to remove residual Galactic foregrounds; after doing so, the residual difference maps exhibit a quadrupole and other large-scale systematic structure. We identify this structure as possibly originating from Planck’s beam sidelobe pick-up, but note that it appears to have insignificant cosmological impact. We develop an extension of the internal linear combination technique to find the minimum-variance difference between the WMAP and Planck sky maps; again we find features that plausibly originate in the Planck data. Lacking access to the Planck time-ordered data we cannot further assess these features. We examine ΛCDM model fits to the angular power spectra and conclude that the ˜2.5% difference in the spectra at multipoles greater than l˜ 100 is significant at the 3-5σ level, depending on how beam uncertainties are handled in the data. We revisit the analysis of WMAP’s beam data to address the power spectrum differences and conclude that previously derived uncertainties are robust and cannot explain the power spectrum differences. In fact, any remaining WMAP errors are most likely to exacerbate the difference. Finally, we examine the consistency of the ΛCDM parameters inferred from each data set taking into account the fact that both experiments observe the same sky, but cover different multipole ranges, apply different sky masks, and have different noise. We find that, while individual parameter values agree within the uncertainties, the six parameters taken together are discrepant at the ˜6σ level, with {χ }2}=56 for 6 degrees of freedom (probability to exceed, PTE = 3× {{10}-10}). The nature of this discrepancy is explored: of the six parameters, {{χ }2} is best improved by marginalizing over {{{Ω}c}{{h}2}, giving {χ }2}=5.2 for 5 degrees of freedom. As an exercise, we find that perturbing the WMAP window function by its dominant beam error profile has little effect on {{{Ω}c}{{h}2}, while perturbing the Planck window function by its corresponding error profile has a much greater effect on {{Ω}c}{{h}2}.

Estimating rainfall time series and model parameter distributions using model data reduction and inversion techniques

NASA Astrophysics Data System (ADS)

Wright, Ashley J.; Walker, Jeffrey P.; Pauwels, Valentijn R. N.

2017-08-01

Floods are devastating natural hazards. To provide accurate, precise, and timely flood forecasts, there is a need to understand the uncertainties associated within an entire rainfall time series, even when rainfall was not observed. The estimation of an entire rainfall time series and model parameter distributions from streamflow observations in complex dynamic catchments adds skill to current areal rainfall estimation methods, allows for the uncertainty of entire rainfall input time series to be considered when estimating model parameters, and provides the ability to improve rainfall estimates from poorly gauged catchments. Current methods to estimate entire rainfall time series from streamflow records are unable to adequately invert complex nonlinear hydrologic systems. This study aims to explore the use of wavelets in the estimation of rainfall time series from streamflow records. Using the Discrete Wavelet Transform (DWT) to reduce rainfall dimensionality for the catchment of Warwick, Queensland, Australia, it is shown that model parameter distributions and an entire rainfall time series can be estimated. Including rainfall in the estimation process improves streamflow simulations by a factor of up to 1.78. This is achieved while estimating an entire rainfall time series, inclusive of days when none was observed. It is shown that the choice of wavelet can have a considerable impact on the robustness of the inversion. Combining the use of a likelihood function that considers rainfall and streamflow errors with the use of the DWT as a model data reduction technique allows the joint inference of hydrologic model parameters along with rainfall.

Methods for exploring uncertainty in groundwater management predictions

USGS Publications Warehouse

Guillaume, Joseph H. A.; Hunt, Randall J.; Comunian, Alessandro; Fu, Baihua; Blakers, Rachel S; Jakeman, Anthony J.; Barreteau, Olivier; Hunt, Randall J.; Rinaudo, Jean-Daniel; Ross, Andrew

2016-01-01

Models of groundwater systems help to integrate knowledge about the natural and human system covering different spatial and temporal scales, often from multiple disciplines, in order to address a range of issues of concern to various stakeholders. A model is simply a tool to express what we think we know. Uncertainty, due to lack of knowledge or natural variability, means that there are always alternative models that may need to be considered. This chapter provides an overview of uncertainty in models and in the definition of a problem to model, highlights approaches to communicating and using predictions of uncertain outcomes and summarises commonly used methods to explore uncertainty in groundwater management predictions. It is intended to raise awareness of how alternative models and hence uncertainty can be explored in order to facilitate the integration of these techniques with groundwater management.

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.

Optimum Design of Forging Process Parameters and Preform Shape under Uncertainties

NASA Astrophysics Data System (ADS)

Repalle, Jalaja; Grandhi, Ramana V.

2004-06-01

Forging is a highly complex non-linear process that is vulnerable to various uncertainties, such as variations in billet geometry, die temperature, material properties, workpiece and forging equipment positional errors and process parameters. A combination of these uncertainties could induce heavy manufacturing losses through premature die failure, final part geometric distortion and production risk. Identifying the sources of uncertainties, quantifying and controlling them will reduce risk in the manufacturing environment, which will minimize the overall cost of production. In this paper, various uncertainties that affect forging tool life and preform design are identified, and their cumulative effect on the forging process is evaluated. Since the forging process simulation is computationally intensive, the response surface approach is used to reduce time by establishing a relationship between the system performance and the critical process design parameters. Variability in system performance due to randomness in the parameters is computed by applying Monte Carlo Simulations (MCS) on generated Response Surface Models (RSM). Finally, a Robust Methodology is developed to optimize forging process parameters and preform shape. The developed method is demonstrated by applying it to an axisymmetric H-cross section disk forging to improve the product quality and robustness.

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.

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.

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.

Dependence of calculated postshock thermodynamic variables on vibrational equilibrium and input uncertainty

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

Campbell, Matthew Frederick; Owen, Kyle G.; Davidson, David F.

The purpose of this article is to explore the dependence of calculated postshock thermodynamic properties in shock tube experiments upon the vibrational state of the test gas and upon the uncertainties inherent to calculation inputs. This paper first offers a comparison between state variables calculated according to a Rankine–Hugoniot–equation-based algorithm, known as FROSH, and those derived from shock tube experiments on vibrationally nonequilibrated gases. It is shown that incorrect vibrational relaxation assumptions could lead to errors in temperature as large as 8% for 25% oxygen/argon mixtures at 3500 K. Following this demonstration, this article employs the algorithm to show themore » importance of correct vibrational equilibration assumptions, noting, for instance, that errors in temperature of up to about 2% at 3500 K may be generated for 10% nitrogen/argon mixtures if vibrational relaxation is not treated properly. Lastly, this article presents an extensive uncertainty analysis, showing that postshock temperatures can be calculated with root-of-sum-of-square errors of better than ±1% given sufficiently accurate experimentally measured input parameters.« less

Dependence of calculated postshock thermodynamic variables on vibrational equilibrium and input uncertainty

DOE PAGES

Campbell, Matthew Frederick; Owen, Kyle G.; Davidson, David F.; ...

2017-01-30

The purpose of this article is to explore the dependence of calculated postshock thermodynamic properties in shock tube experiments upon the vibrational state of the test gas and upon the uncertainties inherent to calculation inputs. This paper first offers a comparison between state variables calculated according to a Rankine–Hugoniot–equation-based algorithm, known as FROSH, and those derived from shock tube experiments on vibrationally nonequilibrated gases. It is shown that incorrect vibrational relaxation assumptions could lead to errors in temperature as large as 8% for 25% oxygen/argon mixtures at 3500 K. Following this demonstration, this article employs the algorithm to show themore » importance of correct vibrational equilibration assumptions, noting, for instance, that errors in temperature of up to about 2% at 3500 K may be generated for 10% nitrogen/argon mixtures if vibrational relaxation is not treated properly. Lastly, this article presents an extensive uncertainty analysis, showing that postshock temperatures can be calculated with root-of-sum-of-square errors of better than ±1% given sufficiently accurate experimentally measured input parameters.« less

Valuing Precaution in Climate Change Policy Analysis (Invited)

NASA Astrophysics Data System (ADS)

Howarth, R. B.

2010-12-01

The U.N. Framework Convention on Climate Change calls for stabilizing greenhouse gas concentrations to prevent “dangerous anthropogenic interference” (DAI) with the global environment. This treaty language emphasizes a precautionary approach to climate change policy in a setting characterized by substantial uncertainty regarding the timing, magnitude, and impacts of climate change. In the economics of climate change, however, analysts often work with deterministic models that assign best-guess values to parameters that are highly uncertain. Such models support a “policy ramp” approach in which only limited steps should be taken to reduce the future growth of greenhouse gas emissions. This presentation will explore how uncertainties related to (a) climate sensitivity and (b) climate-change damages can be satisfactorily addressed in a coupled model of climate-economy dynamics. In this model, capping greenhouse gas concentrations at ~450 ppm of carbon dioxide equivalent provides substantial net benefits by reducing the risk of low-probability, catastrophic impacts. This result formalizes the intuition embodied in the DAI criterion in a manner consistent with rational decision-making under uncertainty.

Sensitivities of seismic velocities to temperature, pressure and composition in the lower mantle

NASA Astrophysics Data System (ADS)

Trampert, Jeannot; Vacher, Pierre; Vlaar, Nico

2001-08-01

We calculated temperature, pressure and compositional sensitivities of seismic velocities in the lower mantle using latest mineral physics data. The compositional variable refers to the volume proportion of perovskite in a simplified perovskite-magnesiowüstite mantle assemblage. The novelty of our approach is the exploration of a reasonable range of input parameters which enter the lower mantle extrapolations. This leads to realistic error bars on the sensitivities. Temperature variations can be inferred throughout the lower mantle within a good degree of precision. Contrary to the uppermost mantle, modest compositional changes in the lower mantle can be detected by seismic tomography, with a larger uncertainty though. A likely trade-off between temperature and composition will be largely determined by uncertainties in tomography itself. Given current sources of uncertainties on recent data, anelastic contributions to the temperature sensitivities (calculated using Karato's approach) appear less significant than previously thought. Recent seismological determinations of the ratio of relative S to P velocity heterogeneity can be entirely explain by thermal effects, although isolated spots beneath Africa and the Central Pacific in the lowermost mantle may ask for a compositional origin.

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.

Insight from uncertainty: bootstrap-derived diffusion metrics differentially predict memory function among older adults.

PubMed

Vorburger, Robert S; Habeck, Christian G; Narkhede, Atul; Guzman, Vanessa A; Manly, Jennifer J; Brickman, Adam M

2016-01-01

Diffusion tensor imaging suffers from an intrinsic low signal-to-noise ratio. Bootstrap algorithms have been introduced to provide a non-parametric method to estimate the uncertainty of the measured diffusion parameters. To quantify the variability of the principal diffusion direction, bootstrap-derived metrics such as the cone of uncertainty have been proposed. However, bootstrap-derived metrics are not independent of the underlying diffusion profile. A higher mean diffusivity causes a smaller signal-to-noise ratio and, thus, increases the measurement uncertainty. Moreover, the goodness of the tensor model, which relies strongly on the complexity of the underlying diffusion profile, influences bootstrap-derived metrics as well. The presented simulations clearly depict the cone of uncertainty as a function of the underlying diffusion profile. Since the relationship of the cone of uncertainty and common diffusion parameters, such as the mean diffusivity and the fractional anisotropy, is not linear, the cone of uncertainty has a different sensitivity. In vivo analysis of the fornix reveals the cone of uncertainty to be a predictor of memory function among older adults. No significant correlation occurs with the common diffusion parameters. The present work not only demonstrates the cone of uncertainty as a function of the actual diffusion profile, but also discloses the cone of uncertainty as a sensitive predictor of memory function. Future studies should incorporate bootstrap-derived metrics to provide more comprehensive analysis.

Investigating the Impact of Uncertainty about Item Parameters on Ability Estimation

ERIC Educational Resources Information Center

Zhang, Jinming; Xie, Minge; Song, Xiaolan; Lu, Ting

2011-01-01

Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee's ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators.…

Combining super-ensembles and statistical emulation to improve a regional climate and vegetation model

NASA Astrophysics Data System (ADS)

Hawkins, L. R.; Rupp, D. E.; Li, S.; Sarah, S.; McNeall, D. J.; Mote, P.; Betts, R. A.; Wallom, D.

2017-12-01

Changing regional patterns of surface temperature, precipitation, and humidity may cause ecosystem-scale changes in vegetation, altering the distribution of trees, shrubs, and grasses. A changing vegetation distribution, in turn, alters the albedo, latent heat flux, and carbon exchanged with the atmosphere with resulting feedbacks onto the regional climate. However, a wide range of earth-system processes that affect the carbon, energy, and hydrologic cycles occur at sub grid scales in climate models and must be parameterized. The appropriate parameter values in such parameterizations are often poorly constrained, leading to uncertainty in predictions of how the ecosystem will respond to changes in forcing. To better understand the sensitivity of regional climate to parameter selection and to improve regional climate and vegetation simulations, we used a large perturbed physics ensemble and a suite of statistical emulators. We dynamically downscaled a super-ensemble (multiple parameter sets and multiple initial conditions) of global climate simulations using a 25-km resolution regional climate model HadRM3p with the land-surface scheme MOSES2 and dynamic vegetation module TRIFFID. We simultaneously perturbed land surface parameters relating to the exchange of carbon, water, and energy between the land surface and atmosphere in a large super-ensemble of regional climate simulations over the western US. Statistical emulation was used as a computationally cost-effective tool to explore uncertainties in interactions. Regions of parameter space that did not satisfy observational constraints were eliminated and an ensemble of parameter sets that reduce regional biases and span a range of plausible interactions among earth system processes were selected. This study demonstrated that by combining super-ensemble simulations with statistical emulation, simulations of regional climate could be improved while simultaneously accounting for a range of plausible land-atmosphere feedback strengths.

Methodological accuracy of image-based electron density assessment using dual-energy computed tomography.

PubMed

Möhler, Christian; Wohlfahrt, Patrick; Richter, Christian; Greilich, Steffen

2017-06-01

Electron density is the most important tissue property influencing photon and ion dose distributions in radiotherapy patients. Dual-energy computed tomography (DECT) enables the determination of electron density by combining the information on photon attenuation obtained at two different effective x-ray energy spectra. Most algorithms suggested so far use the CT numbers provided after image reconstruction as input parameters, i.e., are imaged-based. To explore the accuracy that can be achieved with these approaches, we quantify the intrinsic methodological and calibration uncertainty of the seemingly simplest approach. In the studied approach, electron density is calculated with a one-parametric linear superposition ('alpha blending') of the two DECT images, which is shown to be equivalent to an affine relation between the photon attenuation cross sections of the two x-ray energy spectra. We propose to use the latter relation for empirical calibration of the spectrum-dependent blending parameter. For a conclusive assessment of the electron density uncertainty, we chose to isolate the purely methodological uncertainty component from CT-related effects such as noise and beam hardening. Analyzing calculated spectrally weighted attenuation coefficients, we find universal applicability of the investigated approach to arbitrary mixtures of human tissue with an upper limit of the methodological uncertainty component of 0.2%, excluding high-Z elements such as iodine. The proposed calibration procedure is bias-free and straightforward to perform using standard equipment. Testing the calibration on five published data sets, we obtain very small differences in the calibration result in spite of different experimental setups and CT protocols used. Employing a general calibration per scanner type and voltage combination is thus conceivable. Given the high suitability for clinical application of the alpha-blending approach in combination with a very small methodological uncertainty, we conclude that further refinement of image-based DECT-algorithms for electron density assessment is not advisable. © 2017 American Association of Physicists in Medicine.

The Power of the Spectrum: Combining Numerical Proxy System Models with Analytical Error Spectra to Better Understand Timescale Dependent Proxy Uncertainty

NASA Astrophysics Data System (ADS)

Dolman, A. M.; Laepple, T.; Kunz, T.

2017-12-01

Understanding the uncertainties associated with proxy-based reconstructions of past climate is critical if they are to be used to validate climate models and contribute to a comprehensive understanding of the climate system. Here we present two related and complementary approaches to quantifying proxy uncertainty. The proxy forward model (PFM) "sedproxy" bitbucket.org/ecus/sedproxy numerically simulates the creation, archiving and observation of marine sediment archived proxies such as Mg/Ca in foraminiferal shells and the alkenone unsaturation index UK'37. It includes the effects of bioturbation, bias due to seasonality in the rate of proxy creation, aliasing of the seasonal temperature cycle into lower frequencies, and error due to cleaning, processing and measurement of samples. Numerical PFMs have the advantage of being very flexible, allowing many processes to be modelled and assessed for their importance. However, as more and more proxy-climate data become available, their use in advanced data products necessitates rapid estimates of uncertainties for both the raw reconstructions, and their smoothed/derived products, where individual measurements have been aggregated to coarser time scales or time-slices. To address this, we derive closed-form expressions for power spectral density of the various error sources. The power spectra describe both the magnitude and autocorrelation structure of the error, allowing timescale dependent proxy uncertainty to be estimated from a small number of parameters describing the nature of the proxy, and some simple assumptions about the variance of the true climate signal. We demonstrate and compare both approaches for time-series of the last millennia, Holocene, and the deglaciation. While the numerical forward model can create pseudoproxy records driven by climate model simulations, the analytical model of proxy error allows for a comprehensive exploration of parameter space and mapping of climate signal re-constructability, conditional on the climate and sampling conditions.

