A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

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

Kersaudy, Pierric, E-mail: pierric.kersaudy@orange.com; Whist Lab, 38 avenue du Général Leclerc, 92130 Issy-les-Moulineaux; ESYCOM, Université Paris-Est Marne-la-Vallée, 5 boulevard Descartes, 77700 Marne-la-Vallée

2015-04-01

In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representationmore » of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.« less

Spatial Interpolation of Reference Evapotranspiration in India: Comparison of IDW and Kriging Methods

NASA Astrophysics Data System (ADS)

Hodam, Sanayanbi; Sarkar, Sajal; Marak, Areor G. R.; Bandyopadhyay, A.; Bhadra, A.

2017-12-01

In the present study, to understand the spatial distribution characteristics of the ETo over India, spatial interpolation was performed on the means of 32 years (1971-2002) monthly data of 131 India Meteorological Department stations uniformly distributed over the country by two methods, namely, inverse distance weighted (IDW) interpolation and kriging. Kriging was found to be better while developing the monthly surfaces during cross-validation. However, in station-wise validation, IDW performed better than kriging in almost all the cases, hence is recommended for spatial interpolation of ETo and its governing meteorological parameters. This study also checked if direct kriging of FAO-56 Penman-Monteith (PM) (Allen et al. in Crop evapotranspiration—guidelines for computing crop water requirements, Irrigation and drainage paper 56, Food and Agriculture Organization of the United Nations (FAO), Rome, 1998) point ETo produced comparable results against ETo estimated with individually kriged weather parameters (indirect kriging). Indirect kriging performed marginally well compared to direct kriging. Point ETo values were extended to areal ETo values by IDW and FAO-56 PM mean ETo maps for India were developed to obtain sufficiently accurate ETo estimates at unknown locations.

Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Korte, John J.; Mauery, Timothy M.; Mistree, Farrokh

1998-01-01

In this paper, we compare and contrast the use of second-order response surface models and kriging models for approximating non-random, deterministic computer analyses. After reviewing the response surface method for constructing polynomial approximations, kriging is presented as an alternative approximation method for the design and analysis of computer experiments. Both methods are applied to the multidisciplinary design of an aerospike nozzle which consists of a computational fluid dynamics model and a finite-element model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations, and four optimization problems m formulated and solved using both sets of approximation models. The second-order response surface models and kriging models-using a constant underlying global model and a Gaussian correlation function-yield comparable results.

A kriging metamodel-assisted robust optimization method based on a reverse model

NASA Astrophysics Data System (ADS)

Zhou, Hui; Zhou, Qi; Liu, Congwei; Zhou, Taotao

2018-02-01

The goal of robust optimization methods is to obtain a solution that is both optimum and relatively insensitive to uncertainty factors. Most existing robust optimization approaches use outer-inner nested optimization structures where a large amount of computational effort is required because the robustness of each candidate solution delivered from the outer level should be evaluated in the inner level. In this article, a kriging metamodel-assisted robust optimization method based on a reverse model (K-RMRO) is first proposed, in which the nested optimization structure is reduced into a single-loop optimization structure to ease the computational burden. Ignoring the interpolation uncertainties from kriging, K-RMRO may yield non-robust optima. Hence, an improved kriging-assisted robust optimization method based on a reverse model (IK-RMRO) is presented to take the interpolation uncertainty of kriging metamodel into consideration. In IK-RMRO, an objective switching criterion is introduced to determine whether the inner level robust optimization or the kriging metamodel replacement should be used to evaluate the robustness of design alternatives. The proposed criterion is developed according to whether or not the robust status of the individual can be changed because of the interpolation uncertainties from the kriging metamodel. Numerical and engineering cases are used to demonstrate the applicability and efficiency of the proposed approach.

Distribution of kriging errors, the implications and how to communicate them

NASA Astrophysics Data System (ADS)

Li, Hong Yi; Milne, Alice; Webster, Richard

2016-04-01

Kriging in one form or another has become perhaps the most popular method for spatial prediction in environmental science. Each prediction is unbiased and of minimum variance, which itself is estimated. The kriging variances depend on the mathematical model chosen to describe the spatial variation; different models, however plausible, give rise to different minimized variances. Practitioners often compare models by so-called cross-validation before finally choosing the most appropriate for their kriging. One proceeds as follows. One removes a unit (a sampling point) from the whole set, kriges the value there and compares the kriged value with the value observed to obtain the deviation or error. One repeats the process for each and every point in turn and for all plausible models. One then computes the mean errors (MEs) and the mean of the squared errors (MSEs). Ideally a squared error should equal the corresponding kriging variance (σK2), and so one is advised to choose the model for which on average the squared errors most nearly equal the kriging variances, i.e. the ratio MSDR = MSE/σK2 ≈ 1. Maximum likelihood estimation of models almost guarantees that the MSDR equals 1, and so the kriging variances are unbiased predictors of the squared error across the region. The method is based on the assumption that the errors have a normal distribution. The squared deviation ratio (SDR) should therefore be distributed as χ2 with one degree of freedom with a median of 0.455. We have found that often the median of the SDR (MedSDR) is less, in some instances much less, than 0.455 even though the mean of the SDR is close to 1. It seems that in these cases the distributions of the errors are leptokurtic, i.e. they have an excess of predictions close to the true values, excesses near the extremes and a dearth of predictions in between. In these cases the kriging variances are poor measures of the uncertainty at individual sites. The uncertainty is typically under-estimated for the extreme observations and compensated for by over estimating for other observations. Statisticians must tell users when they present maps of predictions. We illustrate the situation with results from mapping salinity in land reclaimed from the Yangtze delta in the Gulf of Hangzhou, China. There the apparent electrical conductivity (ECa) of the topsoil was measured at 525 points in a field of 2.3 ha. The marginal distribution of the observations was strongly positively skewed, and so the observed ECas were transformed to their logarithms to give an approximately symmetric distribution. That distribution was strongly platykurtic with short tails and no evident outliers. The logarithms were analysed as a mixed model of quadratic drift plus correlated random residuals with a spherical variogram. The kriged predictions that deviated from their true values with an MSDR of 0.993, but with a medSDR=0.324. The coefficient of kurtosis of the deviations was 1.45, i.e. substantially larger than 0 for a normal distribution. The reasons for this behaviour are being sought. The most likely explanation is that there are spatial outliers, i.e. points at which the observed values that differ markedly from those at their their closest neighbours.

Distribution of kriging errors, the implications and how to communicate them

NASA Astrophysics Data System (ADS)

Li, HongYi; Milne, Alice; Webster, Richard

2015-04-01

Kriging in one form or another has become perhaps the most popular method for spatial prediction in environmental science. Each prediction is unbiased and of minimum variance, which itself is estimated. The kriging variances depend on the mathematical model chosen to describe the spatial variation; different models, however plausible, give rise to different minimized variances. Practitioners often compare models by so-called cross-validation before finally choosing the most appropriate for their kriging. One proceeds as follows. One removes a unit (a sampling point) from the whole set, kriges the value there and compares the kriged value with the value observed to obtain the deviation or error. One repeats the process for each and every point in turn and for all plausible models. One then computes the mean errors (MEs) and the mean of the squared errors (MSEs). Ideally a squared error should equal the corresponding kriging variance (σ_K^2), and so one is advised to choose the model for which on average the squared errors most nearly equal the kriging variances, i.e. the ratio MSDR=MSE/ σ_K2 ≈1. Maximum likelihood estimation of models almost guarantees that the MSDR equals 1, and so the kriging variances are unbiased predictors of the squared error across the region. The method is based on the assumption that the errors have a normal distribution. The squared deviation ratio (SDR) should therefore be distributed as χ2 with one degree of freedom with a median of 0.455. We have found that often the median of the SDR (MedSDR) is less, in some instances much less, than 0.455 even though the mean of the SDR is close to 1. It seems that in these cases the distributions of the errors are leptokurtic, i.e. they have an excess of predictions close to the true values, excesses near the extremes and a dearth of predictions in between. In these cases the kriging variances are poor measures of the uncertainty at individual sites. The uncertainty is typically under-estimated for the extreme observations and compensated for by over estimating for other observations. Statisticians must tell users when they present maps of predictions. We illustrate the situation with results from mapping salinity in land reclaimed from the Yangtze delta in the Gulf of Hangzhou, China. There the apparent electrical conductivity (EC_a) of the topsoil was measured at 525 points in a field of 2.3~ha. The marginal distribution of the observations was strongly positively skewed, and so the observed EC_as were transformed to their logarithms to give an approximately symmetric distribution. That distribution was strongly platykurtic with short tails and no evident outliers. The logarithms were analysed as a mixed model of quadratic drift plus correlated random residuals with a spherical variogram. The kriged predictions that deviated from their true values with an MSDR of 0.993, but with a medSDR=0.324. The coefficient of kurtosis of the deviations was 1.45, i.e. substantially larger than 0 for a normal distribution. The reasons for this behaviour are being sought. The most likely explanation is that there are spatial outliers, i.e. points at which the observed values that differ markedly from those at their their closest neighbours.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

PubMed

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-02-27

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10 16 electrons/m²) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

PubMed Central

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-01-01

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area. PMID:28264424

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

NASA Technical Reports Server (NTRS)

Krishnamurthy, Thiagarajan

2005-01-01

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, A.; Künsch, H. R.; Schwierz, C.; Stahel, W. A.

2012-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outlying observations may results from errors (e.g. in data transcription) or from local perturbations in the processes that are responsible for a given pattern of spatial variation. As an example, the spatial distribution of some trace metal in the soils of a region may be distorted by emissions of local anthropogenic sources. Outliers affect the modelling of the large-scale spatial variation, the so-called external drift or trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) [2] proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) [1] for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation. Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and unsampled locations and kriging variances. The method has been implemented in an R package. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis of the Tarrawarra soil moisture data set [3].

A new algorithm combining geostatistics with the surrogate data approach to increase the accuracy of comparisons of point radiation measurements with cloud measurements

NASA Astrophysics Data System (ADS)

Venema, V. K. C.; Lindau, R.; Varnai, T.; Simmer, C.

2009-04-01

Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated on such a kriged field. Stochastic modelling aims at reproducing the structure of the data. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. However, while stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. Because radiative transfer through clouds is a highly nonlinear process it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately as well as the correlations in the cloud field because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. However, up to now we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. The algorithm is tested on cloud fields from large eddy simulations (LES). On these clouds a measurement is simulated. From the pseudo-measurement we estimated the distribution and power spectrum. Furthermore, the pseudo-measurement is kriged to a field the size of the final surrogate cloud. The distribution, spectrum and the kriged field are the inputs to the algorithm. This algorithm is similar to the standard iterative amplitude adjusted Fourier transform (IAAFT) algorithm, but has an additional iterative step in which the surrogate field is nudged towards the kriged field. The nudging strength is gradually reduced to zero. We work with four types of pseudo-measurements: one zenith pointing measurement (which together with the wind produces a line measurement), five zenith pointing measurements, a slow and a fast azimuth scan (which together with the wind produce spirals). Because we work with LES clouds and the truth is known, we can validate the algorithm by performing 3D radiative transfer calculations on the original LES clouds and on the new surrogate clouds. For comparison also the radiative properties of the kriged fields and standard surrogate fields are computed. Preliminary results already show that these new surrogate clouds reproduce the structure of the original clouds very well and the minima and maxima are located where the pseudo-measurements sees them. The main limitation seems to be the amount of data, which is especially very limited in case of just one zenith pointing measurement.

Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.

1998-01-01

The use of response surface models and kriging models are compared for approximating non-random, deterministic computer analyses. After discussing the traditional response surface approach for constructing polynomial models for approximation, kriging is presented as an alternative statistical-based approximation method for the design and analysis of computer experiments. Both approximation methods are applied to the multidisciplinary design and analysis of an aerospike nozzle which consists of a computational fluid dynamics model and a finite element analysis model. Error analysis of the response surface and kriging models is performed along with a graphical comparison of the approximations. Four optimization problems are formulated and solved using both approximation models. While neither approximation technique consistently outperforms the other in this example, the kriging models using only a constant for the underlying global model and a Gaussian correlation function perform as well as the second order polynomial response surface models.

A multi-damages identification method for cantilever beam based on mode shape curvatures and Kriging surrogate model

NASA Astrophysics Data System (ADS)

Xie, Fengle; Jiang, Zhansi; Jiang, Hui

2018-05-01

This paper presents a multi-damages identification method for Cantilever Beam. First, the damage location is identified by using the mode shape curvatures. Second, samples of varying damage severities at the damage location and their corresponding natural frequencies are used to construct the initial Kriging surrogate model. Then a particle swarm optimization (PSO) algorithm is employed to identify the damage severities based on Kriging surrogate model. The simulation study of a double-damaged cantilever beam demonstrated that the proposed method is effective.

Reservoir property grids improve with geostatistics

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

Vogt, J.

1993-09-01

Visualization software, reservoir simulators and many other E and P software applications need reservoir property grids as input. Using geostatistics, as compared to other gridding methods, to produce these grids leads to the best output from the software programs. For the purpose stated herein, geostatistics is simply two types of gridding methods. Mathematically, these methods are based on minimizing or duplicating certain statistical properties of the input data. One geostatical method, called kriging, is used when the highest possible point-by-point accuracy is desired. The other method, called conditional simulation, is used when one wants statistics and texture of the resultingmore » grid to be the same as for the input data. In the following discussion, each method is explained, compared to other gridding methods, and illustrated through example applications. Proper use of geostatistical data in flow simulations, use of geostatistical data for history matching, and situations where geostatistics has no significant advantage over other methods, also will be covered.« less

Structural reliability analysis under evidence theory using the active learning kriging model

NASA Astrophysics Data System (ADS)

Yang, Xufeng; Liu, Yongshou; Ma, Panke

2017-11-01

Structural reliability analysis under evidence theory is investigated. It is rigorously proved that a surrogate model providing only correct sign prediction of the performance function can meet the accuracy requirement of evidence-theory-based reliability analysis. Accordingly, a method based on the active learning kriging model which only correctly predicts the sign of the performance function is proposed. Interval Monte Carlo simulation and a modified optimization method based on Karush-Kuhn-Tucker conditions are introduced to make the method more efficient in estimating the bounds of failure probability based on the kriging model. Four examples are investigated to demonstrate the efficiency and accuracy of the proposed method.

Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater

PubMed Central

Shabbir, Javid; M. AbdEl-Salam, Nasser; Hussain, Tajammal

2016-01-01

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used to predict the sodium concentrations. Spatial simulated annealing is used to generate optimized sampling designs. Different estimation methods (i.e., maximum likelihood, restricted maximum likelihood, ordinary least squares, and weighted least squares) are used to estimate the parameters of the variogram model (i.e, exponential, Gaussian, spherical and cubic). It is concluded that Bayesian universal kriging fits better than universal kriging. It is also observed that the universal kriging predictor provides minimum mean universal kriging variance for both adding and deleting locations during sampling design. PMID:27683016

Geospatial tools effectively estimate nonexceedance probabilities of daily streamflow at ungauged and intermittently gauged locations in Ohio

USGS Publications Warehouse

Farmer, William H.; Koltun, Greg

2017-01-01

Study regionThe state of Ohio in the United States, a humid, continental climate.Study focusThe estimation of nonexceedance probabilities of daily streamflows as an alternative means of establishing the relative magnitudes of streamflows associated with hydrologic and water-quality observations.New hydrological insights for the regionSeveral methods for estimating nonexceedance probabilities of daily mean streamflows are explored, including single-index methodologies (nearest-neighboring index) and geospatial tools (kriging and topological kriging). These methods were evaluated by conducting leave-one-out cross-validations based on analyses of nearly 7 years of daily streamflow data from 79 unregulated streamgages in Ohio and neighboring states. The pooled, ordinary kriging model, with a median Nash–Sutcliffe performance of 0.87, was superior to the single-site index methods, though there was some bias in the tails of the probability distribution. Incorporating network structure through topological kriging did not improve performance. The pooled, ordinary kriging model was applied to 118 locations without systematic streamgaging across Ohio where instantaneous streamflow measurements had been made concurrent with water-quality sampling on at least 3 separate days. Spearman rank correlations between estimated nonexceedance probabilities and measured streamflows were high, with a median value of 0.76. In consideration of application, the degree of regulation in a set of sample sites helped to specify the streamgages required to implement kriging approaches successfully.

Transfer of uncertainty of space-borne high resolution rainfall products at ungauged regions

NASA Astrophysics Data System (ADS)

Tang, Ling

Hydrologically relevant characteristics of high resolution (˜ 0.25 degree, 3 hourly) satellite rainfall uncertainty were derived as a function of season and location using a six year (2002-2007) archive of National Aeronautics and Space Administration (NASA)'s Tropical Rainfall Measuring Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) precipitation data. The Next Generation Radar (NEXRAD) Stage IV rainfall data over the continental United States was used as ground validation (GV) data. A geostatistical mapping scheme was developed and tested for transfer (i.e., spatial interpolation) of uncertainty information from GV regions to the vast non-GV regions by leveraging the error characterization work carried out in the earlier step. The open question explored here was, "If 'error' is defined on the basis of independent ground validation (GV) data, how are error metrics estimated for a satellite rainfall data product without the need for much extensive GV data?" After a quantitative analysis of the spatial and temporal structure of the satellite rainfall uncertainty, a proof-of-concept geostatistical mapping scheme (based on the kriging method) was evaluated. The idea was to understand how realistic the idea of 'transfer' is for the GPM era. It was found that it was indeed technically possible to transfer error metrics from a gauged to an ungauged location for certain error metrics and that a regionalized error metric scheme for GPM may be possible. The uncertainty transfer scheme based on a commonly used kriging method (ordinary kriging) was then assessed further at various timescales (climatologic, seasonal, monthly and weekly), and as a function of the density of GV coverage. The results indicated that if a transfer scheme for estimating uncertainty metrics was finer than seasonal scale (ranging from 3-6 hourly to weekly-monthly), the effectiveness for uncertainty transfer worsened significantly. Next, a comprehensive assessment of different kriging methods for spatial transfer (interpolation) of error metrics was performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method was also performed to quantify the added benefit (if any) of using geostatistical methods. The overall performance ranking of the kriging methods was found to be as follows: OK=DK > IDW > IK. Lastly, various metrics of satellite rainfall uncertainty were identified for two large continental landmasses that share many similar Koppen climate zones, United States and Australia. The dependence of uncertainty as a function of gauge density was then investigated. The investigation revealed that only the first and second ordered moments of error are most amenable to a Koppen-type climate type classification in different continental landmasses.

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

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

He, Xu; Tuo, Rui; Jeff Wu, C. F.

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion

DOE PAGES

He, Xu; Tuo, Rui; Jeff Wu, C. F.

2017-01-31

Computer experiments based on mathematical models are powerful tools for understanding physical processes. This article addresses the problem of kriging-based optimization for deterministic computer experiments with tunable accuracy. Our approach is to use multi- delity computer experiments with increasing accuracy levels and a nonstationary Gaussian process model. We propose an optimization scheme that sequentially adds new computer runs by following two criteria. The first criterion, called EQI, scores candidate inputs with given level of accuracy, and the second criterion, called EQIE, scores candidate combinations of inputs and accuracy. Here, from simulation results and a real example using finite element analysis,more » our method out-performs the expected improvement (EI) criterion which works for single-accuracy experiments.« less

Optimal design criteria - prediction vs. parameter estimation

NASA Astrophysics Data System (ADS)

Waldl, Helmut

2014-05-01

G-optimality is a popular design criterion for optimal prediction, it tries to minimize the kriging variance over the whole design region. A G-optimal design minimizes the maximum variance of all predicted values. If we use kriging methods for prediction it is self-evident to use the kriging variance as a measure of uncertainty for the estimates. Though the computation of the kriging variance and even more the computation of the empirical kriging variance is computationally very costly and finding the maximum kriging variance in high-dimensional regions can be time demanding such that we cannot really find the G-optimal design with nowadays available computer equipment in practice. We cannot always avoid this problem by using space-filling designs because small designs that minimize the empirical kriging variance are often non-space-filling. D-optimality is the design criterion related to parameter estimation. A D-optimal design maximizes the determinant of the information matrix of the estimates. D-optimality in terms of trend parameter estimation and D-optimality in terms of covariance parameter estimation yield basically different designs. The Pareto frontier of these two competing determinant criteria corresponds with designs that perform well under both criteria. Under certain conditions searching the G-optimal design on the above Pareto frontier yields almost as good results as searching the G-optimal design in the whole design region. In doing so the maximum of the empirical kriging variance has to be computed only a few times though. The method is demonstrated by means of a computer simulation experiment based on data provided by the Belgian institute Management Unit of the North Sea Mathematical Models (MUMM) that describe the evolution of inorganic and organic carbon and nutrients, phytoplankton, bacteria and zooplankton in the Southern Bight of the North Sea.

Estimation statistique de donnees manquantes en inventaire du cycle de vie

NASA Astrophysics Data System (ADS)

Moreau, Vincent

The main objective of the research work is to improve the quality of life cycle inventory data by developing a method to estimate missing data and corresponding uncertainties. Contrary to process-based models of mass and energy balance, this approach consists of statistical estimators which model processes from relatively small samples of usually high variability. The research hypothesis is as follows: the so called kriging estimator allows the combined estimation of missing data and their uncertainties in such ways that are more reliable than other linear estimators. Borrowed from spatial statistics, kriging is an estimator with several advantages, the flexibility associated with a choice of model function and the exact estimator property. In other words, kriging shows no statistical errors when estimating observed values, no data is averaged out. An interpretation of the kriging parameters specific to the problems of data uncertainty, offers more advantages. One parameter of the covariance function accounts for small scale variations of the data and taken as a proxy for uncertainty. Whether it be the variety of data sources, the scarcity of the data itself or both, each and every source adds to data variability and uncertainty. The kriging system of equations is therefore modified such as to integrate a factor of uncertainty specific to each observations. Comparisons between the modified and conventional forms of kriging can be drawn. The procedure is based on the relationship between technical specifications, more readily available independent variables, and the dependent material and energy flows of the processes under consideration. Such material and energy requirements as well as emissions are estimated over the entire life cycle of products and processes. The needs for additional data are relatively low compared to other approaches, namely extended input output analysis. For many products, processes and services, electricity generation and consumption account for a sizable share of the impacts. Hydroelectricity in particular is poorly represented within existing inventory data since production facilities vary considerably from one location to another. In other words, generic hydropower plants do not exist. Contrary to inventory flows, the technical specifications or characteristic variables of hydropower plants, such as the installed capacity, annual production or surface area of adjacent reservoirs, are usually publicly available. The kriging model is first tested on a data set which represents windmills of varying power capacity before it is applied to hydroelectricity. The experiment is divided according to data availability, on one hand the energy and materials required during construction, operation and maintenance of hydropower plants. The results show that estimation of inventory data can be improved thanks to kriging. When comparing different forms of kriging and linear regression, the kriging estimates are not only more precise but the standard deviations also cover the data more accurately. Where the observed data are incomplete, that is where inventory flows are missing for part of the observations, the estimation errors are lower for kriging than linear regression. Moreover, univariate kriging of inventory flows based on two characteristic variables, shows lower errors than its multivariate kin, cokriging. On average the statistical errors calculated from cross-validation are lower for kriging than they are for linear regression, whether the observed data are complete or not. The application of several characteristic variables improves the quality of the estimates when they are positively correlated. In addition, the modified form of kriging which accounts for degrees of uncertainty specific to each observations, results in a reduction in the variations of the estimated inventory data. That is, data variability is incorporated directly in the model. Estimates closer to more reliable observations are shown to be less uncertain and vice versa. For each of the data sets, different relationships between dependent and independent variables are tested, for example the linear, exponential, spherical and cubic covariance functions as well as a range of parameter values. For the analysis of electrical generation technologies, these results imply better estimates for data that are difficult to sample and therefore a simplified data collection process. In the case of site specific or variable processes such as hydroelectricity, the estimation of inventory data with kriging accounting for such data variability, proves more representative of the geographical or technological context. The quality of inventory data is consequently higher. Even if kriging has several advantages and its estimation errors are lower on average, some limitations to its application exist. (Abstract shortened by UMI.).

A Geostatistical Toolset for Reconstructing Louisiana's Coastal Stratigraphy using Subsurface Boring and Cone Penetrometer Test Data

NASA Astrophysics Data System (ADS)

Li, A.; Tsai, F. T. C.; Jafari, N.; Chen, Q. J.; Bentley, S. J.

2017-12-01

A vast area of river deltaic wetlands stretches across southern Louisiana coast. The wetlands are suffering from a high rate of land loss, which increasingly threats coastal community and energy infrastructure. A regional stratigraphic framework of the delta plain is now imperative to answer scientific questions (such as how the delta plain grows and decays?) and to provide information to coastal protection and restoration projects (such as marsh creation and construction of levees and floodwalls). Through years, subsurface investigations in Louisiana have been conducted by state and federal agencies (Louisiana Department of Natural Resources, United States Geological Survey, United States Army Corps of Engineers, etc.), research institutes (Louisiana Geological Survey, LSU Coastal Studies Institute, etc.), engineering firms, and oil-gas companies. This has resulted in the availability of various types of data, including geological, geotechnical, and geophysical data. However, it is challenging to integrate different types of data and construct three-dimensional stratigraphy models in regional scale. In this study, a set of geostatistical methods were used to tackle this problem. An ordinary kriging method was used to regionalize continuous data, such as grain size, water content, liquid limit, plasticity index, and cone penetrometer tests (CPTs). Indicator kriging and multiple indicator kriging methods were used to regionalize categorized data, such as soil classification. A compositional kriging method was used to regionalize compositional data, such as soil composition (fractions of sand, silt and clay). Stratigraphy models were constructed for three cases in the coastal zone: (1) Inner Harbor Navigation Canal (IHNC) area: soil classification and soil behavior type (SBT) stratigraphies were constructed using ordinary kriging; (2) Middle Barataria Bay area: a soil classification stratigraphy was constructed using multiple indicator kriging; (3) Lower Barataria Bay and Lower Breton Sound areas: a soil texture stratigraphy was constructed using soil compositional data and compositional kriging. Cross sections were extracted from the three-dimensional stratigraphy models to reveal spatial distributions of different stratigraphic features.

Ionospheric tomography by gradient-enhanced kriging with STEC measurements and ionosonde characteristics

NASA Astrophysics Data System (ADS)

Minkwitz, David; van den Boogaart, Karl Gerald; Gerzen, Tatjana; Hoque, Mainul; Hernández-Pajares, Manuel

2016-11-01

The estimation of the ionospheric electron density by kriging is based on the optimization of a parametric measurement covariance model. First, the extension of kriging with slant total electron content (STEC) measurements based on a spatial covariance to kriging with a spatial-temporal covariance model, assimilating STEC data of a sliding window, is presented. Secondly, a novel tomography approach by gradient-enhanced kriging (GEK) is developed. Beyond the ingestion of STEC measurements, GEK assimilates ionosonde characteristics, providing peak electron density measurements as well as gradient information. Both approaches deploy the 3-D electron density model NeQuick as a priori information and estimate the covariance parameter vector within a maximum likelihood estimation for the dedicated tomography time stamp. The methods are validated in the European region for two periods covering quiet and active ionospheric conditions. The kriging with spatial and spatial-temporal covariance model is analysed regarding its capability to reproduce STEC, differential STEC and foF2. Therefore, the estimates are compared to the NeQuick model results, the 2-D TEC maps of the International GNSS Service and the DLR's Ionospheric Monitoring and Prediction Center, and in the case of foF2 to two independent ionosonde stations. Moreover, simulated STEC and ionosonde measurements are used to investigate the electron density profiles estimated by the GEK in comparison to a kriging with STEC only. The results indicate a crucial improvement in the initial guess by the developed methods and point out the potential compensation for a bias in the peak height hmF2 by means of GEK.

Radioactive source localization in urban environments with sensor networks and the Internet of Things

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

Sullivan, Clair J.

The use of radiation detectors as an element in the so-called “Internet of Things” has recently become viable with the available of low-cost, mobile radiation sensors capable of streaming geo-referenced data. New methods for fusing the data from multiple sensors on such a network is presented. The traditional simple and ordinary Kriging methods present a challenge for such a network since the assumption of a constant mean is not valid in this application. In conclusion, a variety of Kalman filters are introduced in an attempt to solve the problem associated with this variable and unknown mean. Results are presented onmore » a deployed sensor network.« less

Radioactive source localization in urban environments with sensor networks and the Internet of Things

DOE PAGES

Sullivan, Clair J.

2016-01-01

The use of radiation detectors as an element in the so-called “Internet of Things” has recently become viable with the available of low-cost, mobile radiation sensors capable of streaming geo-referenced data. New methods for fusing the data from multiple sensors on such a network is presented. The traditional simple and ordinary Kriging methods present a challenge for such a network since the assumption of a constant mean is not valid in this application. In conclusion, a variety of Kalman filters are introduced in an attempt to solve the problem associated with this variable and unknown mean. Results are presented onmore » a deployed sensor network.« less

Comparison of different wind data interpolation methods for a region with complex terrain in Central Asia

NASA Astrophysics Data System (ADS)

Reinhardt, Katja; Samimi, Cyrus

2018-01-01

While climatological data of high spatial resolution are largely available in most developed countries, the network of climatological stations in many other regions of the world still constitutes large gaps. Especially for those regions, interpolation methods are important tools to fill these gaps and to improve the data base indispensible for climatological research. Over the last years, new hybrid methods of machine learning and geostatistics have been developed which provide innovative prospects in spatial predictive modelling. This study will focus on evaluating the performance of 12 different interpolation methods for the wind components \\overrightarrow{u} and \\overrightarrow{v} in a mountainous region of Central Asia. Thereby, a special focus will be on applying new hybrid methods on spatial interpolation of wind data. This study is the first evaluating and comparing the performance of several of these hybrid methods. The overall aim of this study is to determine whether an optimal interpolation method exists, which can equally be applied for all pressure levels, or whether different interpolation methods have to be used for the different pressure levels. Deterministic (inverse distance weighting) and geostatistical interpolation methods (ordinary kriging) were explored, which take into account only the initial values of \\overrightarrow{u} and \\overrightarrow{v} . In addition, more complex methods (generalized additive model, support vector machine and neural networks as single methods and as hybrid methods as well as regression-kriging) that consider additional variables were applied. The analysis of the error indices revealed that regression-kriging provided the most accurate interpolation results for both wind components and all pressure heights. At 200 and 500 hPa, regression-kriging is followed by the different kinds of neural networks and support vector machines and for 850 hPa it is followed by the different types of support vector machine and ordinary kriging. Overall, explanatory variables improve the interpolation results.

Received Signal Strength Database Interpolation by Kriging for a Wi-Fi Indoor Positioning System

PubMed Central

Jan, Shau-Shiun; Yeh, Shuo-Ju; Liu, Ya-Wen

2015-01-01

The main approach for a Wi-Fi indoor positioning system is based on the received signal strength (RSS) measurements, and the fingerprinting method is utilized to determine the user position by matching the RSS values with the pre-surveyed RSS database. To build a RSS fingerprint database is essential for an RSS based indoor positioning system, and building such a RSS fingerprint database requires lots of time and effort. As the range of the indoor environment becomes larger, labor is increased. To provide better indoor positioning services and to reduce the labor required for the establishment of the positioning system at the same time, an indoor positioning system with an appropriate spatial interpolation method is needed. In addition, the advantage of the RSS approach is that the signal strength decays as the transmission distance increases, and this signal propagation characteristic is applied to an interpolated database with the Kriging algorithm in this paper. Using the distribution of reference points (RPs) at measured points, the signal propagation model of the Wi-Fi access point (AP) in the building can be built and expressed as a function. The function, as the spatial structure of the environment, can create the RSS database quickly in different indoor environments. Thus, in this paper, a Wi-Fi indoor positioning system based on the Kriging fingerprinting method is developed. As shown in the experiment results, with a 72.2% probability, the error of the extended RSS database with Kriging is less than 3 dBm compared to the surveyed RSS database. Importantly, the positioning error of the developed Wi-Fi indoor positioning system with Kriging is reduced by 17.9% in average than that without Kriging. PMID:26343673

Received Signal Strength Database Interpolation by Kriging for a Wi-Fi Indoor Positioning System.

PubMed

Jan, Shau-Shiun; Yeh, Shuo-Ju; Liu, Ya-Wen

2015-08-28

The main approach for a Wi-Fi indoor positioning system is based on the received signal strength (RSS) measurements, and the fingerprinting method is utilized to determine the user position by matching the RSS values with the pre-surveyed RSS database. To build a RSS fingerprint database is essential for an RSS based indoor positioning system, and building such a RSS fingerprint database requires lots of time and effort. As the range of the indoor environment becomes larger, labor is increased. To provide better indoor positioning services and to reduce the labor required for the establishment of the positioning system at the same time, an indoor positioning system with an appropriate spatial interpolation method is needed. In addition, the advantage of the RSS approach is that the signal strength decays as the transmission distance increases, and this signal propagation characteristic is applied to an interpolated database with the Kriging algorithm in this paper. Using the distribution of reference points (RPs) at measured points, the signal propagation model of the Wi-Fi access point (AP) in the building can be built and expressed as a function. The function, as the spatial structure of the environment, can create the RSS database quickly in different indoor environments. Thus, in this paper, a Wi-Fi indoor positioning system based on the Kriging fingerprinting method is developed. As shown in the experiment results, with a 72.2% probability, the error of the extended RSS database with Kriging is less than 3 dBm compared to the surveyed RSS database. Importantly, the positioning error of the developed Wi-Fi indoor positioning system with Kriging is reduced by 17.9% in average than that without Kriging.

Resolving the structure of the Galactic foreground using Herschel measurements and the Kriging technique

NASA Astrophysics Data System (ADS)

Pinter, S.; Bagoly, Z.; Balázs, L. G.; Horvath, I.; Racz, I. I.; Zahorecz, S.; Tóth, L. V.

2018-05-01

Investigating the distant extragalactic Universe requires a subtraction of the Galactic foreground. One of the major difficulties deriving the fine structure of the galactic foreground is the embedded foreground and background point sources appearing in the given fields. It is especially so in the infrared. We report our study subtracting point sources from Herschel images with Kriging, an interpolation method where the interpolated values are modelled by a Gaussian process governed by prior covariances. Using the Kriging method on Herschel multi-wavelength observations the structure of the Galactic foreground can be studied with much higher resolution than previously, leading to a better foreground subtraction at the end.

Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event

NASA Astrophysics Data System (ADS)

Haberlandt, Uwe

2007-01-01

SummaryThe methods kriging with external drift (KED) and indicator kriging with external drift (IKED) are used for the spatial interpolation of hourly rainfall from rain gauges using additional information from radar, daily precipitation of a denser network, and elevation. The techniques are illustrated using data from the storm period of the 10th to the 13th of August 2002 that led to the extreme flood event in the Elbe river basin in Germany. Cross-validation is applied to compare the interpolation performance of the KED and IKED methods using different additional information with the univariate reference methods nearest neighbour (NN) or Thiessen polygons, inverse square distance weighting (IDW), ordinary kriging (OK) and ordinary indicator kriging (IK). Special attention is given to the analysis of the impact of the semivariogram estimation on the interpolation performance. Hourly and average semivariograms are inferred from daily, hourly and radar data considering either isotropic or anisotropic behaviour using automatic and manual fitting procedures. The multivariate methods KED and IKED clearly outperform the univariate ones with the most important additional information being radar, followed by precipitation from the daily network and elevation, which plays only a secondary role here. The best performance is achieved when all additional information are used simultaneously with KED. The indicator-based kriging methods provide, in some cases, smaller root mean square errors than the methods, which use the original data, but at the expense of a significant loss of variance. The impact of the semivariogram on interpolation performance is not very high. The best results are obtained using an automatic fitting procedure with isotropic variograms either from hourly or radar data.

Hybrid surrogate-model-based multi-fidelity efficient global optimization applied to helicopter blade design

NASA Astrophysics Data System (ADS)

Ariyarit, Atthaphon; Sugiura, Masahiko; Tanabe, Yasutada; Kanazaki, Masahiro

2018-06-01

A multi-fidelity optimization technique by an efficient global optimization process using a hybrid surrogate model is investigated for solving real-world design problems. The model constructs the local deviation using the kriging method and the global model using a radial basis function. The expected improvement is computed to decide additional samples that can improve the model. The approach was first investigated by solving mathematical test problems. The results were compared with optimization results from an ordinary kriging method and a co-kriging method, and the proposed method produced the best solution. The proposed method was also applied to aerodynamic design optimization of helicopter blades to obtain the maximum blade efficiency. The optimal shape obtained by the proposed method achieved performance almost equivalent to that obtained using the high-fidelity, evaluation-based single-fidelity optimization. Comparing all three methods, the proposed method required the lowest total number of high-fidelity evaluation runs to obtain a converged solution.

Kriging modeling and SPSA adjusting PID with KPWF compensator control of IPMC gripper for mm-sized objects

NASA Astrophysics Data System (ADS)

Chen, Yang; Hao, Lina; Yang, Hui; Gao, Jinhai

2017-12-01

Ionic polymer metal composite (IPMC) as a new smart material has been widely concerned in the micromanipulation field. In this paper, a novel two-finger gripper which contains an IPMC actuator and an ultrasensitive force sensor is proposed and fabricated. The IPMC as one finger of the gripper for mm-sized objects can achieve gripping and releasing motion, and the other finger works not only as a support finger but also as a force sensor. Because of the feedback signal of the force sensor, this integrated actuating and sensing gripper can complete gripping miniature objects in millimeter scale. The Kriging model is used to describe nonlinear characteristics of the IPMC for the first time, and then the control scheme called simultaneous perturbation stochastic approximation adjusting a proportion integration differentiation parameter controller with a Kriging predictor wavelet filter compensator is applied to track the gripping force of the gripper. The high precision force tracking in the foam ball manipulation process is obtained on a semi-physical experimental platform, which demonstrates that this gripper for mm-sized objects can work well in manipulation applications.

Geostatistical modeling of riparian forest microclimate and its implications for sampling

USGS Publications Warehouse

Eskelson, B.N.I.; Anderson, P.D.; Hagar, J.C.; Temesgen, H.

2011-01-01

Predictive models of microclimate under various site conditions in forested headwater stream - riparian areas are poorly developed, and sampling designs for characterizing underlying riparian microclimate gradients are sparse. We used riparian microclimate data collected at eight headwater streams in the Oregon Coast Range to compare ordinary kriging (OK), universal kriging (UK), and kriging with external drift (KED) for point prediction of mean maximum air temperature (Tair). Several topographic and forest structure characteristics were considered as site-specific parameters. Height above stream and distance to stream were the most important covariates in the KED models, which outperformed OK and UK in terms of root mean square error. Sample patterns were optimized based on the kriging variance and the weighted means of shortest distance criterion using the simulated annealing algorithm. The optimized sample patterns outperformed systematic sample patterns in terms of mean kriging variance mainly for small sample sizes. These findings suggest methods for increasing efficiency of microclimate monitoring in riparian areas.

Accelerating parallel transmit array B1 mapping in high field MRI with slice undersampling and interpolation by kriging.

PubMed

Ferrand, Guillaume; Luong, Michel; Cloos, Martijn A; Amadon, Alexis; Wackernagel, Hans

2014-08-01

Transmit arrays have been developed to mitigate the RF field inhomogeneity commonly observed in high field magnetic resonance imaging (MRI), typically above 3T. To this end, the knowledge of the RF complex-valued B1 transmit-sensitivities of each independent radiating element has become essential. This paper details a method to speed up a currently available B1-calibration method. The principle relies on slice undersampling, slice and channel interleaving and kriging, an interpolation method developed in geostatistics and applicable in many domains. It has been demonstrated that, under certain conditions, kriging gives the best estimator of a field in a region of interest. The resulting accelerated sequence allows mapping a complete set of eight volumetric field maps of the human head in about 1 min. For validation, the accuracy of kriging is first evaluated against a well-known interpolation technique based on Fourier transform as well as to a B1-maps interpolation method presented in the literature. This analysis is carried out on simulated and decimated experimental B1 maps. Finally, the accelerated sequence is compared to the standard sequence on a phantom and a volunteer. The new sequence provides B1 maps three times faster with a loss of accuracy limited potentially to about 5%.

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

Sen, Oishik, E-mail: oishik-sen@uiowa.edu; Gaul, Nicholas J., E-mail: nicholas-gaul@ramdosolutions.com; Choi, K.K., E-mail: kyung-choi@uiowa.edu

Macro-scale computations of shocked particulate flows require closure laws that model the exchange of momentum/energy between the fluid and particle phases. Closure laws are constructed in this work in the form of surrogate models derived from highly resolved mesoscale computations of shock-particle interactions. The mesoscale computations are performed to calculate the drag force on a cluster of particles for different values of Mach Number and particle volume fraction. Two Kriging-based methods, viz. the Dynamic Kriging Method (DKG) and the Modified Bayesian Kriging Method (MBKG) are evaluated for their ability to construct surrogate models with sparse data; i.e. using the leastmore » number of mesoscale simulations. It is shown that if the input data is noise-free, the DKG method converges monotonically; convergence is less robust in the presence of noise. The MBKG method converges monotonically even with noisy input data and is therefore more suitable for surrogate model construction from numerical experiments. This work is the first step towards a full multiscale modeling of interaction of shocked particle laden flows.« less

Polarizable multipolar electrostatics for cholesterol

NASA Astrophysics Data System (ADS)

Fletcher, Timothy L.; Popelier, Paul L. A.

2016-08-01

FFLUX is a novel force field under development for biomolecular modelling, and is based on topological atoms and the machine learning method kriging. Successful kriging models have been obtained for realistic electrostatics of amino acids, small peptides, and some carbohydrates but here, for the first time, we construct kriging models for a sizeable ligand of great importance, which is cholesterol. Cholesterol's mean total (internal) electrostatic energy prediction error amounts to 3.9 kJ mol-1, which pleasingly falls below the threshold of 1 kcal mol-1 often cited for accurate biomolecular modelling. We present a detailed analysis of the error distributions.

Exploring spatial patterns of sudden cardiac arrests in the city of Toronto using Poisson kriging and Hot Spot analyses

PubMed Central

2017-01-01

Introduction Our study looked at out-of-hospital sudden cardiac arrest events in the City of Toronto. These are relatively rare events, yet present a serious global clinical and public health problem. We report on the application of spatial methods and tools that, although relatively well known to geographers and natural resource scientists, need to become better known and used more frequently by health care researchers. Materials and methods Our data came from the population-based Rescu Epistry cardiac arrest database. We limited it to the residents of the City of Toronto who experienced sudden arrest in 2010. The data was aggregated at the Dissemination Area level, and population rates were calculated. Poisson kriging was carried out on one year of data using three different spatial weights. Kriging estimates were then compared in Hot Spot analyses. Results Spatial analysis revealed that Poisson kriging can yield reliable rates using limited data of high quality. We observed the highest rates of sudden arrests in the north and central parts of Etobicoke, western parts of North York as well as the central and southwestern parts of Scarborough while the lowest rates were found in north and eastern parts of Scarborough, downtown Toronto, and East York as well as east central parts of North York. Influence of spatial neighbours on the results did not extend past two rings of adjacent units. Conclusions Poisson kriging has the potential to be applied to a wide range of healthcare research, particularly on rare events. This approach can be successfully combined with other spatial methods. More applied research, is needed to establish a wider acceptance for this method, especially among healthcare researchers and epidemiologists. PMID:28672029

Solving bi-level optimization problems in engineering design using kriging models

NASA Astrophysics Data System (ADS)

Xia, Yi; Liu, Xiaojie; Du, Gang

2018-05-01

Stackelberg game-theoretic approaches are applied extensively in engineering design to handle distributed collaboration decisions. Bi-level genetic algorithms (BLGAs) and response surfaces have been used to solve the corresponding bi-level programming models. However, the computational costs for BLGAs often increase rapidly with the complexity of lower-level programs, and optimal solution functions sometimes cannot be approximated by response surfaces. This article proposes a new method, namely the optimal solution function approximation by kriging model (OSFAKM), in which kriging models are used to approximate the optimal solution functions. A detailed example demonstrates that OSFAKM can obtain better solutions than BLGAs and response surface-based methods, and at the same time reduce the workload of computation remarkably. Five benchmark problems and a case study of the optimal design of a thin-walled pressure vessel are also presented to illustrate the feasibility and potential of the proposed method for bi-level optimization in engineering design.

Model Updating of Complex Structures Using the Combination of Component Mode Synthesis and Kriging Predictor

PubMed Central

Li, Yan; Wang, Dejun; Zhang, Shaoyi

2014-01-01

Updating the structural model of complex structures is time-consuming due to the large size of the finite element model (FEM). Using conventional methods for these cases is computationally expensive or even impossible. A two-level method, which combined the Kriging predictor and the component mode synthesis (CMS) technique, was proposed to ensure the successful implementing of FEM updating of large-scale structures. In the first level, the CMS was applied to build a reasonable condensed FEM of complex structures. In the second level, the Kriging predictor that was deemed as a surrogate FEM in structural dynamics was generated based on the condensed FEM. Some key issues of the application of the metamodel (surrogate FEM) to FEM updating were also discussed. Finally, the effectiveness of the proposed method was demonstrated by updating the FEM of a real arch bridge with the measured modal parameters. PMID:24634612

A hybrid anchored-ANOVA - POD/Kriging method for uncertainty quantification in unsteady high-fidelity CFD simulations

NASA Astrophysics Data System (ADS)

Margheri, Luca; Sagaut, Pierre

2016-11-01

To significantly increase the contribution of numerical computational fluid dynamics (CFD) simulation for risk assessment and decision making, it is important to quantitatively measure the impact of uncertainties to assess the reliability and robustness of the results. As unsteady high-fidelity CFD simulations are becoming the standard for industrial applications, reducing the number of required samples to perform sensitivity (SA) and uncertainty quantification (UQ) analysis is an actual engineering challenge. The novel approach presented in this paper is based on an efficient hybridization between the anchored-ANOVA and the POD/Kriging methods, which have already been used in CFD-UQ realistic applications, and the definition of best practices to achieve global accuracy. The anchored-ANOVA method is used to efficiently reduce the UQ dimension space, while the POD/Kriging is used to smooth and interpolate each anchored-ANOVA term. The main advantages of the proposed method are illustrated through four applications with increasing complexity, most of them based on Large-Eddy Simulation as a high-fidelity CFD tool: the turbulent channel flow, the flow around an isolated bluff-body, a pedestrian wind comfort study in a full scale urban area and an application to toxic gas dispersion in a full scale city area. The proposed c-APK method (anchored-ANOVA-POD/Kriging) inherits the advantages of each key element: interpolation through POD/Kriging precludes the use of quadrature schemes therefore allowing for a more flexible sampling strategy while the ANOVA decomposition allows for a better domain exploration. A comparison of the three methods is given for each application. In addition, the importance of adding flexibility to the control parameters and the choice of the quantity of interest (QoI) are discussed. As a result, global accuracy can be achieved with a reasonable number of samples allowing computationally expensive CFD-UQ analysis.

Near Real-time GNSS-based Ionospheric Model using Expanded Kriging in the East Asia Region

NASA Astrophysics Data System (ADS)

Choi, P. H.; Bang, E.; Lee, J.

2016-12-01

Many applications which utilize radio waves (e.g. navigation, communications, and radio sciences) are influenced by the ionosphere. The technology to provide global ionospheric maps (GIM) which show ionospheric Total Electron Content (TEC) has been progressed by processing GNSS data. However, the GIMs have limited spatial resolution (e.g. 2.5° in latitude and 5° in longitude), because they are generated using globally-distributed and thus relatively sparse GNSS reference station networks. This study presents a near real-time and high spatial resolution TEC model over East Asia by using ionospheric observables from both International GNSS Service (IGS) and local GNSS networks and the expanded kriging method. New signals from multi-constellation (e.g,, GPS L5, Galileo E5) were also used to generate high-precision TEC estimates. The newly proposed estimation method is based on the universal kriging interpolation technique, but integrates TEC data from previous epochs to those from the current epoch to improve the TEC estimation performance by increasing ionospheric observability. To propagate previous measurements to the current epoch, we implemented a Kalman filter whose dynamic model was derived by using the first-order Gauss-Markov process which characterizes temporal ionospheric changes under the nominal ionospheric conditions. Along with the TEC estimates at grids, the method generates the confidence bounds on the estimates using resulting estimation covariance. We also suggest to classify the confidence bounds into several categories to allow users to recognize the quality levels of TEC estimates according to the requirements for user's applications. This paper examines the performance of the proposed method by obtaining estimation results for both nominal and disturbed ionospheric conditions, and compares these results to those provided by GIM of the NASA Jet propulsion Laboratory. In addition, the estimation results based on the expanded kriging method are compared to the results from the universal kriging method for both nominal and disturbed ionospheric conditions.

Kriging - a challenge in geochemical mapping

NASA Astrophysics Data System (ADS)

Stojdl, Jiri; Matys Grygar, Tomas; Elznicova, Jitka; Popelka, Jan; Vachova, Tatina; Hosek, Michal

2017-04-01

Geochemists can easily provide datasets for contamination mapping thanks to recent advances in geographical information systems (GIS) and portable chemical-analytical instrumentation. Kriging is commonly used to visualise the results of such mapping. It is understandable, as kriging is a well-established method of spatial interpolation. It was created in 1950's for geochemical data processing to estimate the most likely distribution of gold based on samples from a few boreholes. However, kriging is based on the assumption of continuous spatial distribution of numeric data that is not realistic in environmental geochemistry. The use of kriging is correct when the data density is sufficient with respect to heterogeneity of the spatial distribution of the geochemical parameters. However, if anomalous geochemical values are focused in hotspots of which boundaries are insufficiently densely sampled, kriging could provide misleading maps with the real contours of hotspots blurred by data smoothing and levelling out individual (isolated) but relevant anomalous values. The data smoothing can thus it results in underestimation of geochemical extremes, which may in fact be of the greatest importance in mapping projects. In our study we characterised hotspots of contamination by uranium and zinc in the floodplain of the Ploučnice River. The first objective of our study was to compare three methods of sampling: random (based on stochastic generation of sampling points), systematic (square grid) and judgemental sampling (based on judgement stemming from principles of fluvial deposition) as the basis for pollution maps. The first detected problem in production of the maps was the reduction of the smoothing effect of kriging using appropriate function of empirical semivariogram and setting the variation of at microscales smaller than the sampling distances to minimum (the "nugget" parameter of semivariogram). Exact interpolators such as Inverse Distance Weighting (IDW) or Radial Basis Functions (RBF) provides better solutions in this respect. The second detected problem was heterogeneous structure of the floodplain: it consists of distinct sedimentary bodies (e.g., natural levees, meander scars, point bars), which have been formed by different process (erosion or deposition on flooding, channel shifts by meandering, channel abandonment). Interpolation through these sedimentary bodies has thus not much sense. Solution is to identify boundaries between sedimentary bodies and interpolation of data with this additional information using exact interpolators with barriers (IDW, RBF or stratified kriging) or regression kriging. Those boundaries can be identified using, e.g., digital elevation model (DEM), dipole electromagnetic profiling (DEMP), gamma spectrometry, or an expertise by a geomorphologist.

Application of universal kriging for prediction pollutant using GStat R

NASA Astrophysics Data System (ADS)

Nur Falah, Annisa; Subartini, Betty; Nurani Ruchjana, Budi

2017-10-01

In the universe, the air and water is a natural resource that is a very big function for living beings. The air is a gas mixture contained in a layer that surrounds the earth and the components of the gas mixture is not always constant. Also in river there is always a pollutant of chemistry concentration more than concentration limit. During the time a lot of air or water pollution caused by industrial waste, coal ash or chemistry pollution is an example of pollution that can pollute the environment and damage the health of humans. To solve this problem we need a method that is able to predict pollutant content in locations that are not observed. In geostatistics, we can use the universal kriging for prediction in a location that unobserved locations. Universal kriging is an interpolation method that has a tendency trend (drift) or a particular valuation method used to deal with non-stationary sample data. GStat R is a program based on open source R software that can be used to predict pollutant in a location that is not observed by the method of universal kriging. In this research, we predicted river pollutant content using trend (drift) equation of first order. GStat R application program in the prediction of river pollutants provides faster computation, more accurate, convenient and can be used as a recommendation for policy makers in the field of environment.

A GIS Tool for evaluating and improving NEXRAD and its application in distributed hydrologic modeling

NASA Astrophysics Data System (ADS)

Zhang, X.; Srinivasan, R.

2008-12-01

In this study, a user friendly GIS tool was developed for evaluating and improving NEXRAD using raingauge data. This GIS tool can automatically read in raingauge and NEXRAD data, evaluate the accuracy of NEXRAD for each time unit, implement several geostatistical methods to improve the accuracy of NEXRAD through raingauge data, and output spatial precipitation map for distributed hydrologic model. The geostatistical methods incorporated in this tool include Simple Kriging with varying local means, Kriging with External Drift, Regression Kriging, Co-Kriging, and a new geostatistical method that was newly developed by Li et al. (2008). This tool was applied in two test watersheds at hourly and daily temporal scale. The preliminary cross-validation results show that incorporating raingauge data to calibrate NEXRAD can pronouncedly change the spatial pattern of NEXRAD and improve its accuracy. Using different geostatistical methods, the GIS tool was applied to produce long term precipitation input for a distributed hydrologic model - Soil and Water Assessment Tool (SWAT). Animated video was generated to vividly illustrate the effect of using different precipitation input data on distributed hydrologic modeling. Currently, this GIS tool is developed as an extension of SWAT, which is used as water quantity and quality modeling tool by USDA and EPA. The flexible module based design of this tool also makes it easy to be adapted for other hydrologic models for hydrological modeling and water resources management.

Robust Design of Sheet Metal Forming Process Based on Kriging Metamodel

NASA Astrophysics Data System (ADS)

Xie, Yanmin

2011-08-01

Nowadays, sheet metal forming processes design is not a trivial task due to the complex issues to be taken into account (conflicting design goals, complex shapes forming and so on). Optimization methods have also been widely applied in sheet metal forming. Therefore, proper design methods to reduce time and costs have to be developed mostly based on computer aided procedures. At the same time, the existence of variations during manufacturing processes significantly may influence final product quality, rendering non-robust optimal solutions. In this paper, a small size of design of experiments is conducted to investigate how a stochastic behavior of noise factors affects drawing quality. The finite element software (LS_DYNA) is used to simulate the complex sheet metal stamping processes. The Kriging metamodel is adopted to map the relation between input process parameters and part quality. Robust design models for sheet metal forming process integrate adaptive importance sampling with Kriging model, in order to minimize impact of the variations and achieve reliable process parameters. In the adaptive sample, an improved criterion is used to provide direction in which additional training samples can be added to better the Kriging model. Nonlinear functions as test functions and a square stamping example (NUMISHEET'93) are employed to verify the proposed method. Final results indicate application feasibility of the aforesaid method proposed for multi-response robust design.

Advances in the regionalization approach: geostatistical techniques for estimating flood quantiles

NASA Astrophysics Data System (ADS)

Chiarello, Valentina; Caporali, Enrica; Matthies, Hermann G.

2015-04-01

The knowledge of peak flow discharges and associated floods is of primary importance in engineering practice for planning of water resources and risk assessment. Streamflow characteristics are usually estimated starting from measurements of river discharges at stream gauging stations. However, the lack of observations at site of interest as well as the measurement inaccuracies, bring inevitably to the necessity of developing predictive models. Regional analysis is a classical approach to estimate river flow characteristics at sites where little or no data exists. Specific techniques are needed to regionalize the hydrological variables over the considered area. Top-kriging or topological kriging, is a kriging interpolation procedure that takes into account the geometric organization and structure of hydrographic network, the catchment area and the nested nature of catchments. The continuous processes in space defined for the point variables are represented by a variogram. In Top-kriging, the measurements are not point values but are defined over a non-zero catchment area. Top-kriging is applied here over the geographical space of Tuscany Region, in Central Italy. The analysis is carried out on the discharge data of 57 consistent runoff gauges, recorded from 1923 to 2014. Top-kriging give also an estimation of the prediction uncertainty in addition to the prediction itself. The results are validated using a cross-validation procedure implemented in the package rtop of the open source statistical environment R The results are compared through different error measurement methods. Top-kriging seems to perform better in nested catchments and larger scale catchments but no for headwater or where there is a high variability for neighbouring catchments.

Combining area-based and individual-level data in the geostatistical mapping of late-stage cancer incidence.

PubMed

Goovaerts, Pierre

2009-01-01

This paper presents a geostatistical approach to incorporate individual-level data (e.g. patient residences) and area-based data (e.g. rates recorded at census tract level) into the mapping of late-stage cancer incidence, with an application to breast cancer in three Michigan counties. Spatial trends in cancer incidence are first estimated from census data using area-to-point binomial kriging. This prior model is then updated using indicator kriging and individual-level data. Simulation studies demonstrate the benefits of this two-step approach over methods (kernel density estimation and indicator kriging) that process only residence data.

Compensating for estimation smoothing in kriging

USGS Publications Warehouse

Olea, R.A.; Pawlowsky, Vera

1996-01-01

Smoothing is a characteristic inherent to all minimum mean-square-error spatial estimators such as kriging. Cross-validation can be used to detect and model such smoothing. Inversion of the model produces a new estimator-compensated kriging. A numerical comparison based on an exhaustive permeability sampling of a 4-fr2 slab of Berea Sandstone shows that the estimation surface generated by compensated kriging has properties intermediate between those generated by ordinary kriging and stochastic realizations resulting from simulated annealing and sequential Gaussian simulation. The frequency distribution is well reproduced by the compensated kriging surface, which also approximates the experimental semivariogram well - better than ordinary kriging, but not as well as stochastic realizations. Compensated kriging produces surfaces that are more accurate than stochastic realizations, but not as accurate as ordinary kriging. ?? 1996 International Association for Mathematical Geology.

Comparison Study on the Estimation of the Spatial Distribution of Regional Soil Metal(loid)s Pollution Based on Kriging Interpolation and BP Neural Network.

PubMed

Jia, Zhenyi; Zhou, Shenglu; Su, Quanlong; Yi, Haomin; Wang, Junxiao

2017-12-26

Soil pollution by metal(loid)s resulting from rapid economic development is a major concern. Accurately estimating the spatial distribution of soil metal(loid) pollution has great significance in preventing and controlling soil pollution. In this study, 126 topsoil samples were collected in Kunshan City and the geo-accumulation index was selected as a pollution index. We used Kriging interpolation and BP neural network methods to estimate the spatial distribution of arsenic (As) and cadmium (Cd) pollution in the study area. Additionally, we introduced a cross-validation method to measure the errors of the estimation results by the two interpolation methods and discussed the accuracy of the information contained in the estimation results. The conclusions are as follows: data distribution characteristics, spatial variability, and mean square errors (MSE) of the different methods showed large differences. Estimation results from BP neural network models have a higher accuracy, the MSE of As and Cd are 0.0661 and 0.1743, respectively. However, the interpolation results show significant skewed distribution, and spatial autocorrelation is strong. Using Kriging interpolation, the MSE of As and Cd are 0.0804 and 0.2983, respectively. The estimation results have poorer accuracy. Combining the two methods can improve the accuracy of the Kriging interpolation and more comprehensively represent the spatial distribution characteristics of metal(loid)s in regional soil. The study may provide a scientific basis and technical support for the regulation of soil metal(loid) pollution.

Optimisation d'un systeme d'antigivrage a air chaud pour aile d'avion basee sur la methode du krigeage dual

NASA Astrophysics Data System (ADS)

Hannat, Ridha

The aim of this thesis is to apply a new methodology of optimization based on the dual kriging method to a hot air anti-icing system for airplanes wings. The anti-icing system consists of a piccolo tube placed along the span of the wing, in the leading edge area. The hot air is injected through small nozzles and impact on the inner wall of the wing. The objective function targeted by the optimization is the effectiveness of the heat transfer of the anti-icing system. This heat transfer effectiveness is regarded as being the ratio of the wing inner wall heat flux and the sum of all the nozzles heat flows of the anti-icing system. The methodology adopted to optimize an anti-icing system consists of three steps. The first step is to build a database according to the Box-Behnken design of experiment. The objective function is then modeled by the dual kriging method and finally the SQP optimization method is applied. One of the advantages of the dual kriging is that the model passes exactly through all measurement points, but it can also take into account the numerical errors and deviates from these points. Moreover, the kriged model can be updated at each new numerical simulation. These features of the dual kriging seem to give a good tool to build the response surfaces necessary for the anti-icing system optimization. The first chapter presents a literature review and the optimization problem related to the antiicing system. Chapters two, three and four present the three articles submitted. Chapter two is devoted to the validation of CFD codes used to perform the numerical simulations of an anti-icing system and to compute the conjugate heat transfer (CHT). The CHT is calculated by taking into account the external flow around the airfoil, the internal flow in the anti-icing system, and the conduction in the wing. The heat transfer coefficient at the external skin of the airfoil is almost the same if the external flow is taken into account or no. Therefore, only the internal flow is considered in the following articles. Chapter three concerns the design of experiment (DoE) matrix and the construction of a second order parametric model. The objective function model is based on the Box-Behnken DoE. The parametric model that results from numerical simulations serve for comparison with the kriged model of the third article. Chapter four applies the dual kriging method to model the heat transfer effectiveness of the anti-icing system and use the model for optimization. The possibility of including the numerical error in the results is explored. For the test cases studied, introduction of the numerical error in the optimization process does not improve the results. Dual kriging method is also used to model the distribution of the local heat flux and to interpolate the local heat flux corresponding to the optimal design of the anti-icing system.

Exploring spatial patterns of sudden cardiac arrests in the city of Toronto using Poisson kriging and Hot Spot analyses.

PubMed

Przybysz, Raymond; Bunch, Martin

2017-01-01

Our study looked at out-of-hospital sudden cardiac arrest events in the City of Toronto. These are relatively rare events, yet present a serious global clinical and public health problem. We report on the application of spatial methods and tools that, although relatively well known to geographers and natural resource scientists, need to become better known and used more frequently by health care researchers. Our data came from the population-based Rescu Epistry cardiac arrest database. We limited it to the residents of the City of Toronto who experienced sudden arrest in 2010. The data was aggregated at the Dissemination Area level, and population rates were calculated. Poisson kriging was carried out on one year of data using three different spatial weights. Kriging estimates were then compared in Hot Spot analyses. Spatial analysis revealed that Poisson kriging can yield reliable rates using limited data of high quality. We observed the highest rates of sudden arrests in the north and central parts of Etobicoke, western parts of North York as well as the central and southwestern parts of Scarborough while the lowest rates were found in north and eastern parts of Scarborough, downtown Toronto, and East York as well as east central parts of North York. Influence of spatial neighbours on the results did not extend past two rings of adjacent units. Poisson kriging has the potential to be applied to a wide range of healthcare research, particularly on rare events. This approach can be successfully combined with other spatial methods. More applied research, is needed to establish a wider acceptance for this method, especially among healthcare researchers and epidemiologists.

A comparison of multiple indicator kriging and area-to-point Poisson kriging for mapping patterns of herbivore species abundance in Kruger National Park, South Africa

PubMed Central

Kerry, Ruth; Goovaerts, Pierre; Smit, Izak P.J.; Ingram, Ben R.

2015-01-01

Kruger National Park (KNP), South Africa, provides protected habitats for the unique animals of the African savannah. For the past 40 years, annual aerial surveys of herbivores have been conducted to aid management decisions based on (1) the spatial distribution of species throughout the park and (2) total species populations in a year. The surveys are extremely time consuming and costly. For many years, the whole park was surveyed, but in 1998 a transect survey approach was adopted. This is cheaper and less time consuming but leaves gaps in the data spatially. Also the distance method currently employed by the park only gives estimates of total species populations but not their spatial distribution. We compare the ability of multiple indicator kriging and area-to-point Poisson kriging to accurately map species distribution in the park. A leave-one-out cross-validation approach indicates that multiple indicator kriging makes poor estimates of the number of animals, particularly the few large counts, as the indicator variograms for such high thresholds are pure nugget. Poisson kriging was applied to the prediction of two types of abundance data: spatial density and proportion of a given species. Both Poisson approaches had standardized mean absolute errors (St. MAEs) of animal counts at least an order of magnitude lower than multiple indicator kriging. The spatial density, Poisson approach (1), gave the lowest St. MAEs for the most abundant species and the proportion, Poisson approach (2), did for the least abundant species. Incorporating environmental data into Poisson approach (2) further reduced St. MAEs. PMID:25729318

A comparison of multiple indicator kriging and area-to-point Poisson kriging for mapping patterns of herbivore species abundance in Kruger National Park, South Africa.

PubMed

Kerry, Ruth; Goovaerts, Pierre; Smit, Izak P J; Ingram, Ben R

Kruger National Park (KNP), South Africa, provides protected habitats for the unique animals of the African savannah. For the past 40 years, annual aerial surveys of herbivores have been conducted to aid management decisions based on (1) the spatial distribution of species throughout the park and (2) total species populations in a year. The surveys are extremely time consuming and costly. For many years, the whole park was surveyed, but in 1998 a transect survey approach was adopted. This is cheaper and less time consuming but leaves gaps in the data spatially. Also the distance method currently employed by the park only gives estimates of total species populations but not their spatial distribution. We compare the ability of multiple indicator kriging and area-to-point Poisson kriging to accurately map species distribution in the park. A leave-one-out cross-validation approach indicates that multiple indicator kriging makes poor estimates of the number of animals, particularly the few large counts, as the indicator variograms for such high thresholds are pure nugget. Poisson kriging was applied to the prediction of two types of abundance data: spatial density and proportion of a given species. Both Poisson approaches had standardized mean absolute errors (St. MAEs) of animal counts at least an order of magnitude lower than multiple indicator kriging. The spatial density, Poisson approach (1), gave the lowest St. MAEs for the most abundant species and the proportion, Poisson approach (2), did for the least abundant species. Incorporating environmental data into Poisson approach (2) further reduced St. MAEs.

Selection of a Geostatistical Method to Interpolate Soil Properties of the State Crop Testing Fields using Attributes of a Digital Terrain Model

NASA Astrophysics Data System (ADS)

Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.

2018-03-01

The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.

Airfoil Shape Optimization based on Surrogate Model

NASA Astrophysics Data System (ADS)

Mukesh, R.; Lingadurai, K.; Selvakumar, U.

2018-02-01

Engineering design problems always require enormous amount of real-time experiments and computational simulations in order to assess and ensure the design objectives of the problems subject to various constraints. In most of the cases, the computational resources and time required per simulation are large. In certain cases like sensitivity analysis, design optimisation etc where thousands and millions of simulations have to be carried out, it leads to have a life time of difficulty for designers. Nowadays approximation models, otherwise called as surrogate models (SM), are more widely employed in order to reduce the requirement of computational resources and time in analysing various engineering systems. Various approaches such as Kriging, neural networks, polynomials, Gaussian processes etc are used to construct the approximation models. The primary intention of this work is to employ the k-fold cross validation approach to study and evaluate the influence of various theoretical variogram models on the accuracy of the surrogate model construction. Ordinary Kriging and design of experiments (DOE) approaches are used to construct the SMs by approximating panel and viscous solution algorithms which are primarily used to solve the flow around airfoils and aircraft wings. The method of coupling the SMs with a suitable optimisation scheme to carryout an aerodynamic design optimisation process for airfoil shapes is also discussed.

in Mapping of Gastric Cancer Incidence in Iran

PubMed

Asmarian, Naeimehossadat; Jafari-Koshki, Tohid; Soleimani, Ali; Taghi Ayatollahi, Seyyed Mohammad

2016-10-01

Background: In many countries gastric cancer has the highest incidence among the gastrointestinal cancers and is the second most common cancer in Iran. The aim of this study was to identify and map high risk gastric cancer regions at the county-level in Iran. Methods: In this study we analyzed gastric cancer data for Iran in the years 2003-2010. Areato- area Poisson kriging and Besag, York and Mollie (BYM) spatial models were applied to smoothing the standardized incidence ratios of gastric cancer for the 373 counties surveyed in this study. The two methods were compared in term of accuracy and precision in identifying high risk regions. Result: The highest smoothed standardized incidence rate (SIR) according to area-to-area Poisson kriging was in Meshkinshahr county in Ardabil province in north-western Iran (2.4,SD=0.05), while the highest smoothed standardized incidence rate (SIR) according to the BYM model was in Ardabil, the capital of that province (2.9,SD=0.09). Conclusion: Both methods of mapping, ATA Poisson kriging and BYM, showed the gastric cancer incidence rate to be highest in north and north-west Iran. However, area-to-area Poisson kriging was more precise than the BYM model and required less smoothing. According to the results obtained, preventive measures and treatment programs should be focused on particular counties of Iran. Creative Commons Attribution License

An adaptive sampling method for variable-fidelity surrogate models using improved hierarchical kriging

NASA Astrophysics Data System (ADS)

Hu, Jiexiang; Zhou, Qi; Jiang, Ping; Shao, Xinyu; Xie, Tingli

2018-01-01

Variable-fidelity (VF) modelling methods have been widely used in complex engineering system design to mitigate the computational burden. Building a VF model generally includes two parts: design of experiments and metamodel construction. In this article, an adaptive sampling method based on improved hierarchical kriging (ASM-IHK) is proposed to refine the improved VF model. First, an improved hierarchical kriging model is developed as the metamodel, in which the low-fidelity model is varied through a polynomial response surface function to capture the characteristics of a high-fidelity model. Secondly, to reduce local approximation errors, an active learning strategy based on a sequential sampling method is introduced to make full use of the already required information on the current sampling points and to guide the sampling process of the high-fidelity model. Finally, two numerical examples and the modelling of the aerodynamic coefficient for an aircraft are provided to demonstrate the approximation capability of the proposed approach, as well as three other metamodelling methods and two sequential sampling methods. The results show that ASM-IHK provides a more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.

Comparison Study on the Estimation of the Spatial Distribution of Regional Soil Metal(loid)s Pollution Based on Kriging Interpolation and BP Neural Network

PubMed Central

Zhou, Shenglu; Su, Quanlong; Yi, Haomin

2017-01-01

Soil pollution by metal(loid)s resulting from rapid economic development is a major concern. Accurately estimating the spatial distribution of soil metal(loid) pollution has great significance in preventing and controlling soil pollution. In this study, 126 topsoil samples were collected in Kunshan City and the geo-accumulation index was selected as a pollution index. We used Kriging interpolation and BP neural network methods to estimate the spatial distribution of arsenic (As) and cadmium (Cd) pollution in the study area. Additionally, we introduced a cross-validation method to measure the errors of the estimation results by the two interpolation methods and discussed the accuracy of the information contained in the estimation results. The conclusions are as follows: data distribution characteristics, spatial variability, and mean square errors (MSE) of the different methods showed large differences. Estimation results from BP neural network models have a higher accuracy, the MSE of As and Cd are 0.0661 and 0.1743, respectively. However, the interpolation results show significant skewed distribution, and spatial autocorrelation is strong. Using Kriging interpolation, the MSE of As and Cd are 0.0804 and 0.2983, respectively. The estimation results have poorer accuracy. Combining the two methods can improve the accuracy of the Kriging interpolation and more comprehensively represent the spatial distribution characteristics of metal(loid)s in regional soil. The study may provide a scientific basis and technical support for the regulation of soil metal(loid) pollution. PMID:29278363

Comparison of the accuracy of kriging and IDW interpolations in estimating groundwater arsenic concentrations in Texas.

PubMed

Gong, Gordon; Mattevada, Sravan; O'Bryant, Sid E

2014-04-01

Exposure to arsenic causes many diseases. Most Americans in rural areas use groundwater for drinking, which may contain arsenic above the currently allowable level, 10µg/L. It is cost-effective to estimate groundwater arsenic levels based on data from wells with known arsenic concentrations. We compared the accuracy of several commonly used interpolation methods in estimating arsenic concentrations in >8000 wells in Texas by the leave-one-out-cross-validation technique. Correlation coefficient between measured and estimated arsenic levels was greater with inverse distance weighted (IDW) than kriging Gaussian, kriging spherical or cokriging interpolations when analyzing data from wells in the entire Texas (p<0.0001). Correlation coefficient was significantly lower with cokriging than any other methods (p<0.006) for wells in Texas, east Texas or the Edwards aquifer. Correlation coefficient was significantly greater for wells in southwestern Texas Panhandle than in east Texas, and was higher for wells in Ogallala aquifer than in Edwards aquifer (p<0.0001) regardless of interpolation methods. In regression analysis, the best models are when well depth and/or elevation were entered into the model as covariates regardless of area/aquifer or interpolation methods, and models with IDW are better than kriging in any area/aquifer. In conclusion, the accuracy in estimating groundwater arsenic level depends on both interpolation methods and wells' geographic distributions and characteristics in Texas. Taking well depth and elevation into regression analysis as covariates significantly increases the accuracy in estimating groundwater arsenic level in Texas with IDW in particular. Published by Elsevier Inc.

Imprecise (fuzzy) information in geostatistics

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

Bardossy, A.; Bogardi, I.; Kelly, W.E.

1988-05-01

A methodology based on fuzzy set theory for the utilization of imprecise data in geostatistics is presented. A common problem preventing a broader use of geostatistics has been the insufficient amount of accurate measurement data. In certain cases, additional but uncertain (soft) information is available and can be encoded as subjective probabilities, and then the soft kriging method can be applied (Journal, 1986). In other cases, a fuzzy encoding of soft information may be more realistic and simplify the numerical calculations. Imprecise (fuzzy) spatial information on the possible variogram is integrated into a single variogram which is used in amore » fuzzy kriging procedure. The overall uncertainty of prediction is represented by the estimation variance and the calculated membership function for each kriged point. The methodology is applied to the permeability prediction of a soil liner for hazardous waste containment. The available number of hard measurement data (20) was not enough for a classical geostatistical analysis. An additional 20 soft data made it possible to prepare kriged contour maps using the fuzzy geostatistical procedure.« less

Mapping the Daily Progression of Large Wildland Fires Using MODIS Active Fire Data

NASA Technical Reports Server (NTRS)

Veraverbeke, Sander; Sedano, Fernando; Hook, Simon J.; Randerson, James T.; Jin, Yufang; Rogers, Brendan

2013-01-01

High temporal resolution information on burned area is a prerequisite for incorporating bottom-up estimates of wildland fire emissions in regional air transport models and for improving models of fire behavior. We used the Moderate Resolution Imaging Spectroradiometer (MODIS) active fire product (MO(Y)D14) as input to a kriging interpolation to derive continuous maps of the evolution of nine large wildland fires. For each fire, local input parameters for the kriging model were defined using variogram analysis. The accuracy of the kriging model was assessed using high resolution daily fire perimeter data available from the U.S. Forest Service. We also assessed the temporal reporting accuracy of the MODIS burned area products (MCD45A1 and MCD64A1). Averaged over the nine fires, the kriging method correctly mapped 73% of the pixels within the accuracy of a single day, compared to 33% for MCD45A1 and 53% for MCD64A1.

Design and Implementation WebGIS for Improving the Quality of Exploration Decisions at Sin-Quyen Copper Mine, Northern Vietnam

NASA Astrophysics Data System (ADS)

Quang Truong, Xuan; Luan Truong, Xuan; Nguyen, Tuan Anh; Nguyen, Dinh Tuan; Cong Nguyen, Chi

2017-12-01

The objective of this study is to design and implement a WebGIS Decision Support System (WDSS) for reducing uncertainty and supporting to improve the quality of exploration decisions in the Sin-Quyen copper mine, northern Vietnam. The main distinctive feature of the Sin-Quyen deposit is an unusual composition of ores. Computer and software applied to the exploration problem have had a significant impact on the exploration process over the past 25 years, but up until now, no online system has been undertaken. The system was completely built on open source technology and the Open Geospatial Consortium Web Services (OWS). The input data includes remote sensing (RS), Geographical Information System (GIS) and data from drillhole explorations, the drillhole exploration data sets were designed as a geodatabase and stored in PostgreSQL. The WDSS must be able to processed exploration data and support users to access 2-dimensional (2D) or 3-dimensional (3D) cross-sections and map of boreholles exploration data and drill holes. The interface was designed in order to interact with based maps (e.g., Digital Elevation Model, Google Map, OpenStreetMap) and thematic maps (e.g., land use and land cover, administrative map, drillholes exploration map), and to provide GIS functions (such as creating a new map, updating an existing map, querying and statistical charts). In addition, the system provides geological cross-sections of ore bodies based on Inverse Distance Weighting (IDW), nearest neighbour interpolation and Kriging methods (e.g., Simple Kriging, Ordinary Kriging, Indicator Kriging and CoKriging). The results based on data available indicate that the best estimation method (of 23 borehole exploration data sets) for estimating geological cross-sections of ore bodies in Sin-Quyen copper mine is Ordinary Kriging. The WDSS could provide useful information to improve drilling efficiency in mineral exploration and for management decision making.

Surrogate models for efficient stability analysis of brake systems

NASA Astrophysics Data System (ADS)

Nechak, Lyes; Gillot, Frédéric; Besset, Sébastien; Sinou, Jean-Jacques

2015-07-01

This study assesses capacities of the global sensitivity analysis combined together with the kriging formalism to be useful in the robust stability analysis of brake systems, which is too costly when performed with the classical complex eigenvalues analysis (CEA) based on finite element models (FEMs). By considering a simplified brake system, the global sensitivity analysis is first shown very helpful for understanding the effects of design parameters on the brake system's stability. This is allowed by the so-called Sobol indices which discriminate design parameters with respect to their influence on the stability. Consequently, only uncertainty of influent parameters is taken into account in the following step, namely, the surrogate modelling based on kriging. The latter is then demonstrated to be an interesting alternative to FEMs since it allowed, with a lower cost, an accurate estimation of the system's proportions of instability corresponding to the influent parameters.

An approach for land suitability evaluation using geostatistics, remote sensing, and geographic information system in arid and semiarid ecosystems.

PubMed

Emadi, Mostafa; Baghernejad, Majid; Pakparvar, Mojtaba; Kowsar, Sayyed Ahang

2010-05-01

This study was undertaken to incorporate geostatistics, remote sensing, and geographic information system (GIS) technologies to improve the qualitative land suitability assessment in arid and semiarid ecosystems of Arsanjan plain, southern Iran. The primary data were obtained from 85 soil samples collected from tree depths (0-30, 30-60, and 60-90 cm); the secondary information was acquired from the remotely sensed data from the linear imaging self-scanner (LISS-III) receiver of the IRS-P6 satellite. Ordinary kriging and simple kriging with varying local means (SKVLM) methods were used to identify the spatial dependency of soil important parameters. It was observed that using the data collected from the spectral values of band 1 of the LISS-III receiver as the secondary variable applying the SKVLM method resulted in the lowest mean square error for mapping the pH and electrical conductivity (ECe) in the 0-30-cm depth. On the other hand, the ordinary kriging method resulted in a reliable accuracy for the other soil properties with moderate to strong spatial dependency in the study area for interpolation in the unstamped points. The parametric land suitability evaluation method was applied on the density points (150 x 150 m(2)) instead of applying on the limited representative profiles conventionally, which were obtained by the kriging or SKVLM methods. Overlaying the information layers of the data was used with the GIS for preparing the final land suitability evaluation. Therefore, changes in land characteristics could be identified in the same soil uniform mapping units over a very short distance. In general, this new method can easily present the squares and limitation factors of the different land suitability classes with considerable accuracy in arbitrary land indices.

[Using sequential indicator simulation method to define risk areas of soil heavy metals in farmland.

PubMed

Yang, Hao; Song, Ying Qiang; Hu, Yue Ming; Chen, Fei Xiang; Zhang, Rui

2018-05-01

The heavy metals in soil have serious impacts on safety, ecological environment and human health due to their toxicity and accumulation. It is necessary to efficiently identify the risk area of heavy metals in farmland soil, which is of important significance for environment protection, pollution warning and farmland risk control. We collected 204 samples and analyzed the contents of seven kinds of heavy metals (Cu, Zn, Pb, Cd, Cr, As, Hg) in Zengcheng District of Guangzhou, China. In order to overcame the problems of the data, including the limitation of abnormal values and skewness distribution and the smooth effect with the traditional kriging methods, we used sequential indicator simulation method (SISIM) to define the spatial distribution of heavy metals, and combined Hakanson index method to identify potential ecological risk area of heavy metals in farmland. The results showed that: (1) Based on the similar accuracy of spatial prediction of soil heavy metals, the SISIM had a better expression of detail rebuild than ordinary kriging in small scale area. Compared to indicator kriging, the SISIM had less error rate (4.9%-17.1%) in uncertainty evaluation of heavy-metal risk identification. The SISIM had less smooth effect and was more applicable to simulate the spatial uncertainty assessment of soil heavy metals and risk identification. (2) There was no pollution in Zengcheng's farmland. Moderate potential ecological risk was found in the southern part of study area due to enterprise production, human activities, and river sediments. This study combined the sequential indicator simulation with Hakanson risk index method, and effectively overcame the outlier information loss and smooth effect of traditional kriging method. It provided a new way to identify the soil heavy metal risk area of farmland in uneven sampling.