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.

Computer-assisted uncertainty assessment of k0-NAA measurement results

NASA Astrophysics Data System (ADS)

Bučar, T.; Smodiš, B.

2008-10-01

In quantifying measurement uncertainty of measurement results obtained by the k0-based neutron activation analysis ( k0-NAA), a number of parameters should be considered and appropriately combined in deriving the final budget. To facilitate this process, a program ERON (ERror propagatiON) was developed, which computes uncertainty propagation factors from the relevant formulae and calculates the combined uncertainty. The program calculates uncertainty of the final result—mass fraction of an element in the measured sample—taking into account the relevant neutron flux parameters such as α and f, including their uncertainties. Nuclear parameters and their uncertainties are taken from the IUPAC database (V.P. Kolotov and F. De Corte, Compilation of k0 and related data for NAA). Furthermore, the program allows for uncertainty calculations of the measured parameters needed in k0-NAA: α (determined with either the Cd-ratio or the Cd-covered multi-monitor method), f (using the Cd-ratio or the bare method), Q0 (using the Cd-ratio or internal comparator method) and k0 (using the Cd-ratio, internal comparator or the Cd subtraction method). The results of calculations can be printed or exported to text or MS Excel format for further analysis. Special care was taken to make the calculation engine portable by having possibility of its incorporation into other applications (e.g., DLL and WWW server). Theoretical basis and the program are described in detail, and typical results obtained under real measurement conditions are presented.

Characteristic Length Scales in Fracture Networks: Hydraulic Connectivity through Periodic Hydraulic Tests

NASA Astrophysics Data System (ADS)

Becker, M.; Bour, O.; Le Borgne, T.; Longuevergne, L.; Lavenant, N.; Cole, M. C.; Guiheneuf, N.

2017-12-01

Determining hydraulic and transport connectivity in fractured bedrock has long been an important objective in contaminant hydrogeology, petroleum engineering, and geothermal operations. A persistent obstacle to making this determination is that the characteristic length scale is nearly impossible to determine in sparsely fractured networks. Both flow and transport occur through an unknown structure of interconnected fracture and/or fracture zones making the actual length that water or solutes travel undetermined. This poses difficulties for flow and transport models. For, example, hydraulic equations require a separation distance between pumping and observation well to determine hydraulic parameters. When wells pairs are close, the structure of the network can influence the interpretation of well separation and the flow dimension of the tested system. This issue is explored using hydraulic tests conducted in a shallow fractured crystalline rock. Periodic (oscillatory) slug tests were performed at the Ploemeur fractured rock test site located in Brittany, France. Hydraulic connectivity was examined between three zones in one well and four zones in another, located 6 m apart in map view. The wells are sufficiently close, however, that the tangential distance between the tested zones ranges between 6 and 30 m. Using standard periodic formulations of radial flow, estimates of storativity scale inversely with the square of the separation distance and hydraulic diffusivity directly with the square of the separation distance. Uncertainty in the connection paths between the two wells leads to an order of magnitude uncertainty in estimates of storativity and hydraulic diffusivity, although estimates of transmissivity are unaffected. The assumed flow dimension results in alternative estimates of hydraulic parameters. In general, one is faced with the prospect of assuming the hydraulic parameter and inverting the separation distance, or vice versa. Similar uncertainties exist, for instance, when trying to invert transport parameters from tracer mean residence time. This field test illustrates that when dealing with fracture networks, there is a need for analytic methods of complexity that lie between simple radial solutions and discrete fracture network models.

Solar neutrinos and the MSW effect for three-neutrino mixing

NASA Technical Reports Server (NTRS)

Shi, X.; Schramm, David N.

1991-01-01

Researchers considered three-neutrino Mikheyev-Smirnov-Wolfenstein (MSW) mixing, assuming m sub 3 is much greater than m sub 2 is greater than m sub 1 as expected from theoretical consideration if neutrinos have mass. They calculated the corresponding mixing parameter space allowed by the Cl-37 and Kamiokande 2 experiments. They also calculated the expected depletion for the Ga-71 experiment. They explored a range of theoretical uncertainty due to possible astrophysical effects by varying the B-8 neutrino flux and redoing the MSW mixing calculation.

Tracing Cosmic Dawn

NASA Astrophysics Data System (ADS)

Fialkov, Anastasia

2018-05-01

Observational effort is on the way to probe the 21-cm of neutral hydrogen from the epochs of Reionization and Cosmic Dawn. Our current poor knowledge of high redshift astrophysics results in a large uncertainty in the theoretically predicted 21-cm signal. A recent parameter study that is highlighted here explores the variety of 21-cm signals resulting from viable astrophysical scenarios. Model-independent relations between the shape of the signal and the underlying astrophysics are discussed. Finally, I briefly note on possible alternative probes of the high redshift Universe, specifically Fast Radio Bursts.

Do not Bet on the Unknown Versus Try to Find Out More: Estimation Uncertainty and “Unexpected Uncertainty” Both Modulate Exploration

PubMed Central

Payzan-LeNestour, Élise; Bossaerts, Peter

2012-01-01

Little is known about how humans solve the exploitation/exploration trade-off. In particular, the evidence for uncertainty-driven exploration is mixed. The current study proposes a novel hypothesis of exploration that helps reconcile prior findings that may seem contradictory at first. According to this hypothesis, uncertainty-driven exploration involves a dilemma between two motives: (i) to speed up learning about the unknown, which may beget novel reward opportunities; (ii) to avoid the unknown because it is potentially dangerous. We provide evidence for our hypothesis using both behavioral and simulated data, and briefly point to recent evidence that the brain differentiates between these two motives. PMID:23087606

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.

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(*)

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 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).

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

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.

Large Uncertainty in Estimating pCO2 From Carbonate Equilibria in Lakes

NASA Astrophysics Data System (ADS)

Golub, Malgorzata; Desai, Ankur R.; McKinley, Galen A.; Remucal, Christina K.; Stanley, Emily H.

2017-11-01

Most estimates of carbon dioxide (CO2) evasion from freshwaters rely on calculating partial pressure of aquatic CO2 (pCO2) from two out of three CO2-related parameters using carbonate equilibria. However, the pCO2 uncertainty has not been systematically evaluated across multiple lake types and equilibria. We quantified random errors in pH, dissolved inorganic carbon, alkalinity, and temperature from the North Temperate Lakes Long-Term Ecological Research site in four lake groups across a broad gradient of chemical composition. These errors were propagated onto pCO2 calculated from three carbonate equilibria, and for overlapping observations, compared against uncertainties in directly measured pCO2. The empirical random errors in CO2-related parameters were mostly below 2% of their median values. Resulting random pCO2 errors ranged from ±3.7% to ±31.5% of the median depending on alkalinity group and choice of input parameter pairs. Temperature uncertainty had a negligible effect on pCO2. When compared with direct pCO2 measurements, all parameter combinations produced biased pCO2 estimates with less than one third of total uncertainty explained by random pCO2 errors, indicating that systematic uncertainty dominates over random error. Multidecadal trend of pCO2 was difficult to reconstruct from uncertain historical observations of CO2-related parameters. Given poor precision and accuracy of pCO2 estimates derived from virtually any combination of two CO2-related parameters, we recommend direct pCO2 measurements where possible. To achieve consistently robust estimates of CO2 emissions from freshwater components of terrestrial carbon balances, future efforts should focus on improving accuracy and precision of CO2-related parameters (including direct pCO2) measurements and associated pCO2 calculations.

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.

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.

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.

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.

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.

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).

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.

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.

A transient stochastic weather generator incorporating climate model uncertainty

NASA Astrophysics Data System (ADS)

Glenis, Vassilis; Pinamonti, Valentina; Hall, Jim W.; Kilsby, Chris G.

2015-11-01

Stochastic weather generators (WGs), which provide long synthetic time series of weather variables such as rainfall and potential evapotranspiration (PET), have found widespread use in water resources modelling. When conditioned upon the changes in climatic statistics (change factors, CFs) predicted by climate models, WGs provide a useful tool for climate impacts assessment and adaption planning. The latest climate modelling exercises have involved large numbers of global and regional climate models integrations, designed to explore the implications of uncertainties in the climate model formulation and parameter settings: so called 'perturbed physics ensembles' (PPEs). In this paper we show how these climate model uncertainties can be propagated through to impact studies by testing multiple vectors of CFs, each vector derived from a different sample from a PPE. We combine this with a new methodology to parameterise the projected time-evolution of CFs. We demonstrate how, when conditioned upon these time-dependent CFs, an existing, well validated and widely used WG can be used to generate non-stationary simulations of future climate that are consistent with probabilistic outputs from the Met Office Hadley Centre's Perturbed Physics Ensemble. The WG enables extensive sampling of natural variability and climate model uncertainty, providing the basis for development of robust water resources management strategies in the context of a non-stationary climate.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

PubMed Central

2011-01-01

Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance. PMID:21324153

Flexibility evaluation of multiechelon supply chains.

PubMed

Almeida, João Flávio de Freitas; Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution.

Flexibility evaluation of multiechelon supply chains

PubMed Central

Conceição, Samuel Vieira; Pinto, Luiz Ricardo; de Camargo, Ricardo Saraiva; Júnior, Gilberto de Miranda

2018-01-01

Multiechelon supply chains are complex logistics systems that require flexibility and coordination at a tactical level to cope with environmental uncertainties in an efficient and effective manner. To cope with these challenges, mathematical programming models are developed to evaluate supply chain flexibility. However, under uncertainty, supply chain models become complex and the scope of flexibility analysis is generally reduced. This paper presents a unified approach that can evaluate the flexibility of a four-echelon supply chain via a robust stochastic programming model. The model simultaneously considers the plans of multiple business divisions such as marketing, logistics, manufacturing, and procurement, whose goals are often conflicting. A numerical example with deterministic parameters is presented to introduce the analysis, and then, the model stochastic parameters are considered to evaluate flexibility. The results of the analysis on supply, manufacturing, and distribution flexibility are presented. Tradeoff analysis of demand variability and service levels is also carried out. The proposed approach facilitates the adoption of different management styles, thus improving supply chain resilience. The model can be extended to contexts pertaining to supply chain disruptions; for example, the model can be used to explore operation strategies when subtle events disrupt supply, manufacturing, or distribution. PMID:29584755

Robust gaze-steering of an active vision system against errors in the estimated parameters

NASA Astrophysics Data System (ADS)

Han, Youngmo

2015-01-01

Gaze-steering is often used to broaden the viewing range of an active vision system. Gaze-steering procedures are usually based on estimated parameters such as image position, image velocity, depth and camera calibration parameters. However, there may be uncertainties in these estimated parameters because of measurement noise and estimation errors. In this case, robust gaze-steering cannot be guaranteed. To compensate for such problems, this paper proposes a gaze-steering method based on a linear matrix inequality (LMI). In this method, we first propose a proportional derivative (PD) control scheme on the unit sphere that does not use depth parameters. This proposed PD control scheme can avoid uncertainties in the estimated depth and camera calibration parameters, as well as inconveniences in their estimation process, including the use of auxiliary feature points and highly non-linear computation. Furthermore, the control gain of the proposed PD control scheme on the unit sphere is designed using LMI such that the designed control is robust in the presence of uncertainties in the other estimated parameters, such as image position and velocity. Simulation results demonstrate that the proposed method provides a better compensation for uncertainties in the estimated parameters than the contemporary linear method and steers the gaze of the camera more steadily over time than the contemporary non-linear method.

Effects of vegetation canopy on the radar backscattering coefficient

NASA Technical Reports Server (NTRS)

Mo, T.; Blanchard, B. J.; Schmugge, T. J.

1983-01-01

Airborne L- and C-band scatterometer data, taken over both vegetation-covered and bare fields, were systematically analyzed and theoretically reproduced, using a recently developed model for calculating radar backscattering coefficients of rough soil surfaces. The results show that the model can reproduce the observed angular variations of radar backscattering coefficient quite well via a least-squares fit method. Best fits to the data provide estimates of the statistical properties of the surface roughness, which is characterized by two parameters: the standard deviation of surface height, and the surface correlation length. In addition, the processes of vegetation attenuation and volume scattering require two canopy parameters, the canopy optical thickness and a volume scattering factor. Canopy parameter values for individual vegetation types, including alfalfa, milo and corn, were also determined from the best-fit results. The uncertainties in the scatterometer data were also explored.

Uncertainty Analysis of Instrument Calibration and Application

NASA Technical Reports Server (NTRS)

Tripp, John S.; Tcheng, Ping

1999-01-01

Experimental aerodynamic researchers require estimated precision and bias uncertainties of measured physical quantities, typically at 95 percent confidence levels. Uncertainties of final computed aerodynamic parameters are obtained by propagation of individual measurement uncertainties through the defining functional expressions. In this paper, rigorous mathematical techniques are extended to determine precision and bias uncertainties of any instrument-sensor system. Through this analysis, instrument uncertainties determined through calibration are now expressed as functions of the corresponding measurement for linear and nonlinear univariate and multivariate processes. Treatment of correlated measurement precision error is developed. During laboratory calibration, calibration standard uncertainties are assumed to be an order of magnitude less than those of the instrument being calibrated. Often calibration standards do not satisfy this assumption. This paper applies rigorous statistical methods for inclusion of calibration standard uncertainty and covariance due to the order of their application. The effects of mathematical modeling error on calibration bias uncertainty are quantified. The effects of experimental design on uncertainty are analyzed. The importance of replication is emphasized, techniques for estimation of both bias and precision uncertainties using replication are developed. Statistical tests for stationarity of calibration parameters over time are obtained.

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.

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

Robustness analysis of bogie suspension components Pareto optimised values

NASA Astrophysics Data System (ADS)

Mousavi Bideleh, Seyed Milad

2017-08-01

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.

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.

A sequential factorial analysis approach to characterize the effects of uncertainties for supporting air quality management

NASA Astrophysics Data System (ADS)

Wang, S.; Huang, G. H.; Veawab, A.

2013-03-01

This study proposes a sequential factorial analysis (SFA) approach for supporting regional air quality management under uncertainty. SFA is capable not only of examining the interactive effects of input parameters, but also of analyzing the effects of constraints. When there are too many factors involved in practical applications, SFA has the advantage of conducting a sequence of factorial analyses for characterizing the effects of factors in a systematic manner. The factor-screening strategy employed in SFA is effective in greatly reducing the computational effort. The proposed SFA approach is applied to a regional air quality management problem for demonstrating its applicability. The results indicate that the effects of factors are evaluated quantitatively, which can help decision makers identify the key factors that have significant influence on system performance and explore the valuable information that may be veiled beneath their interrelationships.

Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach

NASA Astrophysics Data System (ADS)

Chowdhury, R.; Adhikari, S.

2012-10-01

Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RM) or may be infinite-dimensional as in the function space CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.

Energy Signal Tool for Decision Support in Building Energy Systems

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

Henze, G. P.; Pavlak, G. S.; Florita, A. R.

2014-12-01

A prototype energy signal tool is demonstrated for operational whole-building and system-level energy use evaluation. The purpose of the tool is to give a summary of building energy use which allows a building operator to quickly distinguish normal and abnormal energy use. Toward that end, energy use status is displayed as a traffic light, which is a visual metaphor for energy use that is either substantially different from expected (red and yellow lights) or approximately the same as expected (green light). Which light to display for a given energy end use is determined by comparing expected to actual energy use.more » As expected, energy use is necessarily uncertain; we cannot choose the appropriate light with certainty. Instead, the energy signal tool chooses the light by minimizing the expected cost of displaying the wrong light. The expected energy use is represented by a probability distribution. Energy use is modeled by a low-order lumped parameter model. Uncertainty in energy use is quantified by a Monte Carlo exploration of the influence of model parameters on energy use. Distributions over model parameters are updated over time via Bayes' theorem. The simulation study was devised to assess whole-building energy signal accuracy in the presence of uncertainty and faults at the submetered level, which may lead to tradeoffs at the whole-building level that are not detectable without submetering.« less

Sensitivity analysis of TRX-2 lattice parameters with emphasis on epithermal /sup 238/U capture. Final report

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

Tomlinson, E.T.; deSaussure, G.; Weisbin, C.R.

1977-03-01

The main purpose of the study is the determination of the sensitivity of TRX-2 thermal lattice performance parameters to nuclear cross section data, particularly the epithermal resonance capture cross section of /sup 238/U. An energy-dependent sensitivity profile was generated for each of the performance parameters, to the most important cross sections of the various isotopes in the lattice. Uncertainties in the calculated values of the performance parameters due to estimated uncertainties in the basic nuclear data, deduced in this study, were shown to be small compared to the uncertainties in the measured values of the performance parameter and compared tomore » differences among calculations based upon the same data but with different methodologies.« less

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

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

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.

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

A method for approximating acoustic-field-amplitude uncertainty caused by environmental uncertainties.