Use of Principal Components Analysis and Kriging to Predict Groundwater-Sourced Rural Drinking Water Quality in Saskatchewan

PubMed Central

McLeod, Lianne; Bharadwaj, Lalita; Epp, Tasha; Waldner, Cheryl L.

2017-01-01

Groundwater drinking water supply surveillance data were accessed to summarize water quality delivered as public and private water supplies in southern Saskatchewan as part of an exposure assessment for epidemiologic analyses of associations between water quality and type 2 diabetes or cardiovascular disease. Arsenic in drinking water has been linked to a variety of chronic diseases and previous studies have identified multiple wells with arsenic above the drinking water standard of 0.01 mg/L; therefore, arsenic concentrations were of specific interest. Principal components analysis was applied to obtain principal component (PC) scores to summarize mixtures of correlated parameters identified as health standards and those identified as aesthetic objectives in the Saskatchewan Drinking Water Quality Standards and Objective. Ordinary, universal, and empirical Bayesian kriging were used to interpolate arsenic concentrations and PC scores in southern Saskatchewan, and the results were compared. Empirical Bayesian kriging performed best across all analyses, based on having the greatest number of variables for which the root mean square error was lowest. While all of the kriging methods appeared to underestimate high values of arsenic and PC scores, empirical Bayesian kriging was chosen to summarize large scale geographic trends in groundwater-sourced drinking water quality and assess exposure to mixtures of trace metals and ions. PMID:28914824

Use of Principal Components Analysis and Kriging to Predict Groundwater-Sourced Rural Drinking Water Quality in Saskatchewan.

PubMed

McLeod, Lianne; Bharadwaj, Lalita; Epp, Tasha; Waldner, Cheryl L

2017-09-15

Groundwater drinking water supply surveillance data were accessed to summarize water quality delivered as public and private water supplies in southern Saskatchewan as part of an exposure assessment for epidemiologic analyses of associations between water quality and type 2 diabetes or cardiovascular disease. Arsenic in drinking water has been linked to a variety of chronic diseases and previous studies have identified multiple wells with arsenic above the drinking water standard of 0.01 mg/L; therefore, arsenic concentrations were of specific interest. Principal components analysis was applied to obtain principal component (PC) scores to summarize mixtures of correlated parameters identified as health standards and those identified as aesthetic objectives in the Saskatchewan Drinking Water Quality Standards and Objective. Ordinary, universal, and empirical Bayesian kriging were used to interpolate arsenic concentrations and PC scores in southern Saskatchewan, and the results were compared. Empirical Bayesian kriging performed best across all analyses, based on having the greatest number of variables for which the root mean square error was lowest. While all of the kriging methods appeared to underestimate high values of arsenic and PC scores, empirical Bayesian kriging was chosen to summarize large scale geographic trends in groundwater-sourced drinking water quality and assess exposure to mixtures of trace metals and ions.

Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, northwest China.

PubMed

Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong

2016-01-01

Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

Kriging in the Shadows: Geostatistical Interpolation for Remote Sensing

NASA Technical Reports Server (NTRS)

Rossi, Richard E.; Dungan, Jennifer L.; Beck, Louisa R.

1994-01-01

It is often useful to estimate obscured or missing remotely sensed data. Traditional interpolation methods, such as nearest-neighbor or bilinear resampling, do not take full advantage of the spatial information in the image. An alternative method, a geostatistical technique known as indicator kriging, is described and demonstrated using a Landsat Thematic Mapper image in southern Chiapas, Mexico. The image was first classified into pasture and nonpasture land cover. For each pixel that was obscured by cloud or cloud shadow, the probability that it was pasture was assigned by the algorithm. An exponential omnidirectional variogram model was used to characterize the spatial continuity of the image for use in the kriging algorithm. Assuming a cutoff probability level of 50%, the error was shown to be 17% with no obvious spatial bias but with some tendency to categorize nonpasture as pasture (overestimation). While this is a promising result, the method's practical application in other missing data problems for remotely sensed images will depend on the amount and spatial pattern of the unobscured pixels and missing pixels and the success of the spatial continuity model used.

Geostatistical noise filtering of geophysical images : application to unexploded ordnance (UXO) sites.

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

Saito, Hirotaka; McKenna, Sean Andrew; Coburn, Timothy C.

2004-07-01

Geostatistical and non-geostatistical noise filtering methodologies, factorial kriging and a low-pass filter, and a region growing method are applied to analytic signal magnetometer images at two UXO contaminated sites to delineate UXO target areas. Overall delineation performance is improved by removing background noise. Factorial kriging slightly outperforms the low-pass filter but there is no distinct difference between them in terms of finding anomalies of interest.

Spatiotemporal Modeling of Ozone Levels in Quebec (Canada): A Comparison of Kriging, Land-Use Regression (LUR), and Combined Bayesian Maximum Entropy–LUR Approaches

PubMed Central

Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael

2014-01-01

Background: Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. Objectives: We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. Methods: We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. Results: The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Conclusions: Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data. Citation: Adam-Poupart A, Brand A, Fournier M, Jerrett M, Smargiassi A. 2014. Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy–LUR approaches. Environ Health Perspect 122:970–976; http://dx.doi.org/10.1289/ehp.1306566 PMID:24879650

Spatial distribution of soil organic carbon and total nitrogen based on GIS and geostatistics in a small watershed in a hilly area of northern China.

PubMed

Peng, Gao; Bing, Wang; Guangpo, Geng; Guangcan, Zhang

2013-01-01

The spatial variability of soil organic carbon (SOC) and total nitrogen (STN) levels is important in both global carbon-nitrogen cycle and climate change research. There has been little research on the spatial distribution of SOC and STN at the watershed scale based on geographic information systems (GIS) and geostatistics. Ninety-seven soil samples taken at depths of 0-20 cm were collected during October 2010 and 2011 from the Matiyu small watershed (4.2 km(2)) of a hilly area in Shandong Province, northern China. The impacts of different land use types, elevation, vegetation coverage and other factors on SOC and STN spatial distributions were examined using GIS and a geostatistical method, regression-kriging. The results show that the concentration variations of SOC and STN in the Matiyu small watershed were moderate variation based on the mean, median, minimum and maximum, and the coefficients of variation (CV). Residual values of SOC and STN had moderate spatial autocorrelations, and the Nugget/Sill were 0.2% and 0.1%, respectively. Distribution maps of regression-kriging revealed that both SOC and STN concentrations in the Matiyu watershed decreased from southeast to northwest. This result was similar to the watershed DEM trend and significantly correlated with land use type, elevation and aspect. SOC and STN predictions with the regression-kriging method were more accurate than those obtained using ordinary kriging. This research indicates that geostatistical characteristics of SOC and STN concentrations in the watershed were closely related to both land-use type and spatial topographic structure and that regression-kriging is suitable for investigating the spatial distributions of SOC and STN in the complex topography of the watershed.

Spatial Distribution of Soil Organic Carbon and Total Nitrogen Based on GIS and Geostatistics in a Small Watershed in a Hilly Area of Northern China

PubMed Central

Peng, Gao; Bing, Wang; Guangpo, Geng; Guangcan, Zhang

2013-01-01

The spatial variability of soil organic carbon (SOC) and total nitrogen (STN) levels is important in both global carbon-nitrogen cycle and climate change research. There has been little research on the spatial distribution of SOC and STN at the watershed scale based on geographic information systems (GIS) and geostatistics. Ninety-seven soil samples taken at depths of 0–20 cm were collected during October 2010 and 2011 from the Matiyu small watershed (4.2 km2) of a hilly area in Shandong Province, northern China. The impacts of different land use types, elevation, vegetation coverage and other factors on SOC and STN spatial distributions were examined using GIS and a geostatistical method, regression-kriging. The results show that the concentration variations of SOC and STN in the Matiyu small watershed were moderate variation based on the mean, median, minimum and maximum, and the coefficients of variation (CV). Residual values of SOC and STN had moderate spatial autocorrelations, and the Nugget/Sill were 0.2% and 0.1%, respectively. Distribution maps of regression-kriging revealed that both SOC and STN concentrations in the Matiyu watershed decreased from southeast to northwest. This result was similar to the watershed DEM trend and significantly correlated with land use type, elevation and aspect. SOC and STN predictions with the regression-kriging method were more accurate than those obtained using ordinary kriging. This research indicates that geostatistical characteristics of SOC and STN concentrations in the watershed were closely related to both land-use type and spatial topographic structure and that regression-kriging is suitable for investigating the spatial distributions of SOC and STN in the complex topography of the watershed. PMID:24391791

Prediction of DHF disease spreading patterns using inverse distances weighted (IDW), ordinary and universal kriging

NASA Astrophysics Data System (ADS)

Prasetiyowati, S. S.; Sibaroni, Y.

2018-03-01

Dengue hemorrhagic disease, is a disease caused by the Dengue virus of the Flavivirus genus Flaviviridae family. Indonesia is the country with the highest case of dengue in Southeast Asia. In addition to mosquitoes as vectors and humans as hosts, other environmental and social factors are also the cause of widespread dengue fever. To prevent the occurrence of the epidemic of the disease, fast and accurate action is required. Rapid and accurate action can be taken, if there is appropriate information support on the occurrence of the epidemic. Therefore, a complete and accurate information on the spread pattern of endemic areas is necessary, so that precautions can be done as early as possible. The information on dispersal patterns can be obtained by various methods, which are based on empirical and theoretical considerations. One of the methods used is based on the estimated number of infected patients in a region based on spatial and time. The first step of this research is conducted by predicting the number of DHF patients in 2016 until 2018 based on 2010 to 2015 data using GSTAR (1, 1). In the second phase, the distribution pattern prediction of dengue disease area is conducted. Furthermore, based on the characteristics of DHF epidemic trends, i.e. down, stable or rising, the analysis of distribution patterns of dengue fever distribution areas with IDW and Kriging (ordinary and universal Kriging) were conducted in this study. The difference between IDW and Kriging, is the initial process that underlies the prediction process. Based on the experimental results, it is known that the dispersion pattern of epidemic areas of dengue disease with IDW and Ordinary Kriging is similar in the period of time.

Calibration of DEM parameters on shear test experiments using Kriging method

NASA Astrophysics Data System (ADS)

Bednarek, Xavier; Martin, Sylvain; Ndiaye, Abibatou; Peres, Véronique; Bonnefoy, Olivier

2017-06-01

Calibration of powder mixing simulation using Discrete-Element-Method is still an issue. Achieving good agreement with experimental results is difficult because time-efficient use of DEM involves strong assumptions. This work presents a methodology to calibrate DEM parameters using Efficient Global Optimization (EGO) algorithm based on Kriging interpolation method. Classical shear test experiments are used as calibration experiments. The calibration is made on two parameters - Young modulus and friction coefficient. The determination of the minimal number of grains that has to be used is a critical step. Simulations of a too small amount of grains would indeed not represent the realistic behavior of powder when using huge amout of grains will be strongly time consuming. The optimization goal is the minimization of the objective function which is the distance between simulated and measured behaviors. The EGO algorithm uses the maximization of the Expected Improvement criterion to find next point that has to be simulated. This stochastic criterion handles with the two interpolations made by the Kriging method : prediction of the objective function and estimation of the error made. It is thus able to quantify the improvement in the minimization that new simulations at specified DEM parameters would lead to.

Multi-Objective Aerodynamic Optimization of the Streamlined Shape of High-Speed Trains Based on the Kriging Model.

PubMed

Xu, Gang; Liang, Xifeng; Yao, Shuanbao; Chen, Dawei; Li, Zhiwei

2017-01-01

Minimizing the aerodynamic drag and the lift of the train coach remains a key issue for high-speed trains. With the development of computing technology and computational fluid dynamics (CFD) in the engineering field, CFD has been successfully applied to the design process of high-speed trains. However, developing a new streamlined shape for high-speed trains with excellent aerodynamic performance requires huge computational costs. Furthermore, relationships between multiple design variables and the aerodynamic loads are seldom obtained. In the present study, the Kriging surrogate model is used to perform a multi-objective optimization of the streamlined shape of high-speed trains, where the drag and the lift of the train coach are the optimization objectives. To improve the prediction accuracy of the Kriging model, the cross-validation method is used to construct the optimal Kriging model. The optimization results show that the two objectives are efficiently optimized, indicating that the optimization strategy used in the present study can greatly improve the optimization efficiency and meet the engineering requirements.

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2011-05-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.

Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

NASA Astrophysics Data System (ADS)

Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

2010-09-01

Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation period. It is found that both methods yield merged fields of better quality than the original radar field or fields obtained by OK of gauge data. The newly suggested KED formulation is shown to be beneficial, in particular in mountainous regions where the quality of the Swiss radar composite is comparatively low. An analysis of the Kriging variances shows that none of the methods tested here provides a satisfactory uncertainty estimate. A suitable variable transformation is expected to improve this.

Geostatistics for spatial genetic structures: study of wild populations of perennial ryegrass.

PubMed

Monestiez, P; Goulard, M; Charmet, G

1994-04-01

Methods based on geostatistics were applied to quantitative traits of agricultural interest measured on a collection of 547 wild populations of perennial ryegrass in France. The mathematical background of these methods, which resembles spatial autocorrelation analysis, is briefly described. When a single variable is studied, the spatial structure analysis is similar to spatial autocorrelation analysis, and a spatial prediction method, called "kriging", gives a filtered map of the spatial pattern over all the sampled area. When complex interactions of agronomic traits with different evaluation sites define a multivariate structure for the spatial analysis, geostatistical methods allow the spatial variations to be broken down into two main spatial structures with ranges of 120 km and 300 km, respectively. The predicted maps that corresponded to each range were interpreted as a result of the isolation-by-distance model and as a consequence of selection by environmental factors. Practical collecting methodology for breeders may be derived from such spatial structures.

Transfer Learning to Accelerate Interface Structure Searches

NASA Astrophysics Data System (ADS)

Oda, Hiromi; Kiyohara, Shin; Tsuda, Koji; Mizoguchi, Teruyasu

2017-12-01

Interfaces have atomic structures that are significantly different from those in the bulk, and play crucial roles in material properties. The central structures at the interfaces that provide properties have been extensively investigated. However, determination of even one interface structure requires searching for the stable configuration among many thousands of candidates. Here, a powerful combination of machine learning techniques based on kriging and transfer learning (TL) is proposed as a method for unveiling the interface structures. Using the kriging+TL method, thirty-three grain boundaries were systematically determined from 1,650,660 candidates in only 462 calculations, representing an increase in efficiency over conventional all-candidate calculation methods, by a factor of approximately 3,600.

An interpolation method for stream habitat assessments

USGS Publications Warehouse

Sheehan, Kenneth R.; Welsh, Stuart A.

2015-01-01

Interpolation of stream habitat can be very useful for habitat assessment. Using a small number of habitat samples to predict the habitat of larger areas can reduce time and labor costs as long as it provides accurate estimates of habitat. The spatial correlation of stream habitat variables such as substrate and depth improves the accuracy of interpolated data. Several geographical information system interpolation methods (natural neighbor, inverse distance weighted, ordinary kriging, spline, and universal kriging) were used to predict substrate and depth within a 210.7-m2 section of a second-order stream based on 2.5% and 5.0% sampling of the total area. Depth and substrate were recorded for the entire study site and compared with the interpolated values to determine the accuracy of the predictions. In all instances, the 5% interpolations were more accurate for both depth and substrate than the 2.5% interpolations, which achieved accuracies up to 95% and 92%, respectively. Interpolations of depth based on 2.5% sampling attained accuracies of 49–92%, whereas those based on 5% percent sampling attained accuracies of 57–95%. Natural neighbor interpolation was more accurate than that using the inverse distance weighted, ordinary kriging, spline, and universal kriging approaches. Our findings demonstrate the effective use of minimal amounts of small-scale data for the interpolation of habitat over large areas of a stream channel. Use of this method will provide time and cost savings in the assessment of large sections of rivers as well as functional maps to aid the habitat-based management of aquatic species.

A comparison of different interpolation methods for wind data in Central Asia

NASA Astrophysics Data System (ADS)

Reinhardt, Katja; Samimi, Cyrus

2017-04-01

For the assessment of the global climate change and its consequences, the results of computer based climate models are of central importance. The quality of these results and the validity of the derived forecasts are strongly determined by the quality of the underlying climate data. However, in many parts of the world high resolution data are not available. This is particularly true for many regions in Central Asia, where the density of climatological stations has often to be described as thinned out. Due to this insufficient data base the use of statistical methods to improve the resolution of existing climate data is of crucial importance. Only this can provide a substantial data base for a well-founded analysis of past climate changes as well as for a reliable forecast of future climate developments for the particular region. The study presented here shows a comparison of different interpolation methods for the wind components u and v for a region in Central Asia with a pronounced topography. The aim of the study is to find out whether there is an optimal interpolation method which can equally be applied for all pressure levels or if different interpolation methods have to be applied for each pressure level. The European reanalysis data Era-Interim for the years 1989 - 2015 are used as input data for the pressure levels of 850 hPa, 500 hPa and 200 hPa. In order to improve the input data, two different interpolation procedures were applied: On the one hand pure interpolation methods were used, such as inverse distance weighting and ordinary kriging. On the other hand machine learning algorithms, generalized additive models and regression kriging were applied, considering additional influencing factors, e.g. geopotential and topography. As a result it can be concluded that regression kriging provides the best results for all pressure levels, followed by support vector machine, neural networks and ordinary kriging. Inverse distance weighting showed the worst results.

Ordinary kriging as a tool to estimate historical daily streamflow records

USGS Publications Warehouse

Farmer, William H.

2016-01-01

Efficient and responsible management of water resources relies on accurate streamflow records. However, many watersheds are ungaged, limiting the ability to assess and understand local hydrology. Several tools have been developed to alleviate this data scarcity, but few provide continuous daily streamflow records at individual streamgages within an entire region. Building on the history of hydrologic mapping, ordinary kriging was extended to predict daily streamflow time series on a regional basis. Pooling parameters to estimate a single, time-invariant characterization of spatial semivariance structure is shown to produce accurate reproduction of streamflow. This approach is contrasted with a time-varying series of variograms, representing the temporal evolution and behavior of the spatial semivariance structure. Furthermore, the ordinary kriging approach is shown to produce more accurate time series than more common, single-index hydrologic transfers. A comparison between topological kriging and ordinary kriging is less definitive, showing the ordinary kriging approach to be significantly inferior in terms of Nash–Sutcliffe model efficiencies while maintaining significantly superior performance measured by root mean squared errors. Given the similarity of performance and the computational efficiency of ordinary kriging, it is concluded that ordinary kriging is useful for first-order approximation of daily streamflow time series in ungaged watersheds.

Kriging analysis of mean annual precipitation, Powder River Basin, Montana and Wyoming

USGS Publications Warehouse

Karlinger, M.R.; Skrivan, James A.

1981-01-01

Kriging is a statistical estimation technique for regionalized variables which exhibit an autocorrelation structure. Such structure can be described by a semi-variogram of the observed data. The kriging estimate at any point is a weighted average of the data, where the weights are determined using the semi-variogram and an assumed drift, or lack of drift, in the data. Block, or areal, estimates can also be calculated. The kriging algorithm, based on unbiased and minimum-variance estimates, involves a linear system of equations to calculate the weights. Kriging variances can then be used to give confidence intervals of the resulting estimates. Mean annual precipitation in the Powder River basin, Montana and Wyoming, is an important variable when considering restoration of coal-strip-mining lands of the region. Two kriging analyses involving data at 60 stations were made--one assuming no drift in precipitation, and one a partial quadratic drift simulating orographic effects. Contour maps of estimates of mean annual precipitation were similar for both analyses, as were the corresponding contours of kriging variances. Block estimates of mean annual precipitation were made for two subbasins. Runoff estimates were 1-2 percent of the kriged block estimates. (USGS)

[Spatial interpolation of soil organic matter using regression Kriging and geographically weighted regression Kriging].

PubMed

Yang, Shun-hua; Zhang, Hai-tao; Guo, Long; Ren, Yan

2015-06-01

Relative elevation and stream power index were selected as auxiliary variables based on correlation analysis for mapping soil organic matter. Geographically weighted regression Kriging (GWRK) and regression Kriging (RK) were used for spatial interpolation of soil organic matter and compared with ordinary Kriging (OK), which acts as a control. The results indicated that soil or- ganic matter was significantly positively correlated with relative elevation whilst it had a significantly negative correlation with stream power index. Semivariance analysis showed that both soil organic matter content and its residuals (including ordinary least square regression residual and GWR resi- dual) had strong spatial autocorrelation. Interpolation accuracies by different methods were esti- mated based on a data set of 98 validation samples. Results showed that the mean error (ME), mean absolute error (MAE) and root mean square error (RMSE) of RK were respectively 39.2%, 17.7% and 20.6% lower than the corresponding values of OK, with a relative-improvement (RI) of 20.63. GWRK showed a similar tendency, having its ME, MAE and RMSE to be respectively 60.6%, 23.7% and 27.6% lower than those of OK, with a RI of 59.79. Therefore, both RK and GWRK significantly improved the accuracy of OK interpolation of soil organic matter due to their in- corporation of auxiliary variables. In addition, GWRK performed obviously better than RK did in this study, and its improved performance should be attributed to the consideration of sample spatial locations.

Combining natural background levels (NBLs) assessment with indicator kriging analysis to improve groundwater quality data interpretation and management.

PubMed

Ducci, Daniela; de Melo, M Teresa Condesso; Preziosi, Elisabetta; Sellerino, Mariangela; Parrone, Daniele; Ribeiro, Luis

2016-11-01

The natural background level (NBL) concept is revisited and combined with indicator kriging method to analyze the spatial distribution of groundwater quality within a groundwater body (GWB). The aim is to provide a methodology to easily identify areas with the same probability of exceeding a given threshold (which may be a groundwater quality criteria, standards, or recommended limits for selected properties and constituents). Three case studies with different hydrogeological settings and located in two countries (Portugal and Italy) are used to derive NBL using the preselection method and validate the proposed methodology illustrating its main advantages over conventional statistical water quality analysis. Indicator kriging analysis was used to create probability maps of the three potential groundwater contaminants. The results clearly indicate the areas within a groundwater body that are potentially contaminated because the concentrations exceed the drinking water standards or even the local NBL, and cannot be justified by geogenic origin. The combined methodology developed facilitates the management of groundwater quality because it allows for the spatial interpretation of NBL values. Copyright © 2016 Elsevier B.V. All rights reserved.

Using IKONOS Imagery to Estimate Surface Soil Property Variability in Two Alabama Physiographies

NASA Technical Reports Server (NTRS)

Sullivan, Dana; Shaw, Joey; Rickman, Doug

2005-01-01

Knowledge of surface soil properties is used to assess past erosion and predict erodibility, determine nutrient requirements, and assess surface texture for soil survey applications. This study was designed to evaluate high resolution IKONOS multispectral data as a soil- mapping tool. Imagery was acquired over conventionally tilled fields in the Coastal Plain and Tennessee Valley physiographic regions of Alabama. Acquisitions were designed to assess the impact of surface crusting, roughness and tillage on our ability to depict soil property variability. Soils consisted mostly of fine-loamy, kaolinitic, thermic Plinthic Kandiudults at the Coastal Plain site and fine, kaolinitic, thermic Rhodic Paleudults at the Tennessee Valley site. Soils were sampled in 0.20 ha grids to a depth of 15 cm and analyzed for % sand (0.05 - 2 mm), silt (0.002 -0.05 mm), clay (less than 0.002 mm), citrate dithionite extractable iron (Fe(sub d)) and soil organic carbon (SOC). Four methods of evaluating variability in soil attributes were evaluated: 1) kriging of soil attributes, 2) co-kriging with soil attributes and reflectance data, 3) multivariate regression based on the relationship between reflectance and soil properties, and 4) fuzzy c-means clustering of reflectance data. Results indicate that co-kriging with remotely sensed data improved field scale estimates of surface SOC and clay content compared to kriging and regression methods. Fuzzy c-means worked best using RS data acquired over freshly tilled fields, reducing soil property variability within soil zones compared to field scale soil property variability.

Constrained optimization by radial basis function interpolation for high-dimensional expensive black-box problems with infeasible initial points

NASA Astrophysics Data System (ADS)

Regis, Rommel G.

2014-02-01

This article develops two new algorithms for constrained expensive black-box optimization that use radial basis function surrogates for the objective and constraint functions. These algorithms are called COBRA and Extended ConstrLMSRBF and, unlike previous surrogate-based approaches, they can be used for high-dimensional problems where all initial points are infeasible. They both follow a two-phase approach where the first phase finds a feasible point while the second phase improves this feasible point. COBRA and Extended ConstrLMSRBF are compared with alternative methods on 20 test problems and on the MOPTA08 benchmark automotive problem (D.R. Jones, Presented at MOPTA 2008), which has 124 decision variables and 68 black-box inequality constraints. The alternatives include a sequential penalty derivative-free algorithm, a direct search method with kriging surrogates, and two multistart methods. Numerical results show that COBRA algorithms are competitive with Extended ConstrLMSRBF and they generally outperform the alternatives on the MOPTA08 problem and most of the test problems.

A comparison of interpolation methods for predicting spatial variability of soil organic matter content in Eastern Croatia

NASA Astrophysics Data System (ADS)

Đurđević, Boris; Jug, Irena; Jug, Danijel; Vukadinović, Vesna; Bogunović, Igor; Brozović, Bojana; Stipešević, Bojan

2017-04-01

Soil organic matter (SOM) plays crucial role in soil health and productivity and represents one of the key functions for determining soil degradation and soil suitability for crop production. Nowadays, continuing decline of organic matter in soils in agroecosystems, due to inappropriate agricultural practice (burning and removal of crop residue, overgrazing, inappropriate tillage, etc.) and environmental conditions (climate change, extreme weather conditions, erosion) leads to devastating soil degradation processes and decreases soil productivity. The main objectives of this research is to compare three different interpolation methods (Inverse Distance Weighting IDW, Ordinary kriging OK and Empirical Bayesian Kriging EBK) and provide best spatial predictor in order to ensure detailed analysis of the agricultural land in Osijek-Baranja County, Croatia. A number of 9,099 soil samples have been compiled from layer 0-30 cm and analyzed in laboratory. The average value of SOM in the study area was 2.66%, while 70.7 % of samples had SOM value below 3% in Osijek-Baranja County. Among the applied methods, the lowest root mean square error was recorded under Empirical Bayesian Kriging method which had most accurately assessed soil organic matter. The main advantage of EBK is that the process of creating a valid kriging model is automated so the manual parameter adjusting is eliminated, and this resulted with reduced uncertainty of EBK model. Conducted interpolation and visualization of data showed that 85.7% of agricultural land in Osijek-Baranja County has SOM content lower than 3%, which may indicate some sort of soil degradation process. By using interpolation methods combined with visualization of data, we can detect problematic areas much easier and with additional analysis, suggest measures to repair degraded soils. This kind of approach to problem solving in agriculture can be applied on various agroecological conditions and can significantly facilitate and accelerate the decision-making process, and thus directly affect the profitability and sustainability of agricultural production.

Estimation of river pollution index in a tidal stream using kriging analysis.

PubMed

Chen, Yen-Chang; Yeh, Hui-Chung; Wei, Chiang

2012-08-29

Tidal streams are complex watercourses that represent a transitional zone between riverine and marine systems; they occur where fresh and marine waters converge. Because tidal circulation processes cause substantial turbulence in these highly dynamic zones, tidal streams are the most productive of water bodies. Their rich biological diversity, combined with the convenience of land and water transports, provide sites for concentrated populations that evolve into large cities. Domestic wastewater is generally discharged directly into tidal streams in Taiwan, necessitating regular evaluation of the water quality of these streams. Given the complex flow dynamics of tidal streams, only a few models can effectively evaluate and identify pollution levels. This study evaluates the river pollution index (RPI) in tidal streams by using kriging analysis. This is a geostatistical method for interpolating random spatial variation to estimate linear grid points in two or three dimensions. A kriging-based method is developed to evaluate RPI in tidal streams, which is typically considered as 1D in hydraulic engineering. The proposed method efficiently evaluates RPI in tidal streams with the minimum amount of water quality data. Data of the Tanshui River downstream reach available from an estuarine area validate the accuracy and reliability of the proposed method. Results of this study demonstrate that this simple yet reliable method can effectively estimate RPI in tidal streams.

Grundwasserfließgeschehen Mecklenburg-Vorpommerns - Geohydraulische Modellierung mit Detrended Kriging

NASA Astrophysics Data System (ADS)

Hilgert, Toralf; Hennig, Heiko

2017-03-01

Groundwater heads were mapped for the entire State of Mecklenburg-Western Pomerania by applying a Detrended Kriging method based on a numerical geohydraulic model. The general groundwater flow system (trend surface) was represented by a two-dimensional horizontal flow model. Thus deviations of observed groundwater heads from simulated groundwater heads are no longer subject to a regional trend and can be interpolated by means of Ordinary Kriging. Subsequently, the groundwater heads were obtained from the sum of the simulated trend surface and interpolated residuals. Furthermore, the described procedure allowed a plausibility check of observed groundwater heads by comparing them to results of the hydraulic model. If significant deviations were seen, the observation wells could be allocated to different aquifers. The final results are two hydraulically established groundwater head distributions - one for the regional main aquifer and one for the upper aquifer which may differ locally from the main aquifer.

Spatial analysis of groundwater levels using Fuzzy Logic and geostatistical tools

NASA Astrophysics Data System (ADS)

Theodoridou, P. G.; Varouchakis, E. A.; Karatzas, G. P.

2017-12-01

The spatial variability evaluation of the water table of an aquifer provides useful information in water resources management plans. Geostatistical methods are often employed to map the free surface of an aquifer. In geostatistical analysis using Kriging techniques the selection of the optimal variogram is very important for the optimal method performance. This work compares three different criteria to assess the theoretical variogram that fits to the experimental one: the Least Squares Sum method, the Akaike Information Criterion and the Cressie's Indicator. Moreover, variable distance metrics such as the Euclidean, Minkowski, Manhattan, Canberra and Bray-Curtis are applied to calculate the distance between the observation and the prediction points, that affects both the variogram calculation and the Kriging estimator. A Fuzzy Logic System is then applied to define the appropriate neighbors for each estimation point used in the Kriging algorithm. The two criteria used during the Fuzzy Logic process are the distance between observation and estimation points and the groundwater level value at each observation point. The proposed techniques are applied to a data set of 250 hydraulic head measurements distributed over an alluvial aquifer. The analysis showed that the Power-law variogram model and Manhattan distance metric within ordinary kriging provide the best results when the comprehensive geostatistical analysis process is applied. On the other hand, the Fuzzy Logic approach leads to a Gaussian variogram model and significantly improves the estimation performance. The two different variogram models can be explained in terms of a fractional Brownian motion approach and of aquifer behavior at local scale. Finally, maps of hydraulic head spatial variability and of predictions uncertainty are constructed for the area with the two different approaches comparing their advantages and drawbacks.

Ensemble learning for spatial interpolation of soil potassium content based on environmental information.

PubMed

Liu, Wei; Du, Peijun; Wang, Dongchen

2015-01-01

One important method to obtain the continuous surfaces of soil properties from point samples is spatial interpolation. In this paper, we propose a method that combines ensemble learning with ancillary environmental information for improved interpolation of soil properties (hereafter, EL-SP). First, we calculated the trend value for soil potassium contents at the Qinghai Lake region in China based on measured values. Then, based on soil types, geology types, land use types, and slope data, the remaining residual was simulated with the ensemble learning model. Next, the EL-SP method was applied to interpolate soil potassium contents at the study site. To evaluate the utility of the EL-SP method, we compared its performance with other interpolation methods including universal kriging, inverse distance weighting, ordinary kriging, and ordinary kriging combined geographic information. Results show that EL-SP had a lower mean absolute error and root mean square error than the data produced by the other models tested in this paper. Notably, the EL-SP maps can describe more locally detailed information and more accurate spatial patterns for soil potassium content than the other methods because of the combined use of different types of environmental information; these maps are capable of showing abrupt boundary information for soil potassium content. Furthermore, the EL-SP method not only reduces prediction errors, but it also compliments other environmental information, which makes the spatial interpolation of soil potassium content more reasonable and useful.

A modified multi-objective particle swarm optimization approach and its application to the design of a deepwater composite riser

NASA Astrophysics Data System (ADS)

Zheng, Y.; Chen, J.

2017-09-01

A modified multi-objective particle swarm optimization method is proposed for obtaining Pareto-optimal solutions effectively. Different from traditional multi-objective particle swarm optimization methods, Kriging meta-models and the trapezoid index are introduced and integrated with the traditional one. Kriging meta-models are built to match expensive or black-box functions. By applying Kriging meta-models, function evaluation numbers are decreased and the boundary Pareto-optimal solutions are identified rapidly. For bi-objective optimization problems, the trapezoid index is calculated as the sum of the trapezoid's area formed by the Pareto-optimal solutions and one objective axis. It can serve as a measure whether the Pareto-optimal solutions converge to the Pareto front. Illustrative examples indicate that to obtain Pareto-optimal solutions, the method proposed needs fewer function evaluations than the traditional multi-objective particle swarm optimization method and the non-dominated sorting genetic algorithm II method, and both the accuracy and the computational efficiency are improved. The proposed method is also applied to the design of a deepwater composite riser example in which the structural performances are calculated by numerical analysis. The design aim was to enhance the tension strength and minimize the cost. Under the buckling constraint, the optimal trade-off of tensile strength and material volume is obtained. The results demonstrated that the proposed method can effectively deal with multi-objective optimizations with black-box functions.

A regression-kriging model for estimation of rainfall in the Laohahe basin

NASA Astrophysics Data System (ADS)

Wang, Hong; Ren, Li L.; Liu, Gao H.

2009-10-01

This paper presents a multivariate geostatistical algorithm called regression-kriging (RK) for predicting the spatial distribution of rainfall by incorporating five topographic/geographic factors of latitude, longitude, altitude, slope and aspect. The technique is illustrated using rainfall data collected at 52 rain gauges from the Laohahe basis in northeast China during 1986-2005 . Rainfall data from 44 stations were selected for modeling and the remaining 8 stations were used for model validation. To eliminate multicollinearity, the five explanatory factors were first transformed using factor analysis with three Principal Components (PCs) extracted. The rainfall data were then fitted using step-wise regression and residuals interpolated using SK. The regression coefficients were estimated by generalized least squares (GLS), which takes the spatial heteroskedasticity between rainfall and PCs into account. Finally, the rainfall prediction based on RK was compared with that predicted from ordinary kriging (OK) and ordinary least squares (OLS) multiple regression (MR). For correlated topographic factors are taken into account, RK improves the efficiency of predictions. RK achieved a lower relative root mean square error (RMSE) (44.67%) than MR (49.23%) and OK (73.60%) and a lower bias than MR and OK (23.82 versus 30.89 and 32.15 mm) for annual rainfall. It is much more effective for the wet season than for the dry season. RK is suitable for estimation of rainfall in areas where there are no stations nearby and where topography has a major influence on rainfall.

An EGO-like optimization framework for sensor placement optimization in modal analysis

NASA Astrophysics Data System (ADS)

Morlier, Joseph; Basile, Aniello; Chiplunkar, Ankit; Charlotte, Miguel

2018-07-01

In aircraft design, ground/flight vibration tests are conducted to extract aircraft’s modal parameters (natural frequencies, damping ratios and mode shapes) also known as the modal basis. The main problem in aircraft modal identification is the large number of sensors needed, which increases operational time and costs. The goal of this paper is to minimize the number of sensors by optimizing their locations in order to reconstruct a truncated modal basis of N mode shapes with a high level of accuracy in the reconstruction. There are several methods to solve sensors placement optimization (SPO) problems, but for this case an original approach has been established based on an iterative process for mode shapes reconstruction through an adaptive Kriging metamodeling approach so called efficient global optimization (EGO)-SPO. The main idea in this publication is to solve an optimization problem where the sensors locations are variables and the objective function is defined by maximizing the trace of criteria so called AutoMAC. The results on a 2D wing demonstrate a reduction of sensors by 30% using our EGO-SPO strategy.

Interpolations of groundwater table elevation in dissected uplands.

PubMed

Chung, Jae-won; Rogers, J David

2012-01-01

The variable elevation of the groundwater table in the St. Louis area was estimated using multiple linear regression (MLR), ordinary kriging, and cokriging as part of a regional program seeking to assess liquefaction potential. Surface water features were used to determine the minimum water table for MLR and supplement the principal variables for ordinary kriging and cokriging. By evaluating the known depth to the water and the minimum water table elevation, the MLR analysis approximates the groundwater elevation for a contiguous hydrologic system. Ordinary kriging and cokriging estimate values in unsampled areas by calculating the spatial relationships between the unsampled and sampled locations. In this study, ordinary kriging did not incorporate topographic variations as an independent variable, while cokriging included topography as a supporting covariable. Cross validation suggests that cokriging provides a more reliable estimate at known data points with less uncertainty than the other methods. Profiles extending through the dissected uplands terrain suggest that: (1) the groundwater table generated by MLR mimics the ground surface and elicits a exaggerated interpolation of groundwater elevation; (2) the groundwater table estimated by ordinary kriging tends to ignore local topography and exhibits oversmoothing of the actual undulations in the water table; and (3) cokriging appears to give the realistic water surface, which rises and falls in proportion to the overlying topography. The authors concluded that cokriging provided the most realistic estimate of the groundwater surface, which is the key variable in assessing soil liquefaction potential in unconsolidated sediments. © 2011, The Author(s). Ground Water © 2011, National Ground Water Association.

A Residual Kriging method for the reconstruction of 3D high-resolution meteorological fields from airborne and surface observations

NASA Astrophysics Data System (ADS)

Laiti, Lavinia; Zardi, Dino; de Franceschi, Massimiliano; Rampanelli, Gabriele

2013-04-01

Manned light aircrafts and remotely piloted aircrafts represent very valuable and flexible measurement platforms for atmospheric research, as they are able to provide high temporal and spatial resolution observations of the atmosphere above the ground surface. In the present study the application of a geostatistical interpolation technique called Residual Kriging (RK) is proposed for the mapping of airborne measurements of scalar quantities over regularly spaced 3D grids. In RK the dominant (vertical) trend component underlying the original data is first extracted to filter out local anomalies, then the residual field is separately interpolated and finally added back to the trend; the determination of the interpolation weights relies on the estimate of the characteristic covariance function of the residuals, through the computation and modelling of their semivariogram function. RK implementation also allows for the inference of the characteristic spatial scales of variability of the target field and its isotropization, and for an estimate of the interpolation error. The adopted test-bed database consists in a series of flights of an instrumented motorglider exploring the atmosphere of two valleys near the city of Trento (in the southeastern Italian Alps), performed on fair-weather summer days. RK method is used to reconstruct fully 3D high-resolution fields of potential temperature and mixing ratio for specific vertical slices of the valley atmosphere, integrating also ground-based measurements from the nearest surface weather stations. From RK-interpolated meteorological fields, fine-scale features of the atmospheric boundary layer developing over the complex valley topography in connection with the occurrence of thermally-driven slope and valley winds, are detected. The performance of RK mapping is also tested against two other commonly adopted interpolation methods, i.e. the Inverse Distance Weighting and the Delaunay triangulation methods, comparing the results of a cross-validation procedure.

Assessment and Optimization of the Accuracy of an Aircraft-Based Technique Used to Quantify Greenhouse Gas Emission Rates from Point Sources

NASA Astrophysics Data System (ADS)

Shepson, P. B.; Lavoie, T. N.; Kerlo, A. E.; Stirm, B. H.

2016-12-01

Understanding the contribution of anthropogenic activities to atmospheric greenhouse gas concentrations requires an accurate characterization of emission sources. Previously, we have reported the use of a novel aircraft-based mass balance measurement technique to quantify greenhouse gas emission rates from point and area sources, however, the accuracy of this approach has not been evaluated to date. Here, an assessment of method accuracy and precision was performed by conducting a series of six aircraft-based mass balance experiments at a power plant in southern Indiana and comparing the calculated CO2 emission rates to the reported hourly emission measurements made by continuous emissions monitoring systems (CEMS) installed directly in the exhaust stacks at the facility. For all flights, CO2 emissions were quantified before CEMS data were released online to ensure unbiased analysis. Additionally, we assess the uncertainties introduced to the final emission rate caused by our analysis method, which employs a statistical kriging model to interpolate and extrapolate the CO2 fluxes across the flight transects from the ground to the top of the boundary layer. Subsequently, using the results from these flights combined with the known emissions reported by the CEMS, we perform an inter-model comparison of alternative kriging methods to evaluate the performance of the kriging approach.

Accurate prediction of polarised high order electrostatic interactions for hydrogen bonded complexes using the machine learning method kriging.