PubMed

James, Kevin R; Dowling, David R

2008-09-01

In underwater acoustics, the accuracy of computational field predictions is commonly limited by uncertainty in environmental parameters. An approximate technique for determining the probability density function (PDF) of computed field amplitude, A, from known environmental uncertainties is presented here. The technique can be applied to several, N, uncertain parameters simultaneously, requires N+1 field calculations, and can be used with any acoustic field model. The technique implicitly assumes independent input parameters and is based on finding the optimum spatial shift between field calculations completed at two different values of each uncertain parameter. This shift information is used to convert uncertain-environmental-parameter distributions into PDF(A). The technique's accuracy is good when the shifted fields match well. Its accuracy is evaluated in range-independent underwater sound channels via an L(1) error-norm defined between approximate and numerically converged results for PDF(A). In 50-m- and 100-m-deep sound channels with 0.5% uncertainty in depth (N=1) at frequencies between 100 and 800 Hz, and for ranges from 1 to 8 km, 95% of the approximate field-amplitude distributions generated L(1) values less than 0.52 using only two field calculations. Obtaining comparable accuracy from traditional methods requires of order 10 field calculations and up to 10(N) when N>1.

Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

NASA Astrophysics Data System (ADS)

Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

2014-12-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.

Advances in Applications of Hierarchical Bayesian Methods with Hydrological Models

NASA Astrophysics Data System (ADS)

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

2017-12-01

Mechanistic and empirical watershed models are increasingly used to inform water resource decisions. Growing access to historical stream measurements and data from in-situ sensor technologies has increased the need for improved techniques for coupling models with hydrological measurements. Techniques that account for the intrinsic uncertainties of both models and measurements are especially needed. Hierarchical Bayesian methods provide an efficient modeling tool for quantifying model and prediction uncertainties, including those associated with measurements. Hierarchical methods can also be used to explore spatial and temporal variations in model parameters and uncertainties that are informed by hydrological measurements. We used hierarchical Bayesian methods to develop a hybrid (statistical-mechanistic) SPARROW (SPAtially Referenced Regression On Watershed attributes) model of long-term mean annual streamflow across diverse environmental and climatic drainages in 18 U.S. hydrological regions. Our application illustrates the use of a new generation of Bayesian methods that offer more advanced computational efficiencies than the prior generation. Evaluations of the effects of hierarchical (regional) variations in model coefficients and uncertainties on model accuracy indicates improved prediction accuracies (median of 10-50%) but primarily in humid eastern regions, where model uncertainties are one-third of those in arid western regions. Generally moderate regional variability is observed for most hierarchical coefficients. Accounting for measurement and structural uncertainties, using hierarchical state-space techniques, revealed the effects of spatially-heterogeneous, latent hydrological processes in the "localized" drainages between calibration sites; this improved model precision, with only minor changes in regional coefficients. Our study can inform advances in the use of hierarchical methods with hydrological models to improve their integration with stream measurements.

Dealing with deep uncertainties in landslide modelling for disaster risk reduction under climate change

NASA Astrophysics Data System (ADS)

Almeida, Susana; Holcombe, Elizabeth Ann; Pianosi, Francesca; Wagener, Thorsten

2017-02-01

Landslides have large negative economic and societal impacts, including loss of life and damage to infrastructure. Slope stability assessment is a vital tool for landslide risk management, but high levels of uncertainty often challenge its usefulness. Uncertainties are associated with the numerical model used to assess slope stability and its parameters, with the data characterizing the geometric, geotechnic and hydrologic properties of the slope, and with hazard triggers (e.g. rainfall). Uncertainties associated with many of these factors are also likely to be exacerbated further by future climatic and socio-economic changes, such as increased urbanization and resultant land use change. In this study, we illustrate how numerical models can be used to explore the uncertain factors that influence potential future landslide hazard using a bottom-up strategy. Specifically, we link the Combined Hydrology And Stability Model (CHASM) with sensitivity analysis and Classification And Regression Trees (CART) to identify critical thresholds in slope properties and climatic (rainfall) drivers that lead to slope failure. We apply our approach to a slope in the Caribbean, an area that is naturally susceptible to landslides due to a combination of high rainfall rates, steep slopes, and highly weathered residual soils. For this particular slope, we find that uncertainties regarding some slope properties (namely thickness and effective cohesion of topsoil) are as important as the uncertainties related to future rainfall conditions. Furthermore, we show that 89 % of the expected behaviour of the studied slope can be characterized based on only two variables - the ratio of topsoil thickness to cohesion and the ratio of rainfall intensity to duration.

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.

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.

A game theoretic controller for a linear time-invariant system with parameter uncertainty and its application to the Space Station

NASA Technical Reports Server (NTRS)

Rhee, Ihnseok; Speyer, Jason L.

1990-01-01

A game theoretic controller is developed for a linear time-invariant system with parameter uncertainties in system and input matrices. The input-output decomposition modeling for the plant uncertainty is adopted. The uncertain dynamic system is represented as an internal feedback loop in which the system is assumed forced by fictitious disturbance caused by the parameter uncertainty. By considering the input and the fictitious disturbance as two noncooperative players, a differential game problem is constructed. It is shown that the resulting time invariant controller stabilizes the uncertain system for a prescribed uncertainty bound. This game theoretic controller is applied to the momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Inclusion of the external disturbance torque to the design procedure results in a dynamical feedback controller which consists of conventional PID control and cyclic disturbance rejection filter. It is shown that the game theoretic design, comparing to the LQR design or pole placement design, improves the stability robustness with respect to inertia variations.

Uncertainty Quantification in Multi-Scale Coronary Simulations Using Multi-resolution Expansion

NASA Astrophysics Data System (ADS)

Tran, Justin; Schiavazzi, Daniele; Ramachandra, Abhay; Kahn, Andrew; Marsden, Alison

2016-11-01

Computational simulations of coronary flow can provide non-invasive information on hemodynamics that can aid in surgical planning and research on disease propagation. In this study, patient-specific geometries of the aorta and coronary arteries are constructed from CT imaging data and finite element flow simulations are carried out using the open source software SimVascular. Lumped parameter networks (LPN), consisting of circuit representations of vascular hemodynamics and coronary physiology, are used as coupled boundary conditions for the solver. The outputs of these simulations depend on a set of clinically-derived input parameters that define the geometry and boundary conditions, however their values are subjected to uncertainty. We quantify the effects of uncertainty from two sources: uncertainty in the material properties of the vessel wall and uncertainty in the lumped parameter models whose values are estimated by assimilating patient-specific clinical and literature data. We use a generalized multi-resolution chaos approach to propagate the uncertainty. The advantages of this approach lies in its ability to support inputs sampled from arbitrary distributions and its built-in adaptivity that efficiently approximates stochastic responses characterized by steep gradients.

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.

Uncertainty quantification of crustal scale thermo-chemical properties in Southeast Australia

NASA Astrophysics Data System (ADS)

Mather, B.; Moresi, L. N.; Rayner, P. J.

2017-12-01

The thermo-chemical properties of the crust are essential to understanding the mechanical and thermal state of the lithosphere. The uncertainties associated with these parameters are connected to the available geophysical observations and a priori information to constrain the objective function. Often, it is computationally efficient to reduce the parameter space by mapping large portions of the crust into lithologies that have assumed homogeneity. However, the boundaries of these lithologies are, in themselves, uncertain and should also be included in the inverse problem. We assimilate geological uncertainties from an a priori geological model of Southeast Australia with geophysical uncertainties from S-wave tomography and 174 heat flow observations within an adjoint inversion framework. This reduces the computational cost of inverting high dimensional probability spaces, compared to probabilistic inversion techniques that operate in the `forward' mode, but at the sacrifice of uncertainty and covariance information. We overcome this restriction using a sensitivity analysis, that perturbs our observations and a priori information within their probability distributions, to estimate the posterior uncertainty of thermo-chemical parameters in the crust.

The Downwind Hemisphere of the Heliosphere as Observed with IBEX-Lo from 2009 to 2015

NASA Astrophysics Data System (ADS)

Wurz, P.; Galli, A.; Schwadron, N.; Kucharek, H.; Moebius, E.; Bzowski, M.; Sokol, J. M.; Kubiak, M. A.; Funsten, H. O.; Fuselier, S. A.; McComas, D. J.

2017-12-01

The topic of this study is the vast region towards the tail of the heliosphere. To this end, we comprehensively analyzed energetic neutral hydrogen atoms (ENAs) of energies 10 eV to 2.5 keV from the downwind hemisphere of the heliosheath measured during the first 7 years of the IBEX (Interstellar Boundary Explorer) mission. Neutralized ions from the heliosheath (the region of slow solar wind plasma between termination shock and heliopause) can be remotely observed as ENAs down to 10 eV with the IBEX-Lo sensor onboard IBEX. This sensor covers those energies of the ion spectrum that dominate the total plasma pressure in the downwind region. So far, this region of the heliosphere has never been explored in-situ. Converting observations obtained near Earth orbit at these low energies to the original ion distributions in the heliocentric rest frame at 100 AU is very challenging, making the assessment of uncertainties and implicit assumptions crucial. From the maps of observed ENAs from the heliosheath and their uncertainties we derive observational constraints on heliospheric models for the downwind hemisphere. These constraints limit the possible range of 1) the distance of the termination shock, 2) the total plasma pressure across the termination shock, 3) the radial flow velocity of the heliosheath plasma, 4) the extinction length of said plasma, and finally 5) the dimension of the heliosheath in downwind directions. Because these parameters are coupled and because of observational limitations, we also need to characterize the degeneracy, i.e., the fact that different sets of parameters may reproduce the observations.

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...

Methods for handling uncertainty within pharmaceutical funding decisions

NASA Astrophysics Data System (ADS)

Stevenson, Matt; Tappenden, Paul; Squires, Hazel

2014-01-01

This article provides a position statement regarding decision making under uncertainty within the economic evaluation of pharmaceuticals, with a particular focus upon the National Institute for Health and Clinical Excellence context within England and Wales. This area is of importance as funding agencies have a finite budget from which to purchase a selection of competing health care interventions. The objective function generally used is that of maximising societal health with an explicit acknowledgement that there will be opportunity costs associated with purchasing a particular intervention. Three components of uncertainty are discussed within a pharmaceutical funding perspective: methodological uncertainty, parameter uncertainty and structural uncertainty, alongside a discussion of challenges that are particularly pertinent to health economic evaluation. The discipline has focused primarily on handling methodological and parameter uncertainty and a clear reference case has been developed for consistency across evaluations. However, uncertainties still remain. Less attention has been given to methods for handling structural uncertainty. The lack of adequate methods to explicitly incorporate this aspect of model development may result in the true uncertainty surrounding health care investment decisions being underestimated. Research in this area is ongoing as we review.

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

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.

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.

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

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.

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

A Multialgorithm Approach to Land Surface Modeling of Suspended Sediment in the Colorado Front Range

PubMed Central

Stewart, J. R.; Kasprzyk, J. R.; Rajagopalan, B.; Minear, J. T.; Raseman, W. J.

2017-01-01

Abstract A new paradigm of simulating suspended sediment load (SSL) with a Land Surface Model (LSM) is presented here. Five erosion and SSL algorithms were applied within a common LSM framework to quantify uncertainties and evaluate predictability in two steep, forested catchments (>1,000 km2). The algorithms were chosen from among widely used sediment models, including empirically based: monovariate rating curve (MRC) and the Modified Universal Soil Loss Equation (MUSLE); stochastically based: the Load Estimator (LOADEST); conceptually based: the Hydrologic Simulation Program—Fortran (HSPF); and physically based: the Distributed Hydrology Soil Vegetation Model (DHSVM). The algorithms were driven by the hydrologic fluxes and meteorological inputs generated from the Variable Infiltration Capacity (VIC) LSM. A multiobjective calibration was applied to each algorithm and optimized parameter sets were validated over an excluded period, as well as in a transfer experiment to a nearby catchment to explore parameter robustness. Algorithm performance showed consistent decreases when parameter sets were applied to periods with greatly differing SSL variability relative to the calibration period. Of interest was a joint calibration of all sediment algorithm and streamflow parameters simultaneously, from which trade‐offs between streamflow performance and partitioning of runoff and base flow to optimize SSL timing were noted, decreasing the flexibility and robustness of the streamflow to adapt to different time periods. Parameter transferability to another catchment was most successful in more process‐oriented algorithms, the HSPF and the DHSVM. This first‐of‐its‐kind multialgorithm sediment scheme offers a unique capability to portray acute episodic loading while quantifying trade‐offs and uncertainties across a range of algorithm structures. PMID:29399268

Sensitivity of grounding line dynamics to basal conditions

NASA Astrophysics Data System (ADS)

Gagliardini, O.; Brondex, J.; Chauveau, G.; Gillet-chaulet, F.; Durand, G.

2017-12-01

In the context of a warming climate, the dynamical contribution of Antarctica to future sea level rise is still tainted by high uncertainties. Among the processes entering these uncertainties is the link between basal hydrology, friction and grounding line dynamics. Recent works have shown how sensitive is the response of the grounding line retreat to the choice of the form of the friction law. Indeed, starting from the same initial state, grounding line retreat rates can range over almost two orders of magnitude depending on the friction law formulation.Here, we use a phenomenological law that depends on the water pressure and allows a continuous transition from a Weertman-type friction at low water pressure to a Coulomb-type friction at high water pressure. This friction law depends on two main parameters that control the Weertman and Coulomb regimes. The range of values for these two parameters is only weakly physically constrained, and it can be shown that, for a given basal shear stress, different couples of parameters can conduct to the same sliding velocity. In addition, we show that close to the grounding line where basal water pressure is high, determining these two parameters might conduct to an ill-posed inverse problem with no solution.The aim of this presentation is to discuss a methodology to guide the choice of the two friction parameters and explore the sensitivity of the grounding line dynamics to this initial choice. We present results obtained both on a synthetic configuration used by the Marine Ice Sheet Model Intercomparison exercise and for the Amundsen sea sector using the experiments proposed by InitMIP-Antarctica, the first exercise in a series of ISMIP6 ice-sheet model intercomparison activities.

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...

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

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

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

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.

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.

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.

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.

Uncertainty Analysis of the Grazing Flow Impedance Tube

NASA Technical Reports Server (NTRS)

Brown, Martha C.; Jones, Michael G.; Watson, Willie R.

2012-01-01

This paper outlines a methodology to identify the measurement uncertainty of NASA Langley s Grazing Flow Impedance Tube (GFIT) over its operating range, and to identify the parameters that most significantly contribute to the acoustic impedance prediction. Two acoustic liners are used for this study. The first is a single-layer, perforate-over-honeycomb liner that is nonlinear with respect to sound pressure level. The second consists of a wire-mesh facesheet and a honeycomb core, and is linear with respect to sound pressure level. These liners allow for evaluation of the effects of measurement uncertainty on impedances educed with linear and nonlinear liners. In general, the measurement uncertainty is observed to be larger for the nonlinear liners, with the largest uncertainty occurring near anti-resonance. A sensitivity analysis of the aerodynamic parameters (Mach number, static temperature, and static pressure) used in the impedance eduction process is also conducted using a Monte-Carlo approach. This sensitivity analysis demonstrates that the impedance eduction process is virtually insensitive to each of these parameters.

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.

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).

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.

Modelling water table drawdown and recovery during tunnel excavation in fractured rock: estimating environmental impacts and characterizing uncertainties in a heterogeneous domain

NASA Astrophysics Data System (ADS)

Sege, J.; Li, Y.; Chang, C. F.; Chen, J.; Chen, Z.; Rubin, Y.; Li, X.; Hehua, Z.; Wang, C.; Osorio-Murillo, C. A.

2015-12-01

This study will develop a numerical model to characterize the perturbation of local groundwater systems by underground tunnel construction. Tunnels and other underground spaces act as conduits that remove water from the surrounding aquifer, and may lead to drawdown of the water table. Significant declines in water table elevation can cause environmental impacts by altering root zone soil moisture and changing inflows to surface waters. Currently, it is common to use analytical solutions to estimate groundwater fluxes through tunnel walls. However, these solutions often neglect spatial and temporal heterogeneity in aquifer parameters and system stresses. Some heterogeneous parameters, such as fracture densities, can significantly affect tunnel inflows. This study will focus on numerical approaches that incorporate heterogeneity across a range of scales. Time-dependent simulations will be undertaken to compute drawdown at various stages of excavation, and to model water table recovery after low-conductivity liners are applied to the tunnel walls. This approach will assist planners in anticipating environmental impacts to local surface waters and vegetation, and in computing the amount of tunnel inflow reduction required to meet environmental targets. The authors will also focus on managing uncertainty in model parameters. For greater planning applicability, extremes of a priori parameter ranges will be explored in order to anticipate best- and worst-case scenarios. For calibration and verification purposes, the model will be applied to a completed tunnel project in Mount Mingtang, China, where tunnel inflows were recorded throughout the construction process.