PubMed

Hughes, Timothy J; Kandathil, Shaun M; Popelier, Paul L A

2015-02-05

As intermolecular interactions such as the hydrogen bond are electrostatic in origin, rigorous treatment of this term within force field methodologies should be mandatory. We present a method able of accurately reproducing such interactions for seven van der Waals complexes. It uses atomic multipole moments up to hexadecupole moment mapped to the positions of the nuclear coordinates by the machine learning method kriging. Models were built at three levels of theory: HF/6-31G(**), B3LYP/aug-cc-pVDZ and M06-2X/aug-cc-pVDZ. The quality of the kriging models was measured by their ability to predict the electrostatic interaction energy between atoms in external test examples for which the true energies are known. At all levels of theory, >90% of test cases for small van der Waals complexes were predicted within 1 kJ mol(-1), decreasing to 60-70% of test cases for larger base pair complexes. Models built on moments obtained at B3LYP and M06-2X level generally outperformed those at HF level. For all systems the individual interactions were predicted with a mean unsigned error of less than 1 kJ mol(-1). Copyright © 2013 Elsevier B.V. All rights reserved.

Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization.

PubMed

Del Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, Patrícia

2015-04-01

In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Matèrn models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

Arsenic-Safe Aquifers in Coastal Bangladesh: AN Investigation with Ordinary Kriging Estimation

NASA Astrophysics Data System (ADS)

Hassan, M. M.; Ahamed, R.

2017-10-01

Spatial point pattern is one of the most suitable methods for analysing groundwater arsenic concentrations. Groundwater arsenic poisoning in Bangladesh has been one of the biggest environmental health disasters in recent times. About 85 million people are exposed to arsenic more than 50 μg/L in drinking water. The paper seeks to identify the existing suitable aquifers for arsenic-safe drinking water along with "spatial arsenic discontinuity" using GIS-based spatial geostatistical analysis in a small study site (12.69 km2) in the coastal belt of southwest Bangladesh (Dhopakhali union of Bagerhat district). The relevant spatial data were collected with Geographical Positioning Systems (GPS), arsenic data with field testing kits, tubewell attributes with observation and questionnaire survey. Geostatistics with kriging methods can design water quality monitoring in different aquifers with hydrochemical evaluation by spatial mapping. The paper presents the interpolation of the regional estimates of arsenic data for spatial discontinuity mapping with Ordinary Kriging (OK) method that overcomes the areal bias problem for administrative boundary. This paper also demonstrates the suitability of isopleth maps that is easier to read than choropleth maps. The OK method investigated that around 80 percent of the study site are contaminated following the Bangladesh Drinking Water Standards (BDWS) of 50 μg/L. The study identified a very few scattered "pockets" of arsenic-safe zone at the shallow aquifer.

[Downscaling research of spatial distribution of incidence of hand foot and mouth disease based on area-to-area Poisson Kriging method].

PubMed

Wang, J X; Hu, M G; Yu, S C; Xiao, G X

2017-09-10

Objective: To understand the spatial distribution of incidence of hand foot and mouth disease (HFMD) at scale of township and provide evidence for the better prevention and control of HFMD and allocation of medical resources. Methods: The incidence data of HFMD in 108 counties (district) in Shandong province in 2010 were collected. Downscaling interpolation was conducted by using area-to-area Poisson Kriging method. The interpolation results were visualized by using geographic information system (GIS). The county (district) incidence was interpolated into township incidence to get the distribution of spatial distribution of incidence of township. Results: In the downscaling interpolation, the range of the fitting semi-variance equation was 20.38 km. Within the range, the incidence had correlation with each other. The fitting function of scatter diagram of estimated and actual incidence of HFMD at country level was y =1.053 1 x , R (2)=0.99. The incidences at different scale were consistent. Conclusions: The incidence of HFMD had spatial autocorrelation within 20.38 km. When HFMD occurs in one place, it is necessary to strengthen the surveillance and allocation of medical resource in the surrounding area within 20.38 km. Area to area Poisson Kriging method based downscaling research can be used in spatial visualization of HFMD incidence.

[Kriging analysis of vegetation index depression in peak cluster karst area].

PubMed

Yang, Qi-Yong; Jiang, Zhong-Cheng; Ma, Zu-Lu; Cao, Jian-Hua; Luo, Wei-Qun; Li, Wen-Jun; Duan, Xiao-Fang

2012-04-01

In order to master the spatial variability of the normal different vegetation index (NDVI) of the peak cluster karst area, taking into account the problem of the mountain shadow "missing" information of remote sensing images existing in the karst area, NDVI of the non-shaded area were extracted in Guohua Ecological Experimental Area, in Pingguo County, Guangxi applying image processing software, ENVI. The spatial variability of NDVI was analyzed applying geostatistical method, and the NDVI of the mountain shadow areas was predicted and validated. The results indicated that the NDVI of the study area showed strong spatial variability and spatial autocorrelation resulting from the impact of intrinsic factors, and the range was 300 m. The spatial distribution maps of the NDVI interpolated by Kriging interpolation method showed that the mean of NDVI was 0.196, apparently strip and block. The higher NDVI values distributed in the area where the slope was greater than 25 degrees of the peak cluster area, while the lower values distributed in the area such as foot of the peak cluster and depression, where slope was less than 25 degrees. Kriging method validation results show that interpolation has a very high prediction accuracy and could predict the NDVI of the shadow area, which provides a new idea and method for monitoring and evaluation of the karst rocky desertification.

Spatial epidemiology of bovine tuberculosis in Mexico.

PubMed

Martínez, Horacio Zendejas; Suazo, Feliciano Milián; Cuador Gil, José Quintín; Bello, Gustavo Cruz; Anaya Escalera, Ana María; Márquez, Gabriel Huitrón; Casanova, Leticia García

2007-01-01

The purpose of this study was to use geographic information systems (GIS) and geo-statistical methods of ordinary kriging to predict the prevalence and distribution of bovine tuberculosis (TB) in Jalisco, Mexico. A random sample of 2 287 herds selected from a set of 48 766 was used for the analysis. Spatial location of herds was obtained by either a personal global positioning system (GPS), a database from the Instituto Nacional de Estadìstica Geografìa e Informàtica (INEGI) or Google Earth. Information on TB prevalence was provided by the Jalisco Commission for the Control and Eradication of Tuberculosis (COEETB). Prediction of TB was obtained using ordinary kriging in the geostatistical analyst module in ArcView8. A predicted high prevalence area of TB matching the distribution of dairy cattle was observed. This prediction was in agreement with the prevalence calculated on the total 48 766 herds. Validation was performed taking estimated values of TB prevalence at each municipality, extracted from the kriging surface and then compared with the real prevalence values using a correlation test, giving a value of 0.78, indicating that GIS and kriging are reliable tools for the estimation of TB distribution based on a random sample. This resulted in a significant savings of resources.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

NASA Astrophysics Data System (ADS)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

Spatiotemporal modeling of ozone levels in Quebec (Canada): a comparison of kriging, land-use regression (LUR), and combined Bayesian maximum entropy-LUR approaches.

PubMed

Adam-Poupart, Ariane; Brand, Allan; Fournier, Michel; Jerrett, Michael; Smargiassi, Audrey

2014-09-01

Ambient air ozone (O3) is a pulmonary irritant that has been associated with respiratory health effects including increased lung inflammation and permeability, airway hyperreactivity, respiratory symptoms, and decreased lung function. Estimation of O3 exposure is a complex task because the pollutant exhibits complex spatiotemporal patterns. To refine the quality of exposure estimation, various spatiotemporal methods have been developed worldwide. We sought to compare the accuracy of three spatiotemporal models to predict summer ground-level O3 in Quebec, Canada. We developed a land-use mixed-effects regression (LUR) model based on readily available data (air quality and meteorological monitoring data, road networks information, latitude), a Bayesian maximum entropy (BME) model incorporating both O3 monitoring station data and the land-use mixed model outputs (BME-LUR), and a kriging method model based only on available O3 monitoring station data (BME kriging). We performed leave-one-station-out cross-validation and visually assessed the predictive capability of each model by examining the mean temporal and spatial distributions of the average estimated errors. The BME-LUR was the best predictive model (R2 = 0.653) with the lowest root mean-square error (RMSE ;7.06 ppb), followed by the LUR model (R2 = 0.466, RMSE = 8.747) and the BME kriging model (R2 = 0.414, RMSE = 9.164). Our findings suggest that errors of estimation in the interpolation of O3 concentrations with BME can be greatly reduced by incorporating outputs from a LUR model developed with readily available data.

Prediction of soil attributes through interpolators in a deglaciated environment with complex landforms

NASA Astrophysics Data System (ADS)

Schünemann, Adriano Luis; Inácio Fernandes Filho, Elpídio; Rocha Francelino, Marcio; Rodrigues Santos, Gérson; Thomazini, Andre; Batista Pereira, Antônio; Gonçalves Reynaud Schaefer, Carlos Ernesto

2017-04-01

The knowledge of environmental variables values, in non-sampled sites from a minimum data set can be accessed through interpolation technique. Kriging and the classifier Random Forest algorithm are examples of predictors with this aim. The objective of this work was to compare methods of soil attributes spatialization in a recent deglaciated environment with complex landforms. Prediction of the selected soil attributes (potassium, calcium and magnesium) from ice-free areas were tested by using morphometric covariables, and geostatistical models without these covariables. For this, 106 soil samples were collected at 0-10 cm depth in Keller Peninsula, King George Island, Maritime Antarctica. Soil chemical analysis was performed by the gravimetric method, determining values of potassium, calcium and magnesium for each sampled point. Digital terrain models (DTMs) were obtained by using Terrestrial Laser Scanner. DTMs were generated from a cloud of points with spatial resolutions of 1, 5, 10, 20 and 30 m. Hence, 40 morphometric covariates were generated. Simple Kriging was performed using the R package software. The same data set coupled with morphometric covariates, was used to predict values of the studied attributes in non-sampled sites through Random Forest interpolator. Little differences were observed on the DTMs generated by Simple kriging and Random Forest interpolators. Also, DTMs with better spatial resolution did not improved the quality of soil attributes prediction. Results revealed that Simple Kriging can be used as interpolator when morphometric covariates are not available, with little impact regarding quality. It is necessary to go further in soil chemical attributes prediction techniques, especially in periglacial areas with complex landforms.

Stream Kriging: Incremental and recursive ordinary Kriging over spatiotemporal data streams

NASA Astrophysics Data System (ADS)

Zhong, Xu; Kealy, Allison; Duckham, Matt

2016-05-01

Ordinary Kriging is widely used for geospatial interpolation and estimation. Due to the O (n3) time complexity of solving the system of linear equations, ordinary Kriging for a large set of source points is computationally intensive. Conducting real-time Kriging interpolation over continuously varying spatiotemporal data streams can therefore be especially challenging. This paper develops and tests two new strategies for improving the performance of an ordinary Kriging interpolator adapted to a stream-processing environment. These strategies rely on the expectation that, over time, source data points will frequently refer to the same spatial locations (for example, where static sensor nodes are generating repeated observations of a dynamic field). First, an incremental strategy improves efficiency in cases where a relatively small proportion of previously processed spatial locations are absent from the source points at any given iteration. Second, a recursive strategy improves efficiency in cases where there is substantial set overlap between the sets of spatial locations of source points at the current and previous iterations. These two strategies are evaluated in terms of their computational efficiency in comparison to ordinary Kriging algorithm. The results show that these two strategies can reduce the time taken to perform the interpolation by up to 90%, and approach average-case time complexity of O (n2) when most but not all source points refer to the same locations over time. By combining the approaches developed in this paper with existing heuristic ordinary Kriging algorithms, the conclusions indicate how further efficiency gains could potentially be accrued. The work ultimately contributes to the development of online ordinary Kriging interpolation algorithms, capable of real-time spatial interpolation with large streaming data sets.

Spatial probability of soil water repellency in an abandoned agricultural field in Lithuania

NASA Astrophysics Data System (ADS)

Pereira, Paulo; Misiūnė, Ieva

2015-04-01

Water repellency is a natural soil property with implications on infiltration, erosion and plant growth. It depends on soil texture, type and amount of organic matter, fungi, microorganisms, and vegetation cover (Doerr et al., 2000). Human activities as agriculture can have implications on soil water repellency (SWR) due tillage and addition of organic compounds and fertilizers (Blanco-Canqui and Lal, 2009; Gonzalez-Penaloza et al., 2012). It is also assumed that SWR has a high small-scale variability (Doerr et al., 2000). The aim of this work is to study the spatial probability of SWR in an abandoned field testing several geostatistical methods, Organic Kriging (OK), Simple Kriging (SK), Indicator Kriging (IK), Probability Kriging (PK) and Disjunctive Kriging (DK). The study area it is located near Vilnius urban area at (54 49' N, 25 22', 104 masl) in Lithuania (Pereira and Oliva, 2013). It was designed a experimental plot with 21 m2 (07x03 m). Inside this area it was measured SWR was measured every 50 cm using the water drop penetration time (WDPT) (Wessel, 1998). A total of 105 points were measured. The probability of SWR was classified in 0 (No probability) to 1 (High probability). The methods accuracy was assessed with the cross validation method. The best interpolation method was the one with the lowest Root Mean Square Error (RMSE). The results showed that the most accurate probability method was SK (RMSE=0.436), followed by DK (RMSE=0.437), IK (RMSE=0.448), PK (RMSE=0.452) and OK (RMSE=0.537). Significant differences were identified among probability tests (Kruskal-Wallis test =199.7597 p<0.001). On average the probability of SWR was high with the OK (0.58±0.08) followed by PK (0.49±0.18), SK (0.32±0.16), DK (0.32±0.15) and IK (0.31±0.16). The most accurate probability methods predicted a lower probability of SWR in the studied plot. The spatial distribution of SWR was different according to the tested technique. Simple Kriging, DK, IK and PK methods identified the high SWR probabilities in the northeast and central part of the plot, while OK observed mainly in the south-western part of the plot. In conclusion, before predict the spatial probability of SWR it is important to test several methods in order to identify the most accurate. Acknowledgments COST action ES1306 (Connecting European connectivity research). References Blanco-Canqui, H., Lal, R. (2009) Extend of water repellency under long-term no-till soils. Geoderma, 149, 171-180. Doerr, S.H., Shakesby, R.A., Walsh, R.P.D. (2000) Soil water repellency: Its causes, characteristics and hydro-geomorphological significance. Earth-Science Reviews, 51, 33-65. Gonzalez-Penaloza, F.A., Cerda, A., Zavala, L.M., Jordan, A., Gimenez-Morera, A., Arcenegui, V. (2012) Do conservative agriculture practices increase soil water repellency? A case study in citrus-croped soils. Soil and Tillage Research, 124, 233-239. Pereira, P., Oliva, M. (2013) Modelling soil water repellency in an abandoned agricultural field, Visnyk Geology, Visnyk Geology 4, 77-80. Wessel, A.T. (1988) On using the effective contact angle and the water drop penetration time for classification of water repellency in dune soils. Earth Surface Process and Landforms, 13, 555-265.

Application of ordinary kriging to reconstruct and visualise the relief in thelocation of an open pit sand mine. (Polish Title: Zastosowanie krigingu zwyczajnego do rekonstrukcji i wizualizacji reliefu w miejscach odkrywkowej eksploatacji piasku)

NASA Astrophysics Data System (ADS)

Zarychta, R.; Zarychta, A.

2013-12-01

Extraction of mineral resources, including rocks, usually causes some significant changes of the landscape. Transformation of the relief which character and scale can be analysed by means of cartographic materials seems to be the most interesting. Reconstruction of the relief of the period prior to the exploitation is a starting point for such investigation. It can be done basing on archival cartographic materials which are difficult to obtain. However, too varied morphological material of the area can lead to erroneous conclusions which suggests interpretation of three - dimensional models of the relief. Hence, the paper deals with reconstruction and visualisation of the relief (in the period before the exploitation) of four sand fields of the old sand mine excavation "Siemonia". A geological map of Poland (Wojkowice sheet) has been used for the purpose. A geostatical analysis by means of the programmes Surfer 8 and ArcGIS 10.1. has been performed on the map. An estimation method called ordinary kriging, which is related to B.L.U.E. (best linear unbiased estimator), where the condition of the lack of weight of the measurement (the sum of weight is equal to 1) is fulfilled, has been applied. The calculated values of errors (mean error, mean squared error and mean squared standardised error) obtained as a result of application of the cross - validation procedure are, to a large extent, in agreement with predetermined values of errors given by numerous authors in the scientific literature. It confirms proper "manual" adjustment of two mathematic al models of spherical variograms and empirical variograms. The generated contour map of the investigated area (based on estimated points of sampling in nodes of the interpolation grid) together with its three - dimensional digital model are more adequate (due to significant marking of the relief) to the previous state of the investigated area than the two other presented types of cartographic visualisations made without application of the geostatistical methods. Hence, the graphic presentation of results, mentioned as the last one, can be only applied to visualise the relief without any detailed geomorphological interpretations due to its inaccuracy. It seems to be obvious that detailed analyses can be performed basing on a digital model of the terrain accompanied by its contour map obtained when reconstruction of the relief is made by means of geostatistical methods (especially ordinary kriging).

Comparing interpolation techniques for annual temperature mapping across Xinjiang region

NASA Astrophysics Data System (ADS)

Ren-ping, Zhang; Jing, Guo; Tian-gang, Liang; Qi-sheng, Feng; Aimaiti, Yusupujiang

2016-11-01

Interpolating climatic variables such as temperature is challenging due to the highly variable nature of meteorological processes and the difficulty in establishing a representative network of stations. In this paper, based on the monthly temperature data which obtained from the 154 official meteorological stations in the Xinjiang region and surrounding areas, we compared five spatial interpolation techniques: Inverse distance weighting (IDW), Ordinary kriging, Cokriging, thin-plate smoothing splines (ANUSPLIN) and Empirical Bayesian kriging(EBK). Error metrics were used to validate interpolations against independent data. Results indicated that, the ANUSPLIN performed best than the other four interpolation methods.

Area-to-point regression kriging for pan-sharpening

NASA Astrophysics Data System (ADS)

Wang, Qunming; Shi, Wenzhong; Atkinson, Peter M.

2016-04-01

Pan-sharpening is a technique to combine the fine spatial resolution panchromatic (PAN) band with the coarse spatial resolution multispectral bands of the same satellite to create a fine spatial resolution multispectral image. In this paper, area-to-point regression kriging (ATPRK) is proposed for pan-sharpening. ATPRK considers the PAN band as the covariate. Moreover, ATPRK is extended with a local approach, called adaptive ATPRK (AATPRK), which fits a regression model using a local, non-stationary scheme such that the regression coefficients change across the image. The two geostatistical approaches, ATPRK and AATPRK, were compared to the 13 state-of-the-art pan-sharpening approaches summarized in Vivone et al. (2015) in experiments on three separate datasets. ATPRK and AATPRK produced more accurate pan-sharpened images than the 13 benchmark algorithms in all three experiments. Unlike the benchmark algorithms, the two geostatistical solutions precisely preserved the spectral properties of the original coarse data. Furthermore, ATPRK can be enhanced by a local scheme in AATRPK, in cases where the residuals from a global regression model are such that their spatial character varies locally.

Complete Bouguer gravity map of the Medicine Lake Quadrangle, California

USGS Publications Warehouse

Finn, C.

1981-01-01

A mathematical technique, called kriging, was programmed for a computer to interpolate hydrologic data based on a network of measured values in west-central Kansas. The computer program generated estimated values at the center of each 1-mile section in the Western Kansas Groundwater Management District No. 1 and facilitated contouring of selected values that are needed in the effective management of ground water for irrigation. The kriging technique produced objective and reproducible maps that illustrated hydrologic conditions in the Ogallala aquifer, the principal source of water in west-central Kansas. Maps of the aquifer, which use a 3-year average, included the 1978-80 water-table altitudes, which ranged from about 2,580 to 3,720 feet; the 1978-80 saturated thicknesses, which ranged from about 0 to 250 feet; and the percentage changes in saturated thickness from 1950 to 1978-80, which ranged from about a 50-percent increase to a 100-percent decrease. A map showing errors of estimate also was provided as a measure of reliability for the 1978-80 water-table altitudes. Errors of estimate ranged from 2 to 24 feet. (USGS)

The Structure of Optimum Interpolation Functions.

DTIC Science & Technology

1983-02-01

Daniel F. Merriam, ed., Plenum Press, 1970. 2. Hiroshi Akima, "Comments on ’Optimal Contour Mapping Using Universal Kriging’ by Ricardo 0. Olea ," (with...Kriging," Mathematical Geology 14 (1982), 249-257. 21 27. Ricardo 0. Olea , "Optimal Contour Mapping Using Universal Kriging," J. of Geophysical Res. 79

A Probability Co-Kriging Model to Account for Reporting Bias and Recognize Areas at High Risk for Zebra Mussels and Eurasian Watermilfoil Invasions in Minnesota

PubMed Central

Kanankege, Kaushi S. T.; Alkhamis, Moh A.; Phelps, Nicholas B. D.; Perez, Andres M.

2018-01-01

Zebra mussels (ZMs) (Dreissena polymorpha) and Eurasian watermilfoil (EWM) (Myriophyllum spicatum) are aggressive aquatic invasive species posing a conservation burden on Minnesota. Recognizing areas at high risk for invasion is a prerequisite for the implementation of risk-based prevention and mitigation management strategies. The early detection of invasion has been challenging, due in part to the imperfect observation process of invasions including the absence of a surveillance program, reliance on public reporting, and limited resource availability, which results in reporting bias. To predict the areas at high risk for invasions, while accounting for underreporting, we combined network analysis and probability co-kriging to estimate the risk of ZM and EWM invasions. We used network analysis to generate a waterbody-specific variable representing boater traffic, a known high risk activity for human-mediated transportation of invasive species. In addition, co-kriging was used to estimate the probability of species introduction, using waterbody-specific variables. A co-kriging model containing distance to the nearest ZM infested location, boater traffic, and road access was used to recognize the areas at high risk for ZM invasions (AUC = 0.78). The EWM co-kriging model included distance to the nearest EWM infested location, boater traffic, and connectivity to infested waterbodies (AUC = 0.76). Results suggested that, by 2015, nearly 20% of the waterbodies in Minnesota were at high risk of ZM (12.45%) or EWM (12.43%) invasions, whereas only 125/18,411 (0.67%) and 304/18,411 (1.65%) are currently infested, respectively. Prediction methods presented here can support decisions related to solving the problems of imperfect detection, which subsequently improve the early detection of biological invasions. PMID:29354638

Characterizing the risk assessment of heavy metals and sampling uncertainty analysis in paddy field by geostatistics and GIS.

PubMed

Liu, Xingmei; Wu, Jianjun; Xu, Jianming

2006-05-01

For many practical problems in environmental management, information about soil heavy metals, relative to threshold values that may be of practical importance is needed at unsampled sites. The Hangzhou-Jiaxing-Huzhou (HJH) Plain has always been one of the most important rice production areas in Zhejiang province, China, and the soil heavy metal concentration is directly related to the crop quality and ultimately the health of people. Four hundred and fifty soil samples were selected in topsoil in HJH Plain to characterize the spatial variability of Cu, Zn, Pb, Cr and Cd. Ordinary kriging and lognormal kriging were carried out to map the spatial patterns of heavy metals and disjunctive kriging was used to quantify the probability of heavy metal concentrations higher than their guide value. Cokriging method was used to minimize the sampling density for Cu, Zn and Cr. The results of this study could give insight into risk assessment of environmental pollution and decision-making for agriculture.

Using Kriging with a heterogeneous measurement error to improve the accuracy of extreme precipitation return level estimation

NASA Astrophysics Data System (ADS)

Yin, Shui-qing; Wang, Zhonglei; Zhu, Zhengyuan; Zou, Xu-kai; Wang, Wen-ting

2018-07-01

Extreme precipitation can cause flooding and may result in great economic losses and deaths. The return level is a commonly used measure of extreme precipitation events and is required for hydrological engineer designs, including those of sewerage systems, dams, reservoirs and bridges. In this paper, we propose a two-step method to estimate the return level and its uncertainty for a study region. In the first step, we use the generalized extreme value distribution, the L-moment method and the stationary bootstrap to estimate the return level and its uncertainty at the site with observations. In the second step, a spatial model incorporating the heterogeneous measurement errors and covariates is trained to estimate return levels at sites with no observations and to improve the estimates at sites with limited information. The proposed method is applied to the daily rainfall data from 273 weather stations in the Haihe river basin of North China. We compare the proposed method with two alternatives: the first one is based on the ordinary Kriging method without measurement error, and the second one smooths the estimated location and scale parameters of the generalized extreme value distribution by the universal Kriging method. Results show that the proposed method outperforms its counterparts. We also propose a novel approach to assess the two-step method by comparing it with the at-site estimation method with a series of reduced length of observations. Estimates of the 2-, 5-, 10-, 20-, 50- and 100-year return level maps and the corresponding uncertainties are provided for the Haihe river basin, and a comparison with those released by the Hydrology Bureau of Ministry of Water Resources of China is made.

High variation subarctic topsoil pollutant concentration prediction using neural network residual kriging

NASA Astrophysics Data System (ADS)

Sergeev, A. P.; Tarasov, D. A.; Buevich, A. G.; Subbotina, I. E.; Shichkin, A. V.; Sergeeva, M. V.; Lvova, O. A.

2017-06-01

The work deals with the application of neural networks residual kriging (NNRK) to the spatial prediction of the abnormally distributed soil pollutant (Cr). It is known that combination of geostatistical interpolation approaches (kriging) and neural networks leads to significantly better prediction accuracy and productivity. Generalized regression neural networks and multilayer perceptrons are classes of neural networks widely used for the continuous function mapping. Each network has its own pros and cons; however both demonstrated fast training and good mapping possibilities. In the work, we examined and compared two combined techniques: generalized regression neural network residual kriging (GRNNRK) and multilayer perceptron residual kriging (MLPRK). The case study is based on the real data sets on surface contamination by chromium at a particular location of the subarctic Novy Urengoy, Russia, obtained during the previously conducted screening. The proposed models have been built, implemented and validated using ArcGIS and MATLAB environments. The networks structures have been chosen during a computer simulation based on the minimization of the RMSE. MLRPK showed the best predictive accuracy comparing to the geostatistical approach (kriging) and even to GRNNRK.

Combining binary decision tree and geostatistical methods to estimate snow distribution in a mountain watershed

USGS Publications Warehouse

Balk, Benjamin; Elder, Kelly

2000-01-01

We model the spatial distribution of snow across a mountain basin using an approach that combines binary decision tree and geostatistical techniques. In April 1997 and 1998, intensive snow surveys were conducted in the 6.9‐km2 Loch Vale watershed (LVWS), Rocky Mountain National Park, Colorado. Binary decision trees were used to model the large‐scale variations in snow depth, while the small‐scale variations were modeled through kriging interpolation methods. Binary decision trees related depth to the physically based independent variables of net solar radiation, elevation, slope, and vegetation cover type. These decision tree models explained 54–65% of the observed variance in the depth measurements. The tree‐based modeled depths were then subtracted from the measured depths, and the resulting residuals were spatially distributed across LVWS through kriging techniques. The kriged estimates of the residuals were added to the tree‐based modeled depths to produce a combined depth model. The combined depth estimates explained 60–85% of the variance in the measured depths. Snow densities were mapped across LVWS using regression analysis. Snow‐covered area was determined from high‐resolution aerial photographs. Combining the modeled depths and densities with a snow cover map produced estimates of the spatial distribution of snow water equivalence (SWE). This modeling approach offers improvement over previous methods of estimating SWE distribution in mountain basins.

A Bayesian kriging approach for blending satellite and ground precipitation observations

USGS Publications Warehouse

Verdin, Andrew P.; Rajagopalan, Balaji; Kleiber, William; Funk, Christopher C.

2015-01-01

Drought and flood management practices require accurate estimates of precipitation. Gauge observations, however, are often sparse in regions with complicated terrain, clustered in valleys, and of poor quality. Consequently, the spatial extent of wet events is poorly represented. Satellite-derived precipitation data are an attractive alternative, though they tend to underestimate the magnitude of wet events due to their dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Here we offer a Bayesian kriging approach for blending precipitation gauge data and the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates for Central America, Colombia, and Venezuela. First, the gauge observations are modeled as a linear function of satellite-derived estimates and any number of other variables—for this research we include elevation. Prior distributions are defined for all model parameters and the posterior distributions are obtained simultaneously via Markov chain Monte Carlo sampling. The posterior distributions of these parameters are required for spatial estimation, and thus are obtained prior to implementing the spatial kriging model. This functional framework is applied to model parameters obtained by sampling from the posterior distributions, and the residuals of the linear model are subject to a spatial kriging model. Consequently, the posterior distributions and uncertainties of the blended precipitation estimates are obtained. We demonstrate this method by applying it to pentadal and monthly total precipitation fields during 2009. The model's performance and its inherent ability to capture wet events are investigated. We show that this blending method significantly improves upon the satellite-derived estimates and is also competitive in its ability to represent wet events. This procedure also provides a means to estimate a full conditional distribution of the “true” observed precipitation value at each grid cell.

Exploring prediction uncertainty of spatial data in geostatistical and machine learning Approaches

NASA Astrophysics Data System (ADS)

Klump, J. F.; Fouedjio, F.

2017-12-01

Geostatistical methods such as kriging with external drift as well as machine learning techniques such as quantile regression forest have been intensively used for modelling spatial data. In addition to providing predictions for target variables, both approaches are able to deliver a quantification of the uncertainty associated with the prediction at a target location. Geostatistical approaches are, by essence, adequate for providing such prediction uncertainties and their behaviour is well understood. However, they often require significant data pre-processing and rely on assumptions that are rarely met in practice. Machine learning algorithms such as random forest regression, on the other hand, require less data pre-processing and are non-parametric. This makes the application of machine learning algorithms to geostatistical problems an attractive proposition. The objective of this study is to compare kriging with external drift and quantile regression forest with respect to their ability to deliver reliable prediction uncertainties of spatial data. In our comparison we use both simulated and real world datasets. Apart from classical performance indicators, comparisons make use of accuracy plots, probability interval width plots, and the visual examinations of the uncertainty maps provided by the two approaches. By comparing random forest regression to kriging we found that both methods produced comparable maps of estimated values for our variables of interest. However, the measure of uncertainty provided by random forest seems to be quite different to the measure of uncertainty provided by kriging. In particular, the lack of spatial context can give misleading results in areas without ground truth data. These preliminary results raise questions about assessing the risks associated with decisions based on the predictions from geostatistical and machine learning algorithms in a spatial context, e.g. mineral exploration.

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping

PubMed Central

2011-01-01

Background Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. Results In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Conclusions Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset. PMID:21978359

Adjusting for sampling variability in sparse data: geostatistical approaches to disease mapping.

PubMed

Hampton, Kristen H; Serre, Marc L; Gesink, Dionne C; Pilcher, Christopher D; Miller, William C

2011-10-06

Disease maps of crude rates from routinely collected health data indexed at a small geographical resolution pose specific statistical problems due to the sparse nature of the data. Spatial smoothers allow areas to borrow strength from neighboring regions to produce a more stable estimate of the areal value. Geostatistical smoothers are able to quantify the uncertainty in smoothed rate estimates without a high computational burden. In this paper, we introduce a uniform model extension of Bayesian Maximum Entropy (UMBME) and compare its performance to that of Poisson kriging in measures of smoothing strength and estimation accuracy as applied to simulated data and the real data example of HIV infection in North Carolina. The aim is to produce more reliable maps of disease rates in small areas to improve identification of spatial trends at the local level. In all data environments, Poisson kriging exhibited greater smoothing strength than UMBME. With the simulated data where the true latent rate of infection was known, Poisson kriging resulted in greater estimation accuracy with data that displayed low spatial autocorrelation, while UMBME provided more accurate estimators with data that displayed higher spatial autocorrelation. With the HIV data, UMBME performed slightly better than Poisson kriging in cross-validatory predictive checks, with both models performing better than the observed data model with no smoothing. Smoothing methods have different advantages depending upon both internal model assumptions that affect smoothing strength and external data environments, such as spatial correlation of the observed data. Further model comparisons in different data environments are required to provide public health practitioners with guidelines needed in choosing the most appropriate smoothing method for their particular health dataset.

Topological and canonical kriging for design flood prediction in ungauged catchments: an improvement over a traditional regional regression approach?

USGS Publications Warehouse

Archfield, Stacey A.; Pugliese, Alessio; Castellarin, Attilio; Skøien, Jon O.; Kiang, Julie E.

2013-01-01

In the United States, estimation of flood frequency quantiles at ungauged locations has been largely based on regional regression techniques that relate measurable catchment descriptors to flood quantiles. More recently, spatial interpolation techniques of point data have been shown to be effective for predicting streamflow statistics (i.e., flood flows and low-flow indices) in ungauged catchments. Literature reports successful applications of two techniques, canonical kriging, CK (or physiographical-space-based interpolation, PSBI), and topological kriging, TK (or top-kriging). CK performs the spatial interpolation of the streamflow statistic of interest in the two-dimensional space of catchment descriptors. TK predicts the streamflow statistic along river networks taking both the catchment area and nested nature of catchments into account. It is of interest to understand how these spatial interpolation methods compare with generalized least squares (GLS) regression, one of the most common approaches to estimate flood quantiles at ungauged locations. By means of a leave-one-out cross-validation procedure, the performance of CK and TK was compared to GLS regression equations developed for the prediction of 10, 50, 100 and 500 yr floods for 61 streamgauges in the southeast United States. TK substantially outperforms GLS and CK for the study area, particularly for large catchments. The performance of TK over GLS highlights an important distinction between the treatments of spatial correlation when using regression-based or spatial interpolation methods to estimate flood quantiles at ungauged locations. The analysis also shows that coupling TK with CK slightly improves the performance of TK; however, the improvement is marginal when compared to the improvement in performance over GLS.

An evaluation of potential sampling locations in a reservoir with emphasis on conserved spatial correlation structure.

PubMed

Yenilmez, Firdes; Düzgün, Sebnem; Aksoy, Aysegül

2015-01-01

In this study, kernel density estimation (KDE) was coupled with ordinary two-dimensional kriging (OK) to reduce the number of sampling locations in measurement and kriging of dissolved oxygen (DO) concentrations in Porsuk Dam Reservoir (PDR). Conservation of the spatial correlation structure in the DO distribution was a target. KDE was used as a tool to aid in identification of the sampling locations that would be removed from the sampling network in order to decrease the total number of samples. Accordingly, several networks were generated in which sampling locations were reduced from 65 to 10 in increments of 4 or 5 points at a time based on kernel density maps. DO variograms were constructed, and DO values in PDR were kriged. Performance of the networks in DO estimations were evaluated through various error metrics, standard error maps (SEM), and whether the spatial correlation structure was conserved or not. Results indicated that smaller number of sampling points resulted in loss of information in regard to spatial correlation structure in DO. The minimum representative sampling points for PDR was 35. Efficacy of the sampling location selection method was tested against the networks generated by experts. It was shown that the evaluation approach proposed in this study provided a better sampling network design in which the spatial correlation structure of DO was sustained for kriging.

Risk assessment of groundwater level variability using variable Kriging methods

NASA Astrophysics Data System (ADS)

Spanoudaki, Katerina; Kampanis, Nikolaos A.

2015-04-01

Assessment of the water table level spatial variability in aquifers provides useful information regarding optimal groundwater management. This information becomes more important in basins where the water table level has fallen significantly. The spatial variability of the water table level in this work is estimated based on hydraulic head measured during the wet period of the hydrological year 2007-2008, in a sparsely monitored basin in Crete, Greece, which is of high socioeconomic and agricultural interest. Three Kriging-based methodologies are elaborated in Matlab environment to estimate the spatial variability of the water table level in the basin. The first methodology is based on the Ordinary Kriging approach, the second involves auxiliary information from a Digital Elevation Model in terms of Residual Kriging and the third methodology calculates the probability of the groundwater level to fall below a predefined minimum value that could cause significant problems in groundwater resources availability, by means of Indicator Kriging. The Box-Cox methodology is applied to normalize both the data and the residuals for improved prediction results. In addition, various classical variogram models are applied to determine the spatial dependence of the measurements. The Matérn model proves to be the optimal, which in combination with Kriging methodologies provides the most accurate cross validation estimations. Groundwater level and probability maps are constructed to examine the spatial variability of the groundwater level in the basin and the associated risk that certain locations exhibit regarding a predefined minimum value that has been set for the sustainability of the basin's groundwater resources. Acknowledgement The work presented in this paper has been funded by the Greek State Scholarships Foundation (IKY), Fellowships of Excellence for Postdoctoral Studies (Siemens Program), 'A simulation-optimization model for assessing the best practices for the protection of surface water and groundwater in the coastal zone', (2013 - 2015). Varouchakis, E. A. and D. T. Hristopulos (2013). "Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables." Advances in Water Resources 52: 34-49. Kitanidis, P. K. (1997). Introduction to geostatistics, Cambridge: University Press.

Zonal management of arsenic contaminated ground water in Northwestern Bangladesh.

PubMed

Hill, Jason; Hossain, Faisal; Bagtzoglou, Amvrossios C

2009-09-01

This paper used ordinary kriging to spatially map arsenic contamination in shallow aquifers of Northwestern Bangladesh (total area approximately 35,000 km(2)). The Northwestern region was selected because it represents a relatively safer source of large-scale and affordable water supply for the rest of Bangladesh currently faced with extensive arsenic contamination in drinking water (such as the Southern regions). Hence, the work appropriately explored sustainability issues by building upon a previously published study (Hossain et al., 2007; Water Resources Management, vol. 21: 1245-1261) where a more general nation-wide assessment afforded by kriging was identified. The arsenic database for reference comprised the nation-wide survey (of 3534 drinking wells) completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) of Bangladesh. Randomly sampled networks of zones from this reference database were used to develop an empirical variogram and develop maps of zonal arsenic concentration for the Northwestern region. The remaining non-sampled zones from the reference database were used to assess the accuracy of the kriged maps. Two additional criteria were explored: (1) the ability of geostatistical interpolators such as kriging to extrapolate information on spatial structure of arsenic contamination beyond small-scale exploratory domains; (2) the impact of a priori knowledge of anisotropic variability on the effectiveness of geostatistically based management. On the average, the kriging method was found to have a 90% probability of successful prediction of safe zones according to the WHO safe limit of 10ppb while for the Bangladesh safe limit of 50ppb, the safe zone prediction probability was 97%. Compared to the previous study by Hossain et al. (2007) over the rest of the contaminated country side, the probability of successful detection of safe zones in the Northwest is observed to be about 25% higher. An a priori knowledge of anisotropy was found to have inconclusive impact on the effectiveness of kriging. It was, however, hypothesized that a preferential sampling strategy that honored anisotropy could be necessary to reach a more definitive conclusion in regards to this issue.

Spatiotemporal exposure modeling of ambient erythemal ultraviolet radiation.

PubMed

VoPham, Trang; Hart, Jaime E; Bertrand, Kimberly A; Sun, Zhibin; Tamimi, Rulla M; Laden, Francine

2016-11-24

Ultraviolet B (UV-B) radiation plays a multifaceted role in human health, inducing DNA damage and representing the primary source of vitamin D for most humans; however, current U.S. UV exposure models are limited in spatial, temporal, and/or spectral resolution. Area-to-point (ATP) residual kriging is a geostatistical method that can be used to create a spatiotemporal exposure model by downscaling from an area- to point-level spatial resolution using fine-scale ancillary data. A stratified ATP residual kriging approach was used to predict average July noon-time erythemal UV (UV Ery ) (mW/m 2 ) biennially from 1998 to 2012 by downscaling National Aeronautics and Space Administration (NASA) Total Ozone Mapping Spectrometer (TOMS) and Ozone Monitoring Instrument (OMI) gridded remote sensing images to a 1 km spatial resolution. Ancillary data were incorporated in random intercept linear mixed-effects regression models. Modeling was performed separately within nine U.S. regions to satisfy stationarity and account for locally varying associations between UV Ery and predictors. Cross-validation was used to compare ATP residual kriging models and NASA grids to UV-B Monitoring and Research Program (UVMRP) measurements (gold standard). Predictors included in the final regional models included surface albedo, aerosol optical depth (AOD), cloud cover, dew point, elevation, latitude, ozone, surface incoming shortwave flux, sulfur dioxide (SO 2 ), year, and interactions between year and surface albedo, AOD, cloud cover, dew point, elevation, latitude, and SO 2 . ATP residual kriging models more accurately estimated UV Ery at UVMRP monitoring stations on average compared to NASA grids across the contiguous U.S. (average mean absolute error [MAE] for ATP, NASA: 15.8, 20.3; average root mean square error [RMSE]: 21.3, 25.5). ATP residual kriging was associated with positive percent relative improvements in MAE (0.6-31.5%) and RMSE (3.6-29.4%) across all regions compared to NASA grids. ATP residual kriging incorporating fine-scale spatial predictors can provide more accurate, high-resolution UV Ery estimates compared to using NASA grids and can be used in epidemiologic studies examining the health effects of ambient UV.