Quantifying the importance of spatial resolution and other factors through global sensitivity analysis of a flood inundation model

NASA Astrophysics Data System (ADS)

Thomas Steven Savage, James; Pianosi, Francesca; Bates, Paul; Freer, Jim; Wagener, Thorsten

2016-11-01

Where high-resolution topographic data are available, modelers are faced with the decision of whether it is better to spend computational resource on resolving topography at finer resolutions or on running more simulations to account for various uncertain input factors (e.g., model parameters). In this paper we apply global sensitivity analysis to explore how influential the choice of spatial resolution is when compared to uncertainties in the Manning's friction coefficient parameters, the inflow hydrograph, and those stemming from the coarsening of topographic data used to produce Digital Elevation Models (DEMs). We apply the hydraulic model LISFLOOD-FP to produce several temporally and spatially variable model outputs that represent different aspects of flood inundation processes, including flood extent, water depth, and time of inundation. We find that the most influential input factor for flood extent predictions changes during the flood event, starting with the inflow hydrograph during the rising limb before switching to the channel friction parameter during peak flood inundation, and finally to the floodplain friction parameter during the drying phase of the flood event. Spatial resolution and uncertainty introduced by resampling topographic data to coarser resolutions are much more important for water depth predictions, which are also sensitive to different input factors spatially and temporally. Our findings indicate that the sensitivity of LISFLOOD-FP predictions is more complex than previously thought. Consequently, the input factors that modelers should prioritize will differ depending on the model output assessed, and the location and time of when and where this output is most relevant.

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.

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.).

The Interplay between Uncertainty Monitoring and Working Memory: Can Metacognition Become Automatic?

PubMed Central

Coutinho, Mariana V. C.; Redford, Joshua S.; Church, Barbara A.; Zakrzewski, Alexandria C.; Couchman, Justin J.; Smith, J. David

2016-01-01

The uncertainty response has grounded the study of metacognition in nonhuman animals. Recent research has explored the processes supporting uncertainty monitoring in monkeys. It revealed that uncertainty responding in contrast to perceptual responding depends on significant working memory resources. The aim of the present study was to expand this research by examining whether uncertainty monitoring is also working memory demanding in humans. To explore this issue, human participants were tested with or without a cognitive load on a psychophysical discrimination task including either an uncertainty response (allowing the decline of difficult trials) or a middle-perceptual response (labeling the same intermediate trial levels). The results demonstrated that cognitive load reduced uncertainty responding, but increased middle responding. However, this dissociation between uncertainty and middle responding was only observed when participants either lacked training or had very little training with the uncertainty response. If more training was provided, the effect of load was small. These results suggest that uncertainty responding is resource demanding, but with sufficient training, human participants can respond to uncertainty either by using minimal working memory resources or effectively sharing resources. These results are discussed in relation to the literature on animal and human metacognition. PMID:25971878

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

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

Hock, Kiel; Earle, Keith

2016-02-06

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

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

Quantum corrections to newtonian potential and generalized uncertainty principle

NASA Astrophysics Data System (ADS)

Scardigli, Fabio; Lambiase, Gaetano; Vagenas, Elias

2017-08-01

We use the leading quantum corrections to the newtonian potential to compute the deformation parameter of the generalized uncertainty principle. By assuming just only General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum, our calculation gives, to first order, a specific numerical result. We briefly discuss the physical meaning of this value, and compare it with the previously obtained bounds on the generalized uncertainty principle deformation parameter.

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.

Exact results for the finite time thermodynamic uncertainty relation

NASA Astrophysics Data System (ADS)

Manikandan, Sreekanth K.; Krishnamurthy, Supriya

2018-03-01

We obtain exact results for the recently discovered finite-time thermodynamic uncertainty relation, for the dissipated work W d , in a stochastically driven system with non-Gaussian work statistics, both in the steady state and transient regimes, by obtaining exact expressions for any moment of W d at arbitrary times. The uncertainty function (the Fano factor of W d ) is bounded from below by 2k_BT as expected, for all times τ, in both steady state and transient regimes. The lower bound is reached at τ=0 as well as when certain system parameters vanish (corresponding to an equilibrium state). Surprisingly, we find that the uncertainty function also reaches a constant value at large τ for all the cases we have looked at. For a system starting and remaining in steady state, the uncertainty function increases monotonically, as a function of τ as well as other system parameters, implying that the large τ value is also an upper bound. For the same system in the transient regime, however, we find that the uncertainty function can have a local minimum at an accessible time τm , for a range of parameter values. The large τ value for the uncertainty function is hence not a bound in this case. The non-monotonicity suggests, rather counter-intuitively, that there might be an optimal time for the working of microscopic machines, as well as an optimal configuration in the phase space of parameter values. Our solutions show that the ratios of higher moments of the dissipated work are also bounded from below by 2k_BT . For another model, also solvable by our methods, which never reaches a steady state, the uncertainty function, is in some cases, bounded from below by a value less than 2k_BT .

Abschätzung des Einflusses von Parameterunsicherheiten bei der Planung und Auswertung von Tracertests unter Verwendung von Ensembleprognosen

NASA Astrophysics Data System (ADS)

Klotzsch, Stephan; Binder, Martin; Händel, Falk

2017-06-01

While planning tracer tests, uncertainties in geohydraulic parameters should be considered as an important factor. Neglecting these uncertainties can lead to missing the tracer breakthrough, for example. One way to consider uncertainties during tracer test design is the so called ensemble forecast. The applicability of this method to geohydrological problems is demonstrated by coupling the method with two analytical solute transport models. The algorithm presented in this article is suitable for prediction as well as parameter estimation. The parameter estimation function can be used in a tracer test for reducing the uncertainties in the measured data which can improve the initial prediction. The algorithm was implemented into a software tool which is freely downloadable from the website of the Institute for Groundwater Management at TU Dresden, Germany.

Position uncertainty distribution for articulated arm coordinate measuring machine based on simplified definite integration

NASA Astrophysics Data System (ADS)

You, Xu; Zhi-jian, Zong; Qun, Gao

2018-07-01

This paper describes a methodology for the position uncertainty distribution of an articulated arm coordinate measuring machine (AACMM). First, a model of the structural parameter uncertainties was established by statistical method. Second, the position uncertainty space volume of the AACMM in a certain configuration was expressed using a simplified definite integration method based on the structural parameter uncertainties; it was then used to evaluate the position accuracy of the AACMM in a certain configuration. Third, the configurations of a certain working point were calculated by an inverse solution, and the position uncertainty distribution of a certain working point was determined; working point uncertainty can be evaluated by the weighting method. Lastly, the position uncertainty distribution in the workspace of the ACCMM was described by a map. A single-point contrast test of a 6-joint AACMM was carried out to verify the effectiveness of the proposed method, and it was shown that the method can describe the position uncertainty of the AACMM and it was used to guide the calibration of the AACMM and the choice of AACMM’s accuracy area.

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

Bayesian inference of spectral induced polarization parameters for laboratory complex resistivity measurements of rocks and soils

NASA Astrophysics Data System (ADS)

Bérubé, Charles L.; Chouteau, Michel; Shamsipour, Pejman; Enkin, Randolph J.; Olivo, Gema R.

2017-08-01

Spectral induced polarization (SIP) measurements are now widely used to infer mineralogical or hydrogeological properties from the low-frequency electrical properties of the subsurface in both mineral exploration and environmental sciences. We present an open-source program that performs fast multi-model inversion of laboratory complex resistivity measurements using Markov-chain Monte Carlo simulation. Using this stochastic method, SIP parameters and their uncertainties may be obtained from the Cole-Cole and Dias models, or from the Debye and Warburg decomposition approaches. The program is tested on synthetic and laboratory data to show that the posterior distribution of a multiple Cole-Cole model is multimodal in particular cases. The Warburg and Debye decomposition approaches yield unique solutions in all cases. It is shown that an adaptive Metropolis algorithm performs faster and is less dependent on the initial parameter values than the Metropolis-Hastings step method when inverting SIP data through the decomposition schemes. There are no advantages in using an adaptive step method for well-defined Cole-Cole inversion. Finally, the influence of measurement noise on the recovered relaxation time distribution is explored. We provide the geophysics community with a open-source platform that can serve as a base for further developments in stochastic SIP data inversion and that may be used to perform parameter analysis with various SIP models.

Machine Learning Techniques for Global Sensitivity Analysis in Climate Models

NASA Astrophysics Data System (ADS)

Safta, C.; Sargsyan, K.; Ricciuto, D. M.

2017-12-01

Climate models studies are not only challenged by the compute intensive nature of these models but also by the high-dimensionality of the input parameter space. In our previous work with the land model components (Sargsyan et al., 2014) we identified subsets of 10 to 20 parameters relevant for each QoI via Bayesian compressive sensing and variance-based decomposition. Nevertheless the algorithms were challenged by the nonlinear input-output dependencies for some of the relevant QoIs. In this work we will explore a combination of techniques to extract relevant parameters for each QoI and subsequently construct surrogate models with quantified uncertainty necessary to future developments, e.g. model calibration and prediction studies. In the first step, we will compare the skill of machine-learning models (e.g. neural networks, support vector machine) to identify the optimal number of classes in selected QoIs and construct robust multi-class classifiers that will partition the parameter space in regions with smooth input-output dependencies. These classifiers will be coupled with techniques aimed at building sparse and/or low-rank surrogate models tailored to each class. Specifically we will explore and compare sparse learning techniques with low-rank tensor decompositions. These models will be used to identify parameters that are important for each QoI. Surrogate accuracy requirements are higher for subsequent model calibration studies and we will ascertain the performance of this workflow for multi-site ALM simulation ensembles.

A review of uncertainty research in impact assessment

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

Leung, Wanda, E-mail: wanda.leung@usask.ca; Noble, Bram, E-mail: b.noble@usask.ca; Gunn, Jill, E-mail: jill.gunn@usask.ca

2015-01-15

This paper examines uncertainty research in Impact Assessment (IA) and the focus of attention of the IA scholarly literature. We do so by first exploring ‘outside’ the IA literature, identifying three main themes of uncertainty research, and then apply these themes to examine the focus of scholarly research on uncertainty ‘inside’ IA. Based on a search of the database Scopus, we identified 134 journal papers published between 1970 and 2013 that address uncertainty in IA, 75% of which were published since 2005. We found that 90% of IA research addressing uncertainty focused on uncertainty in the practice of IA, includingmore » uncertainty in impact predictions, models and managing environmental impacts. Notwithstanding early guidance on uncertainty treatment in IA from the 1980s, we found no common, underlying conceptual framework that was guiding research on uncertainty in IA practice. Considerably less attention, only 9% of papers, focused on uncertainty communication, disclosure and decision-making under uncertain conditions, the majority of which focused on the need to disclose uncertainties as opposed to providing guidance on how to do so and effectively use that information to inform decisions. Finally, research focused on theory building for explaining human behavior with respect to uncertainty avoidance constituted only 1% of the IA published literature. We suggest the need for further conceptual framework development for researchers focused on identifying and addressing uncertainty in IA practice; the need for guidance on how best to communicate uncertainties in practice, versus criticizing practitioners for not doing so; research that explores how best to interpret and use disclosures about uncertainty when making decisions about project approvals, and the implications of doing so; and academic theory building and exploring the utility of existing theories to better understand and explain uncertainty avoidance behavior in IA. - Highlights: • We identified three main themes of uncertainty research in 134 papers from the scholarly literature. • The majority of research has focused on better methods for managing uncertainty in predictions. • Uncertainty disclosure is demanded of practitioners, but there is little guidance on how to do so. • There is limited theoretical explanation as to why uncertainty is avoided or not disclosed. • Conceptual, practical and theoretical guidance are required for IA uncertainty consideration.« less

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.

COMMUNICATING THE PARAMETER UNCERTAINTY IN THE IQWIG EFFICIENCY FRONTIER TO DECISION-MAKERS

PubMed Central

Stollenwerk, Björn; Lhachimi, Stefan K; Briggs, Andrew; Fenwick, Elisabeth; Caro, Jaime J; Siebert, Uwe; Danner, Marion; Gerber-Grote, Andreas

2015-01-01

The Institute for Quality and Efficiency in Health Care (IQWiG) developed—in a consultation process with an international expert panel—the efficiency frontier (EF) approach to satisfy a range of legal requirements for economic evaluation in Germany's statutory health insurance system. The EF approach is distinctly different from other health economic approaches. Here, we evaluate established tools for assessing and communicating parameter uncertainty in terms of their applicability to the EF approach. Among these are tools that perform the following: (i) graphically display overall uncertainty within the IQWiG EF (scatter plots, confidence bands, and contour plots) and (ii) communicate the uncertainty around the reimbursable price. We found that, within the EF approach, most established plots were not always easy to interpret. Hence, we propose the use of price reimbursement acceptability curves—a modification of the well-known cost-effectiveness acceptability curves. Furthermore, it emerges that the net monetary benefit allows an intuitive interpretation of parameter uncertainty within the EF approach. This research closes a gap for handling uncertainty in the economic evaluation approach of the IQWiG methods when using the EF. However, the precise consequences of uncertainty when determining prices are yet to be defined. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd. PMID:24590819

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.

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.

Predicting critical transitions in dynamical systems from time series using nonstationary probability density modeling.

PubMed

Kwasniok, Frank

2013-11-01

A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter uncertainty is taken. The technique is generic, independent of the underlying dynamics of the system. The method is verified on simulated data and then applied to prediction of Arctic sea-ice extent.

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.

Uncertainty and sensitivity assessment of flood risk assessments

NASA Astrophysics Data System (ADS)

de Moel, H.; Aerts, J. C.

2009-12-01

Floods are one of the most frequent and costly natural disasters. In order to protect human lifes and valuable assets from the effect of floods many defensive structures have been build. Despite these efforts economic losses due to catastrophic flood events have, however, risen substantially during the past couple of decades because of continuing economic developments in flood prone areas. On top of that, climate change is expected to affect the magnitude and frequency of flood events. Because these ongoing trends are expected to continue, a transition can be observed in various countries to move from a protective flood management approach to a more risk based flood management approach. In a risk based approach, flood risk assessments play an important role in supporting decision making. Most flood risk assessments assess flood risks in monetary terms (damage estimated for specific situations or expected annual damage) in order to feed cost-benefit analysis of management measures. Such flood risk assessments contain, however, considerable uncertainties. This is the result from uncertainties in the many different input parameters propagating through the risk assessment and accumulating in the final estimate. Whilst common in some other disciplines, as with integrated assessment models, full uncertainty and sensitivity analyses of flood risk assessments are not so common. Various studies have addressed uncertainties regarding flood risk assessments, but have mainly focussed on the hydrological conditions. However, uncertainties in other components of the risk assessment, like the relation between water depth and monetary damage, can be substantial as well. This research therefore tries to assess the uncertainties of all components of monetary flood risk assessments, using a Monte Carlo based approach. Furthermore, the total uncertainty will also be attributed to the different input parameters using a variance based sensitivity analysis. Assessing and visualizing the uncertainties of the final risk estimate will be helpful to decision makers to make better informed decisions and attributing this uncertainty to the input parameters helps to identify which parameters are most important when it comes to uncertainty in the final estimate and should therefore deserve additional attention in further research.

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.

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

Effect of information, uncertainty and parameter variability on profits in a queue with various pricing strategies

NASA Astrophysics Data System (ADS)

Sun, Wei; Li, Shiyong

2014-08-01

This paper presents an unobservable single-server queueing system with three types of uncertainty, where the service rate, or waiting cost or service quality is random variable that may obtain n(n > 2) values. The information about the realised values of parameters is only known to the server. We are concerned about the server's behaviour: revealing or concealing the information to customers. The n-value assumption and the server's behaviour enable us to consider various pricing strategies. In this paper, we analyse the effect of information and uncertainty on profits and make comparisons between the profits under different pricing strategies. Moreover, as for parameter variability reflected by the number of each parameter's possible choices n, we observe the effect of variable n on all types of profits and find that revealing the parameter information can much more benefit the server with the increase of n.

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.

Sensitivity to Uncertainty in Asteroid Impact Risk Assessment

NASA Astrophysics Data System (ADS)

Mathias, D.; Wheeler, L.; Prabhu, D. K.; Aftosmis, M.; Dotson, J.; Robertson, D. K.

2015-12-01

The Engineering Risk Assessment (ERA) team at NASA Ames Research Center is developing a physics-based impact risk model for probabilistically assessing threats from potential asteroid impacts on Earth. The model integrates probabilistic sampling of asteroid parameter ranges with physics-based analyses of entry, breakup, and impact to estimate damage areas and casualties from various impact scenarios. Assessing these threats is a highly coupled, dynamic problem involving significant uncertainties in the range of expected asteroid characteristics, how those characteristics may affect the level of damage, and the fidelity of various modeling approaches and assumptions. The presented model is used to explore the sensitivity of impact risk estimates to these uncertainties in order to gain insight into what additional data or modeling refinements are most important for producing effective, meaningful risk assessments. In the extreme cases of very small or very large impacts, the results are generally insensitive to many of the characterization and modeling assumptions. However, the nature of the sensitivity can change across moderate-sized impacts. Results will focus on the value of additional information in this critical, mid-size range, and how this additional data can support more robust mitigation decisions.

Bayesian inversion of the global present-day GIA signal uncertainty from RSL data

NASA Astrophysics Data System (ADS)

Caron, Lambert; Ivins, Erik R.; Adhikari, Surendra; Larour, Eric

2017-04-01

Various geophysical signals measured in the process of studying the present-day climate change (such as changes in the Earth gravitational potential, ocean altimery or GPS data) include a secular Glacial Isostatic Adjustment contribution that has to be corrected for. Yet, one of the current major challenges that Glacial Isostatic Adjustment modelling is currently struggling with is to accurately determine the uncertainty of the predicted present-day GIA signal. This is especially true at the global scale, where coupling between ice history and mantle rheology greatly contributes to the non-uniqueness of the solutions. Here we propose to use more than 11000 paleo sea level records to constrain a set of GIA Bayesian inversions and thoroughly explore its parameters space. We include two linearly relaxing models to represent the mantle rheology and couple them with a scalable ice history model in order to better assess the non-uniqueness of the solutions. From the resulting estimates of the Probability Density Function, we then extract maps of uncertainty affecting the present-day vertical land motion and geoid due to GIA at the global scale, and their associated expectation of the signal.

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

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.

Exploring Several Methods of Groundwater Model Selection

NASA Astrophysics Data System (ADS)

Samani, Saeideh; Ye, Ming; Asghari Moghaddam, Asghar

2017-04-01

Selecting reliable models for simulating groundwater flow and solute transport is essential to groundwater resources management and protection. This work is to explore several model selection methods for avoiding over-complex and/or over-parameterized groundwater models. We consider six groundwater flow models with different numbers (6, 10, 10, 13, 13 and 15) of model parameters. These models represent alternative geological interpretations, recharge estimates, and boundary conditions at a study site in Iran. The models were developed with Model Muse, and calibrated against observations of hydraulic head using UCODE. Model selection was conducted by using the following four approaches: (1) Rank the models using their root mean square error (RMSE) obtained after UCODE-based model calibration, (2) Calculate model probability using GLUE method, (3) Evaluate model probability using model selection criteria (AIC, AICc, BIC, and KIC), and (4) Evaluate model weights using the Fuzzy Multi-Criteria-Decision-Making (MCDM) approach. MCDM is based on the fuzzy analytical hierarchy process (AHP) and fuzzy technique for order performance, which is to identify the ideal solution by a gradual expansion from the local to the global scale of model parameters. The KIC and MCDM methods are superior to other methods, as they consider not only the fit between observed and simulated data and the number of parameter, but also uncertainty in model parameters. Considering these factors can prevent from occurring over-complexity and over-parameterization, when selecting the appropriate groundwater flow models. These methods selected, as the best model, one with average complexity (10 parameters) and the best parameter estimation (model 3).

Numerical simulations of high-energy flows in accreting magnetic white dwarfs

NASA Astrophysics Data System (ADS)

Van Box Som, Lucile; Falize, É.; Bonnet-Bidaud, J.-M.; Mouchet, M.; Busschaert, C.; Ciardi, A.

2018-01-01

Some polars show quasi-periodic oscillations (QPOs) in their optical light curves that have been interpreted as the result of shock oscillations driven by the cooling instability. Although numerical simulations can recover this physics, they wrongly predict QPOs in the X-ray luminosity and have also failed to reproduce the observed frequencies, at least for the limited range of parameters explored so far. Given the uncertainties on the observed polar parameters, it is still unclear whether simulations can reproduce the observations. The aim of this work is to study QPOs covering all relevant polars showing QPOs. We perform numerical simulations including gravity, cyclotron and bremsstrahlung radiative losses, for a wide range of polar parameters, and compare our results with the astronomical data using synthetic X-ray and optical luminosities. We show that shock oscillations are the result of complex shock dynamics triggered by the interplay of two radiative instabilities. The secondary shock forms at the acoustic horizon in the post-shock region in agreement with our estimates from steady-state solutions. We also demonstrate that the secondary shock is essential to sustain the accretion shock oscillations at the average height predicted by our steady-state accretion model. Finally, in spite of the large explored parameter space, matching the observed QPO parameters requires a combination of parameters inconsistent with the observed ones. This difficulty highlights the limits of one-dimensional simulations, suggesting that multi-dimensional effects are needed to understand the non-linear dynamics of accretion columns in polars and the origins of QPOs.

Bayesian approach to the analysis of neutron Brillouin scattering data on liquid metals

NASA Astrophysics Data System (ADS)

De Francesco, A.; Guarini, E.; Bafile, U.; Formisano, F.; Scaccia, L.

2016-08-01

When the dynamics of liquids and disordered systems at mesoscopic level is investigated by means of inelastic scattering (e.g., neutron or x ray), spectra are often characterized by a poor definition of the excitation lines and spectroscopic features in general and one important issue is to establish how many of these lines need to be included in the modeling function and to estimate their parameters. Furthermore, when strongly damped excitations are present, commonly used and widespread fitting algorithms are particularly affected by the choice of initial values of the parameters. An inadequate choice may lead to an inefficient exploration of the parameter space, resulting in the algorithm getting stuck in a local minimum. In this paper, we present a Bayesian approach to the analysis of neutron Brillouin scattering data in which the number of excitation lines is treated as unknown and estimated along with the other model parameters. We propose a joint estimation procedure based on a reversible-jump Markov chain Monte Carlo algorithm, which efficiently explores the parameter space, producing a probabilistic measure to quantify the uncertainty on the number of excitation lines as well as reliable parameter estimates. The method proposed could turn out of great importance in extracting physical information from experimental data, especially when the detection of spectral features is complicated not only because of the properties of the sample, but also because of the limited instrumental resolution and count statistics. The approach is tested on generated data set and then applied to real experimental spectra of neutron Brillouin scattering from a liquid metal, previously analyzed in a more traditional way.

Bayesian and Frequentist Methods for Estimating Joint Uncertainty of Freundlich Adsorption Isotherm Fitting Parameters

EPA Science Inventory

In this paper, we present methods for estimating Freundlich isotherm fitting parameters (K and N) and their joint uncertainty, which have been implemented into the freeware software platforms R and WinBUGS. These estimates were determined by both Frequentist and Bayesian analyse...

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.

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

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.

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.

Imputation approaches for animal movement modeling

USGS Publications Warehouse

Scharf, Henry; Hooten, Mevin B.; Johnson, Devin S.

2017-01-01

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.

Uncertainties on [Formula: see text] in the MMHT2014 global PDF analysis and implications for SM predictions.

PubMed

Harland-Lang, L A; Martin, A D; Motylinski, P; Thorne, R S

We investigate the uncertainty in the strong coupling [Formula: see text] when allowing it to be a free parameter in the recent MMHT global analyses of deep-inelastic and related hard scattering data that was undertaken to determine the parton distribution functions (PDFs) of the proton. The analysis uses the standard framework of leading twist fixed-order collinear factorisation in the [Formula: see text] scheme. We study the constraints on [Formula: see text] coming from individual data sets by repeating the NNLO and NLO fits spanning the range 0.108 to 0.128 in units of 0.001, making all PDFs sets available. The inclusion of the cross section for inclusive [Formula: see text] production allows us to explore the correlation between the mass [Formula: see text] of the top quark and [Formula: see text]. We find that the best-fit values are [Formula: see text] and [Formula: see text] at NLO and NNLO, respectively, with the central values changing to [Formula: see text] and 0.1178 when the world average of [Formula: see text] is used as a data point. We investigate the interplay between the uncertainties on [Formula: see text] and on the PDFs. In particular we calculate the cross sections for key processes at the LHC and show how the uncertainties from the PDFs and from [Formula: see text] can be provided independently and be combined.

Quantifying Risks and Uncertainties Associated with Induced Seismicity due to CO2 Injection into Geologic Formations with Faults

NASA Astrophysics Data System (ADS)

Hou, Z.; Nguyen, B. N.; Bacon, D. H.; White, M. D.; Murray, C. J.

2016-12-01

A multiphase flow and reactive transport simulator named STOMP-CO2-R has been developed and coupled to the ABAQUS® finite element package for geomechanical analysis enabling comprehensive thermo-hydro-geochemical-mechanical (THMC) analyses. The coupled THMC simulator has been applied to analyze faulted CO2 reservoir responses (e.g., stress and strain distributions, pressure buildup, slip tendency factor, pressure margin to fracture) with various complexities in fault and reservoir structures and mineralogy. Depending on the geological and reaction network settings, long-term injection of CO2 can have a significant effect on the elastic stiffness and permeability of formation rocks. In parallel, an uncertainty quantification framework (UQ-CO2), which consists of entropy-based prior uncertainty representation, efficient sampling, geostatistical reservoir modeling, and effective response surface analysis, has been developed for quantifying risks and uncertainties associated with CO2 sequestration. It has been demonstrated for evaluating risks in CO2 leakage through natural pathways and wellbores, and for developing predictive reduced order models. Recently, a parallel STOMP-CO2-R has been developed and the updated STOMP/ABAQUS model has been proven to have a great scalability, which makes it possible to integrate the model with the UQ framework to effectively and efficiently explore multidimensional parameter space (e.g., permeability, elastic modulus, crack orientation, fault friction coefficient) for a more systematic analysis of induced seismicity risks.

Making predictions in a changing world-inference, uncertainty, and learning.

PubMed

O'Reilly, Jill X

2013-01-01

To function effectively, brains need to make predictions about their environment based on past experience, i.e., they need to learn about their environment. The algorithms by which learning occurs are of interest to neuroscientists, both in their own right (because they exist in the brain) and as a tool to model participants' incomplete knowledge of task parameters and hence, to better understand their behavior. This review focusses on a particular challenge for learning algorithms-how to match the rate at which they learn to the rate of change in the environment, so that they use as much observed data as possible whilst disregarding irrelevant, old observations. To do this algorithms must evaluate whether the environment is changing. We discuss the concepts of likelihood, priors and transition functions, and how these relate to change detection. We review expected and estimation uncertainty, and how these relate to change detection and learning rate. Finally, we consider the neural correlates of uncertainty and learning. We argue that the neural correlates of uncertainty bear a resemblance to neural systems that are active when agents actively explore their environments, suggesting that the mechanisms by which the rate of learning is set may be subject to top down control (in circumstances when agents actively seek new information) as well as bottom up control (by observations that imply change in the environment).

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.

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.

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.

A vulnerability driven approach to identify adverse climate and land use change combinations for critical hydrologic indicator thresholds: Application to a watershed in Pennsylvania, USA

NASA Astrophysics Data System (ADS)

Singh, R.; Wagener, T.; Crane, R.; Mann, M. E.; Ning, L.

2014-04-01

Large uncertainties in streamflow projections derived from downscaled climate projections of precipitation and temperature can render such simulations of limited value for decision making in the context of water resources management. New approaches are being sought to provide decision makers with robust information in the face of such large uncertainties. We present an alternative approach that starts with the stakeholder's definition of vulnerable ranges for relevant hydrologic indicators. Then the modeled system is analyzed to assess under what conditions these thresholds are exceeded. The space of possible climates and land use combinations for a watershed is explored to isolate subspaces that lead to vulnerability, while considering model parameter uncertainty in the analysis. We implement this concept using classification and regression trees (CART) that separate the input space of climate and land use change into those combinations that lead to vulnerability and those that do not. We test our method in a Pennsylvania watershed for nine ecological and water resources related streamflow indicators for which an increase in temperature between 3°C and 6°C and change in precipitation between -17% and 19% is projected. Our approach provides several new insights, for example, we show that even small decreases in precipitation (˜5%) combined with temperature increases greater than 2.5°C can push the mean annual runoff into a slightly vulnerable regime. Using this impact and stakeholder driven strategy, we explore the decision-relevant space more fully and provide information to the decision maker even if climate change projections are ambiguous.

Uncertainty relations as Hilbert space geometry

NASA Technical Reports Server (NTRS)

Braunstein, Samuel L.

1994-01-01

Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

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.

Statistical errors and systematic biases in the calibration of the convective core overshooting with eclipsing binaries. A case study: TZ Fornacis

NASA Astrophysics Data System (ADS)

Valle, G.; Dell'Omodarme, M.; Prada Moroni, P. G.; Degl'Innocenti, S.

2017-04-01

Context. Recently published work has made high-precision fundamental parameters available for the binary system TZ Fornacis, making it an ideal target for the calibration of stellar models. Aims: Relying on these observations, we attempt to constrain the initial helium abundance, the age and the efficiency of the convective core overshooting. Our main aim is in pointing out the biases in the results due to not accounting for some sources of uncertainty. Methods: We adopt the SCEPtER pipeline, a maximum likelihood technique based on fine grids of stellar models computed for various values of metallicity, initial helium abundance and overshooting efficiency by means of two independent stellar evolutionary codes, namely FRANEC and MESA. Results: Beside the degeneracy between the estimated age and overshooting efficiency, we found the existence of multiple independent groups of solutions. The best one suggests a system of age 1.10 ± 0.07 Gyr composed of a primary star in the central helium burning stage and a secondary in the sub-giant branch (SGB). The resulting initial helium abundance is consistent with a helium-to-metal enrichment ratio of ΔY/ ΔZ = 1; the core overshooting parameter is β = 0.15 ± 0.01 for FRANEC and fov = 0.013 ± 0.001 for MESA. The second class of solutions, characterised by a worse goodness-of-fit, still suggest a primary star in the central helium-burning stage but a secondary in the overall contraction phase, at the end of the main sequence (MS). In this case, the FRANEC grid provides an age of Gyr and a core overshooting parameter , while the MESA grid gives 1.23 ± 0.03 Gyr and fov = 0.025 ± 0.003. We analyse the impact on the results of a larger, but typical, mass uncertainty and of neglecting the uncertainty in the initial helium content of the system. We show that very precise mass determinations with uncertainty of a few thousandths of solar mass are required to obtain reliable determinations of stellar parameters, as mass errors larger than approximately 1% lead to estimates that are not only less precise but also biased. Moreover, we show that a fit obtained with a grid of models computed at a fixed ΔY/ ΔZ - thus neglecting the current uncertainty in the initial helium content of the system - can provide severely biased age and overshooting estimates. The possibility of independent overshooting efficiencies for the two stars of the system is also explored. Conclusions: The present analysis confirms that to constrain the core overshooting parameter by means of binary systems is a very difficult task that requires an observational precision still rarely achieved and a robust statistical treatment of the error sources.

Colour pairs for constraining the age and metallicity of stellar populations

NASA Astrophysics Data System (ADS)

Li, Zhongmu; Han, Zhanwen

2008-04-01

Using a widely used stellar-population synthesis model, we study the possibility of using pairs of AB system colours to break the well-known stellar age-metallicity degeneracy and to give constraints on two luminosity-weighted stellar-population parameters (age and metallicity). We present the relative age and metallicity sensitivities of the AB system colours that relate to the u,B,g,V,r,R,i, I,z,J,H and K bands, and we quantify the ability of various colour pairs to break the age-metallicity degeneracy. Our results suggest that a few pairs of colours can be used to constrain the above two stellar-population parameters. This will be very useful for exploring the stellar populations of distant galaxies. In detail, colour pairs [(r-K), (u-R)] and [(r-K), (u-r)] are shown to be the best pairs for estimating the luminosity-weighted stellar ages and metallicities of galaxies. They can constrain two stellar-population parameters on average with age uncertainties less than 3.89 Gyr and metallicity uncertainties less than 0.34 dex for typical colour uncertainties. The typical age uncertainties for young populations (age < 4.6 Gyr) and metal-rich populations (Z >= 0.001) are small (about 2.26 Gyr) while those for old populations (age >= 4.6 Gyr) and metal-poor populations (Z < 0.001) are much larger (about 6.88 Gyr). However, the metallicity uncertainties for metal-poor populations (about 0.0024) are much smaller than for other populations (about 0.015). Some other colour pairs can also possibly be used for constraining the two parameters. On the whole, the estimation of stellar-population parameters is likely to be reliable only for early-type galaxies with small colour errors and globular clusters, because such objects contain less dust. In fact, no galaxy is totally dust-free and early-type galaxies are also likely have some dust [e.g. E(B- V) ~ 0.05], which can change the stellar ages by about 2.5 Gyr and metallicities (Z) by about 0.015. When we compare the photometric estimates with previous spectroscopic estimates, we find some differences, especially when comparing the stellar ages determined by two methods. The differences mainly result from the young populations of galaxies. Therefore, it is difficult to obtain the absolute values of stellar ages and metallicities, but the results are useful for obtaining some relative values. In addition, our results suggest that colours relating to both UBVRIJHK and ugriz magnitudes are much better than either UBVRIJHK or ugriz colours for breaking the well-known degeneracy. The results also show that the stellar ages and metallicities of galaxies observed by the Sloan Digital Sky Survey and the Two-Micron All-Sky Survey can be estimated via photometry data. The data are available at the Centre de Données astronomiques de Strabourg (CDS) or on request to the authors. E-mail: zhongmu.li@gmail.com

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.