Spatiotemporal Interpolation of Elevation Changes Derived from Satellite Altimetry for Jakobshavn Isbrae, Greenland

NASA Technical Reports Server (NTRS)

Hurkmans, R.T.W.L.; Bamber, J.L.; Sorensen, L. S.; Joughin, I. R.; Davis, C. H.; Krabill, W. B.

2012-01-01

Estimation of ice sheet mass balance from satellite altimetry requires interpolation of point-scale elevation change (dHdt) data over the area of interest. The largest dHdt values occur over narrow, fast-flowing outlet glaciers, where data coverage of current satellite altimetry is poorest. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns of dHdt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbr, an outlet glacier for which widespread airborne validation data are available from NASAs Airborne Topographic Mapper (ATM). The four methods are ordinary kriging (OK), kriging with external drift (KED), where the spatial pattern of surface velocity is used as a proxy for that of dHdt, and their spatiotemporal equivalents (ST-OK and ST-KED).

Uncertainty Estimation using Bootstrapped Kriging Predictions for Precipitation Isoscapes

NASA Astrophysics Data System (ADS)

Ma, C.; Bowen, G. J.; Vander Zanden, H.; Wunder, M.

2017-12-01

Isoscapes are spatial models representing the distribution of stable isotope values across landscapes. Isoscapes of hydrogen and oxygen in precipitation are now widely used in a diversity of fields, including geology, biology, hydrology, and atmospheric science. To generate isoscapes, geostatistical methods are typically applied to extend predictions from limited data measurements. Kriging is a popular method in isoscape modeling, but quantifying the uncertainty associated with the resulting isoscapes is challenging. Applications that use precipitation isoscapes to determine sample origin require estimation of uncertainty. Here we present a simple bootstrap method (SBM) to estimate the mean and uncertainty of the krigged isoscape and compare these results with a generalized bootstrap method (GBM) applied in previous studies. We used hydrogen isotopic data from IsoMAP to explore these two approaches for estimating uncertainty. We conducted 10 simulations for each bootstrap method and found that SBM results in more kriging predictions (9/10) compared to GBM (4/10). Prediction from SBM was closer to the original prediction generated without bootstrapping and had less variance than GBM. SBM was tested on different datasets from IsoMAP with different numbers of observation sites. We determined that predictions from the datasets with fewer than 40 observation sites using SBM were more variable than the original prediction. The approaches we used for estimating uncertainty will be compiled in an R package that is under development. We expect that these robust estimates of precipitation isoscape uncertainty can be applied in diagnosing the origin of samples ranging from various type of waters to migratory animals, food products, and humans.

spMC: an R-package for 3D lithological reconstructions based on spatial Markov chains

NASA Astrophysics Data System (ADS)

Sartore, Luca; Fabbri, Paolo; Gaetan, Carlo

2016-09-01

The paper presents the spatial Markov Chains (spMC) R-package and a case study of subsoil simulation/prediction located in a plain site of Northeastern Italy. spMC is a quite complete collection of advanced methods for data inspection, besides spMC implements Markov Chain models to estimate experimental transition probabilities of categorical lithological data. Furthermore, simulation methods based on most known prediction methods (as indicator Kriging and CoKriging) were implemented in spMC package. Moreover, other more advanced methods are available for simulations, e.g. path methods and Bayesian procedures, that exploit the maximum entropy. Since the spMC package was developed for intensive geostatistical computations, part of the code is implemented for parallel computations via the OpenMP constructs. A final analysis of this computational efficiency compares the simulation/prediction algorithms by using different numbers of CPU cores, and considering the example data set of the case study included in the package.

A Nonparametric Geostatistical Method For Estimating Species Importance

Treesearch

Andrew J. Lister; Rachel Riemann; Michael Hoppus

2001-01-01

Parametric statistical methods are not always appropriate for conducting spatial analyses of forest inventory data. Parametric geostatistical methods such as variography and kriging are essentially averaging procedures, and thus can be affected by extreme values. Furthermore, non normal distributions violate the assumptions of analyses in which test statistics are...

Estimating the spatial distribution of soil moisture based on Bayesian maximum entropy method with auxiliary data from remote sensing

NASA Astrophysics Data System (ADS)

Gao, Shengguo; Zhu, Zhongli; Liu, Shaomin; Jin, Rui; Yang, Guangchao; Tan, Lei

2014-10-01

Soil moisture (SM) plays a fundamental role in the land-atmosphere exchange process. Spatial estimation based on multi in situ (network) data is a critical way to understand the spatial structure and variation of land surface soil moisture. Theoretically, integrating densely sampled auxiliary data spatially correlated with soil moisture into the procedure of spatial estimation can improve its accuracy. In this study, we present a novel approach to estimate the spatial pattern of soil moisture by using the BME method based on wireless sensor network data and auxiliary information from ASTER (Terra) land surface temperature measurements. For comparison, three traditional geostatistic methods were also applied: ordinary kriging (OK), which used the wireless sensor network data only, regression kriging (RK) and ordinary co-kriging (Co-OK) which both integrated the ASTER land surface temperature as a covariate. In Co-OK, LST was linearly contained in the estimator, in RK, estimator is expressed as the sum of the regression estimate and the kriged estimate of the spatially correlated residual, but in BME, the ASTER land surface temperature was first retrieved as soil moisture based on the linear regression, then, the t-distributed prediction interval (PI) of soil moisture was estimated and used as soft data in probability form. The results indicate that all three methods provide reasonable estimations. Co-OK, RK and BME can provide a more accurate spatial estimation by integrating the auxiliary information Compared to OK. RK and BME shows more obvious improvement compared to Co-OK, and even BME can perform slightly better than RK. The inherent issue of spatial estimation (overestimation in the range of low values and underestimation in the range of high values) can also be further improved in both RK and BME. We can conclude that integrating auxiliary data into spatial estimation can indeed improve the accuracy, BME and RK take better advantage of the auxiliary information compared to Co-OK, and BME outperforms RK by integrating the auxiliary data in a probability form.

A study on exposure assessment for fine dust by using Kriging method: The case of Seoul Metropolitan city

NASA Astrophysics Data System (ADS)

Seo, J. H.; Sohn, J. R.; Mo, R.

2017-12-01

According to the OECD, South Korea is expected to have the highest morality and the biggest economic damage due to the air pollution among OECD members in 2060. Korea's air quality monitoring network is provided by Air Korea of the Korea Environment Corporation under the Ministry of Environment. There are 323 measurement stations installed in 97 different places in Korea. The monitoring network is classified into city atmosphere, roadside, country background concentration, and suburban atmosphere monitoring network, which operate according to each measurement purpose. However, the data from this network shows a large difference in pollutant concentration by region and there is a limit to explain the concentration of pollutants in Seoul, which has a very high population density. The data of the fine dust concentration in Korea University is provided by Seongbuk-gu, but actually Korea University is closer to the measuring station in Dongdaemun-gu. Therefore, a difference will occur if the data from Seongbuk-gu is used to the exposure assessment of residents in nearby Korea University for air pollution. Therefore, this study is aimed to acquire estimated value about areas that have not been measured and implement more precise exposure assessment by comparing it with measured value. On May 8, 2017, when the fine dust concentration was the highest, we calculated the pollutant concentration estimates near Korea University by using measuring network of Seongbukgu and Dongdaemun through Kriging method and compared them with actual measured value which was acquired in this study. Analysis results showed that air pollution concentration near Korea University tends to be overestimated when using the data from Seongbukgu. On the other hand, it showed a similarity to measured value when using data from both Seongbukgu and Dongdaemungu through Kriging method. Therefore, it is necessary to estimate the data about blind spots through Kriging method rather than using the existing national atmospheric monitoring data. In addition, it is required to acquire measured data through government agencies and research institutes in addition to the measurement networking data to calculate more accurate pollution concentration and utilize it for the exposure evaluation.

Geostatistical interpolation of available copper in orchard soil as influenced by planting duration.

PubMed

Fu, Chuancheng; Zhang, Haibo; Tu, Chen; Li, Lianzhen; Luo, Yongming

2018-01-01

Mapping the spatial distribution of available copper (A-Cu) in orchard soils is important in agriculture and environmental management. However, data on the distribution of A-Cu in orchard soils is usually highly variable and severely skewed due to the continuous input of fungicides. In this study, ordinary kriging combined with planting duration (OK_PD) is proposed as a method for improving the interpolation of soil A-Cu. Four normal distribution transformation methods, namely, the Box-Cox, Johnson, rank order, and normal score methods, were utilized prior to interpolation. A total of 317 soil samples were collected in the orchards of the Northeast Jiaodong Peninsula. Moreover, 1472 orchards were investigated to obtain a map of planting duration using Voronoi tessellations. The soil A-Cu content ranged from 0.09 to 106.05 with a mean of 18.10 mg kg -1 , reflecting the high availability of Cu in the soils. Soil A-Cu concentrations exhibited a moderate spatial dependency and increased significantly with increasing planting duration. All the normal transformation methods successfully decreased the skewness and kurtosis of the soil A-Cu and the associated residuals, and also computed more robust variograms. OK_PD could generate better spatial prediction accuracy than ordinary kriging (OK) for all transformation methods tested, and it also provided a more detailed map of soil A-Cu. Normal score transformation produced satisfactory accuracy and showed an advantage in ameliorating smoothing effect derived from the interpolation methods. Thus, normal score transformation prior to kriging combined with planting duration (NSOK_PD) is recommended for the interpolation of soil A-Cu in this area.

The geostatistic-based spatial distribution variations of soil salts under long-term wastewater irrigation.

PubMed

Wu, Wenyong; Yin, Shiyang; Liu, Honglu; Niu, Yong; Bao, Zhe

2014-10-01

The purpose of this study was to determine and evaluate the spatial changes in soil salinity by using geostatistical methods. The study focused on the suburb area of Beijing, where urban development led to water shortage and accelerated wastewater reuse to farm irrigation for more than 30 years. The data were then processed by GIS using three different interpolation techniques of ordinary kriging (OK), disjunctive kriging (DK), and universal kriging (UK). The normality test and overall trend analysis were applied for each interpolation technique to select the best fitted model for soil parameters. Results showed that OK was suitable for soil sodium adsorption ratio (SAR) and Na(+) interpolation; UK was suitable for soil Cl(-) and pH; DK was suitable for soil Ca(2+). The nugget-to-sill ratio was applied to evaluate the effects of structural and stochastic factors. The maps showed that the areas of non-saline soil and slight salinity soil accounted for 6.39 and 93.61%, respectively. The spatial distribution and accumulation of soil salt were significantly affected by the irrigation probabilities and drainage situation under long-term wastewater irrigation.

[Application of ordinary Kriging method in entomologic ecology].

PubMed

Zhang, Runjie; Zhou, Qiang; Chen, Cuixian; Wang, Shousong

2003-01-01

Geostatistics is a statistic method based on regional variables and using the tool of variogram to analyze the spatial structure and the patterns of organism. In simulating the variogram within a great range, though optimal simulation cannot be obtained, the simulation method of a dialogue between human and computer can be used to optimize the parameters of the spherical models. In this paper, the method mentioned above and the weighted polynomial regression were utilized to simulate the one-step spherical model, the two-step spherical model and linear function model, and the available nearby samples were used to draw on the ordinary Kriging procedure, which provided a best linear unbiased estimate of the constraint of the unbiased estimation. The sum of square deviation between the estimating and measuring values of varying theory models were figured out, and the relative graphs were shown. It was showed that the simulation based on the two-step spherical model was the best simulation, and the one-step spherical model was better than the linear function model.

Geographic and temporal trends in influenzalike illness, Japan, 1992-1999.

PubMed

Sakai, Takatsugu; Suzuki, Hiroshi; Sasaki, Asami; Saito, Reiko; Tanabe, Naohito; Taniguchi, Kiyosu

2004-10-01

From 1992 to 1999, we analyzed >2.5 million cases of influenzalike illness (ILI). Nationwide influenza epidemics generally lasted 3-4 months in winter. Kriging analysis, which illustrates geographic movement, showed that the starting areas of peak ILI activity were mostly found in western Japan. Two spreading patterns, monotonous and multitonous, were observed. Monotonous patterns in two seasons featured peak ILI activity that covered all of Japan within 3 to 5 weeks in larger epidemics with new antigenic variants of A/H3N2. Multitonous patterns, observed in the other five seasons, featured peak ILI activity within 12 to 15 weeks in small epidemics without new variants. Applying the kriging method allowed better visualization and understanding of spatiotemporal trends in seasonal ILI activity. This method will likely be an important tool for future influenza surveillance in Japan.

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer.

PubMed

Davie, Stuart J; Di Pasquale, Nicodemo; Popelier, Paul L A

2016-10-15

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra-atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom-of-interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Spatial uncertainty analysis: Propagation of interpolation errors in spatially distributed models

USGS Publications Warehouse

Phillips, D.L.; Marks, D.G.

1996-01-01

In simulation modelling, it is desirable to quantify model uncertainties and provide not only point estimates for output variables but confidence intervals as well. Spatially distributed physical and ecological process models are becoming widely used, with runs being made over a grid of points that represent the landscape. This requires input values at each grid point, which often have to be interpolated from irregularly scattered measurement sites, e.g., weather stations. Interpolation introduces spatially varying errors which propagate through the model We extended established uncertainty analysis methods to a spatial domain for quantifying spatial patterns of input variable interpolation errors and how they propagate through a model to affect the uncertainty of the model output. We applied this to a model of potential evapotranspiration (PET) as a demonstration. We modelled PET for three time periods in 1990 as a function of temperature, humidity, and wind on a 10-km grid across the U.S. portion of the Columbia River Basin. Temperature, humidity, and wind speed were interpolated using kriging from 700- 1000 supporting data points. Kriging standard deviations (SD) were used to quantify the spatially varying interpolation uncertainties. For each of 5693 grid points, 100 Monte Carlo simulations were done, using the kriged values of temperature, humidity, and wind, plus random error terms determined by the kriging SDs and the correlations of interpolation errors among the three variables. For the spring season example, kriging SDs averaged 2.6??C for temperature, 8.7% for relative humidity, and 0.38 m s-1 for wind. The resultant PET estimates had coefficients of variation (CVs) ranging from 14% to 27% for the 10-km grid cells. Maps of PET means and CVs showed the spatial patterns of PET with a measure of its uncertainty due to interpolation of the input variables. This methodology should be applicable to a variety of spatially distributed models using interpolated inputs.

Spatial prediction of soil texture in region Centre (France) from summary data

NASA Astrophysics Data System (ADS)

Dobarco, Mercedes Roman; Saby, Nicolas; Paroissien, Jean-Baptiste; Orton, Tom G.

2015-04-01

Soil texture is a key controlling factor of important soil functions like water and nutrient holding capacity, retention of pollutants, drainage, soil biodiversity, and C cycling. High resolution soil texture maps enhance our understanding of the spatial distribution of soil properties and provide valuable information for decision making and crop management, environmental protection, and hydrological planning. We predicted the soil texture of agricultural topsoils in the Region Centre (France) combining regression and area-to-point kriging. Soil texture data was collected from the French soil-test database (BDAT), which is populated with soil analysis performed by farmers' demand. To protect the anonymity of the farms the data was treated by commune. In a first step, summary statistics of environmental covariates by commune were used to develop prediction models with Cubist, boosted regression trees, and random forests. In a second step the residuals of each individual observation were summarized by commune and kriged following the method developed by Orton et al. (2012). This approach allowed to include non-linear relationships among covariates and soil texture while accounting for the uncertainty on areal means in the area-to-point kriging step. Independent validation of the models was done using data from the systematic soil monitoring network of French soils. Future work will compare the performance of these models with a non-stationary variance geostatistical model using the most important covariates and summary statistics of texture data. The results will inform on whether the later and statistically more-challenging approach improves significantly texture predictions or whether the more simple area-to-point regression kriging can offer satisfactory results. The application of area-to-point regression kriging at national level using BDAT data has the potential to improve soil texture predictions for agricultural topsoils, especially when combined with existing maps (i.e., model ensemble).

Wet-season spatial variability of N2O emissions from a tea field in subtropical central China

NASA Astrophysics Data System (ADS)

Fu, X.; Liu, X.; Li, Y.; Shen, J.; Wang, Y.; Zou, G.; Li, H.; Song, L.; Wu, J.

2015-01-01

Tea fields emit large amounts of nitrous oxide (N2O) to the atmosphere. Obtaining accurate estimations of N2O emissions from tea-planted soils is challenging due to strong spatial variability. We examined the spatial variability of N2O emissions from a red-soil tea field in Hunan province, China, on 22 April 2012 (in a wet season) using 147 static mini chambers approximately regular gridded in a 4.0 ha tea field. The N2O fluxes for a 30 min snapshot (10-10.30 a.m.) ranged from -1.73 to 1659.11 g N ha-1 d-1 and were positively skewed with an average flux of 102.24 g N ha-1 d-1. The N2O flux data were transformed to a normal distribution by using a logit function. The geostatistical analyses of our data indicated that the logit-transformed N2O fluxes (FLUX30t) exhibited strong spatial autocorrelation, which was characterized by an exponential semivariogram model with an effective range of 25.2 m. As observed in the wet season, the logit-transformed soil ammonium-N (NH4Nt), soil nitrate-N (NO3Nt), soil organic carbon (SOCt), total soil nitrogen (TSNt) were all found to be significantly correlated with FLUX30t (r=0.57-0.71, p<0.001). Three spatial interpolation methods (ordinary kriging, regression kriging and cokriging) were applied to estimate the spatial distribution of N2O emissions over the study area. Cokriging with NH4Nt and NO3Nt as covariables (r= 0.74 and RMSE =1.18) outperformed ordinary kriging (r= 0.18 and RMSE =1.74), regression kriging with the sample position as a predictor (r= 0.49 and RMSE =1.55) and cokriging with SOCt as a covariable (r= 0.58 and RMSE =1.44). The predictions of the three kriging interpolation methods for the total N2O emissions of the 4.0 ha tea field ranged from 148.2 to 208.1 g N d-1, based on the 30 min snapshots obtained during the wet season. Our findings suggested that to accurately estimate the total N2O emissions over a region, the environmental variables (e.g., soil properties) and the current land use pattern (e.g., tea row transects in the present study) must be included in spatial interpolation. Additionally, compared with other kriging approaches, the cokriging prediction approach showed great advantages in being easily deployed, and more importantly providing accurate regional estimation of N2O emissions from tea-planted soils.

Wet-season spatial variability in N2O emissions from a tea field in subtropical central China

NASA Astrophysics Data System (ADS)

Fu, X.; Liu, X.; Li, Y.; Shen, J.; Wang, Y.; Zou, G.; Li, H.; Song, L.; Wu, J.

2015-06-01

Tea fields emit large amounts of nitrous oxide (N2O) to the atmosphere. Obtaining accurate estimations of N2O emissions from tea-planted soils is challenging due to strong spatial variability. We examined the spatial variability in N2O emissions from a red-soil tea field in Hunan Province, China, on 22 April 2012 (in a wet season) using 147 static mini chambers approximately regular gridded in a 4.0 ha tea field. The N2O fluxes for a 30 min snapshot (10:00-10:30 a.m.) ranged from -1.73 to 1659.11 g N ha-1 d-1 and were positively skewed with an average flux of 102.24 g N ha-1 d-1. The N2O flux data were transformed to a normal distribution by using a logit function. The geostatistical analyses of our data indicated that the logit-transformed N2O fluxes (FLUX30t) exhibited strong spatial autocorrelation, which was characterized by an exponential semivariogram model with an effective range of 25.2 m. As observed in the wet season, the logit-transformed soil ammonium-N (NH4Nt), soil nitrate-N (NO3Nt), soil organic carbon (SOCt) and total soil nitrogen (TSNt) were all found to be significantly correlated with FLUX30t (r = 0.57-0.71, p < 0.001). Three spatial interpolation methods (ordinary kriging, regression kriging and cokriging) were applied to estimate the spatial distribution of N2O emissions over the study area. Cokriging with NH4Nt and NO3Nt as covariables (r = 0.74 and RMSE = 1.18) outperformed ordinary kriging (r = 0.18 and RMSE = 1.74), regression kriging with the sample position as a predictor (r = 0.49 and RMSE = 1.55) and cokriging with SOCt as a covariable (r = 0.58 and RMSE = 1.44). The predictions of the three kriging interpolation methods for the total N2O emissions of 4.0 ha tea field ranged from 148.2 to 208.1 g N d-1, based on the 30 min snapshots obtained during the wet season. Our findings suggested that to accurately estimate the total N2O emissions over a region, the environmental variables (e.g., soil properties) and the current land use pattern (e.g., tea row transects in the present study) must be included in spatial interpolation. Additionally, compared with other kriging approaches, the cokriging prediction approach showed great advantages in being easily deployed and, more importantly, providing accurate regional estimation of N2O emissions from tea-planted soils.

A robust method of thin plate spline and its application to DEM construction

NASA Astrophysics Data System (ADS)

Chen, Chuanfa; Li, Yanyan

2012-11-01

In order to avoid the ill-conditioning problem of thin plate spline (TPS), the orthogonal least squares (OLS) method was introduced, and a modified OLS (MOLS) was developed. The MOLS of TPS (TPS-M) can not only select significant points, termed knots, from large and dense sampling data sets, but also easily compute the weights of the knots in terms of back-substitution. For interpolating large sampling points, we developed a local TPS-M, where some neighbor sampling points around the point being estimated are selected for computation. Numerical tests indicate that irrespective of sampling noise level, the average performance of TPS-M can advantage with smoothing TPS. Under the same simulation accuracy, the computational time of TPS-M decreases with the increase of the number of sampling points. The smooth fitting results on lidar-derived noise data indicate that TPS-M has an obvious smoothing effect, which is on par with smoothing TPS. The example of constructing a series of large scale DEMs, located in Shandong province, China, was employed to comparatively analyze the estimation accuracies of the two versions of TPS and the classical interpolation methods including inverse distance weighting (IDW), ordinary kriging (OK) and universal kriging with the second-order drift function (UK). Results show that regardless of sampling interval and spatial resolution, TPS-M is more accurate than the classical interpolation methods, except for the smoothing TPS at the finest sampling interval of 20 m, and the two versions of kriging at the spatial resolution of 15 m. In conclusion, TPS-M, which avoids the ill-conditioning problem, is considered as a robust method for DEM construction.

Kriging for Spatial-Temporal Data on the Bridges Supercomputer

NASA Astrophysics Data System (ADS)

Hodgess, E. M.

2017-12-01

Currently, kriging of spatial-temporal data is slow and limited to relatively small vector sizes. We have developed a method on the Bridges supercomputer, at the Pittsburgh supercomputer center, which uses a combination of the tools R, Fortran, the Message Passage Interface (MPI), OpenACC, and special R packages for big data. This combination of tools now permits us to complete tasks which could previously not be completed, or takes literally hours to complete. We ran simulation studies from a laptop against the supercomputer. We also look at "real world" data sets, such as the Irish wind data, and some weather data. We compare the timings. We note that the timings are suprising good.

Effective Solar Indices for Ionospheric Modeling: A Review and a Proposal for a Real-Time Regional IRI

NASA Astrophysics Data System (ADS)

Pignalberi, A.; Pezzopane, M.; Rizzi, R.; Galkin, I.

2018-01-01

The first part of this paper reviews methods using effective solar indices to update a background ionospheric model focusing on those employing the Kriging method to perform the spatial interpolation. Then, it proposes a method to update the International Reference Ionosphere (IRI) model through the assimilation of data collected by a European ionosonde network. The method, called International Reference Ionosphere UPdate (IRI UP), that can potentially operate in real time, is mathematically described and validated for the period 9-25 March 2015 (a time window including the well-known St. Patrick storm occurred on 17 March), using IRI and IRI Real Time Assimilative Model (IRTAM) models as the reference. It relies on foF2 and M(3000)F2 ionospheric characteristics, recorded routinely by a network of 12 European ionosonde stations, which are used to calculate for each station effective values of IRI indices IG_{12} and R_{12} (identified as IG_{{12{eff}}} and R_{{12{eff}}}); then, starting from this discrete dataset of values, two-dimensional (2D) maps of IG_{{12{eff}}} and R_{{12{eff}}} are generated through the universal Kriging method. Five variogram models are proposed and tested statistically to select the best performer for each effective index. Then, computed maps of IG_{{12{eff}}} and R_{{12{eff}}} are used in the IRI model to synthesize updated values of foF2 and hmF2. To evaluate the ability of the proposed method to reproduce rapid local changes that are common under disturbed conditions, quality metrics are calculated for two test stations whose measurements were not assimilated in IRI UP, Fairford (51.7°N, 1.5°W) and San Vito (40.6°N, 17.8°E), for IRI, IRI UP, and IRTAM models. The proposed method turns out to be very effective under highly disturbed conditions, with significant improvements of the foF2 representation and noticeable improvements of the hmF2 one. Important improvements have been verified also for quiet and moderately disturbed conditions. A visual analysis of foF2 and hmF2 maps highlights the ability of the IRI UP method to catch small-scale changes occurring under disturbed conditions which are not seen by IRI.

Traffic volume estimation using network interpolation techniques.

DOT National Transportation Integrated Search

2013-12-01

Kriging method is a frequently used interpolation methodology in geography, which enables estimations of unknown values at : certain places with the considerations of distances among locations. When it is used in transportation field, network distanc...

Modeling of surface dust concentration in snow cover at industrial area using neural networks and kriging

NASA Astrophysics Data System (ADS)

Sergeev, A. P.; Tarasov, D. A.; Buevich, A. G.; Shichkin, A. V.; Tyagunov, A. G.; Medvedev, A. N.

2017-06-01

Modeling of spatial distribution of pollutants in the urbanized territories is difficult, especially if there are multiple emission sources. When monitoring such territories, it is often impossible to arrange the necessary detailed sampling. Because of this, the usual methods of analysis and forecasting based on geostatistics are often less effective. Approaches based on artificial neural networks (ANNs) demonstrate the best results under these circumstances. This study compares two models based on ANNs, which are multilayer perceptron (MLP) and generalized regression neural networks (GRNNs) with the base geostatistical method - kriging. Models of the spatial dust distribution in the snow cover around the existing copper quarry and in the area of emissions of a nickel factory were created. To assess the effectiveness of the models three indices were used: the mean absolute error (MAE), the root-mean-square error (RMSE), and the relative root-mean-square error (RRMSE). Taking into account all indices the model of GRNN proved to be the most accurate which included coordinates of the sampling points and the distance to the likely emission source as input parameters for the modeling. Maps of spatial dust distribution in the snow cover were created in the study area. It has been shown that the models based on ANNs were more accurate than the kriging, particularly in the context of a limited data set.

[Prediction of soil nutrients spatial distribution based on neural network model combined with goestatistics].

PubMed

Li, Qi-Quan; Wang, Chang-Quan; Zhang, Wen-Jiang; Yu, Yong; Li, Bing; Yang, Juan; Bai, Gen-Chuan; Cai, Yan

2013-02-01

In this study, a radial basis function neural network model combined with ordinary kriging (RBFNN_OK) was adopted to predict the spatial distribution of soil nutrients (organic matter and total N) in a typical hilly region of Sichuan Basin, Southwest China, and the performance of this method was compared with that of ordinary kriging (OK) and regression kriging (RK). All the three methods produced the similar soil nutrient maps. However, as compared with those obtained by multiple linear regression model, the correlation coefficients between the measured values and the predicted values of soil organic matter and total N obtained by neural network model increased by 12. 3% and 16. 5% , respectively, suggesting that neural network model could more accurately capture the complicated relationships between soil nutrients and quantitative environmental factors. The error analyses of the prediction values of 469 validation points indicated that the mean absolute error (MAE) , mean relative error (MRE), and root mean squared error (RMSE) of RBFNN_OK were 6.9%, 7.4%, and 5. 1% (for soil organic matter), and 4.9%, 6.1% , and 4.6% (for soil total N) smaller than those of OK (P<0.01), and 2.4%, 2.6% , and 1.8% (for soil organic matter), and 2.1%, 2.8%, and 2.2% (for soil total N) smaller than those of RK, respectively (P<0.05).

Integrating Map Algebra and Statistical Modeling for Spatio- Temporal Analysis of Monthly Mean Daily Incident Photosynthetically Active Radiation (PAR) over a Complex Terrain.

PubMed

Evrendilek, Fatih

2007-12-12

This study aims at quantifying spatio-temporal dynamics of monthly mean dailyincident photosynthetically active radiation (PAR) over a vast and complex terrain such asTurkey. The spatial interpolation method of universal kriging, and the combination ofmultiple linear regression (MLR) models and map algebra techniques were implemented togenerate surface maps of PAR with a grid resolution of 500 x 500 m as a function of fivegeographical and 14 climatic variables. Performance of the geostatistical and MLR modelswas compared using mean prediction error (MPE), root-mean-square prediction error(RMSPE), average standard prediction error (ASE), mean standardized prediction error(MSPE), root-mean-square standardized prediction error (RMSSPE), and adjustedcoefficient of determination (R² adj. ). The best-fit MLR- and universal kriging-generatedmodels of monthly mean daily PAR were validated against an independent 37-year observeddataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifingmethod. The spatial variability patterns of monthly mean daily incident PAR were moreaccurately reflected in the surface maps created by the MLR-based models than in thosecreated by the universal kriging method, in particular, for spring (May) and autumn(November). The MLR-based spatial interpolation algorithms of PAR described in thisstudy indicated the significance of the multifactor approach to understanding and mappingspatio-temporal dynamics of PAR for a complex terrain over meso-scales.

High-resolution spatial databases of monthly climate variables (1961-2010) over a complex terrain region in southwestern China

NASA Astrophysics Data System (ADS)

Wu, Wei; Xu, An-Ding; Liu, Hong-Bin

2015-01-01

Climate data in gridded format are critical for understanding climate change and its impact on eco-environment. The aim of the current study is to develop spatial databases for three climate variables (maximum, minimum temperatures, and relative humidity) over a large region with complex topography in southwestern China. Five widely used approaches including inverse distance weighting, ordinary kriging, universal kriging, co-kriging, and thin-plate smoothing spline were tested. Root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) showed that thin-plate smoothing spline with latitude, longitude, and elevation outperformed other models. Average RMSE, MAE, and MAPE of the best models were 1.16 °C, 0.74 °C, and 7.38 % for maximum temperature; 0.826 °C, 0.58 °C, and 6.41 % for minimum temperature; and 3.44, 2.28, and 3.21 % for relative humidity, respectively. Spatial datasets of annual and monthly climate variables with 1-km resolution covering the period 1961-2010 were then obtained using the best performance methods. Comparative study showed that the current outcomes were in well agreement with public datasets. Based on the gridded datasets, changes in temperature variables were investigated across the study area. Future study might be needed to capture the uncertainty induced by environmental conditions through remote sensing and knowledge-based methods.

Geostatistical analysis of disease data: accounting for spatial support and population density in the isopleth mapping of cancer mortality risk using area-to-point Poisson kriging

PubMed Central

Goovaerts, Pierre

2006-01-01

Background Geostatistical techniques that account for spatially varying population sizes and spatial patterns in the filtering of choropleth maps of cancer mortality were recently developed. Their implementation was facilitated by the initial assumption that all geographical units are the same size and shape, which allowed the use of geographic centroids in semivariogram estimation and kriging. Another implicit assumption was that the population at risk is uniformly distributed within each unit. This paper presents a generalization of Poisson kriging whereby the size and shape of administrative units, as well as the population density, is incorporated into the filtering of noisy mortality rates and the creation of isopleth risk maps. An innovative procedure to infer the point-support semivariogram of the risk from aggregated rates (i.e. areal data) is also proposed. Results The novel methodology is applied to age-adjusted lung and cervix cancer mortality rates recorded for white females in two contrasted county geographies: 1) state of Indiana that consists of 92 counties of fairly similar size and shape, and 2) four states in the Western US (Arizona, California, Nevada and Utah) forming a set of 118 counties that are vastly different geographical units. Area-to-point (ATP) Poisson kriging produces risk surfaces that are less smooth than the maps created by a naïve point kriging of empirical Bayesian smoothed rates. The coherence constraint of ATP kriging also ensures that the population-weighted average of risk estimates within each geographical unit equals the areal data for this unit. Simulation studies showed that the new approach yields more accurate predictions and confidence intervals than point kriging of areal data where all counties are simply collapsed into their respective polygon centroids. Its benefit over point kriging increases as the county geography becomes more heterogeneous. Conclusion A major limitation of choropleth maps is the common biased visual perception that larger rural and sparsely populated areas are of greater importance. The approach presented in this paper allows the continuous mapping of mortality risk, while accounting locally for population density and areal data through the coherence constraint. This form of Poisson kriging will facilitate the analysis of relationships between health data and putative covariates that are typically measured over different spatial supports. PMID:17137504

Identification of land degradation evidences in an organic farm using probability maps (Croatia)

NASA Astrophysics Data System (ADS)

Pereira, Paulo; Bogunovic, Igor; Estebaranz, Ferran

2017-04-01

Land degradation is a biophysical process with important impacts on society, economy and policy. Areas affected by land degradation do not provide services in quality and with capacity to full-field the communities that depends on them (Amaya-Romero et al., 2015; Beyene, 2015; Lanckriet et al., 2015). Agricultural activities are one of the main causes of land degradation (Kraaijvanger and Veldkamp, 2015), especially when they decrease soil organic matter (SOM), a crucial element for soil fertility. In temperate areas, the critical level of SOM concentration in agricultural soils is 3.4%. Below this level there is a potential decrease of soil quality (Loveland and Weeb, 2003). However, no previous work was carried out in other environments, such as the Mediterranean. The spatial distribution of potential degraded land is important to be identified and mapped, in order to identify the areas that need restoration (Brevik et al., 2016; Pereira et al., 2017). The aim of this work is to assess the spatial distribution of areas with evidences of land degradation (SOM bellow 3.4%) using probability maps in an organic farm located in Croatia. In order to find the best method, we compared several probability methods, such as Ordinary Kriging (OK), Simple Kriging (SK), Universal Kriging (UK), Indicator Kriging (IK), Probability Kriging (PK) and Disjunctive Kriging (DK). The study area is located on the Istria peninsula (45°3' N; 14°2' E), with a total area of 182 ha. One hundred eighty-two soil samples (0-30 cm) were collected during July of 2015 and SOM was assessed using wet combustion procedure. The assessment of the best probability method was carried out using leave one out cross validation method. The probability method with the lowest Root Mean Squared Error (RMSE) was the most accurate. The results showed that the best method to predict the probability of potential land degradation was SK with an RMSE of 0.635, followed by DK (RMSE=0.636), UK (RMSE=0.660), OK (RMSE=0.660), IK (RMSE=0.722) and PK (RMSE=1.661). According to the most accurate method, it is observed that the majority of the area studied has a high probability to be degraded. Measures are needed to restore this area. References Amaya-Romero, M., Abd-Elmabod, S., Munoz-Rojas, M., Castellano, G., Ceacero, C., Alvarez, S., Mendez, M., De la Rosa, D. (2015) Evaluating soil threats under climate change scenarios in the Andalusia region, Southern Spain. Land Degradation and Development, 26, 441-449. Beyene, F. (2015) Incentives and challenges in community based rangeland management: Evidence from Eastern Ethiopia. Land Degradation and Development, 26, 502-509. Brevik, E., Calzolari, C., Miller, B., Pereira, P., Kabala, C., Baumgarten, A., Jordán, A. (2016) Historical perspectives and future needs in soil mapping, classification and pedological modelling, Geoderma, 264, Part B, 256-274. Kraaijvanger, R., Veldkamp, T. (2015) Grain productivity, fertilizer response and nutrient balance of farming systems in Tigray, Ethiopia: A Multiprespective view in relation do soil fertility degradation. Land Degradation and Development, 26, 701-710. Lanckriet, S., Derudder, B., Naudts, J., Bauer, H., Deckers, J., Haile, M., Nyssen, J. (2015) A political ecology perspective of land degradation in the North Ethiopian Highlands. Land Degradation and Development, 26, 521-530. Loveland, P., Weeb, J. (2003) Is there a critical level of organic matter in the agricultural soils of temperate regions: a review. Soil & Tillage Research, 70, 1-18. Pereira, P., Brevik, E., Munoz-Rojas, M., Miller, B., Smetanova, A., Depellegrin, D., Misiune, I., Novara, A., Cerda, A. Soil mapping and process modelling for sustainable land management. In: Pereira, P., Brevik, E., Munoz-Rojas, M., Miller, B. (Eds.) Soil mapping and process modelling for sustainable land use management (Elsevier Publishing House) ISBN: 9780128052006

Trace elements of concern affecting urban agriculture in industrialized areas: A multivariate approach.

PubMed

Boente, C; Matanzas, N; García-González, N; Rodríguez-Valdés, E; Gallego, J R

2017-09-01

The urban and peri-urban soils used for agriculture could be contaminated by atmospheric deposition or industrial releases, thus raising concerns about the potential risk to public health. Here we propose a method to evaluate potential soil pollution based on multivariate statistics, geostatistics (kriging), a novel soil pollution index, and bioavailability assessments. This approach was tested in two districts of a highly populated and industrialized city (Gijón, Spain). The soils showed anomalous content of several trace elements, such as As and Pb (up to 80 and 585 mg kg -1 respectively). In addition, factor analyses associated these elements with anthropogenic activity, whereas other elements were attributed to natural sources. Subsequent clustering also facilitated the differentiation between the northern area studied (only limited Pb pollution found) and the southern area (pattern of coal combustion, including simultaneous anomalies of trace elements and benzo(a)pyrene). A normalized soil pollution index (SPI) was calculated by kriging, using only the elements falling above threshold levels; therefore point-source polluted zones in the northern area and diffuse contamination in the south were identified. In addition, in the six mapping units with the highest SPIs of the fifty studied, we observed low bioavailability for most of the elements that surpassed the threshold levels. However, some anomalies of Pb contents and the pollution fingerprint in the central area of the southern grid call for further site-specific studies. On the whole, the combination of a multivariate (geo) statistic approach and a bioavailability assessment allowed us to efficiently identify sources of contamination and potential risks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Robust geostatistical analysis of spatial data

NASA Astrophysics Data System (ADS)

Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.

2013-04-01

Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R.M. 2007. Robust estimation of the variogram by residual maximum likelihood. Geoderma 140: 62-72. Richardson, A.M. and Welsh, A.H. 1995. Robust restricted maximum likelihood in mixed linear models. Biometrics 51: 1429-1439. Welsh, A.H. and Richardson, A.M. 1997. Approaches to the robust estimation of mixed models. In: Handbook of Statistics Vol. 15, Elsevier, pp. 343-384.

Spatial Variability of Plant Available Water, Soil Organic Carbon, and Microbial Biomass under Divergent Land Uses: A Comparison among Regression-Kriging, Cokriging, and Regression-Cokriging

NASA Astrophysics Data System (ADS)

Kiani, M.; Hernandez Ramirez, G.; Quideau, S.

2016-12-01

Improved knowledge about the spatial variability of plant available water (PAW), soil organic carbon (SOC), and microbial biomass carbon (MBC) as affected by land-use systems can underpin the identification and inventory of beneficial ecosystem good and services in both agricultural and wild lands. Little research has been done that addresses the spatial patterns of PAW, SOC, and MBC under different land use types at a field scale. Therefore, we collected 56 soil samples (5-10 cm depth increment), using a nested cyclic sampling design within both a native grassland (NG) site and an irrigated cultivated (IC) site located near Brooks, Alberta. Using classical statistical and geostatistical methods, we characterized the spatial heterogeneities of PAW, SOC, and MBC under NG and IC using several geostatistical methods such as ordinary kriging (OK), regression-kriging (RK), cokriging (COK), and regression-cokriging (RCOK). Converting the native grassland to irrigated cultivated land altered soil pore distribution by reducing macroporosity which led to lower saturated water content and half hydraulic conductivity in IC compared to NG. This conversion also decreased the relative abundance of gram-negative bacteria, while increasing both the proportion of gram-positive bacteria and MBC concentration. At both studied sites, the best fitted spatial model was Gaussian based on lower RSS and higher R2 as criteria. The IC had stronger degree of spatial dependence and longer range of spatial auto-correlation revealing a homogenization of the spatial variability of soil properties as a result of intensive, recurrent agricultural activities. Comparison of OK, RK, COK, and RCOK approaches indicated that cokriging method had the best performance demonstrating a profound improvement in the accuracy of spatial estimations of PAW, SOC, and MBC. It seems that the combination of terrain covariates such as elevation and depth-to-water with kriging techniques offers more capability for incorporating explicit ancillary information in predictive soil mapping. Overall, identification of spatial patterns of soil properties in agricultural lands gives a bird's eye view to land owners to implement and improve management practices which lead to more sustainable production.