Observing binary black hole ringdowns by advanced gravitational wave detectors

NASA Astrophysics Data System (ADS)

Maselli, Andrea; Kokkotas, Kostas D.; Laguna, Pablo

2017-05-01

The direct discovery of gravitational waves from compact binary systems leads for the first time to explore the possibility of black hole spectroscopy. Newly formed black holes produced by coalescing events are copious emitters of gravitational radiation, in the form of damped sinusoids, the quasinormal modes. The latter provides a precious source of information on the nature of gravity in the strong field regime, as they represent a powerful tool to investigate the validity of the no-hair theorem. In this work we perform a systematic study on the accuracy with which current and future interferometers will measure the fundamental parameters of ringdown events, such as frequencies and damping times. We analyze how these errors affect the estimate of the mass and the angular momentum of the final black hole, constraining the parameter space which will lead to the most precise measurements. We explore both single and multimode events, showing how the uncertainties evolve when multiple detectors are available. We also prove that, for the second generation of interferometers, a network of instruments is a crucial and necessary ingredient to perform strong-gravity tests of the no-hair theorem. Finally, we analyze the constraints that a third generation of detectors may be able to set on the mode's parameters, comparing the projected bounds against those obtained for current facilities.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Licatta, Angelo; Griffin, Devon

2007-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

Risk Assessment of Bone Fracture During Space Exploration Missions to the Moon and Mars

NASA Technical Reports Server (NTRS)

Lewandowski, Beth E.; Myers, Jerry G.; Nelson, Emily S.; Griffin, Devon

2008-01-01

The possibility of a traumatic bone fracture in space is a concern due to the observed decrease in astronaut bone mineral density (BMD) during spaceflight and because of the physical demands of the mission. The Bone Fracture Risk Module (BFxRM) was developed to quantify the probability of fracture at the femoral neck and lumbar spine during space exploration missions. The BFxRM is scenario-based, providing predictions for specific activities or events during a particular space mission. The key elements of the BFxRM are the mission parameters, the biomechanical loading models, the bone loss and fracture models and the incidence rate of the activity or event. Uncertainties in the model parameters arise due to variations within the population and unknowns associated with the effects of the space environment. Consequently, parameter distributions were used in Monte Carlo simulations to obtain an estimate of fracture probability under real mission scenarios. The model predicts an increase in the probability of fracture as the mission length increases and fracture is more likely in the higher gravitational field of Mars than on the moon. The resulting probability predictions and sensitivity analyses of the BFxRM can be used as an engineering tool for mission operation and resource planning in order to mitigate the risk of bone fracture in space.

The Importance of Behavioral Thresholds and Objective Functions in Contaminant Transport Uncertainty Analysis

NASA Astrophysics Data System (ADS)

Sykes, J. F.; Kang, M.; Thomson, N. R.

2007-12-01

The TCE release from The Lockformer Company in Lisle Illinois resulted in a plume in a confined aquifer that is more than 4 km long and impacted more than 300 residential wells. Many of the wells are on the fringe of the plume and have concentrations that did not exceed 5 ppb. The settlement for the Chapter 11 bankruptcy protection of Lockformer involved the establishment of a trust fund that compensates individuals with cancers with payments being based on cancer type, estimated TCE concentration in the well and the duration of exposure to TCE. The estimation of early arrival times and hence low likelihood events is critical in the determination of the eligibility of an individual for compensation. Thus, an emphasis must be placed on the accuracy of the leading tail region in the likelihood distribution of possible arrival times at a well. The estimation of TCE arrival time, using a three-dimensional analytical solution, involved parameter estimation and uncertainty analysis. Parameters in the model included TCE source parameters, groundwater velocities, dispersivities and the TCE decay coefficient for both the confining layer and the bedrock aquifer. Numerous objective functions, which include the well-known L2-estimator, robust estimators (L1-estimators and M-estimators), penalty functions, and dead zones, were incorporated in the parameter estimation process to treat insufficiencies in both the model and observational data due to errors, biases, and limitations. The concept of equifinality was adopted and multiple maximum likelihood parameter sets were accepted if pre-defined physical criteria were met. The criteria ensured that a valid solution predicted TCE concentrations for all TCE impacted areas. Monte Carlo samples are found to be inadequate for uncertainty analysis of this case study due to its inability to find parameter sets that meet the predefined physical criteria. Successful results are achieved using a Dynamically-Dimensioned Search sampling methodology that inherently accounts for parameter correlations and does not require assumptions regarding parameter distributions. For uncertainty analysis, multiple parameter sets were obtained using a modified Cauchy's M-estimator. Penalty functions had to be incorporated into the objective function definitions to generate a sufficient number of acceptable parameter sets. The combined effect of optimization and the application of the physical criteria perform the function of behavioral thresholds by reducing anomalies and by removing parameter sets with high objective function values. The factors that are important to the creation of an uncertainty envelope for TCE arrival at wells are outlined in the work. In general, greater uncertainty appears to be present at the tails of the distribution. For a refinement of the uncertainty envelopes, the application of additional physical criteria or behavioral thresholds is recommended.

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.

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

Effect of Biological and Mass Transfer Parameter Uncertainty on N₂O Emission Estimates from WRRFs.

PubMed

Song, Kang; Harper, Willie F; Takeuchi, Yuki; Hosomi, Masaaki; Terada, Akihiko

2017-07-01

  This research used the detailed activated sludge model (ASM) to investigate the effect of parameter uncertainty on nitrous oxide (N2O) emissions from biological wastewater treatment systems. Monte Carlo simulations accounted for uncertainty in the values of the microbial growth parameters and in the volumetric mass transfer coefficient for dissolved oxygen (kLaDO), and the results show that the detailed ASM predicted N2O emission of less than 4% (typically 1%) of the total influent loading. Uncertainties in kLaDO were further investigated in experiments, which showed that lower values of kLaDO generated higher soluble N2O levels. The detailed ASM likely requires revision to account for abiotic reactions and other factors that cause higher levels of N2O emission.

Effect of Small Numbers of Test Results on Accuracy of Hoek-Brown Strength Parameter Estimations: A Statistical Simulation Study

NASA Astrophysics Data System (ADS)

Bozorgzadeh, Nezam; Yanagimura, Yoko; Harrison, John P.

2017-12-01

The Hoek-Brown empirical strength criterion for intact rock is widely used as the basis for estimating the strength of rock masses. Estimations of the intact rock H-B parameters, namely the empirical constant m and the uniaxial compressive strength σc, are commonly obtained by fitting the criterion to triaxial strength data sets of small sample size. This paper investigates how such small sample sizes affect the uncertainty associated with the H-B parameter estimations. We use Monte Carlo (MC) simulation to generate data sets of different sizes and different combinations of H-B parameters, and then investigate the uncertainty in H-B parameters estimated from these limited data sets. We show that the uncertainties depend not only on the level of variability but also on the particular combination of parameters being investigated. As particular combinations of H-B parameters can informally be considered to represent specific rock types, we discuss that as the minimum number of required samples depends on rock type it should correspond to some acceptable level of uncertainty in the estimations. Also, a comparison of the results from our analysis with actual rock strength data shows that the probability of obtaining reliable strength parameter estimations using small samples may be very low. We further discuss the impact of this on ongoing implementation of reliability-based design protocols and conclude with suggestions for improvements in this respect.

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.

The notion of ``distinguishability'' between bulk elastic parameters on the basis of the Gibbs deformation energy

NASA Astrophysics Data System (ADS)

Pavese, Alessandro; Diella, Valeria

2010-09-01

The present work aims in discussing a principle that distinguishes between elastic parameters sets, \\{ Upphi \\} equiv \\{ K0 , K^', V0 ,ldots\\} , on the basis of an energetic criterion: once a reference set, \\{ UpphiR \\} , is given, another one can be fixed, left\\{ {Upphi_{ min } } right\\} , so that they are as close as possible to each other, but yield non-equivalent deformation energy curves Updelta G(\\{ Upphi \\} )_{text{deform}} , i.e. they give Updelta G(\\{ UpphiR \\} )_{text{deform}} and Updelta G(\\{ Upphi_{ min } \\} )_{text{deform}} such that left| {Updelta G(\\{ Upphi_{ min } \\} )_{text{deform}} - Updelta G(\\{ UpphiR \\} )_{text{deform}} } right| ge 1× σ [Updelta G_{text{deform}} ]. Δ G deform, calculated using the equation of state (EoS), and its uncertainty σ[Δ G deform], obtained by a propagation of the errors affecting \\{ Upphi \\} are crucial to fix which mineral assemblage forms at P- T conditions and allow one to assess the reliability of such a prediction. We explore some properties related to the principle introduced, using the average values of the elastic parameters found in literature and related uncertainties for di-octahedral mica, olivine, garnet and clinopyroxene. Two elementary applications are briefly discussed: the effect of refining V 0 in fitting EoSs to P-V experimental data, in the case of garnet and omphacite, and the phengite 3 T-2 M 1 relative stability, controlled by pressure.

Uncertainty estimation of a complex water quality model: The influence of Box-Cox transformation on Bayesian approaches and comparison with a non-Bayesian method

NASA Astrophysics Data System (ADS)

Freni, Gabriele; Mannina, Giorgio

In urban drainage modelling, uncertainty analysis is of undoubted necessity. However, uncertainty analysis in urban water-quality modelling is still in its infancy and only few studies have been carried out. Therefore, several methodological aspects still need to be experienced and clarified especially regarding water quality modelling. The use of the Bayesian approach for uncertainty analysis has been stimulated by its rigorous theoretical framework and by the possibility of evaluating the impact of new knowledge on the modelling predictions. Nevertheless, the Bayesian approach relies on some restrictive hypotheses that are not present in less formal methods like the Generalised Likelihood Uncertainty Estimation (GLUE). One crucial point in the application of Bayesian method is the formulation of a likelihood function that is conditioned by the hypotheses made regarding model residuals. Statistical transformations, such as the use of Box-Cox equation, are generally used to ensure the homoscedasticity of residuals. However, this practice may affect the reliability of the analysis leading to a wrong uncertainty estimation. The present paper aims to explore the influence of the Box-Cox equation for environmental water quality models. To this end, five cases were considered one of which was the “real” residuals distributions (i.e. drawn from available data). The analysis was applied to the Nocella experimental catchment (Italy) which is an agricultural and semi-urbanised basin where two sewer systems, two wastewater treatment plants and a river reach were monitored during both dry and wet weather periods. The results show that the uncertainty estimation is greatly affected by residual transformation and a wrong assumption may also affect the evaluation of model uncertainty. The use of less formal methods always provide an overestimation of modelling uncertainty with respect to Bayesian method but such effect is reduced if a wrong assumption is made regarding the residuals distribution. If residuals are not normally distributed, the uncertainty is over-estimated if Box-Cox transformation is not applied or non-calibrated parameter is used.

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.

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.

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

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.

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.

Parameter uncertainty and variability in evaluative fate and exposure models

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

Hertwich, E.G.; McKone, T.E.; Pease, W.S.

The human toxicity potential, a weighting scheme used to evaluate toxic emissions for life cycle assessment and toxics release inventories, is based on potential dose calculations and toxicity factors. This paper evaluates the variance in potential dose calculations that can be attributed to the uncertainty in chemical-specific input parameters as well as the variability in exposure factors and landscape parameters. A knowledge of the uncertainty allows us to assess the robustness of a decision based on the toxicity potential; a knowledge of the sources of uncertainty allows one to focus resources if the uncertainty is to be reduced. The potentialmore » does of 236 chemicals was assessed. The chemicals were grouped by dominant exposure route, and a Monte Carlo analysis was conducted for one representative chemical in each group. The variance is typically one to two orders of magnitude. For comparison, the point estimates in potential dose for 236 chemicals span ten orders of magnitude. Most of the variance in the potential dose is due to chemical-specific input parameters, especially half-lives, although exposure factors such as fish intake and the source of drinking water can be important for chemicals whose dominant exposure is through indirect routes. Landscape characteristics are generally of minor importance.« less

Estimating the uncertainty in thermochemical calculations for oxygen-hydrogen combustors

NASA Astrophysics Data System (ADS)

Sims, Joseph David

The thermochemistry program CEA2 was combined with the statistical thermodynamics program PAC99 in a Monte Carlo simulation to determine the uncertainty in several CEA2 output variables due to uncertainty in thermodynamic reference values for the reactant and combustion species. In all, six typical performance parameters were examined, along with the required intermediate calculations (five gas properties and eight stoichiometric coefficients), for three hydrogen-oxygen combustors: a main combustor, an oxidizer preburner and a fuel preburner. The three combustors were analyzed in two different modes: design mode, where, for the first time, the uncertainty in thermodynamic reference values---taken from the literature---was considered (inputs to CEA2 were specified and so had no uncertainty); and data reduction mode, where inputs to CEA2 did have uncertainty. The inputs to CEA2 were contrived experimental measurements that were intended to represent the typical combustor testing facility. In design mode, uncertainties in the performance parameters were on the order of 0.1% for the main combustor, on the order of 0.05% for the oxidizer preburner and on the order of 0.01% for the fuel preburner. Thermodynamic reference values for H2O were the dominant sources of uncertainty, as was the assigned enthalpy for liquid oxygen. In data reduction mode, uncertainties in performance parameters increased significantly as a result of the uncertainties in experimental measurements compared to uncertainties in thermodynamic reference values. Main combustor and fuel preburner theoretical performance values had uncertainties of about 0.5%, while the oxidizer preburner had nearly 2%. Associated experimentally-determined performance values for all three combustors were 3% to 4%. The dominant sources of uncertainty in this mode were the propellant flowrates. These results only apply to hydrogen-oxygen combustors and should not be generalized to every propellant combination. Species for a hydrogen-oxygen system are relatively simple, thereby resulting in low thermodynamic reference value uncertainties. Hydrocarbon combustors, solid rocket motors and hybrid rocket motors have combustion gases containing complex molecules that will likely have thermodynamic reference values with large uncertainties. Thus, every chemical system should be analyzed in a similar manner as that shown in this work.

MEASURING REDDENING WITH SLOAN DIGITAL SKY SURVEY STELLAR SPECTRA AND RECALIBRATING SFD

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

Schlafly, Edward F.; Finkbeiner, Douglas P.

2011-08-20

We present measurements of dust reddening using the colors of stars with spectra in the Sloan Digital Sky Survey. We measure reddening as the difference between the measured and predicted colors of a star, as derived from stellar parameters from the Sloan Extension for Galactic Understanding and Exploration Stellar Parameter Pipeline. We achieve uncertainties of 56, 34, 25, and 29 mmag in the colors u - g, g - r, r - i, and i - z, per star, though the uncertainty varies depending on the stellar type and the magnitude of the star. The spectrum-based reddening measurements confirm ourmore » earlier 'blue tip' reddening measurements, finding reddening coefficients different by -3%, 1%, 1%, and 2% in u - g, g - r, r - i, and i - z from those found by the blue tip method, after removing a 4% normalization difference. These results prefer an R{sub V} = 3.1 Fitzpatrick reddening law to O'Donnell or Cardelli et al. reddening laws. We provide a table of conversion coefficients from the Schlegel et al. (SFD) maps of E(B - V) to extinction in 88 bandpasses for four values of R{sub V} , using this reddening law and the 14% recalibration of SFD first reported by Schlafly et al. and confirmed in this work.« less

Defining Uncertainty and Error in Planktic Foraminiferal Oxygen Isotope Measurements

NASA Astrophysics Data System (ADS)

Fraass, A. J.; Lowery, C.

2016-12-01

Foraminifera are the backbone of paleoceanography, and planktic foraminifera are one of the leading tools for reconstructing water column structure. Currently, there are unconstrained variables when dealing with the reproducibility of oxygen isotope measurements. This study presents the first results from a simple model of foraminiferal calcification (Foraminiferal Isotope Reproducibility Model; FIRM), designed to estimate the precision and accuracy of oxygen isotope measurements. FIRM produces synthetic isotope data using parameters including location, depth habitat, season, number of individuals included in measurement, diagenesis, misidentification, size variation, and vital effects. Reproducibility is then tested using Monte Carlo simulations. The results from a series of experiments show that reproducibility is largely controlled by the number of individuals in each measurement, but also strongly a function of local oceanography if the number of individuals is held constant. Parameters like diagenesis or misidentification have an impact on both the precision and the accuracy of the data. Currently FIRM is a tool to estimate isotopic error values best employed in the Holocene. It is also a tool to explore the impact of myriad factors on the fidelity of paleoceanographic records. FIRM was constructed in the open-source computing environment R and is freely available via GitHub. We invite modification and expansion, and have planned inclusions for benthic foram reproducibility and stratigraphic uncertainty.

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.

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

UNCERTAINTY IN EARLY OCCUPATIONAL ASPIRATIONS: ROLE EXPLORATION OR AIMLESSNESS?

PubMed Central

Staff, Jeremy; Harris, Angel; Sabates, Ricardo; Briddell, Laine

2014-01-01

Many youth in the United States lack clear occupational aspirations. This uncertainty in achievement ambitions may benefit socioeconomic attainment if it signifies “role exploration,” characterized by career development, continued education, and enduring partnerships. By contrast, uncertainty may diminish attainment if it instead leads to “aimlessness,” involving prolonged education without the acquisition of a degree, residential dependence, and frequent job changes. We use nationally representative data from the National Education Longitudinal Study (NELS) to examine how uncertainty in occupational aspirations in adolescence (age 16) affects wage attainments in young adulthood (age 26). Results suggest that youth with uncertain career ambitions earn significantly lower hourly wages in young adulthood than youth with professional and non-professional aspirations, supporting the view that uncertainty heightens the risk of labor-market problems. PMID:25540465

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.

Uncertainty Representation in Visualizations of Learning Analytics for Learners: Current Approaches and Opportunities

ERIC Educational Resources Information Center

Demmans Epp, Carrie; Bull, Susan

2015-01-01

Adding uncertainty information to visualizations is becoming increasingly common across domains since its addition helps ensure that informed decisions are made. This work has shown the difficulty that is inherent to representing uncertainty. Moreover, the representation of uncertainty has yet to be thoroughly explored in educational domains even…

Are You Sure? The Role of Uncertainty in Career

ERIC Educational Resources Information Center

Trevor-Roberts, Edwin

2006-01-01

Although uncertainty is a fundamental human experience, professionals in the career field have largely overlooked the role that it plays in people's careers. The changed nature of careers has resulted in people experiencing increased uncertainty in their career that is beyond the uncertainty experienced in their job. The author explores the role…

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.

Accessing the uncertainties of seismic velocity and anisotropy structure of Northern Great Plains using a transdimensional Bayesian approach

NASA Astrophysics Data System (ADS)

Gao, C.; Lekic, V.

2017-12-01

Seismic imaging utilizing complementary seismic data provides unique insight on the formation, evolution and current structure of continental lithosphere. While numerous efforts have improved the resolution of seismic structure, the quantification of uncertainties remains challenging due to the non-linearity and the non-uniqueness of geophysical inverse problem. In this project, we use a reverse jump Markov chain Monte Carlo (rjMcMC) algorithm to incorporate seismic observables including Rayleigh and Love wave dispersion, Ps and Sp receiver function to invert for shear velocity (Vs), compressional velocity (Vp), density, and radial anisotropy of the lithospheric structure. The Bayesian nature and the transdimensionality of this approach allow the quantification of the model parameter uncertainties while keeping the models parsimonious. Both synthetic test and inversion of actual data for Ps and Sp receiver functions are performed. We quantify the information gained in different inversions by calculating the Kullback-Leibler divergence. Furthermore, we explore the ability of Rayleigh and Love wave dispersion data to constrain radial anisotropy. We show that when multiple types of model parameters (Vsv, Vsh, and Vp) are inverted simultaneously, the constraints on radial anisotropy are limited by relatively large data uncertainties and trade-off strongly with Vp. We then perform joint inversion of the surface wave dispersion (SWD) and Ps, Sp receiver functions, and show that the constraints on both isotropic Vs and radial anisotropy are significantly improved. To achieve faster convergence of the rjMcMC, we propose a progressive inclusion scheme, and invert SWD measurements and receiver functions from about 400 USArray stations in the Northern Great Plains. We start by only using SWD data due to its fast convergence rate. We then use the average of the ensemble as a starting model for the joint inversion, which is able to resolve distinct seismic signatures of geological structures including the trans-Hudson orogen, Wyoming craton and Yellowstone hotspot. Various analyses are done to access the uncertainties of the seismic velocities and Moho depths. We also address the importance of careful data processing of receiver functions by illustrating artifacts due to unmodelled sediment reverberations.

Impact of Martian atmosphere parameter uncertainties on entry vehicles aerodynamic for hypersonic rarefied conditions

NASA Astrophysics Data System (ADS)

Fei, Huang; Xu-hong, Jin; Jun-ming, Lv; Xiao-li, Cheng

2016-11-01

An attempt has been made to analyze impact of Martian atmosphere parameter uncertainties on entry vehicle aerodynamics for hypersonic rarefied conditions with a DSMC code. The code has been validated by comparing Viking vehicle flight data with present computational results. Then, by simulating flows around the Mars Science Laboratory, the impact of errors of free stream parameter uncertainties on aerodynamics is investigated. The validation results show that the present numerical approach can show good agreement with the Viking flight data. The physical and chemical properties of CO2 has strong impact on aerodynamics of Mars entry vehicles, so it is necessary to make proper corrections to the data obtained with air model in hypersonic rarefied conditions, which is consistent with the conclusions drawn in continuum regime. Uncertainties of free stream density and velocity weakly influence aerodynamics and pitching moment. However, aerodynamics appears to be little influenced by free stream temperature, the maximum error of what is below 0.5%. Center of pressure position is not sensitive to free stream parameters.

New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.

PubMed

Han, Jubong; Lee, K B; Lee, Jong-Man; Park, Tae Soon; Oh, J S; Oh, Pil-Jei

2016-03-01

We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods. Copyright © 2015. Published by Elsevier Ltd.

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.

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.

Stochastic Inversion of 2D Magnetotelluric Data

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

Chen, Jinsong

2010-07-01

The algorithm is developed to invert 2D magnetotelluric (MT) data based on sharp boundary parametrization using a Bayesian framework. Within the algorithm, we consider the locations and the resistivity of regions formed by the interfaces are as unknowns. We use a parallel, adaptive finite-element algorithm to forward simulate frequency-domain MT responses of 2D conductivity structure. Those unknown parameters are spatially correlated and are described by a geostatistical model. The joint posterior probability distribution function is explored by Markov Chain Monte Carlo (MCMC) sampling methods. The developed stochastic model is effective for estimating the interface locations and resistivity. Most importantly, itmore » provides details uncertainty information on each unknown parameter. Hardware requirements: PC, Supercomputer, Multi-platform, Workstation; Software requirements C and Fortan; Operation Systems/version is Linux/Unix or Windows« less

Making Invasion models useful for decision makers; incorporating uncertainty, knowledge gaps, and decision-making preferences

Treesearch

Denys Yemshanov; Frank H Koch; Mark Ducey

2015-01-01

Uncertainty is inherent in model-based forecasts of ecological invasions. In this chapter, we explore how the perceptions of that uncertainty can be incorporated into the pest risk assessment process. Uncertainty changes a decision maker’s perceptions of risk; therefore, the direct incorporation of uncertainty may provide a more appropriate depiction of risk. Our...

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

NASA Technical Reports Server (NTRS)

Brown, Andrew M.; Peck, Jeffrey A.; Stewart, Eric C.

2018-01-01

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Design Analysis Kit for Optimization and Terascale Applications 6.0

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

2015-10-19

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: (1) enhance understanding of risk, (2) improve products, and (3) assess simulation credibility. In its simplest mode, Dakota can automate typical parameter variation studies through a generic interface to a computational model. However, Dakota also delivers advanced parametric analysis techniques enabling design exploration, optimization, model calibration, risk analysis, and quantification of margins and uncertainty with such models. It directly supports verificationmore » and validation activities. The algorithms implemented in Dakota aim to address challenges in performing these analyses with complex science and engineering models from desktop to high performance computers.« less

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.

Measurements for liquid rocket engine performance code verification

NASA Technical Reports Server (NTRS)

Praharaj, Sarat C.; Palko, Richard L.

1986-01-01

The goal of the rocket engine performance code verification tests is to obtain the I sub sp with an accuracy of 0.25% or less. This needs to be done during the sequence of four related tests (two reactive and two hot gas simulation) to best utilize the loss separation technique recommended in this study. In addition to I sub sp, the measurements of the input and output parameters for the codes are needed. This study has shown two things in regard to obtaining the I sub sp uncertainty within the 0.25% target. First, this target is generally not being realized at the present time, and second, the instrumentation and testing technology does exist to obtain this 0.25% uncertainty goal. However, to achieve this goal will require carefully planned, designed, and conducted testing. In addition, the test-stand (or system) dynamics must be evaluated in the pre-test and post-test phases of the design of the experiment and data analysis, respectively always keeping in mind that a .25% overall uncertainty in I sub sp is targeted. A table gives the maximum allowable uncertainty required for obtaining I sub sp with 0.25% uncertainty, the currently-quoted instrument specification, and present test uncertainty for the parameters. In general, it appears that measurement of the mass flow parameter within the required uncertainty may be the most difficult.

Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

NASA Astrophysics Data System (ADS)

Pachhai, S.; Masters, G.; Laske, G.

2017-12-01

Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

Evaluation of assigned-value uncertainty for complex calibrator value assignment processes: a prealbumin example.

PubMed

Middleton, John; Vaks, Jeffrey E

2007-04-01

Errors of calibrator-assigned values lead to errors in the testing of patient samples. The ability to estimate the uncertainties of calibrator-assigned values and other variables minimizes errors in testing processes. International Organization of Standardization guidelines provide simple equations for the estimation of calibrator uncertainty with simple value-assignment processes, but other methods are needed to estimate uncertainty in complex processes. We estimated the assigned-value uncertainty with a Monte Carlo computer simulation of a complex value-assignment process, based on a formalized description of the process, with measurement parameters estimated experimentally. This method was applied to study uncertainty of a multilevel calibrator value assignment for a prealbumin immunoassay. The simulation results showed that the component of the uncertainty added by the process of value transfer from the reference material CRM470 to the calibrator is smaller than that of the reference material itself (<0.8% vs 3.7%). Varying the process parameters in the simulation model allowed for optimizing the process, while keeping the added uncertainty small. The patient result uncertainty caused by the calibrator uncertainty was also found to be small. This method of estimating uncertainty is a powerful tool that allows for estimation of calibrator uncertainty for optimization of various value assignment processes, with a reduced number of measurements and reagent costs, while satisfying the requirements to uncertainty. The new method expands and augments existing methods to allow estimation of uncertainty in complex processes.

Model Reduction via Principe Component Analysis and Markov Chain Monte Carlo (MCMC) Methods

NASA Astrophysics Data System (ADS)

Gong, R.; Chen, J.; Hoversten, M. G.; Luo, J.

2011-12-01

Geophysical and hydrogeological inverse problems often include a large number of unknown parameters, ranging from hundreds to millions, depending on parameterization and problems undertaking. This makes inverse estimation and uncertainty quantification very challenging, especially for those problems in two- or three-dimensional spatial domains. Model reduction technique has the potential of mitigating the curse of dimensionality by reducing total numbers of unknowns while describing the complex subsurface systems adequately. In this study, we explore the use of principal component analysis (PCA) and Markov chain Monte Carlo (MCMC) sampling methods for model reduction through the use of synthetic datasets. We compare the performances of three different but closely related model reduction approaches: (1) PCA methods with geometric sampling (referred to as 'Method 1'), (2) PCA methods with MCMC sampling (referred to as 'Method 2'), and (3) PCA methods with MCMC sampling and inclusion of random effects (referred to as 'Method 3'). We consider a simple convolution model with five unknown parameters as our goal is to understand and visualize the advantages and disadvantages of each method by comparing their inversion results with the corresponding analytical solutions. We generated synthetic data with noise added and invert them under two different situations: (1) the noised data and the covariance matrix for PCA analysis are consistent (referred to as the unbiased case), and (2) the noise data and the covariance matrix are inconsistent (referred to as biased case). In the unbiased case, comparison between the analytical solutions and the inversion results show that all three methods provide good estimates of the true values and Method 1 is computationally more efficient. In terms of uncertainty quantification, Method 1 performs poorly because of relatively small number of samples obtained, Method 2 performs best, and Method 3 overestimates uncertainty due to inclusion of random effects. However, in the biased case, only Method 3 correctly estimates all the unknown parameters, and both Methods 1 and 2 provide wrong values for the biased parameters. The synthetic case study demonstrates that if the covariance matrix for PCA analysis is inconsistent with true models, the PCA methods with geometric or MCMC sampling will provide incorrect estimates.

Quantifying the Uncertainties and Multi-parameter Trade-offs in Joint Inversion of Receiver Functions and Surface Wave Velocity and Ellipticity

NASA Astrophysics Data System (ADS)

Gao, C.; Lekic, V.

2016-12-01

When constraining the structure of the Earth's continental lithosphere, multiple seismic observables are often combined due to their complementary sensitivities.The transdimensional Bayesian (TB) approach in seismic inversion allows model parameter uncertainties and trade-offs to be quantified with few assumptions. TB sampling yields an adaptive parameterization that enables simultaneous inversion for different model parameters (Vp, Vs, density, radial anisotropy), without the need for strong prior information or regularization. We use a reversible jump Markov chain Monte Carlo (rjMcMC) algorithm to incorporate different seismic observables - surface wave dispersion (SWD), Rayleigh wave ellipticity (ZH ratio), and receiver functions - into the inversion for the profiles of shear velocity (Vs), compressional velocity (Vp), density (ρ), and radial anisotropy (ξ) beneath a seismic station. By analyzing all three data types individually and together, we show that TB sampling can eliminate the need for a fixed parameterization based on prior information, and reduce trade-offs in model estimates. We then explore the effect of different types of misfit functions for receiver function inversion, which is a highly non-unique problem. We compare the synthetic inversion results using the L2 norm, cross-correlation type and integral type misfit function by their convergence rates and retrieved seismic structures. In inversions in which only one type of model parameter (Vs for the case of SWD) is inverted, assumed scaling relationships are often applied to account for sensitivity to other model parameters (e.g. Vp, ρ, ξ). Here we show that under a TB framework, we can eliminate scaling assumptions, while simultaneously constraining multiple model parameters to varying degrees. Furthermore, we compare the performance of TB inversion when different types of model parameters either share the same or use independent parameterizations. We show that different parameterizations can lead to differences in retrieved model parameters, consistent with limited data constraints. We then quantitatively examine the model parameter trade-offs and find that trade-offs between Vp and radial anisotropy might limit our ability to constrain shallow-layer radial anisotropy using current seismic observables.

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

NASA Astrophysics Data System (ADS)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete empirical interpolation method (DEIM) to approximate the nonlinearity in the forward problem. We show that using only a limited number of forward solves, the resulting subspaces lead to an efficient method to explore the high-dimensional posterior.

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).

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.

Modeling the value for money of changing clinical practice change: a stochastic application in diabetes care.

PubMed

Hoomans, Ties; Abrams, Keith R; Ament, Andre J H A; Evers, Silvia M A A; Severens, Johan L

2009-10-01

Decision making about resource allocation for guideline implementation to change clinical practice is inevitably undertaken in a context of uncertainty surrounding the cost-effectiveness of both clinical guidelines and implementation strategies. Adopting a total net benefit approach, a model was recently developed to overcome problems with the use of combined ratio statistics when analyzing decision uncertainty. To demonstrate the stochastic application of the model for informing decision making about the adoption of an audit and feedback strategy for implementing a guideline recommending intensive blood glucose control in type 2 diabetes in primary care in the Netherlands. An integrated Bayesian approach to decision modeling and evidence synthesis is adopted, using Markov Chain Monte Carlo simulation in WinBUGs. Data on model parameters is gathered from various sources, with effectiveness of implementation being estimated using pooled, random-effects meta-analysis. Decision uncertainty is illustrated using cost-effectiveness acceptability curves and frontier. Decisions about whether to adopt intensified glycemic control and whether to adopt audit and feedback alter for the maximum values that decision makers are willing to pay for health gain. Through simultaneously incorporating uncertain economic evidence on both guidance and implementation strategy, the cost-effectiveness acceptability curves and cost-effectiveness acceptability frontier show an increase in decision uncertainty concerning guideline implementation. The stochastic application in diabetes care demonstrates that the model provides a simple and useful tool for quantifying and exploring the (combined) uncertainty associated with decision making about adopting guidelines and implementation strategies and, therefore, for informing decisions about efficient resource allocation to change clinical practice.

Quantifying Uncertainty in Near Surface Electromagnetic Imaging Using Bayesian Methods

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Ray, A.; Key, K.

2017-12-01

Geoscientists commonly use electromagnetic methods to image the Earth's near surface. Field measurements of EM fields are made (often with the aid an artificial EM source) and then used to infer near surface electrical conductivity via a process known as inversion. In geophysics, the standard inversion tool kit is robust and can provide an estimate of the Earth's near surface conductivity that is both geologically reasonable and compatible with the measured field data. However, standard inverse methods struggle to provide a sense of the uncertainty in the estimate they provide. This is because the task of finding an Earth model that explains the data to within measurement error is non-unique - that is, there are many, many such models; but the standard methods provide only one "answer." An alternative method, known as Bayesian inversion, seeks to explore the full range of Earth model parameters that can adequately explain the measured data, rather than attempting to find a single, "ideal" model. Bayesian inverse methods can therefore provide a quantitative assessment of the uncertainty inherent in trying to infer near surface conductivity from noisy, measured field data. This study applies a Bayesian inverse method (called trans-dimensional Markov chain Monte Carlo) to transient airborne EM data previously collected over Taylor Valley - one of the McMurdo Dry Valleys in Antarctica. Our results confirm the reasonableness of previous estimates (made using standard methods) of near surface conductivity beneath Taylor Valley. In addition, we demonstrate quantitatively the uncertainty associated with those estimates. We demonstrate that Bayesian inverse methods can provide quantitative uncertainty to estimates of near surface conductivity.

Estimation of the uncertainty of analyte concentration from the measurement uncertainty.

PubMed

Brown, Simon; Cooke, Delwyn G; Blackwell, Leonard F

2015-09-01

Ligand-binding assays, such as immunoassays, are usually analysed using standard curves based on the four-parameter and five-parameter logistic models. An estimate of the uncertainty of an analyte concentration obtained from such curves is needed for confidence intervals or precision profiles. Using a numerical simulation approach, it is shown that the uncertainty of the analyte concentration estimate becomes significant at the extremes of the concentration range and that this is affected significantly by the steepness of the standard curve. We also provide expressions for the coefficient of variation of the analyte concentration estimate from which confidence intervals and the precision profile can be obtained. Using three examples, we show that the expressions perform well.

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.

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.

An MCMC determination of the primordial helium abundance

NASA Astrophysics Data System (ADS)

Aver, Erik; Olive, Keith A.; Skillman, Evan D.