Accounting for rate instability and spatial patterns in the boundary analysis of cancer mortality maps

PubMed Central

Goovaerts, Pierre

2006-01-01

Boundary analysis of cancer maps may highlight areas where causative exposures change through geographic space, the presence of local populations with distinct cancer incidences, or the impact of different cancer control methods. Too often, such analysis ignores the spatial pattern of incidence or mortality rates and overlooks the fact that rates computed from sparsely populated geographic entities can be very unreliable. This paper proposes a new methodology that accounts for the uncertainty and spatial correlation of rate data in the detection of significant edges between adjacent entities or polygons. Poisson kriging is first used to estimate the risk value and the associated standard error within each polygon, accounting for the population size and the risk semivariogram computed from raw rates. The boundary statistic is then defined as half the absolute difference between kriged risks. Its reference distribution, under the null hypothesis of no boundary, is derived through the generation of multiple realizations of the spatial distribution of cancer risk values. This paper presents three types of neutral models generated using methods of increasing complexity: the common random shuffle of estimated risk values, a spatial re-ordering of these risks, or p-field simulation that accounts for the population size within each polygon. The approach is illustrated using age-adjusted pancreatic cancer mortality rates for white females in 295 US counties of the Northeast (1970–1994). Simulation studies demonstrate that Poisson kriging yields more accurate estimates of the cancer risk and how its value changes between polygons (i.e. boundary statistic), relatively to the use of raw rates or local empirical Bayes smoother. When used in conjunction with spatial neutral models generated by p-field simulation, the boundary analysis based on Poisson kriging estimates minimizes the proportion of type I errors (i.e. edges wrongly declared significant) while the frequency of these errors is predicted well by the p-value of the statistical test. PMID:19023455

GEOSTATISTICAL SAMPLING DESIGNS FOR HAZARDOUS WASTE SITES

EPA Science Inventory

This chapter discusses field sampling design for environmental sites and hazardous waste sites with respect to random variable sampling theory, Gy's sampling theory, and geostatistical (kriging) sampling theory. The literature often presents these sampling methods as an adversari...

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors.

PubMed

Ma, Xiaolei; Luan, Sen; Du, Bowen; Yu, Bin

2017-09-21

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks.

Distributed database kriging for adaptive sampling (D²KAS)

DOE PAGES

Roehm, Dominic; Pavel, Robert S.; Barros, Kipton; ...

2015-03-18

We present an adaptive sampling method supplemented by a distributed database and a prediction method for multiscale simulations using the Heterogeneous Multiscale Method. A finite-volume scheme integrates the macro-scale conservation laws for elastodynamics, which are closed by momentum and energy fluxes evaluated at the micro-scale. In the original approach, molecular dynamics (MD) simulations are launched for every macro-scale volume element. Our adaptive sampling scheme replaces a large fraction of costly micro-scale MD simulations with fast table lookup and prediction. The cloud database Redis provides the plain table lookup, and with locality aware hashing we gather input data for our predictionmore » scheme. For the latter we use kriging, which estimates an unknown value and its uncertainty (error) at a specific location in parameter space by using weighted averages of the neighboring points. We find that our adaptive scheme significantly improves simulation performance by a factor of 2.5 to 25, while retaining high accuracy for various choices of the algorithm parameters.« less

Spatio-Temporal Field Estimation Using Kriged Kalman Filter (KKF) with Sparsity-Enforcing Sensor Placement.

PubMed

Roy, Venkat; Simonetto, Andrea; Leus, Geert

2018-06-01

We propose a sensor placement method for spatio-temporal field estimation based on a kriged Kalman filter (KKF) using a network of static or mobile sensors. The developed framework dynamically designs the optimal constellation to place the sensors. We combine the estimation error (for the stationary as well as non-stationary component of the field) minimization problem with a sparsity-enforcing penalty to design the optimal sensor constellation in an economic manner. The developed sensor placement method can be directly used for a general class of covariance matrices (ill-conditioned or well-conditioned) modelling the spatial variability of the stationary component of the field, which acts as a correlated observation noise, while estimating the non-stationary component of the field. Finally, a KKF estimator is used to estimate the field using the measurements from the selected sensing locations. Numerical results are provided to exhibit the feasibility of the proposed dynamic sensor placement followed by the KKF estimation method.

Topsoil moisture mapping using geostatistical techniques under different Mediterranean climatic conditions.

PubMed

Martínez-Murillo, J F; Hueso-González, P; Ruiz-Sinoga, J D

2017-10-01

Soil mapping has been considered as an important factor in the widening of Soil Science and giving response to many different environmental questions. Geostatistical techniques, through kriging and co-kriging techniques, have made possible to improve the understanding of eco-geomorphologic variables, e.g., soil moisture. This study is focused on mapping of topsoil moisture using geostatistical techniques under different Mediterranean climatic conditions (humid, dry and semiarid) in three small watersheds and considering topography and soil properties as key factors. A Digital Elevation Model (DEM) with a resolution of 1×1m was derived from a topographical survey as well as soils were sampled to analyzed soil properties controlling topsoil moisture, which was measured during 4-years. Afterwards, some topography attributes were derived from the DEM, the soil properties analyzed in laboratory, and the topsoil moisture was modeled for the entire watersheds applying three geostatistical techniques: i) ordinary kriging; ii) co-kriging considering as co-variate topography attributes; and iii) co-kriging ta considering as co-variates topography attributes and gravel content. The results indicated topsoil moisture was more accurately mapped in the dry and semiarid watersheds when co-kriging procedure was performed. The study is a contribution to improve the efficiency and accuracy of studies about the Mediterranean eco-geomorphologic system and soil hydrology in field conditions. Copyright © 2017 Elsevier B.V. All rights reserved.

Development of Spatial Scaling Technique of Forest Health Sample Point Information

NASA Astrophysics Data System (ADS)

Lee, J. H.; Ryu, J. E.; Chung, H. I.; Choi, Y. Y.; Jeon, S. W.; Kim, S. H.

2018-04-01

Forests provide many goods, Ecosystem services, and resources to humans such as recreation air purification and water protection functions. In rececnt years, there has been an increase in the factors that threaten the health of forests such as global warming due to climate change, environmental pollution, and the increase in interest in forests, and efforts are being made in various countries for forest management. Thus, existing forest ecosystem survey method is a monitoring method of sampling points, and it is difficult to utilize forests for forest management because Korea is surveying only a small part of the forest area occupying 63.7 % of the country (Ministry of Land Infrastructure and Transport Korea, 2016). Therefore, in order to manage large forests, a method of interpolating and spatializing data is needed. In this study, The 1st Korea Forest Health Management biodiversity Shannon;s index data (National Institute of Forests Science, 2015) were used for spatial interpolation. Two widely used methods of interpolation, Kriging method and IDW(Inverse Distance Weighted) method were used to interpolate the biodiversity index. Vegetation indices SAVI, NDVI, LAI and SR were used. As a result, Kriging method was the most accurate method.

A comparative research of different ensemble surrogate models based on set pair analysis for the DNAPL-contaminated aquifer remediation strategy optimization.

PubMed

Hou, Zeyu; Lu, Wenxi; Xue, Haibo; Lin, Jin

2017-08-01

Surrogate-based simulation-optimization technique is an effective approach for optimizing the surfactant enhanced aquifer remediation (SEAR) strategy for clearing DNAPLs. The performance of the surrogate model, which is used to replace the simulation model for the aim of reducing computation burden, is the key of corresponding researches. However, previous researches are generally based on a stand-alone surrogate model, and rarely make efforts to improve the approximation accuracy of the surrogate model to the simulation model sufficiently by combining various methods. In this regard, we present set pair analysis (SPA) as a new method to build ensemble surrogate (ES) model, and conducted a comparative research to select a better ES modeling pattern for the SEAR strategy optimization problems. Surrogate models were developed using radial basis function artificial neural network (RBFANN), support vector regression (SVR), and Kriging. One ES model is assembling RBFANN model, SVR model, and Kriging model using set pair weights according their performance, and the other is assembling several Kriging (the best surrogate modeling method of three) models built with different training sample datasets. Finally, an optimization model, in which the ES model was embedded, was established to obtain the optimal remediation strategy. The results showed the residuals of the outputs between the best ES model and simulation model for 100 testing samples were lower than 1.5%. Using an ES model instead of the simulation model was critical for considerably reducing the computation time of simulation-optimization process and maintaining high computation accuracy simultaneously. Copyright © 2017 Elsevier B.V. All rights reserved.

Study and Optimization of Helicopter Subfloor Energy Absorption Structure with Foldcore Sandwich Structures

NASA Astrophysics Data System (ADS)

HuaZhi, Zhou; ZhiJin, Wang

2017-11-01

The intersection element is an important part of the helicopter subfloor structure. In order to improve the crashworthiness properties, the floor and the skin of the intersection element are replaced with foldcore sandwich structures. Foldcore is a kind of high-energy absorption structure. Compared with original structure, the new intersection element shows better buffering capacity and energy-absorption capacity. To reduce structure’s mass while maintaining the crashworthiness requirements satisfied, optimization of the intersection element geometric parameters is conducted. An optimization method using NSGA-II and Anisotropic Kriging is used. A significant CPU time saving can be obtained by replacing numerical model with Anisotropic Kriging surrogate model. The operation allows 17.15% reduce of the intersection element mass.

Uncertainty in Random Forests: What does it mean in a spatial context?

NASA Astrophysics Data System (ADS)

Klump, Jens; Fouedjio, Francky

2017-04-01

Geochemical surveys are an important part of exploration for mineral resources and in environmental studies. The samples and chemical analyses are often laborious and difficult to obtain and therefore come at a high cost. As a consequence, these surveys are characterised by datasets with large numbers of variables but relatively few data points when compared to conventional big data problems. With more remote sensing platforms and sensor networks being deployed, large volumes of auxiliary data of the surveyed areas are becoming available. The use of these auxiliary data has the potential to improve the prediction of chemical element concentrations over the whole study area. Kriging is a well established geostatistical method for the prediction of spatial data but requires significant pre-processing and makes some basic assumptions about the underlying distribution of the data. Some machine learning algorithms, on the other hand, may require less data pre-processing and are non-parametric. In this study we used a dataset provided by Kirkwood et al. [1] to explore the potential use of Random Forest in geochemical mapping. We chose Random Forest because it is a well understood machine learning method and has the advantage that it provides us with a measure of uncertainty. By comparing Random Forest to Kriging we found that both methods produced comparable maps of estimated values for our variables of interest. Kriging outperformed Random Forest for variables of interest with relatively strong spatial correlation. The measure of uncertainty provided by Random Forest seems to be quite different to the measure of uncertainty provided by Kriging. In particular, the lack of spatial context can give misleading results in areas without ground truth data. In conclusion, our preliminary results show that the model driven approach in geostatistics gives us more reliable estimates for our target variables than Random Forest for variables with relatively strong spatial correlation. However, in cases of weak spatial correlation Random Forest, as a nonparametric method, may give the better results once we have a better understanding of the meaning of its uncertainty measures in a spatial context. References [1] Kirkwood, C., M. Cave, D. Beamish, S. Grebby, and A. Ferreira (2016), A machine learning approach to geochemical mapping, Journal of Geochemical Exploration, 163, 28-40, doi:10.1016/j.gexplo.2016.05.003.

Methods for Data-based Delineation of Spatial Regions

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

Wilson, John E.

In data analysis, it is often useful to delineate or segregate areas of interest from the general population of data in order to concentrate further analysis efforts on smaller areas. Three methods are presented here for automatically generating polygons around spatial data of interest. Each method addresses a distinct data type. These methods were developed for and implemented in the sample planning tool called Visual Sample Plan (VSP). Method A is used to delineate areas of elevated values in a rectangular grid of data (raster). The data used for this method are spatially related. Although VSP uses data from amore » kriging process for this method, it will work for any type of data that is spatially coherent and appears on a regular grid. Method B is used to surround areas of interest characterized by individual data points that are congregated within a certain distance of each other. Areas where data are “clumped” together spatially will be delineated. Method C is used to recreate the original boundary in a raster of data that separated data values from non-values. This is useful when a rectangular raster of data contains non-values (missing data) that indicate they were outside of some original boundary. If the original boundary is not delivered with the raster, this method will approximate the original boundary.« less

The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.

PubMed

Thamareerat, N; Luadsong, A; Aschariyaphotha, N

2016-01-01

In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier-Stokes equations in two dimensions. We first employ the meshless local Petrov-Galerkin (MLPG) method based on a local weak formulation to form the system of discretized equations and then we will approximate the time fractional derivative interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging interpolation which possesses the Kronecker delta property is applied to construct shape functions. This research aims to extend and develop further the applicability of the truly MLPG method to the generalized incompressible Navier-Stokes equations. Two numerical examples are provided to illustrate the accuracy and efficiency of the proposed algorithm. Very good agreement between the numerically and analytically computed solutions can be observed in the verification. The present MLPG method has proved its efficiency and reliability for solving the two-dimensional time fractional Navier-Stokes equations arising in fluid dynamics as well as several other problems in science and engineering.

Distributed processing of a GPS receiver network for a regional ionosphere map

NASA Astrophysics Data System (ADS)

Choi, Kwang Ho; Hoo Lim, Joon; Yoo, Won Jae; Lee, Hyung Keun

2018-01-01

This paper proposes a distributed processing method applicable to GPS receivers in a network to generate a regional ionosphere map accurately and reliably. For accuracy, the proposed method is operated by multiple local Kalman filters and Kriging estimators. Each local Kalman filter is applied to a dual-frequency receiver to estimate the receiver’s differential code bias and vertical ionospheric delays (VIDs) at different ionospheric pierce points. The Kriging estimator selects and combines several VID estimates provided by the local Kalman filters to generate the VID estimate at each ionospheric grid point. For reliability, the proposed method uses receiver fault detectors and satellite fault detectors. Each receiver fault detector compares the VID estimates of the same local area provided by different local Kalman filters. Each satellite fault detector compares the VID estimate of each local area with that projected from the other local areas. Compared with the traditional centralized processing method, the proposed method is advantageous in that it considerably reduces the computational burden of each single Kalman filter and enables flexible fault detection, isolation, and reconfiguration capability. To evaluate the performance of the proposed method, several experiments with field collected measurements were performed.

Field Scale Spatial Modelling of Surface Soil Quality Attributes in Controlled Traffic Farming

NASA Astrophysics Data System (ADS)

Guenette, Kris; Hernandez-Ramirez, Guillermo

2017-04-01

The employment of controlled traffic farming (CTF) can yield improvements to soil quality attributes through the confinement of equipment traffic to tramlines with the field. There is a need to quantify and explain the spatial heterogeneity of soil quality attributes affected by CTF to further improve our understanding and modelling ability of field scale soil dynamics. Soil properties such as available nitrogen (AN), pH, soil total nitrogen (STN), soil organic carbon (SOC), bulk density, macroporosity, soil quality S-Index, plant available water capacity (PAWC) and unsaturated hydraulic conductivity (Km) were analysed and compared among trafficked and un-trafficked areas. We contrasted standard geostatistical methods such as ordinary kriging (OK) and covariate kriging (COK) as well as the hybrid method of regression kriging (ROK) to predict the spatial distribution of soil properties across two annual cropland sites actively employing CTF in Alberta, Canada. Field scale variability was quantified more accurately through the inclusion of covariates; however, the use of ROK was shown to improve model accuracy despite the regression model composition limiting the robustness of the ROK method. The exclusion of traffic from the un-trafficked areas displayed significant improvements to bulk density, macroporosity and Km while subsequently enhancing AN, STN and SOC. The ability of the regression models and the ROK method to account for spatial trends led to the highest goodness-of-fit and lowest error achieved for the soil physical properties, as the rigid traffic regime of CTF altered their spatial distribution at the field scale. Conversely, the COK method produced the most optimal predictions for the soil nutrient properties and Km. The use of terrain covariates derived from light ranging and detection (LiDAR), such as of elevation and topographic position index (TPI), yielded the best models in the COK method at the field scale.

Evaluation and correction of uncertainty due to Gaussian approximation in radar - rain gauge merging using kriging with external drift

NASA Astrophysics Data System (ADS)

Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.

2016-12-01

It is widely recognised that merging radar rainfall estimates (RRE) with rain gauge data can improve the RRE and provide areal and temporal coverage that rain gauges cannot offer. Many methods to merge radar and rain gauge data are based on kriging and require an assumption of Gaussianity on the variable of interest. In particular, this work looks at kriging with external drift (KED), because it is an efficient, widely used, and well performing merging method. Rainfall, especially at finer temporal scale, does not have a normal distribution and presents a bi-modal skewed distribution. In some applications a Gaussianity assumption is made, without any correction. In other cases, variables are transformed in order to obtain a distribution closer to Gaussian. This work has two objectives: 1) compare different transformation methods in merging applications; 2) evaluate the uncertainty arising when untransformed rainfall data is used in KED. The comparison of transformation methods is addressed under two points of view. On the one hand, the ability to reproduce the original probability distribution after back-transformation of merged products is evaluated with qq-plots, on the other hand the rainfall estimates are compared with an independent set of rain gauge measurements. The tested methods are 1) no transformation, 2) Box-Cox transformations with parameter equal to λ=0.5 (square root), 3) λ=0.25 (square root - square root), and 4) λ=0.1 (almost logarithmic), 5) normal quantile transformation, and 6) singularity analysis. The uncertainty associated with the use of non-transformed data in KED is evaluated in comparison with the best performing product. The methods are tested on a case study in Northern England, using hourly data from 211 tipping bucket rain gauges from the Environment Agency and radar rainfall data at 1 km/5-min resolutions from the UK Met Office. In addition, 25 independent rain gauges from the UK Met Office were used to assess the merged products.

Assessing groundwater quality for irrigation using indicator kriging method

NASA Astrophysics Data System (ADS)

Delbari, Masoomeh; Amiri, Meysam; Motlagh, Masoud Bahraini

2016-11-01

One of the key parameters influencing sprinkler irrigation performance is water quality. In this study, the spatial variability of groundwater quality parameters (EC, SAR, Na+, Cl-, HCO3 - and pH) was investigated by geostatistical methods and the most suitable areas for implementation of sprinkler irrigation systems in terms of water quality are determined. The study was performed in Fasa county of Fars province using 91 water samples. Results indicated that all parameters are moderately to strongly spatially correlated over the study area. The spatial distribution of pH and HCO3 - was mapped using ordinary kriging. The probability of concentrations of EC, SAR, Na+ and Cl- exceeding a threshold limit in groundwater was obtained using indicator kriging (IK). The experimental indicator semivariograms were often fitted well by a spherical model for SAR, EC, Na+ and Cl-. For HCO3 - and pH, an exponential model was fitted to the experimental semivariograms. Probability maps showed that the risk of EC, SAR, Na+ and Cl- exceeding the given critical threshold is higher in lower half of the study area. The most proper agricultural lands for sprinkler irrigation implementation were identified by evaluating all probability maps. The suitable areas for sprinkler irrigation design were determined to be 25,240 hectares, which is about 34 percent of total agricultural lands and are located in northern and eastern parts. Overall the results of this study showed that IK is an appropriate approach for risk assessment of groundwater pollution, which is useful for a proper groundwater resources management.

Building on crossvalidation for increasing the quality of geostatistical modeling

USGS Publications Warehouse

Olea, R.A.

2012-01-01

The random function is a mathematical model commonly used in the assessment of uncertainty associated with a spatially correlated attribute that has been partially sampled. There are multiple algorithms for modeling such random functions, all sharing the requirement of specifying various parameters that have critical influence on the results. The importance of finding ways to compare the methods and setting parameters to obtain results that better model uncertainty has increased as these algorithms have grown in number and complexity. Crossvalidation has been used in spatial statistics, mostly in kriging, for the analysis of mean square errors. An appeal of this approach is its ability to work with the same empirical sample available for running the algorithms. This paper goes beyond checking estimates by formulating a function sensitive to conditional bias. Under ideal conditions, such function turns into a straight line, which can be used as a reference for preparing measures of performance. Applied to kriging, deviations from the ideal line provide sensitivity to the semivariogram lacking in crossvalidation of kriging errors and are more sensitive to conditional bias than analyses of errors. In terms of stochastic simulation, in addition to finding better parameters, the deviations allow comparison of the realizations resulting from the applications of different methods. Examples show improvements of about 30% in the deviations and approximately 10% in the square root of mean square errors between reasonable starting modelling and the solutions according to the new criteria. ?? 2011 US Government.

Spatial Analysis of Geothermal Resource Potential in New York and Pennsylvania: A Stratified Kriging Approach

NASA Astrophysics Data System (ADS)

Smith, J. D.; Whealton, C. A.; Stedinger, J. R.

2014-12-01

Resource assessments for low-grade geothermal applications employ available well temperature measurements to determine if the resource potential is sufficient for supporting district heating opportunities. This study used a compilation of bottomhole temperature (BHT) data from recent unconventional shale oil and gas wells, along with legacy oil, gas, and storage wells, in Pennsylvania (PA) and New York (NY). Our study's goal was to predict the geothermal resource potential and associated uncertainty for the NY-PA region using kriging interpolation. The dataset was scanned for outliers, and some observations were removed. Because these wells were drilled for reasons other than geothermal resource assessment, their spatial density varied widely. An exploratory spatial statistical analysis revealed differences in the spatial structure of the geothermal gradient data (the kriging semi-variogram and its nugget variance, shape, sill, and the degree of anisotropy). As a result, a stratified kriging procedure was adopted to better capture the statistical structure of the data, to generate an interpolated surface, and to quantify the uncertainty of the computed surface. The area was stratified reflecting different physiographic provinces in NY and PA that have geologic properties likely related to variations in the value of the geothermal gradient. The kriging prediction and the variance-of-prediction were determined for each province by the generation of a semi-variogram using only the wells that were located within that province. A leave-one-out cross validation (LOOCV) was conducted as a diagnostic tool. The results of stratified kriging were compared to kriging using the whole region to determine the impact of stratification. The two approaches provided similar predictions of the geothermal gradient. However, the variance-of-prediction was different. The stratified approach is recommended because it gave a more appropriate site-specific characterization of uncertainty based upon a more realistic description of the statistical structure of the data given the geologic characteristics of each province.

Mapping the spatial pattern of temperate forest above ground biomass by integrating airborne lidar with Radarsat-2 imagery via geostatistical models

NASA Astrophysics Data System (ADS)

Li, Wang; Niu, Zheng; Gao, Shuai; Wang, Cheng

2014-11-01

Light Detection and Ranging (LiDAR) and Synthetic Aperture Radar (SAR) are two competitive active remote sensing techniques in forest above ground biomass estimation, which is important for forest management and global climate change study. This study aims to further explore their capabilities in temperate forest above ground biomass (AGB) estimation by emphasizing the spatial auto-correlation of variables obtained from these two remote sensing tools, which is a usually overlooked aspect in remote sensing applications to vegetation studies. Remote sensing variables including airborne LiDAR metrics, backscattering coefficient for different SAR polarizations and their ratio variables for Radarsat-2 imagery were calculated. First, simple linear regression models (SLR) was established between the field-estimated above ground biomass and the remote sensing variables. Pearson's correlation coefficient (R2) was used to find which LiDAR metric showed the most significant correlation with the regression residuals and could be selected as co-variable in regression co-kriging (RCoKrig). Second, regression co-kriging was conducted by choosing the regression residuals as dependent variable and the LiDAR metric (Hmean) with highest R2 as co-variable. Third, above ground biomass over the study area was estimated using SLR model and RCoKrig model, respectively. The results for these two models were validated using the same ground points. Results showed that both of these two methods achieved satisfactory prediction accuracy, while regression co-kriging showed the lower estimation error. It is proved that regression co-kriging model is feasible and effective in mapping the spatial pattern of AGB in the temperate forest using Radarsat-2 data calibrated by airborne LiDAR metrics.

Geostatistical simulations for radon indoor with a nested model including the housing factor.

PubMed

Cafaro, C; Giovani, C; Garavaglia, M

2016-01-01

The radon prone areas definition is matter of many researches in radioecology, since radon is considered a leading cause of lung tumours, therefore the authorities ask for support to develop an appropriate sanitary prevention strategy. In this paper, we use geostatistical tools to elaborate a definition accounting for some of the available information about the dwellings. Co-kriging is the proper interpolator used in geostatistics to refine the predictions by using external covariates. In advance, co-kriging is not guaranteed to improve significantly the results obtained by applying the common lognormal kriging. Here, instead, such multivariate approach leads to reduce the cross-validation residual variance to an extent which is deemed as satisfying. Furthermore, with the application of Monte Carlo simulations, the paradigm provides a more conservative radon prone areas definition than the one previously made by lognormal kriging. Copyright © 2015 Elsevier Ltd. All rights reserved.

Geostatistical methods in evaluating spatial variability of groundwater quality in Al-Kharj Region, Saudi Arabia

NASA Astrophysics Data System (ADS)

Al-Omran, Abdulrasoul M.; Aly, Anwar A.; Al-Wabel, Mohammad I.; Al-Shayaa, Mohammad S.; Sallam, Abdulazeam S.; Nadeem, Mahmoud E.

2017-11-01

The analyses of 180 groundwater samples of Al-Kharj, Saudi Arabia, recorded that most groundwaters are unsuitable for drinking uses due to high salinity; however, they can be used for irrigation with some restriction. The electric conductivity of studied groundwater ranged between 1.05 and 10.15 dS m-1 with an average of 3.0 dS m-1. Nitrate was also found in high concentration in some groundwater. Piper diagrams revealed that the majority of water samples are magnesium-calcium/sulfate-chloride water type. The Gibbs's diagram revealed that the chemical weathering of rock-forming minerals and evaporation are influencing the groundwater chemistry. A kriging method was used for predicting spatial distribution of salinity (EC dS m-1) and NO3 - (mg L-1) in Al-Kharj's groundwater using data of 180 different locations. After normalization of data, variogram was drawn, for selecting suitable model for fitness on experimental variogram, less residual sum of squares value was used. Then cross-validation and root mean square error were used to select the best method for interpolation. The kriging method was found suitable methods for groundwater interpolation and management using either GS+ or ArcGIS.

Comparison of regression and geostatistical methods for mapping Leaf Area Index (LAI) with Landsat ETM+ data over a boreal forest.

Treesearch

Mercedes Berterretche; Andrew T. Hudak; Warren B. Cohen; Thomas K. Maiersperger; Stith T. Gower; Jennifer Dungan

2005-01-01

This study compared aspatial and spatial methods of using remote sensing and field data to predict maximum growing season leaf area index (LAI) maps in a boreal forest in Manitoba, Canada. The methods tested were orthogonal regression analysis (reduced major axis, RMA) and two geostatistical techniques: kriging with an external drift (KED) and sequential Gaussian...

Spatial Copula Model for Imputing Traffic Flow Data from Remote Microwave Sensors

PubMed Central

Ma, Xiaolei; Du, Bowen; Yu, Bin

2017-01-01

Issues of missing data have become increasingly serious with the rapid increase in usage of traffic sensors. Analyses of the Beijing ring expressway have showed that up to 50% of microwave sensors pose missing values. The imputation of missing traffic data must be urgently solved although a precise solution that cannot be easily achieved due to the significant number of missing portions. In this study, copula-based models are proposed for the spatial interpolation of traffic flow from remote traffic microwave sensors. Most existing interpolation methods only rely on covariance functions to depict spatial correlation and are unsuitable for coping with anomalies due to Gaussian consumption. Copula theory overcomes this issue and provides a connection between the correlation function and the marginal distribution function of traffic flow. To validate copula-based models, a comparison with three kriging methods is conducted. Results indicate that copula-based models outperform kriging methods, especially on roads with irregular traffic patterns. Copula-based models demonstrate significant potential to impute missing data in large-scale transportation networks. PMID:28934164

Optimization and Analysis of Centrifugal Pump considering Fluid-Structure Interaction

PubMed Central

Hu, Sanbao

2014-01-01

This paper presents the optimization of vibrations of centrifugal pump considering fluid-structure interaction (FSI). A set of centrifugal pumps with various blade shapes were studied using FSI method, in order to investigate the transient vibration performance. The Kriging model, based on the results of the FSI simulations, was established to approximate the relationship between the geometrical parameters of pump impeller and the root mean square (RMS) values of the displacement response at the pump bearing block. Hence, multi-island genetic algorithm (MIGA) has been implemented to minimize the RMS value of the impeller displacement. A prototype of centrifugal pump has been manufactured and an experimental validation of the optimization results has been carried out. The comparison among results of Kriging surrogate model, FSI simulation, and experimental test showed a good consistency of the three approaches. Finally, the transient mechanical behavior of pump impeller has been investigated using FSI method based on the optimized geometry parameters of pump impeller. PMID:25197690

Using geostatistical methods to estimate snow water equivalence distribution in a mountain watershed

USGS Publications Warehouse

Balk, B.; Elder, K.; Baron, Jill S.

1998-01-01

Knowledge of the spatial distribution of snow water equivalence (SWE) is necessary to adequately forecast the volume and timing of snowmelt runoff.  In April 1997, peak accumulation snow depth and density measurements were independently taken in the Loch Vale watershed (6.6 km2), Rocky Mountain National Park, Colorado.  Geostatistics and classical statistics were used to estimate SWE distribution across the watershed.  Snow depths were spatially distributed across the watershed through kriging interpolation methods which provide unbiased estimates that have minimum variances.  Snow densities were spatially modeled through regression analysis.  Combining the modeled depth and density with snow-covered area (SCA produced an estimate of the spatial distribution of SWE.  The kriged estimates of snow depth explained 37-68% of the observed variance in the measured depths.  Steep slopes, variably strong winds, and complex energy balance in the watershed contribute to a large degree of heterogeneity in snow depth.

Combining Ordinary Kriging with wind directions to identify sources of industrial odors in Portland, Oregon.

PubMed

Eckmann, Ted C; Wright, Samantha G; Simpson, Logan K; Walker, Joe L; Kolmes, Steven A; Houck, James E; Velasquez, Sandra C

2018-01-01

This study combines Ordinary Kriging, odor monitoring, and wind direction data to demonstrate how these elements can be applied to identify the source of an industrial odor. The specific case study used as an example of how to address this issue was the University Park neighborhood of Portland, Oregon (USA) where residents frequently complain about industrial odors, and suspect the main source to be a nearby Daimler Trucks North America LLC manufacturing plant. We collected 19,665 odor observations plus 105,120 wind measurements, using an automated weather station to measure winds in the area at five-minute intervals, logging continuously from December 2014 through November 2015, while we also measured odors at 19 locations, three times per day, using methods from the American Society of the International Association for Testing and Materials. Our results quantify how winds vary with season and time of day when industrial odors were observed versus when they were not observed, while also mapping spatiotemporal patterns in these odors using Ordinary Kriging. Our analyses show that industrial odors were detected most frequently to the northwest of the Daimler plant, mostly when winds blew from the southeast, suggesting Daimler's facility is a likely source for much of this odor.

Applicability of Various Interpolation Approaches for High Resolution Spatial Mapping of Climate Data in Korea

NASA Astrophysics Data System (ADS)

Jo, A.; Ryu, J.; Chung, H.; Choi, Y.; Jeon, S.

2018-04-01

The purpose of this study is to create a new dataset of spatially interpolated monthly climate data for South Korea at high spatial resolution (approximately 30m) by performing various spatio-statistical interpolation and comparing with forecast LDAPS gridded climate data provided from Korea Meterological Administration (KMA). Automatic Weather System (AWS) and Automated Synoptic Observing System (ASOS) data in 2017 obtained from KMA were included for the spatial mapping of temperature and rainfall; instantaneous temperature and 1-hour accumulated precipitation at 09:00 am on 31th March, 21th June, 23th September, and 24th December. Among observation data, 80 percent of the total point (478) and remaining 120 points were used for interpolations and for quantification, respectively. With the training data and digital elevation model (DEM) with 30 m resolution, inverse distance weighting (IDW), co-kriging, and kriging were performed by using ArcGIS10.3.1 software and Python 3.6.4. Bias and root mean square were computed to compare prediction performance quantitatively. When statistical analysis was performed for each cluster using 20 % validation data, co kriging was more suitable for spatialization of instantaneous temperature than other interpolation method. On the other hand, IDW technique was appropriate for spatialization of precipitation.

Combining Ordinary Kriging with wind directions to identify sources of industrial odors in Portland, Oregon

PubMed Central

Kolmes, Steven A.; Houck, James E.; Velasquez, Sandra C.

2018-01-01

This study combines Ordinary Kriging, odor monitoring, and wind direction data to demonstrate how these elements can be applied to identify the source of an industrial odor. The specific case study used as an example of how to address this issue was the University Park neighborhood of Portland, Oregon (USA) where residents frequently complain about industrial odors, and suspect the main source to be a nearby Daimler Trucks North America LLC manufacturing plant. We collected 19,665 odor observations plus 105,120 wind measurements, using an automated weather station to measure winds in the area at five-minute intervals, logging continuously from December 2014 through November 2015, while we also measured odors at 19 locations, three times per day, using methods from the American Society of the International Association for Testing and Materials. Our results quantify how winds vary with season and time of day when industrial odors were observed versus when they were not observed, while also mapping spatiotemporal patterns in these odors using Ordinary Kriging. Our analyses show that industrial odors were detected most frequently to the northwest of the Daimler plant, mostly when winds blew from the southeast, suggesting Daimler’s facility is a likely source for much of this odor. PMID:29385136

Assessment of methane emission and oxidation at Air Hitam Landfill site cover soil in wet tropical climate.

PubMed

Abushammala, Mohammed F M; Basri, Noor Ezlin Ahmad; Elfithri, Rahmah

2013-12-01

Methane (CH₄) emissions and oxidation were measured at the Air Hitam sanitary landfill in Malaysia and were modeled using the Intergovernmental Panel on Climate Change waste model to estimate the CH₄ generation rate constant, k. The emissions were measured at several locations using a fabricated static flux chamber. A combination of gas concentrations in soil profiles and surface CH₄ and carbon dioxide (CO₂) emissions at four monitoring locations were used to estimate the CH₄ oxidation capacity. The temporal variations in CH₄ and CO₂ emissions were also investigated in this study. Geospatial means using point kriging and inverse distance weight (IDW), as well as arithmetic and geometric means, were used to estimate total CH₄ emissions. The point kriging, IDW, and arithmetic means were almost identical and were two times higher than the geometric mean. The CH₄ emission geospatial means estimated using the kriging and IDW methods were 30.81 and 30.49 gm(−2) day(−1), respectively. The total CH₄ emissions from the studied area were 53.8 kg day(−1). The mean of the CH₄ oxidation capacity was 27.5 %. The estimated value of k is 0.138 year(−1). Special consideration must be given to the CH₄ oxidation in the wet tropical climate for enhancing CH₄ emission reduction.

Determination of Semivariogram Models to Krige Hourly and Daily Solar Irradiance in Western Nebraska(.

NASA Astrophysics Data System (ADS)

Merino, G. G.; Jones, D.; Stooksbury, D. E.; Hubbard, K. G.

2001-06-01

In this paper, linear and spherical semivariogram models were determined for use in kriging hourly and daily solar irradiation for every season of the year. The data used to generate the models were from 18 weather stations in western Nebraska. The models generated were tested using cross validation. The performance of the spherical and linear semivariogram models were compared with each other and also with the semivariogram models based on the best fit to the sample semivariogram of a particular day or hour. There were no significant differences in the performance of the three models. This result and the comparable errors produced by the models in kriging indicated that the linear and spherical models could be used to perform kriging at any hour and day of the year without deriving an individual semivariogram model for that day or hour.The seasonal mean absolute errors associated with kriging, within the network, when using the spherical or the linear semivariograms models were between 10% and 13% of the mean irradiation for daily irradiation and between 12% and 20% for hourly irradiation. These errors represent an improvement of 1%-2% when compared with replacing data at a given site with the data of the nearest weather station.

CPLFD-GDPT5: high-resolution gridded daily precipitation and temperature dataset for two largest Polish river basins

NASA Astrophysics Data System (ADS)

Berezowski, T.; Szcześniak, M.; Kardel, I.; Michałowski, R.; Okruszko, T.; Mezghani, A.; Piniewski, M.

2015-12-01

The CHASE-PL Forcing Data-Gridded Daily Precipitation and Temperature Dataset-5 km (CPLFD-GDPT5) consists of 1951-2013 daily minimum and maximum air temperatures and precipitation totals interpolated onto a 5 km grid based on daily meteorological observations from Institute of Meteorology and Water Management (IMGW-PIB; Polish stations), Deutscher Wetterdienst (DWD, German and Czech stations), ECAD and NOAA-NCDC (Slovak, Ukrainian and Belarus stations). The main purpose for constructing this product was the need for long-term aerial precipitation and temperature data for earth-system modelling, especially hydrological modelling. The spatial coverage is the union of Vistula and Odra basin and Polish territory. The number of available meteorological stations for precipitation and temperature varies in time from about 100 for temperature and 300 for precipitation in 1950 up to about 180 for temperature and 700 for precipitation in 1990. The precipitation dataset was corrected for snowfall and rainfall under-catch with the Richter method. The interpolation methods were: kriging with elevation as external drift for temperatures and indicator kriging combined with universal kriging for precipitation. The kriging cross-validation revealed low root mean squared errors expressed as a fraction of standard deviation (SD): 0.54 and 0.47 for minimum and maximum temperature, respectively and 0.79 for precipitation. The correlation scores were 0.84 for minimum temperatures, 0.88 for maximum temperatures and 0.65 for precipitation. The CPLFD-GDPT5 product is consistent with 1971-2000 climatic data published by IMGW-PIB. We also confirm good skill of the product for hydrological modelling by performing an application using the Soil and Water Assessment Tool (SWAT) in the Vistula and Odra basins. Link to the dataset: http://data.3tu.nl/repository/uuid:e939aec0-bdd1-440f-bd1e-c49ff10d0a07

Transferring Error Characteristics of Satellite Rainfall Data from Ground Validation (gauged) into Non-ground Validation (ungauged)

NASA Astrophysics Data System (ADS)

Tang, L.; Hossain, F.

2009-12-01

Understanding the error characteristics of satellite rainfall data at different spatial/temporal scales is critical, especially when the scheduled Global Precipitation Mission (GPM) plans to provide High Resolution Precipitation Products (HRPPs) at global scales. Satellite rainfall data contain errors which need ground validation (GV) data for characterization, while satellite rainfall data will be most useful in the regions that are lacking in GV. Therefore, a critical step is to develop a spatial interpolation scheme for transferring the error characteristics of satellite rainfall data from GV regions to Non-GV regions. As a prelude to GPM, The TRMM Multi-satellite Precipitation Analysis (TMPA) products of 3B41RT and 3B42RT (Huffman et al., 2007) over the US spanning a record of 6 years are used as a representative example of satellite rainfall data. Next Generation Radar (NEXRAD) Stage IV rainfall data are used as the reference for GV data. Initial work by the authors (Tang et al., 2009, GRL) has shown promise in transferring error from GV to Non-GV regions, based on a six-year climatologic average of satellite rainfall data assuming only 50% of GV coverage. However, this transfer of error characteristics needs to be investigated for a range of GV data coverage. In addition, it is also important to investigate if proxy-GV data from an accurate space-borne sensor, such as the TRMM PR (or the GPM DPR), can be leveraged for the transfer of error at sparsely gauged regions. The specific question we ask in this study is, “what is the minimum coverage of GV data required for error transfer scheme to be implemented at acceptable accuracy in hydrological relevant scale?” Three geostatistical interpolation methods are compared: ordinary kriging, indicator kriging and disjunctive kriging. Various error metrics are assessed for transfer such as, Probability of Detection for rain and no rain, False Alarm Ratio, Frequency Bias, Critical Success Index, RMSE etc. Understanding the proper space-time scales at which these metrics can be reasonably transferred is also explored in this study. Keyword: Satellite rainfall, error transfer, spatial interpolation, kriging methods.

Factors affecting paddy soil arsenic concentration in Bangladesh: prediction and uncertainty of geostatistical risk mapping.