2012-04-01

Spectroscopic observations of the chemical abundances in metal-poor H II regions provide an independent method for estimating the primordial helium abundance. H II regions are described by several physical parameters such as electron density, electron temperature, and reddening, in addition to y, the ratio of helium to hydrogen. It had been customary to estimate or determine self-consistently these parameters to calculate y. Frequentist analyses of the parameter space have been shown to be successful in these parameter determinations, and Markov Chain Monte Carlo (MCMC) techniques have proven to be very efficient in sampling this parameter space. Nevertheless, accurate determination of the primordial helium abundance from observations of H II regions is constrained by both systematic and statistical uncertainties. In an attempt to better reduce the latter, and continue to better characterize the former, we apply MCMC methods to the large dataset recently compiled by Izotov, Thuan, & Stasińska (2007). To improve the reliability of the determination, a high quality dataset is needed. In pursuit of this, a variety of cuts are explored. The efficacy of the He I λ4026 emission line as a constraint on the solutions is first examined, revealing the introduction of systematic bias through its absence. As a clear measure of the quality of the physical solution, a χ2 analysis proves instrumental in the selection of data compatible with the theoretical model. Nearly two-thirds of the observations fall outside a standard 95% confidence level cut, which highlights the care necessary in selecting systems and warrants further investigation into potential deficiencies of the model or data. In addition, the method also allows us to exclude systems for which parameter estimations are statistical outliers. As a result, the final selected dataset gains in reliability and exhibits improved consistency. Regression to zero metallicity yields Yp = 0.2534 ± 0.0083, in broad agreement with the WMAP result. The inclusion of more observations shows promise for further reducing the uncertainty, but more high quality spectra are required.

Bayesian model comparison and parameter inference in systems biology using nested sampling.

PubMed

Pullen, Nick; Morris, Richard J

2014-01-01

Inferring parameters for models of biological processes is a current challenge in systems biology, as is the related problem of comparing competing models that explain the data. In this work we apply Skilling's nested sampling to address both of these problems. Nested sampling is a Bayesian method for exploring parameter space that transforms a multi-dimensional integral to a 1D integration over likelihood space. This approach focuses on the computation of the marginal likelihood or evidence. The ratio of evidences of different models leads to the Bayes factor, which can be used for model comparison. We demonstrate how nested sampling can be used to reverse-engineer a system's behaviour whilst accounting for the uncertainty in the results. The effect of missing initial conditions of the variables as well as unknown parameters is investigated. We show how the evidence and the model ranking can change as a function of the available data. Furthermore, the addition of data from extra variables of the system can deliver more information for model comparison than increasing the data from one variable, thus providing a basis for experimental design.

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.

Uncertainty associated with the gravimetric measurement of particulate matter concentration in ambient air.

PubMed

Lacey, Ronald E; Faulkner, William Brock

2015-07-01

This work applied a propagation of uncertainty method to typical total suspended particulate (TSP) sampling apparatus in order to estimate the overall measurement uncertainty. The objectives of this study were to estimate the uncertainty for three TSP samplers, develop an uncertainty budget, and determine the sensitivity of the total uncertainty to environmental parameters. The samplers evaluated were the TAMU High Volume TSP Sampler at a nominal volumetric flow rate of 1.42 m3 min(-1) (50 CFM), the TAMU Low Volume TSP Sampler at a nominal volumetric flow rate of 17 L min(-1) (0.6 CFM) and the EPA TSP Sampler at the nominal volumetric flow rates of 1.1 and 1.7 m3 min(-1) (39 and 60 CFM). Under nominal operating conditions the overall measurement uncertainty was found to vary from 6.1x10(-6) g m(-3) to 18.0x10(-6) g m(-3), which represented an uncertainty of 1.7% to 5.2% of the measurement. Analysis of the uncertainty budget determined that three of the instrument parameters contributed significantly to the overall uncertainty: the uncertainty in the pressure drop measurement across the orifice meter during both calibration and testing and the uncertainty of the airflow standard used during calibration of the orifice meter. Five environmental parameters occurring during field measurements were considered for their effect on overall uncertainty: ambient TSP concentration, volumetric airflow rate, ambient temperature, ambient pressure, and ambient relative humidity. Of these, only ambient TSP concentration and volumetric airflow rate were found to have a strong effect on the overall uncertainty. The technique described in this paper can be applied to other measurement systems and is especially useful where there are no methods available to generate these values empirically. This work addresses measurement uncertainty of TSP samplers used in ambient conditions. Estimation of uncertainty in gravimetric measurements is of particular interest, since as ambient particulate matter (PM) concentrations approach regulatory limits, the uncertainty of the measurement is essential in determining the sample size and the probability of type II errors in hypothesis testing. This is an important factor in determining if ambient PM concentrations exceed regulatory limits. The technique described in this paper can be applied to other measurement systems and is especially useful where there are no methods available to generate these values empirically.

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.

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.

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.

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.

A Reduced Set of Features for Chronic Kidney Disease Prediction

PubMed Central

Misir, Rajesh; Mitra, Malay; Samanta, Ranjit Kumar

2017-01-01

Chronic kidney disease (CKD) is one of the life-threatening diseases. Early detection and proper management are solicited for augmenting survivability. As per the UCI data set, there are 24 attributes for predicting CKD or non-CKD. At least there are 16 attributes need pathological investigations involving more resources, money, time, and uncertainties. The objective of this work is to explore whether we can predict CKD or non-CKD with reasonable accuracy using less number of features. An intelligent system development approach has been used in this study. We attempted one important feature selection technique to discover reduced features that explain the data set much better. Two intelligent binary classification techniques have been adopted for the validity of the reduced feature set. Performances were evaluated in terms of four important classification evaluation parameters. As suggested from our results, we may more concentrate on those reduced features for identifying CKD and thereby reduces uncertainty, saves time, and reduces costs. PMID:28706750

The Impact of Measurement Noise in GPA Diagnostic Analysis of a Gas Turbine Engine

NASA Astrophysics Data System (ADS)

Ntantis, Efstratios L.; Li, Y. G.

2013-12-01

The performance diagnostic analysis of a gas turbine is accomplished by estimating a set of internal engine health parameters from available sensor measurements. No physical measuring instruments however can ever completely eliminate the presence of measurement uncertainties. Sensor measurements are often distorted by noise and bias leading to inaccurate estimation results. This paper explores the impact of measurement noise on Gas Turbine GPA analysis. The analysis is demonstrated with a test case where gas turbine performance simulation and diagnostics code TURBOMATCH is used to build a performance model of a model engine similar to Rolls-Royce Trent 500 turbofan engine, and carry out the diagnostic analysis with the presence of different levels of measurement noise. Conclusively, to improve the reliability of the diagnostic results, a statistical analysis of the data scattering caused by sensor uncertainties is made. The diagnostic tool used to deal with the statistical analysis of measurement noise impact is a model-based method utilizing a non-linear GPA.

A Flexible Approach for the Statistical Visualization of Ensemble Data

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

Potter, K.; Wilson, A.; Bremer, P.

2009-09-29

Scientists are increasingly moving towards ensemble data sets to explore relationships present in dynamic systems. Ensemble data sets combine spatio-temporal simulation results generated using multiple numerical models, sampled input conditions and perturbed parameters. While ensemble data sets are a powerful tool for mitigating uncertainty, they pose significant visualization and analysis challenges due to their complexity. We present a collection of overview and statistical displays linked through a high level of interactivity to provide a framework for gaining key scientific insight into the distribution of the simulation results as well as the uncertainty associated with the data. In contrast to methodsmore » that present large amounts of diverse information in a single display, we argue that combining multiple linked statistical displays yields a clearer presentation of the data and facilitates a greater level of visual data analysis. We demonstrate this approach using driving problems from climate modeling and meteorology and discuss generalizations to other fields.« less

Validation Study of Unnotched Charpy and Taylor-Anvil Impact Experiments using Kayenta

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

Kamojjala, Krishna; Lacy, Jeffrey; Chu, Henry S.

2015-03-01

Validation of a single computational model with multiple available strain-to-failure fracture theories is presented through experimental tests and numerical simulations of the standardized unnotched Charpy and Taylor-anvil impact tests, both run using the same material model (Kayenta). Unnotched Charpy tests are performed on rolled homogeneous armor steel. The fracture patterns using Kayenta’s various failure options that include aleatory uncertainty and scale effects are compared against the experiments. Other quantities of interest include the average value of the absorbed energy and bend angle of the specimen. Taylor-anvil impact tests are performed on Ti6Al4V titanium alloy. The impact speeds of the specimenmore » are 321 m/s and 393 m/s. The goal of the numerical work is to reproduce the damage patterns observed in the laboratory. For the numerical study, the Johnson-Cook failure model is used as the ductile fracture criterion, and aleatory uncertainty is applied to rate-dependence parameters to explore its effect on the fracture patterns.« less

A statistical approach to the brittle fracture of a multi-phase solid

NASA Technical Reports Server (NTRS)

Liu, W. K.; Lua, Y. I.; Belytschko, T.

1991-01-01

A stochastic damage model is proposed to quantify the inherent statistical distribution of the fracture toughness of a brittle, multi-phase solid. The model, based on the macrocrack-microcrack interaction, incorporates uncertainties in locations and orientations of microcracks. Due to the high concentration of microcracks near the macro-tip, a higher order analysis based on traction boundary integral equations is formulated first for an arbitrary array of cracks. The effects of uncertainties in locations and orientations of microcracks at a macro-tip are analyzed quantitatively by using the boundary integral equations method in conjunction with the computer simulation of the random microcrack array. The short range interactions resulting from surrounding microcracks closet to the main crack tip are investigated. The effects of microcrack density parameter are also explored in the present study. The validity of the present model is demonstrated by comparing its statistical output with the Neville distribution function, which gives correct fits to sets of experimental data from multi-phase solids.

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

Unleashing Empirical Equations with "Nonlinear Fitting" and "GUM Tree Calculator"

NASA Astrophysics Data System (ADS)

Lovell-Smith, J. W.; Saunders, P.; Feistel, R.

2017-10-01

Empirical equations having large numbers of fitted parameters, such as the international standard reference equations published by the International Association for the Properties of Water and Steam (IAPWS), which form the basis of the "Thermodynamic Equation of Seawater—2010" (TEOS-10), provide the means to calculate many quantities very accurately. The parameters of these equations are found by least-squares fitting to large bodies of measurement data. However, the usefulness of these equations is limited since uncertainties are not readily available for most of the quantities able to be calculated, the covariance of the measurement data is not considered, and further propagation of the uncertainty in the calculated result is restricted since the covariance of calculated quantities is unknown. In this paper, we present two tools developed at MSL that are particularly useful in unleashing the full power of such empirical equations. "Nonlinear Fitting" enables propagation of the covariance of the measurement data into the parameters using generalized least-squares methods. The parameter covariance then may be published along with the equations. Then, when using these large, complex equations, "GUM Tree Calculator" enables the simultaneous calculation of any derived quantity and its uncertainty, by automatic propagation of the parameter covariance into the calculated quantity. We demonstrate these tools in exploratory work to determine and propagate uncertainties associated with the IAPWS-95 parameters.

Experimental design for estimating parameters of rate-limited mass transfer: Analysis of stream tracer studies

USGS Publications Warehouse

Wagner, Brian J.; Harvey, Judson W.

1997-01-01

Tracer experiments are valuable tools for analyzing the transport characteristics of streams and their interactions with shallow groundwater. The focus of this work is the design of tracer studies in high-gradient stream systems subject to advection, dispersion, groundwater inflow, and exchange between the active channel and zones in surface or subsurface water where flow is stagnant or slow moving. We present a methodology for (1) evaluating and comparing alternative stream tracer experiment designs and (2) identifying those combinations of stream transport properties that pose limitations to parameter estimation and therefore a challenge to tracer test design. The methodology uses the concept of global parameter uncertainty analysis, which couples solute transport simulation with parameter uncertainty analysis in a Monte Carlo framework. Two general conclusions resulted from this work. First, the solute injection and sampling strategy has an important effect on the reliability of transport parameter estimates. We found that constant injection with sampling through concentration rise, plateau, and fall provided considerably more reliable parameter estimates than a pulse injection across the spectrum of transport scenarios likely encountered in high-gradient streams. Second, for a given tracer test design, the uncertainties in mass transfer and storage-zone parameter estimates are strongly dependent on the experimental Damkohler number, DaI, which is a dimensionless combination of the rates of exchange between the stream and storage zones, the stream-water velocity, and the stream reach length of the experiment. Parameter uncertainties are lowest at DaI values on the order of 1.0. When DaI values are much less than 1.0 (owing to high velocity, long exchange timescale, and/or short reach length), parameter uncertainties are high because only a small amount of tracer interacts with storage zones in the reach. For the opposite conditions (DaI ≫ 1.0), solute exchange rates are fast relative to stream-water velocity and all solute is exchanged with the storage zone over the experimental reach. As DaI increases, tracer dispersion caused by hyporheic exchange eventually reaches an equilibrium condition and storage-zone exchange parameters become essentially nonidentifiable.

Physical properties of asteroids derived from a novel approach to modeling of optical lightcurves and WISE thermalinfrared data

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Delbo, Marco; Ali-Lagoa, Victor; Carry, Benoit

2014-11-01

Convex shape models and spin vectors of asteroids are now routinely derived from their disk-integrated lightcurves by the lightcurve inversion method of Kaasalainen et al. (2001, Icarus 153, 37). These shape models can be then used in combination with thermal infrared data and a thermophysical model to derive other physical parameters - size, albedo, macroscopic roughness and thermal inertia of the surface. In this classical two-step approach, the shape and spin parameters are kept fixed during the thermophysical modeling when the emitted thermal flux is computed from the surface temperature, which is computed by solving a 1-D heat diffusion equation in sub-surface layers. A novel method of simultaneous inversion of optical and infrared data was presented by Durech et al. (2012, LPI Contribution No. 1667, id.6118). The new algorithm uses the same convex shape representation as the lightcurve inversion but optimizes all relevant physical parameters simultaneously (including the shape, size, rotation vector, thermal inertia, albedo, surface roughness, etc.), which leads to a better fit to the thermal data and a reliable estimation of model uncertainties. We applied this method to selected asteroids using their optical lightcurves from archives and thermal infrared data observed by the Wide-field Infrared Survey Explorer (WISE) satellite. We will (i) show several examples of how well our model fits both optical and infrared data, (ii) discuss the uncertainty of derived parameters (namely the thermal inertia), (iii) compare results obtained with the two-step approach with those obtained by our method, (iv) discuss the advantages of this simultaneous approach with respect to the classical two-step approach, and (v) advertise the possibility to use this approach to tens of thousands asteroids for which enough WISE and optical data exist.

CALIBRATION, OPTIMIZATION, AND SENSITIVITY AND UNCERTAINTY ALGORITHMS APPLICATION PROGRAMMING INTERFACE (COSU-API)

EPA Science Inventory

The Application Programming Interface (API) for Uncertainty Analysis, Sensitivity Analysis, and Parameter Estimation (UA/SA/PE API) tool development, here fore referred to as the Calibration, Optimization, and Sensitivity and Uncertainty Algorithms API (COSU-API), was initially d...

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.

Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

NASA Technical Reports Server (NTRS)

Gao, Zhiqiang; Antsaklis, Panos J.

1993-01-01

The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

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...

Robust stability for stochastic bidirectional associative memory neural networks with time delays

NASA Astrophysics Data System (ADS)

Shu, H. S.; Lv, Z. W.; Wei, G. L.

2008-02-01

In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

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.

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.

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

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.

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.

Parameter uncertainty and nonstationarity in regional extreme rainfall frequency analysis in Qu River Basin, East China

NASA Astrophysics Data System (ADS)

Zhu, Q.; Xu, Y. P.; Gu, H.

2014-12-01

Traditionally, regional frequency analysis methods were developed for stationary environmental conditions. Nevertheless, recent studies have identified significant changes in hydrological records, leading to the 'death' of stationarity. Besides, uncertainty in hydrological frequency analysis is persistent. This study aims to investigate the impact of one of the most important uncertainty sources, parameter uncertainty, together with nonstationarity, on design rainfall depth in Qu River Basin, East China. A spatial bootstrap is first proposed to analyze the uncertainty of design rainfall depth estimated by regional frequency analysis based on L-moments and estimated on at-site scale. Meanwhile, a method combining the generalized additive models with 30-year moving window is employed to analyze non-stationarity existed in the extreme rainfall regime. The results show that the uncertainties of design rainfall depth with 100-year return period under stationary conditions estimated by regional spatial bootstrap can reach 15.07% and 12.22% with GEV and PE3 respectively. On at-site scale, the uncertainties can reach 17.18% and 15.44% with GEV and PE3 respectively. In non-stationary conditions, the uncertainties of maximum rainfall depth (corresponding to design rainfall depth) with 0.01 annual exceedance probability (corresponding to 100-year return period) are 23.09% and 13.83% with GEV and PE3 respectively. Comparing the 90% confidence interval, the uncertainty of design rainfall depth resulted from parameter uncertainty is less than that from non-stationarity frequency analysis with GEV, however, slightly larger with PE3. This study indicates that the spatial bootstrap can be successfully applied to analyze the uncertainty of design rainfall depth on both regional and at-site scales. And the non-stationary analysis shows that the differences between non-stationary quantiles and their stationary equivalents are important for decision makes of water resources management and risk management.