PubMed

Ahmed, Zia U; Panaullah, Golam M; DeGloria, Stephen D; Duxbury, John M

2011-12-15

Knowledge of the spatial correlation of soil arsenic (As) concentrations with environmental variables is needed to assess the nature and extent of the risk of As contamination from irrigation water in Bangladesh. We analyzed 263 paired groundwater and paddy soil samples covering highland (HL) and medium highland-1 (MHL-1) land types for geostatistical mapping of soil As and delineation of As contaminated areas in Tala Upazilla, Satkhira district. We also collected 74 non-rice soil samples to assess the baseline concentration of soil As for this area. The mean soil As concentrations (mg/kg) for different land types under rice and non-rice crops were: rice-MHL-1 (21.2)>rice-HL (14.1)>non-rice-MHL-1 (11.9)>non-rice-HL (7.2). Multiple regression analyses showed that irrigation water As, Fe, land elevation and years of tubewell operation are the important factors affecting the concentrations of As in HL paddy soils. Only years of tubewell operation affected As concentration in the MHL-1 paddy soils. Quantitatively similar increases in soil As above the estimated baseline-As concentration were observed for rice soils on HL and MHL-1 after 6-8 years of groundwater irrigation, implying strong retention of As added in irrigation water in both land types. Application of single geostatistical methods with secondary variables such as regression kriging (RK) and ordinary co-kriging (OCK) gave little improvement in prediction of soil As over ordinary kriging (OK). Comparing single prediction methods, kriging within strata (KWS), the combination of RK for HL and OCK for MHL-1, gave more accurate soil As predictions and showed the lowest misclassification of declaring a location "contaminated" with respect to 14.8 mg As/kg, the highest value obtained for the baseline soil As concentration. Prediction of soil As buildup over time indicated that 75% or the soils cropped to rice would contain at least 30 mg/L As by the year 2020. Copyright © 2011 Elsevier B.V. All rights reserved.

Structural similarity based kriging for quantitative structure activity and property relationship modeling.

PubMed

Teixeira, Ana L; Falcao, Andre O

2014-07-28

Structurally similar molecules tend to have similar properties, i.e. closer molecules in the molecular space are more likely to yield similar property values while distant molecules are more likely to yield different values. Based on this principle, we propose the use of a new method that takes into account the high dimensionality of the molecular space, predicting chemical, physical, or biological properties based on the most similar compounds with measured properties. This methodology uses ordinary kriging coupled with three different molecular similarity approaches (based on molecular descriptors, fingerprints, and atom matching) which creates an interpolation map over the molecular space that is capable of predicting properties/activities for diverse chemical data sets. The proposed method was tested in two data sets of diverse chemical compounds collected from the literature and preprocessed. One of the data sets contained dihydrofolate reductase inhibition activity data, and the second molecules for which aqueous solubility was known. The overall predictive results using kriging for both data sets comply with the results obtained in the literature using typical QSPR/QSAR approaches. However, the procedure did not involve any type of descriptor selection or even minimal information about each problem, suggesting that this approach is directly applicable to a large spectrum of problems in QSAR/QSPR. Furthermore, the predictive results improve significantly with the similarity threshold between the training and testing compounds, allowing the definition of a confidence threshold of similarity and error estimation for each case inferred. The use of kriging for interpolation over the molecular metric space is independent of the training data set size, and no reparametrizations are necessary when more compounds are added or removed from the set, and increasing the size of the database will consequentially improve the quality of the estimations. Finally it is shown that this model can be used for checking the consistency of measured data and for guiding an extension of the training set by determining the regions of the molecular space for which new experimental measurements could be used to maximize the model's predictive performance.

New numerical methods for open-loop and feedback solutions to dynamic optimization problems

NASA Astrophysics Data System (ADS)

Ghosh, Pradipto

The topic of the first part of this research is trajectory optimization of dynamical systems via computational swarm intelligence. Particle swarm optimization is a nature-inspired heuristic search method that relies on a group of potential solutions to explore the fitness landscape. Conceptually, each particle in the swarm uses its own memory as well as the knowledge accumulated by the entire swarm to iteratively converge on an optimal or near-optimal solution. It is relatively straightforward to implement and unlike gradient-based solvers, does not require an initial guess or continuity in the problem definition. Although particle swarm optimization has been successfully employed in solving static optimization problems, its application in dynamic optimization, as posed in optimal control theory, is still relatively new. In the first half of this thesis particle swarm optimization is used to generate near-optimal solutions to several nontrivial trajectory optimization problems including thrust programming for minimum fuel, multi-burn spacecraft orbit transfer, and computing minimum-time rest-to-rest trajectories for a robotic manipulator. A distinct feature of the particle swarm optimization implementation in this work is the runtime selection of the optimal solution structure. Optimal trajectories are generated by solving instances of constrained nonlinear mixed-integer programming problems with the swarming technique. For each solved optimal programming problem, the particle swarm optimization result is compared with a nearly exact solution found via a direct method using nonlinear programming. Numerical experiments indicate that swarm search can locate solutions to very great accuracy. The second half of this research develops a new extremal-field approach for synthesizing nearly optimal feedback controllers for optimal control and two-player pursuit-evasion games described by general nonlinear differential equations. A notable revelation from this development is that the resulting control law has an algebraic closed-form structure. The proposed method uses an optimal spatial statistical predictor called universal kriging to construct the surrogate model of a feedback controller, which is capable of quickly predicting an optimal control estimate based on current state (and time) information. With universal kriging, an approximation to the optimal feedback map is computed by conceptualizing a set of state-control samples from pre-computed extremals to be a particular realization of a jointly Gaussian spatial process. Feedback policies are computed for a variety of example dynamic optimization problems in order to evaluate the effectiveness of this methodology. This feedback synthesis approach is found to combine good numerical accuracy with low computational overhead, making it a suitable candidate for real-time applications. Particle swarm and universal kriging are combined for a capstone example, a near optimal, near-admissible, full-state feedback control law is computed and tested for the heat-load-limited atmospheric-turn guidance of an aeroassisted transfer vehicle. The performance of this explicit guidance scheme is found to be very promising; initial errors in atmospheric entry due to simulated thruster misfirings are found to be accurately corrected while closely respecting the algebraic state-inequality constraint.

A local space time kriging approach applied to a national outpatient malaria data set

NASA Astrophysics Data System (ADS)

Gething, P. W.; Atkinson, P. M.; Noor, A. M.; Gikandi, P. W.; Hay, S. I.; Nixon, M. S.

2007-10-01

Increases in the availability of reliable health data are widely recognised as essential for efforts to strengthen health-care systems in resource-poor settings worldwide. Effective health-system planning requires comprehensive and up-to-date information on a range of health metrics and this requirement is generally addressed by a Health Management Information System (HMIS) that coordinates the routine collection of data at individual health facilities and their compilation into national databases. In many resource-poor settings, these systems are inadequate and national databases often contain only a small proportion of the expected records. In this paper, we take an important health metric in Kenya (the proportion of outpatient treatments for malaria (MP)) from the national HMIS database and predict the values of MP at facilities where monthly records are missing. The available MP data were densely distributed across a spatiotemporal domain and displayed second-order heterogeneity. We used three different kriging methodologies to make cross-validation predictions of MP in order to test the effect on prediction accuracy of (a) the extension of a spatial-only to a space-time prediction approach, and (b) the replacement of a globally stationary with a locally varying random function model. Space-time kriging was found to produce predictions with 98.4% less mean bias and 14.8% smaller mean imprecision than conventional spatial-only kriging. A modification of space-time kriging that allowed space-time variograms to be recalculated for every prediction location within a spatially local neighbourhood resulted in a larger decrease in mean imprecision over ordinary kriging (18.3%) although the mean bias was reduced less (87.5%).

A local space–time kriging approach applied to a national outpatient malaria data set

PubMed Central

Gething, P.W.; Atkinson, P.M.; Noor, A.M.; Gikandi, P.W.; Hay, S.I.; Nixon, M.S.

2007-01-01

Increases in the availability of reliable health data are widely recognised as essential for efforts to strengthen health-care systems in resource-poor settings worldwide. Effective health-system planning requires comprehensive and up-to-date information on a range of health metrics and this requirement is generally addressed by a Health Management Information System (HMIS) that coordinates the routine collection of data at individual health facilities and their compilation into national databases. In many resource-poor settings, these systems are inadequate and national databases often contain only a small proportion of the expected records. In this paper, we take an important health metric in Kenya (the proportion of outpatient treatments for malaria (MP)) from the national HMIS database and predict the values of MP at facilities where monthly records are missing. The available MP data were densely distributed across a spatiotemporal domain and displayed second-order heterogeneity. We used three different kriging methodologies to make cross-validation predictions of MP in order to test the effect on prediction accuracy of (a) the extension of a spatial-only to a space–time prediction approach, and (b) the replacement of a globally stationary with a locally varying random function model. Space–time kriging was found to produce predictions with 98.4% less mean bias and 14.8% smaller mean imprecision than conventional spatial-only kriging. A modification of space–time kriging that allowed space–time variograms to be recalculated for every prediction location within a spatially local neighbourhood resulted in a larger decrease in mean imprecision over ordinary kriging (18.3%) although the mean bias was reduced less (87.5%). PMID:19424510

Methods to estimate distribution and range extent of grizzly bears in the Greater Yellowstone Ecosystem

USGS Publications Warehouse

Haroldson, Mark A.; Schwartz, Charles C.; Thompson, Daniel J.; Bjornlie, Daniel D.; Gunther, Kerry A.; Cain, Steven L.; Tyers, Daniel B.; Frey, Kevin L.; Aber, Bryan C.

2014-01-01

The distribution of the Greater Yellowstone Ecosystem grizzly bear (Ursus arctos) population has expanded into areas unoccupied since the early 20th century. Up-to-date information on the area and extent of this distribution is crucial for federal, state, and tribal wildlife and land managers to make informed decisions regarding grizzly bear management. The most recent estimate of grizzly bear distribution (2004) utilized fixed-kernel density estimators to describe distribution. This method was complex and computationally time consuming and excluded observations of unmarked bears. Our objective was to develop a technique to estimate grizzly bear distribution that would allow for the use of all verified grizzly bear location data, as well as provide the simplicity to be updated more frequently. We placed all verified grizzly bear locations from all sources from 1990 to 2004 and 1990 to 2010 onto a 3-km × 3-km grid and used zonal analysis and ordinary kriging to develop a predicted surface of grizzly bear distribution. We compared the area and extent of the 2004 kriging surface with the previous 2004 effort and evaluated changes in grizzly bear distribution from 2004 to 2010. The 2004 kriging surface was 2.4% smaller than the previous fixed-kernel estimate, but more closely represented the data. Grizzly bear distribution increased 38.3% from 2004 to 2010, with most expansion in the northern and southern regions of the range. This technique can be used to provide a current estimate of grizzly bear distribution for management and conservation applications.

On the optimal selection of interpolation methods for groundwater contouring: An example of propagation of uncertainty regarding inter-aquifer exchange

NASA Astrophysics Data System (ADS)

Ohmer, Marc; Liesch, Tanja; Goeppert, Nadine; Goldscheider, Nico

2017-11-01

The selection of the best possible method to interpolate a continuous groundwater surface from point data of groundwater levels is a controversial issue. In the present study four deterministic and five geostatistical interpolation methods (global polynomial interpolation, local polynomial interpolation, inverse distance weighting, radial basis function, simple-, ordinary-, universal-, empirical Bayesian and co-Kriging) and six error statistics (ME, MAE, MAPE, RMSE, RMSSE, Pearson R) were examined for a Jurassic karst aquifer and a Quaternary alluvial aquifer. We investigated the possible propagation of uncertainty of the chosen interpolation method on the calculation of the estimated vertical groundwater exchange between the aquifers. Furthermore, we validated the results with eco-hydrogeological data including the comparison between calculated groundwater depths and geographic locations of karst springs, wetlands and surface waters. These results show, that calculated inter-aquifer exchange rates based on different interpolations of groundwater potentials may vary greatly depending on the chosen interpolation method (by factor >10). Therefore, the choice of an interpolation method should be made with care, taking different error measures as well as additional data for plausibility control into account. The most accurate results have been obtained with co-Kriging incorporating secondary data (e.g. topography, river levels).

Overview and technical and practical aspects for use of geostatistics in hazardous-, toxic-, and radioactive-waste-site investigations

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

Bossong, C.R.; Karlinger, M.R.; Troutman, B.M.

1999-10-01

Technical and practical aspects of applying geostatistics are developed for individuals involved in investigation at hazardous-, toxic-, and radioactive-waste sites. Important geostatistical concepts, such as variograms and ordinary, universal, and indicator kriging, are described in general terms for introductory purposes and in more detail for practical applications. Variogram modeling using measured ground-water elevation data is described in detail to illustrate principles of stationarity, anisotropy, transformations, and cross validation. Several examples of kriging applications are described using ground-water-level elevations, bedrock elevations, and ground-water-quality data. A review of contemporary literature and selected public domain software associated with geostatistics also is provided, asmore » is a discussion of alternative methods for spatial modeling, including inverse distance weighting, triangulation, splines, trend-surface analysis, and simulation.« less

A new statistic to express the uncertainty of kriging predictions for purposes of survey planning.

NASA Astrophysics Data System (ADS)

Lark, R. M.; Lapworth, D. J.

2014-05-01

It is well-known that one advantage of kriging for spatial prediction is that, given the random effects model, the prediction error variance can be computed a priori for alternative sampling designs. This allows one to compare sampling schemes, in particular sampling at different densities, and so to decide on one which meets requirements in terms of the uncertainty of the resulting predictions. However, the planning of sampling schemes must account not only for statistical considerations, but also logistics and cost. This requires effective communication between statisticians, soil scientists and data users/sponsors such as managers, regulators or civil servants. In our experience the latter parties are not necessarily able to interpret the prediction error variance as a measure of uncertainty for decision making. In some contexts (particularly the solution of very specific problems at large cartographic scales, e.g. site remediation and precision farming) it is possible to translate uncertainty of predictions into a loss function directly comparable with the cost incurred in increasing precision. Often, however, sampling must be planned for more generic purposes (e.g. baseline or exploratory geochemical surveys). In this latter context the prediction error variance may be of limited value to a non-statistician who has to make a decision on sample intensity and associated cost. We propose an alternative criterion for these circumstances to aid communication between statisticians and data users about the uncertainty of geostatistical surveys based on different sampling intensities. The criterion is the consistency of estimates made from two non-coincident instantiations of a proposed sample design. We consider square sample grids, one instantiation is offset from the second by half the grid spacing along the rows and along the columns. If a sample grid is coarse relative to the important scales of variation in the target property then the consistency of predictions from two instantiations is expected to be small, and can be increased by reducing the grid spacing. The measure of consistency is the correlation between estimates from the two instantiations of the sample grid, averaged over a grid cell. We call this the offset correlation, it can be calculated from the variogram. We propose that this measure is easier to grasp intuitively than the prediction error variance, and has the advantage of having an upper bound (1.0) which will aid its interpretation. This quality measure is illustrated for some hypothetical examples, considering both ordinary kriging and factorial kriging of the variable of interest. It is also illustrated using data on metal concentrations in the soil of north-east England.

Regional flow duration curves: Geostatistical techniques versus multivariate regression

USGS Publications Warehouse

Pugliese, Alessio; Farmer, William H.; Castellarin, Attilio; Archfield, Stacey A.; Vogel, Richard M.

2016-01-01

A period-of-record flow duration curve (FDC) represents the relationship between the magnitude and frequency of daily streamflows. Prediction of FDCs is of great importance for locations characterized by sparse or missing streamflow observations. We present a detailed comparison of two methods which are capable of predicting an FDC at ungauged basins: (1) an adaptation of the geostatistical method, Top-kriging, employing a linear weighted average of dimensionless empirical FDCs, standardised with a reference streamflow value; and (2) regional multiple linear regression of streamflow quantiles, perhaps the most common method for the prediction of FDCs at ungauged sites. In particular, Top-kriging relies on a metric for expressing the similarity between catchments computed as the negative deviation of the FDC from a reference streamflow value, which we termed total negative deviation (TND). Comparisons of these two methods are made in 182 largely unregulated river catchments in the southeastern U.S. using a three-fold cross-validation algorithm. Our results reveal that the two methods perform similarly throughout flow-regimes, with average Nash-Sutcliffe Efficiencies 0.566 and 0.662, (0.883 and 0.829 on log-transformed quantiles) for the geostatistical and the linear regression models, respectively. The differences between the reproduction of FDC's occurred mostly for low flows with exceedance probability (i.e. duration) above 0.98.

Application of Multiregressive Linear Models, Dynamic Kriging Models and Neural Network Models to Predictive Maintenance of Hydroelectric Power Systems

NASA Astrophysics Data System (ADS)

Lucifredi, A.; Mazzieri, C.; Rossi, M.

2000-05-01

Since the operational conditions of a hydroelectric unit can vary within a wide range, the monitoring system must be able to distinguish between the variations of the monitored variable caused by variations of the operation conditions and those due to arising and progressing of failures and misoperations. The paper aims to identify the best technique to be adopted for the monitoring system. Three different methods have been implemented and compared. Two of them use statistical techniques: the first, the linear multiple regression, expresses the monitored variable as a linear function of the process parameters (independent variables), while the second, the dynamic kriging technique, is a modified technique of multiple linear regression representing the monitored variable as a linear combination of the process variables in such a way as to minimize the variance of the estimate error. The third is based on neural networks. Tests have shown that the monitoring system based on the kriging technique is not affected by some problems common to the other two models e.g. the requirement of a large amount of data for their tuning, both for training the neural network and defining the optimum plane for the multiple regression, not only in the system starting phase but also after a trivial operation of maintenance involving the substitution of machinery components having a direct impact on the observed variable. Or, in addition, the necessity of different models to describe in a satisfactory way the different ranges of operation of the plant. The monitoring system based on the kriging statistical technique overrides the previous difficulties: it does not require a large amount of data to be tuned and is immediately operational: given two points, the third can be immediately estimated; in addition the model follows the system without adapting itself to it. The results of the experimentation performed seem to indicate that a model based on a neural network or on a linear multiple regression is not optimal, and that a different approach is necessary to reduce the amount of work during the learning phase using, when available, all the information stored during the initial phase of the plant to build the reference baseline, elaborating, if it is the case, the raw information available. A mixed approach using the kriging statistical technique and neural network techniques could optimise the result.

Spatial analysis and hazard assessment on soil total nitrogen in the middle subtropical zone of China

NASA Astrophysics Data System (ADS)

Lu, Peng; Lin, Wenpeng; Niu, Zheng; Su, Yirong; Wu, Jinshui

2006-10-01

Nitrogen (N) is one of the main factors affecting environmental pollution. In recent years, non-point source pollution and water body eutrophication have become increasing concerns for both scientists and the policy-makers. In order to assess the environmental hazard of soil total N pollution, a typical ecological unit was selected as the experimental site. This paper showed that Box-Cox transformation achieved normality in the data set, and dampened the effect of outliers. The best theoretical model of soil total N was a Gaussian model. Spatial variability of soil total N at NE60° and NE150° directions showed that it had a strip anisotropic structure. The ordinary kriging estimate of soil total N concentration was mapped. The spatial distribution pattern of soil total N in the direction of NE150° displayed a strip-shaped structure. Kriging standard deviations (KSD) provided valuable information that will increase the accuracy of total N mapping. The probability kriging method is useful to assess the hazard of N pollution by providing the conditional probability of N concentration exceeding the threshold value, where we found soil total N>2.0g/kg. The probability distribution of soil total N will be helpful to conduct hazard assessment, optimal fertilization, and develop management practices to control the non-point sources of N pollution.

A statistical evaluation of non-ergodic variogram estimators

USGS Publications Warehouse

Curriero, F.C.; Hohn, M.E.; Liebhold, A.M.; Lele, S.R.

2002-01-01

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.

Assessment and modeling of the groundwater hydrogeochemical quality parameters via geostatistical approaches

NASA Astrophysics Data System (ADS)

Karami, Shawgar; Madani, Hassan; Katibeh, Homayoon; Fatehi Marj, Ahmad

2018-03-01

Geostatistical methods are one of the advanced techniques used for interpolation of groundwater quality data. The results obtained from geostatistics will be useful for decision makers to adopt suitable remedial measures to protect the quality of groundwater sources. Data used in this study were collected from 78 wells in Varamin plain aquifer located in southeast of Tehran, Iran, in 2013. Ordinary kriging method was used in this study to evaluate groundwater quality parameters. According to what has been mentioned in this paper, seven main quality parameters (i.e. total dissolved solids (TDS), sodium adsorption ratio (SAR), electrical conductivity (EC), sodium (Na+), total hardness (TH), chloride (Cl-) and sulfate (SO4 2-)), have been analyzed and interpreted by statistical and geostatistical methods. After data normalization by Nscore method in WinGslib software, variography as a geostatistical tool to define spatial regression was compiled and experimental variograms were plotted by GS+ software. Then, the best theoretical model was fitted to each variogram based on the minimum RSS. Cross validation method was used to determine the accuracy of the estimated data. Eventually, estimation maps of groundwater quality were prepared in WinGslib software and estimation variance map and estimation error map were presented to evaluate the quality of estimation in each estimated point. Results showed that kriging method is more accurate than the traditional interpolation methods.

Accuracy and uncertainty analysis of soil Bbf spatial distribution estimation at a coking plant-contaminated site based on normalization geostatistical technologies.

PubMed

Liu, Geng; Niu, Junjie; Zhang, Chao; Guo, Guanlin

2015-12-01

Data distribution is usually skewed severely by the presence of hot spots in contaminated sites. This causes difficulties for accurate geostatistical data transformation. Three types of typical normal distribution transformation methods termed the normal score, Johnson, and Box-Cox transformations were applied to compare the effects of spatial interpolation with normal distribution transformation data of benzo(b)fluoranthene in a large-scale coking plant-contaminated site in north China. Three normal transformation methods decreased the skewness and kurtosis of the benzo(b)fluoranthene, and all the transformed data passed the Kolmogorov-Smirnov test threshold. Cross validation showed that Johnson ordinary kriging has a minimum root-mean-square error of 1.17 and a mean error of 0.19, which was more accurate than the other two models. The area with fewer sampling points and that with high levels of contamination showed the largest prediction standard errors based on the Johnson ordinary kriging prediction map. We introduce an ideal normal transformation method prior to geostatistical estimation for severely skewed data, which enhances the reliability of risk estimation and improves the accuracy for determination of remediation boundaries.

Where and when should sensors move? Sampling using the expected value of information.

PubMed

de Bruin, Sytze; Ballari, Daniela; Bregt, Arnold K

2012-11-26

In case of an environmental accident, initially available data are often insufficient for properly managing the situation. In this paper, new sensor observations are iteratively added to an initial sample by maximising the global expected value of information of the points for decision making. This is equivalent to minimizing the aggregated expected misclassification costs over the study area. The method considers measurement error and different costs for class omissions and false class commissions. Constraints imposed by a mobile sensor web are accounted for using cost distances to decide which sensor should move to the next sample location. The method is demonstrated using synthetic examples of static and dynamic phenomena. This allowed computation of the true misclassification costs and comparison with other sampling approaches. The probability of local contamination levels being above a given critical threshold were computed by indicator kriging. In the case of multiple sensors being relocated simultaneously, a genetic algorithm was used to find sets of suitable new measurement locations. Otherwise, all grid nodes were searched exhaustively, which is computationally demanding. In terms of true misclassification costs, the method outperformed random sampling and sampling based on minimisation of the kriging variance.

Where and When Should Sensors Move? Sampling Using the Expected Value of Information

PubMed Central

de Bruin, Sytze; Ballari, Daniela; Bregt, Arnold K.

2012-01-01

In case of an environmental accident, initially available data are often insufficient for properly managing the situation. In this paper, new sensor observations are iteratively added to an initial sample by maximising the global expected value of information of the points for decision making. This is equivalent to minimizing the aggregated expected misclassification costs over the study area. The method considers measurement error and different costs for class omissions and false class commissions. Constraints imposed by a mobile sensor web are accounted for using cost distances to decide which sensor should move to the next sample location. The method is demonstrated using synthetic examples of static and dynamic phenomena. This allowed computation of the true misclassification costs and comparison with other sampling approaches. The probability of local contamination levels being above a given critical threshold were computed by indicator kriging. In the case of multiple sensors being relocated simultaneously, a genetic algorithm was used to find sets of suitable new measurement locations. Otherwise, all grid nodes were searched exhaustively, which is computationally demanding. In terms of true misclassification costs, the method outperformed random sampling and sampling based on minimisation of the kriging variance. PMID:23443379

Reliability Analysis of Sealing Structure of Electromechanical System Based on Kriging Model

NASA Astrophysics Data System (ADS)

Zhang, F.; Wang, Y. M.; Chen, R. W.; Deng, W. W.; Gao, Y.

2018-05-01

The sealing performance of aircraft electromechanical system has a great influence on flight safety, and the reliability of its typical seal structure is analyzed by researcher. In this paper, we regard reciprocating seal structure as a research object to study structural reliability. Having been based on the finite element numerical simulation method, the contact stress between the rubber sealing ring and the cylinder wall is calculated, and the relationship between the contact stress and the pressure of the hydraulic medium is built, and the friction force on different working conditions are compared. Through the co-simulation, the adaptive Kriging model obtained by EFF learning mechanism is used to describe the failure probability of the seal ring, so as to evaluate the reliability of the sealing structure. This article proposes a new idea of numerical evaluation for the reliability analysis of sealing structure, and also provides a theoretical basis for the optimal design of sealing structure.

Comparison of Highly Resolved Model-Based Exposure Metrics for Traffic-Related Air Pollutants to Support Environmental Health Studies

EPA Science Inventory

Human exposure to air pollution in many studies is represented by ambient concentrations from space-time kriging of observed values. Space-time kriging techniques based on a limited number of ambient monitors may fail to capture the concentration from local sources. Further, beca...

The design, deployment, and testing of kriging models in GEOframe with SIK-0.9.8

NASA Astrophysics Data System (ADS)

Bancheri, Marialaura; Serafin, Francesco; Bottazzi, Michele; Abera, Wuletawu; Formetta, Giuseppe; Rigon, Riccardo

2018-06-01

This work presents a software package for the interpolation of climatological variables, such as temperature and precipitation, using kriging techniques. The purposes of the paper are (1) to present a geostatistical software that is easy to use and easy to plug in to a hydrological model; (2) to provide a practical example of an accurately designed software from the perspective of reproducible research; and (3) to demonstrate the goodness of the results of the software and so have a reliable alternative to other, more traditional tools. A total of 11 types of theoretical semivariograms and four types of kriging were implemented and gathered into Object Modeling System-compliant components. The package provides real-time optimization for semivariogram and kriging parameters. The software was tested using a year's worth of hourly temperature readings and a rain storm event (11 h) recorded in 2008 and retrieved from 97 meteorological stations in the Isarco River basin, Italy. For both the variables, good interpolation results were obtained and then compared to the results from the R package gstat.

Multipolar electrostatics based on the Kriging machine learning method: an application to serine.

PubMed

Yuan, Yongna; Mills, Matthew J L; Popelier, Paul L A

2014-04-01

A multipolar, polarizable electrostatic method for future use in a novel force field is described. Quantum Chemical Topology (QCT) is used to partition the electron density of a chemical system into atoms, then the machine learning method Kriging is used to build models that relate the multipole moments of the atoms to the positions of their surrounding nuclei. The pilot system serine is used to study both the influence of the level of theory and the set of data generator methods used. The latter consists of: (i) sampling of protein structures deposited in the Protein Data Bank (PDB), or (ii) normal mode distortion along either (a) Cartesian coordinates, or (b) redundant internal coordinates. Wavefunctions for the sampled geometries were obtained at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory, prior to calculation of the atomic multipole moments by volume integration. The average absolute error (over an independent test set of conformations) in the total atom-atom electrostatic interaction energy of serine, using Kriging models built with the three data generator methods is 11.3 kJ mol⁻¹ (PDB), 8.2 kJ mol⁻¹ (Cartesian distortion), and 10.1 kJ mol⁻¹ (redundant internal distortion) at the HF/6-31G(d,p) level. At the B3LYP/apc-1 level, the respective errors are 7.7 kJ mol⁻¹, 6.7 kJ mol⁻¹, and 4.9 kJ mol⁻¹, while at the MP2/cc-pVDZ level they are 6.5 kJ mol⁻¹, 5.3 kJ mol⁻¹, and 4.0 kJ mol⁻¹. The ranges of geometries generated by the redundant internal coordinate distortion and by extraction from the PDB are much wider than the range generated by Cartesian distortion. The atomic multipole moment and electrostatic interaction energy predictions for the B3LYP/apc-1 and MP2/cc-pVDZ levels are similar, and both are better than the corresponding predictions at the HF/6-31G(d,p) level.

Kriging and local polynomial methods for blending satellite-derived and gauge precipitation estimates to support hydrologic early warning systems

USGS Publications Warehouse

Verdin, Andrew; Funk, Christopher C.; Rajagopalan, Balaji; Kleiber, William

2016-01-01

Robust estimates of precipitation in space and time are important for efficient natural resource management and for mitigating natural hazards. This is particularly true in regions with developing infrastructure and regions that are frequently exposed to extreme events. Gauge observations of rainfall are sparse but capture the precipitation process with high fidelity. Due to its high resolution and complete spatial coverage, satellite-derived rainfall data are an attractive alternative in data-sparse regions and are often used to support hydrometeorological early warning systems. Satellite-derived precipitation data, however, tend to underrepresent extreme precipitation events. Thus, it is often desirable to blend spatially extensive satellite-derived rainfall estimates with high-fidelity rain gauge observations to obtain more accurate precipitation estimates. In this research, we use two different methods, namely, ordinary kriging and κ-nearest neighbor local polynomials, to blend rain gauge observations with the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates in data-sparse Central America and Colombia. The utility of these methods in producing blended precipitation estimates at pentadal (five-day) and monthly time scales is demonstrated. We find that these blending methods significantly improve the satellite-derived estimates and are competitive in their ability to capture extreme precipitation.

Delineation of estuarine management areas using multivariate geostatistics: the case of Sado Estuary.

PubMed

Caeiro, Sandra; Goovaerts, Pierre; Painho, Marco; Costa, M Helena

2003-09-15

The Sado Estuary is a coastal zone located in the south of Portugal where conflicts between conservation and development exist because of its location near industrialized urban zones and its designation as a natural reserve. The aim of this paper is to evaluate a set of multivariate geostatistical approaches to delineate spatially contiguous regions of sediment structure for Sado Estuary. These areas will be the supporting infrastructure of an environmental management system for this estuary. The boundaries of each homogeneous area were derived from three sediment characterization attributes through three different approaches: (1) cluster analysis of dissimilarity matrix function of geographical separation followed by indicator kriging of the cluster data, (2) discriminant analysis of kriged values of the three sediment attributes, and (3) a combination of methods 1 and 2. Final maximum likelihood classification was integrated into a geographical information system. All methods generated fairly spatially contiguous management areas that reproduce well the environment of the estuary. Map comparison techniques based on kappa statistics showed thatthe resultant three maps are similar, supporting the choice of any of the methods as appropriate for management of the Sado Estuary. However, the results of method 1 seem to be in better agreement with estuary behavior, assessment of contamination sources, and previous work conducted at this site.

Sandwich mapping of schistosomiasis risk in Anhui Province, China.

PubMed

Hu, Yi; Bergquist, Robert; Lynn, Henry; Gao, Fenghua; Wang, Qizhi; Zhang, Shiqing; Li, Rui; Sun, Liqian; Xia, Congcong; Xiong, Chenglong; Zhang, Zhijie; Jiang, Qingwu

2015-06-03

Schistosomiasis mapping using data obtained from parasitological surveys is frequently used in planning and evaluation of disease control strategies. The available geostatistical approaches are, however, subject to the assumption of stationarity, a stochastic process whose joint probability distribution does not change when shifted in time. As this is impractical for large areas, we introduce here the sandwich method, the basic idea of which is to divide the study area (with its attributes) into homogeneous subareas and estimate the values for the reporting units using spatial stratified sampling. The sandwich method was applied to map the county-level prevalence of schistosomiasis japonica in Anhui Province, China based on parasitological data collected from sample villages and land use data. We first mapped the county-level prevalence using the sandwich method, then compared our findings with block Kriging. The sandwich estimates ranged from 0.17 to 0.21% with a lower level of uncertainty, while the Kriging estimates varied from 0 to 0.97% with a higher level of uncertainty, indicating that the former is more smoothed and stable compared to latter. Aside from various forms of reporting units, the sandwich method has the particular merit of simple model assumption coupled with full utilization of sample data. It performs well when a disease presents stratified heterogeneity over space.

Spatial Variability of the Topsoil Organic Carbon in the Moso Bamboo Forests of Southern China in Association with Soil Properties

PubMed Central

Zhang, Houxi; Zhuang, Shunyao; Qian, Haiyan; Wang, Feng; Ji, Haibao

2015-01-01

Understanding the spatial variability of soil organic carbon (SOC) must be enhanced to improve sampling design and to develop soil management strategies in terrestrial ecosystems. Moso bamboo (Phyllostachys pubescens Mazel ex Houz.) forests have a high SOC storage potential; however, they also vary significantly spatially. This study investigated the spatial variability of SOC (0-20 cm) in association with other soil properties and with spatial variables in the Moso bamboo forests of Jian’ou City, which is a typical bamboo hometown in China. 209 soil samples were collected from Moso bamboo stands and then analyzed for SOC, bulk density (BD), pH, cation exchange capacity (CEC), and gravel content (GC) based on spatial distribution. The spatial variability of SOC was then examined using geostatistics. A Kriging map was produced through ordinary interpolation and required sample numbers were calculated by classical and Kriging methods. An aggregated boosted tree (ABT) analysis was also conducted. A semivariogram analysis indicated that ln(SOC) was best fitted with an exponential model and that it exhibited moderate spatial dependence, with a nugget/sill ratio of 0.462. SOC was significantly and linearly correlated with BD (r = −0.373**), pH (r = −0.429**), GC (r = −0.163*), CEC (r = 0.263**), and elevation (r = 0.192**). Moreover, the Kriging method requires fewer samples than the classical method given an expected standard error level as per a variance analysis. ABT analysis indicated that the physicochemical variables of soil affected SOC variation more significantly than spatial variables did, thus suggesting that the SOC in Moso bamboo forests can be strongly influenced by management practices. Thus, this study provides valuable information in relation to sampling strategy and insight into the potential of adjustments in agronomic measure, such as in fertilization for Moso bamboo production. PMID:25789615

Spatiotemporal approaches to analyzing pedestrian fatalities: the case of Cali, Colombia.

PubMed

Fox, Lani; Serre, Marc L; Lippmann, Steven J; Rodríguez, Daniel A; Bangdiwala, Shrikant I; Gutiérrez, María Isabel; Escobar, Guido; Villaveces, Andrés

2015-01-01

Injuries among pedestrians are a major public health concern in Colombian cities such as Cali. This is one of the first studies in Latin America to apply Bayesian maximum entropy (BME) methods to visualize and produce fine-scale, highly accurate estimates of citywide pedestrian fatalities. The purpose of this study is to determine the BME method that best estimates pedestrian mortality rates and reduces statistical noise. We further utilized BME methods to identify and differentiate spatial patterns and persistent versus transient pedestrian mortality hotspots. In this multiyear study, geocoded pedestrian mortality data from the Cali Injury Surveillance System (2008 to 2010) and census data were utilized to accurately visualize and estimate pedestrian fatalities. We investigated the effects of temporal and spatial scales, addressing issues arising from the rarity of pedestrian fatality events using 3 BME methods (simple kriging, Poisson kriging, and uniform model Bayesian maximum entropy). To reduce statistical noise while retaining a fine spatial and temporal scale, data were aggregated over 9-month incidence periods and censal sectors. Based on a cross-validation of BME methods, Poisson kriging was selected as the best BME method. Finally, the spatiotemporal and urban built environment characteristics of Cali pedestrian mortality hotspots were linked to intervention measures provided in Mead et al.'s (2014) pedestrian mortality review. The BME space-time analysis in Cali resulted in maps displaying hotspots of high pedestrian fatalities extending over small areas with radii of 0.25 to 1.1 km and temporal durations of 1 month to 3 years. Mapping the spatiotemporal distribution of pedestrian mortality rates identified high-priority areas for prevention strategies. The BME results allow us to identify possible intervention strategies according to the persistence and built environment of the hotspot; for example, through enforcement or long-term environmental modifications. BME methods provide useful information on the time and place of injuries and can inform policy strategies by isolating priority areas for interventions, contributing to intervention evaluation, and helping to generate hypotheses and identify the preventative strategies that may be suitable to those areas (e.g., street-level methods: pedestrian crossings, enforcement interventions; or citywide approaches: limiting vehicle speeds). This specific information is highly relevant for public health interventions because it provides the ability to target precise locations.

CPLFD-GDPT5: High-resolution gridded daily precipitation and temperature data set for two largest Polish river basins

NASA Astrophysics Data System (ADS)

Berezowski, Tomasz; Szcześniak, Mateusz; Kardel, Ignacy; Michałowski, Robert; Okruszko, Tomasz; Mezghani, Abdelkader; Piniewski, Mikołaj

2016-03-01

The CHASE-PL (Climate change impact assessment for selected sectors in Poland) Forcing Data-Gridded Daily Precipitation & Temperature Dataset-5 km (CPLFD-GDPT5) consists of 1951-2013 daily minimum and maximum air temperatures and precipitation totals interpolated onto a 5 km grid based on daily meteorological observations from the Institute of Meteorology and Water Management (IMGW-PIB; Polish stations), Deutscher Wetterdienst (DWD, German and Czech stations), and European Climate Assessment and Dataset (ECAD) and National Oceanic and Atmosphere Administration-National Climatic Data Center (NOAA-NCDC) (Slovak, Ukrainian, and Belarusian stations). The main purpose for constructing this product was the need for long-term aerial precipitation and temperature data for earth-system modelling, especially hydrological modelling. The spatial coverage is the union of the Vistula and Oder basins and Polish territory. The number of available meteorological stations for precipitation and temperature varies in time from about 100 for temperature and 300 for precipitation in the 1950s up to about 180 for temperature and 700 for precipitation in the 1990s. The precipitation data set was corrected for snowfall and rainfall under-catch with the Richter method. The interpolation methods were kriging with elevation as external drift for temperatures and indicator kriging combined with universal kriging for precipitation. The kriging cross validation revealed low root-mean-squared errors expressed as a fraction of standard deviation (SD): 0.54 and 0.47 for minimum and maximum temperature, respectively, and 0.79 for precipitation. The correlation scores were 0.84 for minimum temperatures, 0.88 for maximum temperatures, and 0.65 for precipitation. The CPLFD-GDPT5 product is consistent with 1971-2000 climatic data published by IMGW-PIB. We also confirm good skill of the product for hydrological modelling by performing an application using the Soil and Water Assessment Tool (SWAT) in the Vistula and Oder basins. Link to the data set: doi:10.4121/uuid:e939aec0-bdd1-440f-bd1e-c49ff10d0a07.

Analysis of thrips distribution: application of spatial statistics and Kriging

Treesearch

John Aleong; Bruce L. Parker; Margaret Skinner; Diantha Howard

1991-01-01

Kriging is a statistical technique that provides predictions for spatially and temporally correlated data. Observations of thrips distribution and density in Vermont soils are made in both space and time. Traditional statistical analysis of such data assumes that the counts taken over space and time are independent, which is not necessarily true. Therefore, to analyze...

Geostatistics: a new tool for describing spatially-varied surface conditions from timber harvested and burned hillslopes

Treesearch

Peter R. Robichaud

1997-01-01

Geostatistics provides a method to describe the spatial continuity of many natural phenomena. Spatial models are based upon the concept of scaling, kriging and conditional simulation. These techniques were used to describe the spatially-varied surface conditions on timber harvest and burned hillslopes. Geostatistical techniques provided estimates of the ground cover (...

Kriging Direct and Indirect Estimates of Sulfate Deposition: A Comparison

Treesearch

Gregory A. Reams; Manuela M.P. Huso; Richard J. Vong; Joseph M. McCollum

1997-01-01

Due to logistical and cost constraints, acidic deposition is rarely measured at forest research or sampling locations. A crucial first step to assessing the effects of acid rain on forests is an accurate estimate of acidic deposition at forest sample sites. We examine two methods (direct and indirect) for estimating sulfate deposition at atmospherically unmonitored...

Evaluating kriging as a tool to improve moderate resolution maps of forest biomass

Treesearch

Elizabeth A. Freeman; Gretchen G. Moisen

2007-01-01

The USDA Forest Service, Forest Inventory and Analysis program (FIA) recently produced a nationwide map of forest biomass by modeling biomass collected on forest inventory plots as nonparametric functions of moderate resolution satellite data and other environmental variables using Cubist software. Efforts are underway to develop methods to enhance this initial map. We...

Volumetric calculations in an oil field: The basis method

USGS Publications Warehouse

Olea, R.A.; Pawlowsky, V.; Davis, J.C.

1993-01-01

The basis method for estimating oil reserves in place is compared to a traditional procedure that uses ordinary kriging. In the basis method, auxiliary variables that sum to the net thickness of pay are estimated by cokriging. In theory, the procedure should be more powerful because it makes full use of the cross-correlation between variables and forces the original variables to honor interval constraints. However, at least in our case study, the practical advantages of cokriging for estimating oil in place are marginal. ?? 1993.

Comparison of geostatistical interpolation and remote sensing techniques for estimating long-term exposure to ambient PM2.5 concentrations across the continental United States.

PubMed

Lee, Seung-Jae; Serre, Marc L; van Donkelaar, Aaron; Martin, Randall V; Burnett, Richard T; Jerrett, Michael

2012-12-01

A better understanding of the adverse health effects of chronic exposure to fine particulate matter (PM2.5) requires accurate estimates of PM2.5 variation at fine spatial scales. Remote sensing has emerged as an important means of estimating PM2.5 exposures, but relatively few studies have compared remote-sensing estimates to those derived from monitor-based data. We evaluated and compared the predictive capabilities of remote sensing and geostatistical interpolation. We developed a space-time geostatistical kriging model to predict PM2.5 over the continental United States and compared resulting predictions to estimates derived from satellite retrievals. The kriging estimate was more accurate for locations that were about 100 km from a monitoring station, whereas the remote sensing estimate was more accurate for locations that were > 100 km from a monitoring station. Based on this finding, we developed a hybrid map that combines the kriging and satellite-based PM2.5 estimates. We found that for most of the populated areas of the continental United States, geostatistical interpolation produced more accurate estimates than remote sensing. The differences between the estimates resulting from the two methods, however, were relatively small. In areas with extensive monitoring networks, the interpolation may provide more accurate estimates, but in the many areas of the world without such monitoring, remote sensing can provide useful exposure estimates that perform nearly as well.

A Kriging based spatiotemporal approach for traffic volume data imputation

PubMed Central

Han, Lee D.; Liu, Xiaohan; Pu, Li; Chin, Shih-miao; Hwang, Ho-ling

2018-01-01

Along with the rapid development of Intelligent Transportation Systems, traffic data collection technologies have progressed fast. The emergence of innovative data collection technologies such as remote traffic microwave sensor, Bluetooth sensor, GPS-based floating car method, and automated license plate recognition, has significantly increased the variety and volume of traffic data. Despite the development of these technologies, the missing data issue is still a problem that poses great challenge for data based applications such as traffic forecasting, real-time incident detection, dynamic route guidance, and massive evacuation optimization. A thorough literature review suggests most current imputation models either focus on the temporal nature of the traffic data and fail to consider the spatial information of neighboring locations or assume the data follow a certain distribution. These two issues reduce the imputation accuracy and limit the use of the corresponding imputation methods respectively. As a result, this paper presents a Kriging based data imputation approach that is able to fully utilize the spatiotemporal correlation in the traffic data and that does not assume the data follow any distribution. A set of scenarios with different missing rates are used to evaluate the performance of the proposed method. The performance of the proposed method was compared with that of two other widely used methods, historical average and K-nearest neighborhood. Comparison results indicate that the proposed method has the highest imputation accuracy and is more flexible compared to other methods. PMID:29664928

Three-Dimensional Mapping of Soil Organic Carbon by Combining Kriging Method with Profile Depth Function.

PubMed

Chen, Chong; Hu, Kelin; Li, Hong; Yun, Anping; Li, Baoguo

2015-01-01

Understanding spatial variation of soil organic carbon (SOC) in three-dimensional direction is helpful for land use management. Due to the effect of profile depths and soil texture on vertical distribution of SOC, the stationary assumption for SOC cannot be met in the vertical direction. Therefore the three-dimensional (3D) ordinary kriging technique cannot be directly used to map the distribution of SOC at a regional scale. The objectives of this study were to map the 3D distribution of SOC at a regional scale by combining kriging method with the profile depth function of SOC (KPDF), and to explore the effects of soil texture and land use type on vertical distribution of SOC in a fluvial plain. A total of 605 samples were collected from 121 soil profiles (0.0 to 1.0 m, 0.20 m increment) in Quzhou County, China and SOC contents were determined for each soil sample. The KPDF method was used to obtain the 3D map of SOC at the county scale. The results showed that the exponential equation well described the vertical distribution of mean values of the SOC contents. The coefficients of determination, root mean squared error and mean prediction error between the measured and the predicted SOC contents were 0.52, 1.82 and -0.24 g kg(-1) respectively, suggesting that the KPDF method could be used to produce a 3D map of SOC content. The surface SOC contents were high in the mid-west and south regions, and low values lay in the southeast corner. The SOC contents showed significant positive correlations between the five different depths and the correlations of SOC contents were larger in adjacent layers than in non-adjacent layers. Soil texture and land use type had significant effects on the spatial distribution of SOC. The influence of land use type was more important than that of soil texture in the surface soil, and soil texture played a more important role in influencing the SOC levels for 0.2-0.4 m layer.

Three-Dimensional Mapping of Soil Organic Carbon by Combining Kriging Method with Profile Depth Function

PubMed Central

Chen, Chong; Hu, Kelin; Li, Hong; Yun, Anping; Li, Baoguo

2015-01-01

Understanding spatial variation of soil organic carbon (SOC) in three-dimensional direction is helpful for land use management. Due to the effect of profile depths and soil texture on vertical distribution of SOC, the stationary assumption for SOC cannot be met in the vertical direction. Therefore the three-dimensional (3D) ordinary kriging technique cannot be directly used to map the distribution of SOC at a regional scale. The objectives of this study were to map the 3D distribution of SOC at a regional scale by combining kriging method with the profile depth function of SOC (KPDF), and to explore the effects of soil texture and land use type on vertical distribution of SOC in a fluvial plain. A total of 605 samples were collected from 121 soil profiles (0.0 to 1.0 m, 0.20 m increment) in Quzhou County, China and SOC contents were determined for each soil sample. The KPDF method was used to obtain the 3D map of SOC at the county scale. The results showed that the exponential equation well described the vertical distribution of mean values of the SOC contents. The coefficients of determination, root mean squared error and mean prediction error between the measured and the predicted SOC contents were 0.52, 1.82 and -0.24 g kg-1 respectively, suggesting that the KPDF method could be used to produce a 3D map of SOC content. The surface SOC contents were high in the mid-west and south regions, and low values lay in the southeast corner. The SOC contents showed significant positive correlations between the five different depths and the correlations of SOC contents were larger in adjacent layers than in non-adjacent layers. Soil texture and land use type had significant effects on the spatial distribution of SOC. The influence of land use type was more important than that of soil texture in the surface soil, and soil texture played a more important role in influencing the SOC levels for 0.2-0.4 m layer. PMID:26047012

Application of spatial methods to identify areas with lime requirement in eastern Croatia

NASA Astrophysics Data System (ADS)

Bogunović, Igor; Kisic, Ivica; Mesic, Milan; Zgorelec, Zeljka; Percin, Aleksandra; Pereira, Paulo

2016-04-01

With more than 50% of acid soils in all agricultural land in Croatia, soil acidity is recognized as a big problem. Low soil pH leads to a series of negative phenomena in plant production and therefore as a compulsory measure for reclamation of acid soils is liming, recommended on the base of soil analysis. The need for liming is often erroneously determined only on the basis of the soil pH, because the determination of cation exchange capacity, the hydrolytic acidity and base saturation is a major cost to producers. Therefore, in Croatia, as well as some other countries, the amount of liming material needed to ameliorate acid soils is calculated by considering their hydrolytic acidity. For this research, several interpolation methods were tested to identify the best spatial predictor of hidrolitic acidity. The purpose of this study was to: test several interpolation methods to identify the best spatial predictor of hidrolitic acidity; and to determine the possibility of using multivariate geostatistics in order to reduce the number of needed samples for determination the hydrolytic acidity, all with an aim that the accuracy of the spatial distribution of liming requirement is not significantly reduced. Soil pH (in KCl) and hydrolytic acidity (Y1) is determined in the 1004 samples (from 0-30 cm) randomized collected in agricultural fields near Orahovica in eastern Croatia. This study tested 14 univariate interpolation models (part of ArcGIS software package) in order to provide most accurate spatial map of hydrolytic acidity on a base of: all samples (Y1 100%), and the datasets with 15% (Y1 85%), 30% (Y1 70%) and 50% fewer samples (Y1 50%). Parallel to univariate interpolation methods, the precision of the spatial distribution of the Y1 was tested by the co-kriging method with exchangeable acidity (pH in KCl) as a covariate. The soils at studied area had an average pH (KCl) 4,81, while the average Y1 10,52 cmol+ kg-1. These data suggest that liming is necessary agrotechnical measure for soil conditioning. The results show that ordinary kriging was most accurate univariate interpolation method with smallest error (RMSE) in all four data sets, while the least precise showed Radial Basis Functions (Thin Plate Spline and Inverse Multiquadratic). Furthermore, it is noticeable a trend of increasing errors (RMSE) with a reduced number of samples tested on the most accurate univariate interpolation model: 3,096 (Y1 100%), 3,258 (Y1 85%), 3,317 (Y1 70%), 3,546 (Y1 50%). The best-fit semivariograms show a strong spatial dependence in Y1 100% (Nugget/Sill 20.19) and Y1 85% (Nugget/Sill 23.83), while a further reduction of the number of samples resulted with moderate spatial dependence (Y1 70% -35,85% and Y1 50% - 32,01). Co-kriging method resulted in a reduction in RMSE compared with univariate interpolation methods for each data set with: 2,054, 1,731 and 1,734 for Y1 85%, Y1 70%, Y1 50%, respectively. The results show the possibility for reducing sampling costs by using co-kriging method which is useful from the practical viewpoint. Reduced number of samples by half for determination of hydrolytic acidity in the interaction with the soil pH provides a higher precision for variable liming compared to the univariate interpolation methods of the entire set of data. These data provide new opportunities to reduce costs in the practical plant production in Croatia.

Integrating bathymetric and topographic data

NASA Astrophysics Data System (ADS)

Teh, Su Yean; Koh, Hock Lye; Lim, Yong Hui; Tan, Wai Kiat

2017-11-01

The quality of bathymetric and topographic resolution significantly affect the accuracy of tsunami run-up and inundation simulation. However, high resolution gridded bathymetric and topographic data sets for Malaysia are not freely available online. It is desirable to have seamless integration of high resolution bathymetric and topographic data. The bathymetric data available from the National Hydrographic Centre (NHC) of the Royal Malaysian Navy are in scattered form; while the topographic data from the Department of Survey and Mapping Malaysia (JUPEM) are given in regularly spaced grid systems. Hence, interpolation is required to integrate the bathymetric and topographic data into regularly-spaced grid systems for tsunami simulation. The objective of this research is to analyze the most suitable interpolation methods for integrating bathymetric and topographic data with minimal errors. We analyze four commonly used interpolation methods for generating gridded topographic and bathymetric surfaces, namely (i) Kriging, (ii) Multiquadric (MQ), (iii) Thin Plate Spline (TPS) and (iv) Inverse Distance to Power (IDP). Based upon the bathymetric and topographic data for the southern part of Penang Island, our study concluded, via qualitative visual comparison and Root Mean Square Error (RMSE) assessment, that the Kriging interpolation method produces an interpolated bathymetric and topographic surface that best approximate the admiralty nautical chart of south Penang Island.

Estimation of geotechnical parameters on the basis of geophysical methods and geostatistics

NASA Astrophysics Data System (ADS)

Brom, Aleksander; Natonik, Adrianna

2017-12-01

The paper presents possible implementation of ordinary cokriging and geophysical investigation on humidity data acquired in geotechnical studies. The Author describes concept of geostatistics, terminology of geostatistical modelling, spatial correlation functions, principles of solving cokriging systems, advantages of (co-)kriging in comparison with other interpolation methods, obstacles in this type of attempt. Cross validation and discussion of results was performed with an indication of prospect of applying similar procedures in various researches..

Numerical Optimization Using Computer Experiments

NASA Technical Reports Server (NTRS)

Trosset, Michael W.; Torczon, Virginia

1997-01-01

Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Improved interpolation of meteorological forcings for hydrologic applications in a Swiss Alpine region

NASA Astrophysics Data System (ADS)

Tobin, Cara; Nicotina, Ludovico; Parlange, Marc B.; Berne, Alexis; Rinaldo, Andrea

2011-04-01

SummaryThis paper presents a comparative study on the mapping of temperature and precipitation fields in complex Alpine terrain. Its relevance hinges on the major impact that inadequate interpolations of meteorological forcings bear on the accuracy of hydrologic predictions regardless of the specifics of the models, particularly during flood events. Three flood events measured in the Swiss Alps are analyzed in detail to determine the interpolation methods which best capture the distribution of intense, orographically-induced precipitation. The interpolation techniques comparatively examined include: Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Kriging with External Drift (KED). Geostatistical methods rely on a robust anisotropic variogram for the definition of the spatial rainfall structure. Results indicate that IDW tends to significantly underestimate rainfall volumes whereas OK and KED methods capture spatial patterns and rainfall volumes induced by storm advection. Using numerical weather forecasts and elevation data as covariates for precipitation, we provide evidence for KED to outperform the other methods. Most significantly, the use of elevation as auxiliary information in KED of temperatures demonstrates minimal errors in estimated instantaneous rainfall volumes and provides instantaneous lapse rates which better capture snow/rainfall partitioning. Incorporation of the temperature and precipitation input fields into a hydrological model used for operational management was found to provide vastly improved outputs with respect to measured discharge volumes and flood peaks, with notable implications for flood modeling.

Spatial dynamics of the invasive defoliator amber-marked birch leafminer across the Anchorage landscape

Treesearch

J.E. Lundquist; R.M. Reich; M. Tuffly

2012-01-01

The amber-marked birch leafminer has caused severe infestations of birch species in Anchorage, AK, since 2002. Its spatial distribution has been monitored since 2006 and summarized using interpolated surfaces based on simple kriging. In this study, we developed methods of assessing and describing spatial distribution of the leafminer as they vary from year to year, and...

Characterization of shallow groundwater quality in the Lower St. Johns River Basin: a case study.

PubMed

Ouyang, Ying; Zhang, Jia-En; Parajuli, Prem

2013-12-01

Characterization of groundwater quality allows the evaluation of groundwater pollution and provides information for better management of groundwater resources. This study characterized the shallow groundwater quality and its spatial and seasonal variations in the Lower St. Johns River Basin, Florida, USA, under agricultural, forest, wastewater, and residential land uses using field measurements and two-dimensional kriging analysis. Comparison of the concentrations of groundwater quality constituents against the US EPA's water quality criteria showed that the maximum nitrate/nitrite (NO x ) and arsenic (As) concentrations exceeded the EPA's drinking water standard limits, while the maximum Cl, SO 4 (2-) , and Mn concentrations exceeded the EPA's national secondary drinking water regulations. In general, high kriging estimated groundwater NH 4 (+) concentrations were found around the agricultural areas, while high kriging estimated groundwater NO x concentrations were observed in the residential areas with a high density of septic tank distribution. Our study further revealed that more areas were found with high estimated NO x concentrations in summer than in spring. This occurred partially because of more NO x leaching into the shallow groundwater due to the wetter summer and partially because of faster nitrification rate due to the higher temperature in summer. Large extent and high kriging estimated total phosphorus concentrations were found in the residential areas. Overall, the groundwater Na and Mg concentration distributions were relatively more even in summer than in spring. Higher kriging estimated groundwater As concentrations were found around the agricultural areas, which exceeded the EPA's drinking water standard limit. Very small variations in groundwater dissolved organic carbon concentrations were observed between spring and summer. This study demonstrated that the concentrations of groundwater quality constituents varied from location to location, and impacts of land uses on groundwater quality variation were profound.

Optimization of a hydrometric network extension using specific flow, kriging and simulated annealing

NASA Astrophysics Data System (ADS)

Chebbi, Afef; Kebaili Bargaoui, Zoubeida; Abid, Nesrine; da Conceição Cunha, Maria

2017-12-01

In hydrometric stations, water levels are continuously observed and discharge rating curves are constantly updated to achieve accurate river levels and discharge observations. An adequate spatial distribution of hydrological gauging stations presents a lot of interest in linkage with the river regime characterization, water infrastructures design, water resources management and ecological survey. Due to the increase of riverside population and the associated flood risk, hydrological networks constantly need to be developed. This paper suggests taking advantage of kriging approaches to improve the design of a hydrometric network. The context deals with the application of an optimization approach using ordinary kriging and simulated annealing (SA) in order to identify the best locations to install new hydrometric gauges. The task at hand is to extend an existing hydrometric network in order to estimate, at ungauged sites, the average specific annual discharge which is a key basin descriptor. This methodology is developed for the hydrometric network of the transboundary Medjerda River in the North of Tunisia. A Geographic Information System (GIS) is adopted to delineate basin limits and centroids. The latter are adopted to assign the location of basins in kriging development. Scenarios where the size of an existing 12 stations network is alternatively increased by 1, 2, 3, 4 and 5 new station(s) are investigated using geo-regression and minimization of the variance of kriging errors. The analysis of the optimized locations from a scenario to another shows a perfect conformity with respect to the location of the new sites. The new locations insure a better spatial coverage of the study area as seen with the increase of both the average and the maximum of inter-station distances after optimization. The optimization procedure selects the basins that insure the shifting of the mean drainage area towards higher specific discharges.

An accurate Kriging-based regional ionospheric model using combined GPS/BeiDou observations

NASA Astrophysics Data System (ADS)

Abdelazeem, Mohamed; Çelik, Rahmi N.; El-Rabbany, Ahmed

2018-01-01

In this study, we propose a regional ionospheric model (RIM) based on both of the GPS-only and the combined GPS/BeiDou observations for single-frequency precise point positioning (SF-PPP) users in Europe. GPS/BeiDou observations from 16 reference stations are processed in the zero-difference mode. A least-squares algorithm is developed to determine the vertical total electron content (VTEC) bi-linear function parameters for a 15-minute time interval. The Kriging interpolation method is used to estimate the VTEC values at a 1 ° × 1 ° grid. The resulting RIMs are validated for PPP applications using GNSS observations from another set of stations. The SF-PPP accuracy and convergence time obtained through the proposed RIMs are computed and compared with those obtained through the international GNSS service global ionospheric maps (IGS-GIM). The results show that the RIMs speed up the convergence time and enhance the overall positioning accuracy in comparison with the IGS-GIM model, particularly the combined GPS/BeiDou-based model.

Use of geostatistics for remediation planning to transcend urban political boundaries.

PubMed

Milillo, Tammy M; Sinha, Gaurav; Gardella, Joseph A

2012-11-01

Soil remediation plans are often dictated by areas of jurisdiction or property lines instead of scientific information. This study exemplifies how geostatistically interpolated surfaces can substantially improve remediation planning. Ordinary kriging, ordinary co-kriging, and inverse distance weighting spatial interpolation methods were compared for analyzing surface and sub-surface soil sample data originally collected by the US EPA and researchers at the University at Buffalo in Hickory Woods, an industrial-residential neighborhood in Buffalo, NY, where both lead and arsenic contamination is present. Past clean-up efforts estimated contamination levels from point samples, but parcel and agency jurisdiction boundaries were used to define remediation sites, rather than geostatistical models estimating the spatial behavior of the contaminants in the soil. Residents were understandably dissatisfied with the arbitrariness of the remediation plan. In this study we show how geostatistical mapping and participatory assessment can make soil remediation scientifically defensible, socially acceptable, and economically feasible. Copyright © 2012 Elsevier Ltd. All rights reserved.

Sampling design optimization for spatial functions

USGS Publications Warehouse

Olea, R.A.

1984-01-01

A new procedure is presented for minimizing the sampling requirements necessary to estimate a mappable spatial function at a specified level of accuracy. The technique is based on universal kriging, an estimation method within the theory of regionalized variables. Neither actual implementation of the sampling nor universal kriging estimations are necessary to make an optimal design. The average standard error and maximum standard error of estimation over the sampling domain are used as global indices of sampling efficiency. The procedure optimally selects those parameters controlling the magnitude of the indices, including the density and spatial pattern of the sample elements and the number of nearest sample elements used in the estimation. As an illustration, the network of observation wells used to monitor the water table in the Equus Beds of Kansas is analyzed and an improved sampling pattern suggested. This example demonstrates the practical utility of the procedure, which can be applied equally well to other spatial sampling problems, as the procedure is not limited by the nature of the spatial function. ?? 1984 Plenum Publishing Corporation.

NTS radiological assessment project: comparison of delta-surface interpolation with kriging for the Frenchman Lake region of area 5

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

Foley, T.A. Jr.

The primary objective of this report is to compare the results of delta surface interpolation with kriging on four large sets of radiological data sampled in the Frenchman Lake region at the Nevada Test Site. The results of kriging, described in Barnes, Giacomini, Reiman, and Elliott, are very similar to those using the delta surface interpolant. The other topic studied is in reducing the number of sample points and obtaining results similar to those using all of the data. The positive results here suggest that great savings of time and money can be made. Furthermore, the delta surface interpolant ismore » viewed as a contour map and as a three dimensional surface. These graphical representations help in the analysis of the large sets of radiological data.« less

Long-Term Large-Scale Bias-Adjusted Precipitation Estimates at High Spatial and Temporal Resolution Derived from the National Mosaic and Multi-Sensor QPE (NMQ/Q2) Precipitation Reanalysis over CONUS

NASA Astrophysics Data System (ADS)

Prat, O. P.; Nelson, B. R.; Stevens, S. E.; Seo, D. J.; Kim, B.

2014-12-01

The processing of radar-only precipitation via the reanalysis from the National Mosaic and Multi-Sensor Quantitative (NMQ/Q2) based on the WSR-88D Next-generation Radar (Nexrad) network over Continental United States (CONUS) is nearly completed for the period covering from 2000 to 2012. This important milestone constitutes a unique opportunity to study precipitation processes at a 1-km spatial resolution for a 5-min temporal resolution. However, in order to be suitable for hydrological, meteorological and climatological applications, the radar-only product needs to be bias-adjusted and merged with in-situ rain gauge information. Rain gauge networks such as the Hydrometeorological Automated Data System (HADS), the Automated Surface Observing Systems (ASOS), the Climate Reference Network (CRN), and the Global Historical Climatology Network - Daily (GHCN-D) are used to adjust for those biases and to merge with the radar only product to provide a multi-sensor estimate. The challenges related to incorporating non-homogeneous networks over a vast area and for a long-term record are enormous. Among the challenges we are facing are the difficulties incorporating differing resolution and quality surface measurements to adjust gridded estimates of precipitation. Another challenge is the type of adjustment technique. After assessing the bias and applying reduction or elimination techniques, we are investigating the kriging method and its variants such as simple kriging (SK), ordinary kriging (OK), and conditional bias-penalized Kriging (CBPK) among others. In addition we hope to generate estimates of uncertainty for the gridded estimate. In this work the methodology is presented as well as a comparison between the radar-only product and the final multi-sensor QPE product. The comparison is performed at various time scales from the sub-hourly, to annual. In addition, comparisons over the same period with a suite of lower resolution QPEs derived from ground based radar measurements (Stage IV) and satellite products (TMPA, CMORPH, PERSIANN) are provided in order to give a detailed picture of the improvements and remaining challenges.

Three-dimensional mapping of soil chemical characteristics at micrometric scale: Statistical prediction by combining 2D SEM-EDX data and 3D X-ray computed micro-tomographic images

NASA Astrophysics Data System (ADS)

Hapca, Simona

2015-04-01

Many soil properties and functions emerge from interactions of physical, chemical and biological processes at microscopic scales, which can be understood only by integrating techniques that traditionally are developed within separate disciplines. While recent advances in imaging techniques, such as X-ray computed tomography (X-ray CT), offer the possibility to reconstruct the 3D physical structure at fine resolutions, for the distribution of chemicals in soil, existing methods, based on scanning electron microscope (SEM) and energy dispersive X-ray detection (EDX), allow for characterization of the chemical composition only on 2D surfaces. At present, direct 3D measurement techniques are still lacking, sequential sectioning of soils, followed by 2D mapping of chemical elements and interpolation to 3D, being an alternative which is explored in this study. Specifically, we develop an integrated experimental and theoretical framework which combines 3D X-ray CT imaging technique with 2D SEM-EDX and use spatial statistics methods to map the chemical composition of soil in 3D. The procedure involves three stages 1) scanning a resin impregnated soil cube by X-ray CT, followed by precision cutting to produce parallel thin slices, the surfaces of which are scanned by SEM-EDX, 2) alignment of the 2D chemical maps within the internal 3D structure of the soil cube, and 3) development, of spatial statistics methods to predict the chemical composition of 3D soil based on the observed 2D chemical and 3D physical data. Specifically, three statistical models consisting of a regression tree, a regression tree kriging and cokriging model were used to predict the 3D spatial distribution of carbon, silicon, iron and oxygen in soil, these chemical elements showing a good spatial agreement between the X-ray grayscale intensities and the corresponding 2D SEM-EDX data. Due to the spatial correlation between the physical and chemical data, the regression-tree model showed a great potential in predicting chemical composition in particular for iron, which is generally sparsely distributed in soil. For carbon, silicon and oxygen, which are more densely distributed, the additional kriging of the regression tree residuals improved significantly the prediction, whereas prediction based on co-kriging was less consistent across replicates, underperforming regression-tree kriging. The present study shows a great potential in integrating geo-statistical methods with imaging techniques to unveil the 3D chemical structure of soil at very fine scales, the framework being suitable to be further applied to other types of imaging data such as images of biological thin sections for characterization of microbial distribution. Key words: X-ray CT, SEM-EDX, segmentation techniques, spatial correlation, 3D soil images, 2D chemical maps.

Rtop - an R package for interpolation of data with a variable spatial support - examples from river networks

NASA Astrophysics Data System (ADS)

Olav Skøien, Jon; Laaha, Gregor; Koffler, Daniel; Blöschl, Günter; Pebesma, Edzer; Parajka, Juraj; Viglione, Alberto

2013-04-01

Geostatistical methods have been applied only to a limited extent for spatial interpolation in applications where the observations have an irregular support, such as runoff characteristics or population health data. Several studies have shown the potential of such methods (Gottschalk 1993, Sauquet et al. 2000, Gottschalk et al. 2006, Skøien et al. 2006, Goovaerts 2008), but these developments have so far not led to easily accessible, versatile, easy to apply and open source software. Based on the top-kriging approach suggested by Skøien et al. (2006), we will here present the package rtop, which has been implemented in the statistical environment R (R Core Team 2012). Taking advantage of the existing methods in R for analysis of spatial objects (Bivand et al. 2008), and the extensive possibilities for visualizing the results, rtop makes it easy to apply geostatistical interpolation methods when observations have a non-point spatial support. Although the package is flexible regarding data input, the main application so far has been for interpolation along river networks. We will present some examples showing how the package can easily be used for such interpolation. The model will soon be uploaded to CRAN, but is in the meantime also available from R-forge and can be installed by: > install.packages("rtop", repos="http://R-Forge.R-project.org") Bivand, R.S., Pebesma, E.J. & Gómez-Rubio, V., 2008. Applied spatial data analysis with r: Springer. Goovaerts, P., 2008. Kriging and semivariogram deconvolution in the presence of irregular geographical units. Mathematical Geosciences, 40 (1), 101-128. Gottschalk, L., 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., Krasovskaia, I., Leblois, E. & Sauquet, E., 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Core Team, 2012. R: A language and environment for statistical computing. Vienna, Austria, ISBN 3-900051-07-0. Sauquet, E., Gottschalk, L. & Leblois, E., 2000. Mapping average annual runoff: A hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J.O., Merz, R. & Blöschl, G., 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

Topsoil pollution forecasting using artificial neural networks on the example of the abnormally distributed heavy metal at Russian subarctic

NASA Astrophysics Data System (ADS)

Tarasov, D. A.; Buevich, A. G.; Sergeev, A. P.; Shichkin, A. V.; Baglaeva, E. M.

2017-06-01

Forecasting the soil pollution is a considerable field of study in the light of the general concern of environmental protection issues. Due to the variation of content and spatial heterogeneity of pollutants distribution at urban areas, the conventional spatial interpolation models implemented in many GIS packages mostly cannot provide appreciate interpolation accuracy. Moreover, the problem of prediction the distribution of the element with high variability in the concentration at the study site is particularly difficult. The work presents two neural networks models forecasting a spatial content of the abnormally distributed soil pollutant (Cr) at a particular location of the subarctic Novy Urengoy, Russia. A method of generalized regression neural network (GRNN) was compared to a common multilayer perceptron (MLP) model. The proposed techniques have been built, implemented and tested using ArcGIS and MATLAB. To verify the models performances, 150 scattered input data points (pollutant concentrations) have been selected from 8.5 km2 area and then split into independent training data set (105 points) and validation data set (45 points). The training data set was generated for the interpolation using ordinary kriging while the validation data set was used to test their accuracies. The networks structures have been chosen during a computer simulation based on the minimization of the RMSE. The predictive accuracy of both models was confirmed to be significantly higher than those achieved by the geostatistical approach (kriging). It is shown that MLP could achieve better accuracy than both kriging and even GRNN for interpolating surfaces.

Spatiotemporal interpolation of discharge across a river network by using synthetic SWOT satellite data

NASA Astrophysics Data System (ADS)

Paiva, Rodrigo C. D.; Durand, Michael T.; Hossain, Faisal

2015-01-01

Recent efforts have sought to estimate river discharge and other surface water-related quantities using spaceborne sensors, with better spatial coverage but worse temporal sampling as compared with in situ measurements. The Surface Water and Ocean Topography (SWOT) mission will provide river discharge estimates globally from space. However, questions on how to optimally use the spatially distributed but asynchronous satellite observations to generate continuous fields still exist. This paper presents a statistical model (River Kriging-RK), for estimating discharge time series in a river network in the context of the SWOT mission. RK uses discharge estimates at different locations and times to produce a continuous field using spatiotemporal kriging. A key component of RK is the space-time river discharge covariance, which was derived analytically from the diffusive wave approximation of Saint Venant's equations. The RK covariance also accounts for the loss of correlation at confluences. The model performed well in a case study on Ganges-Brahmaputra-Meghna (GBM) River system in Bangladesh using synthetic SWOT observations. The correlation model reproduced empirically derived values. RK (R2=0.83) outperformed other kriging-based methods (R2=0.80), as well as a simple time series linear interpolation (R2=0.72). RK was used to combine discharge from SWOT and in situ observations, improving estimates when the latter is included (R2=0.91). The proposed statistical concepts may eventually provide a feasible framework to estimate continuous discharge time series across a river network based on SWOT data, other altimetry missions, and/or in situ data.

A Modified Kriging Method to Interpolate the Soil Moisture Measured by Wireless Sensor Network with the Aid of Remote Sensing Images

NASA Astrophysics Data System (ADS)

Zhang, J.; Liu, Q.; Li, X.; Niu, H.; Cai, E.

2015-12-01

In recent years, wireless sensor network (WSN) emerges to collect Earth observation data at relatively low cost and light labor load, while its observations are still point-data. To learn the spatial distribution of a land surface parameter, interpolating the point data is necessary. Taking soil moisture (SM) for example, its spatial distribution is critical information for agriculture management, hydrological and ecological researches. This study developed a method to interpolate the WSN-measured SM to acquire the spatial distribution in a 5km*5km study area, located in the middle reaches of HEIHE River, western China. As SM is related to many factors such as topology, soil type, vegetation and etc., even the WSN observation grid is not dense enough to reflect the SM distribution pattern. Our idea is to revise the traditional Kriging algorithm, introducing spectral variables, i.e., vegetation index (VI) and abledo, from satellite imagery as supplementary information to aid the interpolation. Thus, the new Extended-Kriging algorithm operates on the spatial & spectral combined space. To run the algorithm, first we need to estimate the SM variance function, which is also extended to the combined space. As the number of WSN samples in the study area is not enough to gather robust statistics, we have to assume that the SM variance function is invariant over time. So, the variance function is estimated from a SM map, derived from the airborne CASI/TASI images acquired in July 10, 2012, and then applied to interpolate WSN data in that season. Data analysis indicates that the new algorithm can provide more details to the variation of land SM. Then, the Leave-one-out cross-validation is adopted to estimate the interpolation accuracy. Although a reasonable accuracy can be achieved, the result is not yet satisfactory. Besides improving the algorithm, the uncertainties in WSN measurements may also need to be controlled in our further work.

High-resolution daily gridded datasets of air temperature and wind speed for Europe

NASA Astrophysics Data System (ADS)

Brinckmann, S.; Krähenmann, S.; Bissolli, P.

2015-08-01

New high-resolution datasets for near surface daily air temperature (minimum, maximum and mean) and daily mean wind speed for Europe (the CORDEX domain) are provided for the period 2001-2010 for the purpose of regional model validation in the framework of DecReg, a sub-project of the German MiKlip project, which aims to develop decadal climate predictions. The main input data sources are hourly SYNOP observations, partly supplemented by station data from the ECA&D dataset (http://www.ecad.eu). These data are quality tested to eliminate erroneous data and various kinds of inhomogeneities. Grids in a resolution of 0.044° (5 km) are derived by spatial interpolation of these station data into the CORDEX area. For temperature interpolation a modified version of a regression kriging method developed by Krähenmann et al. (2011) is used. At first, predictor fields of altitude, continentality and zonal mean temperature are chosen for a regression applied to monthly station data. The residuals of the monthly regression and the deviations of the daily data from the monthly averages are interpolated using simple kriging in a second and third step. For wind speed a new method based on the concept used for temperature was developed, involving predictor fields of exposure, roughness length, coastal distance and ERA Interim reanalysis wind speed at 850 hPa. Interpolation uncertainty is estimated by means of the kriging variance and regression uncertainties. Furthermore, to assess the quality of the final daily grid data, cross validation is performed. Explained variance ranges from 70 to 90 % for monthly temperature and from 50 to 60 % for monthly wind speed. The resulting RMSE for the final daily grid data amounts to 1-2 °C and 1-1.5 m s-1 (depending on season and parameter) for daily temperature parameters and daily mean wind speed, respectively. The datasets presented in this article are published at http://dx.doi.org/10.5676/DWD_CDC/DECREG0110v1.

Geostatistical Approach to Estimating the Gold Ore Characteristics and Gold Reserves: A Case Study Daksa Area, Quang Nam Province, Viet Nam

NASA Astrophysics Data System (ADS)

Luan Truong, Xuan; Luong Le, Van; Quang Truong, Xuan

2015-04-01

Daksa gold deposit is the biggest gold deposits in Vietnam. The Daksa geological structure complicated, distributed mainly metamorphosed sedimentary NuiVu formation (PR3-?1nv2). The sulfide gold ore bodies distributed in quartz schist, quartz - biotite related to faut and distribution wing anticline. The gold ore bodies form circuits, network circuits, circuits lenses; fill the cup surface layer of the developing northeast - southwest; is the less than or west longitude north - SE. The results show that, Au and accompanying elements (Ag, Pb and Zn) have correlated pretty closely. All of its consistent with the logarithmic distribution standard, in accordance with the law of distribution of content mineral rare. The structure functions have nugget effect and spherical models with show that Au and accompanying elements special variation are changes. Au contents shown local anisotropy, no clearly anisotropy (K=1,17) and weakly anisotropy (K=1,4). Intensity mineralization of the ore bodies are quite high with demand spherical conversion coefficient ranging from 0.49 to 0.75 and from 0.66 to 0.97 (for other body). With nugget effects, ore bodies shown that it is consistent with mineralization in the ore bodies study, ore erasable, micro vein, infilling fractures in quartz vein. All of variogram presents local anisotropy, indicated gold mineralization at study area has least two-mineralization stages, consistent with the analysis of mineralography samples. By the results of the structure function study, the authors present the system optimization for exploration deposit and used to evaluate gold reserves by Ordinary Kriging. High accuracy of Kriging estimation results are expressed in the minimum Kriging variance, by compare the results calculated by some other methods (such as distance inverse weighting method, ..) and specially compare to the results of a some blocks have been exploited. Key words: Geostat and gold deposits VN. Daksa and gold mineralization. Geostat and gold mine Daksa.

Combining kriging, multispectral and multimodal microscopy to resolve malaria-infected erythrocyte contents.

PubMed

Dabo-Niang, S; Zoueu, J T

2012-09-01

In this communication, we demonstrate how kriging, combine with multispectral and multimodal microscopy can enhance the resolution of malaria-infected images and provide more details on their composition, for analysis and diagnosis. The results of this interpolation applied to the two principal components of multispectral and multimodal images illustrate that the examination of the content of Plasmodium falciparum infected human erythrocyte is improved. © 2012 The Authors Journal of Microscopy © 2012 Royal Microscopical Society.

Simulation-Based Methodologies for Global Optimization and Planning

DTIC Science & Technology

2013-10-11

GESK ) Stochastic kriging (SK) was introduced by Ankenman, Nelson, and Staum [1] to handle the stochastic simulation setting, where the noise in the...is used for the kriging. Four experiments will be used to illustrate some charac- teristics of SK, SKG, and GESK , with respect to the choice of...samples at each point. Because GESK is able to explore the design space more via extrapolation, it does a better job of capturing the fluctuations of the

Enhancing Groundwater Cost Estimation with the Interpolation of Water Tables across the United States

NASA Astrophysics Data System (ADS)

Rosli, A. U. M.; Lall, U.; Josset, L.; Rising, J. A.; Russo, T. A.; Eisenhart, T.

2017-12-01

Analyzing the trends in water use and supply across the United States is fundamental to efforts in ensuring water sustainability. As part of this, estimating the costs of producing or obtaining water (water extraction) and the correlation with water use is an important aspect in understanding the underlying trends. This study estimates groundwater costs by interpolating the depth to water level across the US in each county. We use Ordinary and Universal Kriging, accounting for the differences between aquifers. Kriging generates a best linear unbiased estimate at each location and has been widely used to map ground-water surfaces (Alley, 1993).The spatial covariates included in the universal Kriging were land-surface elevation as well as aquifer information. The average water table is computed for each county using block kriging to obtain a national map of groundwater cost, which we compare with survey estimates of depth to the water table performed by the USDA. Groundwater extraction costs were then assumed to be proportional to water table depth. Beyond estimating the water cost, the approach can provide an indication of groundwater-stress by exploring the historical evolution of depth to the water table using time series information between 1960 and 2015. Despite data limitations, we hope to enable a more compelling and meaningful national-level analysis through the quantification of cost and stress for more economically efficient water management.

Time-REferenced data Kriging (TREK): mapping hydrological statistics given their time of reference

NASA Astrophysics Data System (ADS)

Porcheron, Delphine; Leblois, Etienne; Sauquet, Eric

2016-04-01

A major issue in water sciences is to predict runoff parameters at ungauged sites. Estimates can be obtained by various methods. Among them, geostatistical approaches provide interpolation methods that consequently use explicit assumptions on the variable of interest. Geostatistical techniques have been applied to precipitation and temperature fields and later extended to estimate runoff features considered as basin-support variates along the river network (e.g. Gottschalk, 1993; Sauquet et al., 2000; Skoien et al., 2006; Gottschalk et al., 2011). To obtain robust estimations, the first step is to collect a relevant dataset. Sauquet et al. (2000) and Sauquet (2006) suggest including a large number of catchments with long and common observation periods to ensure both reliability and temporal consistency in runoff estimates. However most observation networks evolve with time. Several choices are thus possible to define an optimal reference period maximizing either spatial or temporal overlap. However, the constraints usually lead to discard a significant number of stations. Time-REferenced data Kriging method (TREK) has been developed to overcome this issue. Here is proposed a method of geostatistical estimation considering the temporal support over which a hydrological statistic has been estimated. This allows attenuating the loss of data previously caused by the application of a strict reference period. The time reference remains for the targeted map itself. The weights depend on the observation period of the data included in the dataset and how near this is to the target period. In this presentation, the concepts of TREK will be introduced and thereafter illustrated to map mean annual runoff in France. References Gottschalk, L., 1993, Correlation and covariance of runoff. Stochastic Hydrology and Hydraulics 7(2), 85-101. Sauquet, E., Gottschalk, L. and Leblois, E., 2000, Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal 45(6), 799-815. Skoien, J.O., Merz, R. and Bloschl, G., 2006, Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences 10(2), 277-287. Gottschalk, L., Leblois, E. and Skoien, J.O., 2011, Correlation and covariance of runoff revisited. Journal of Hydrology 398(1-2), 76-90. Sauquet, E., 2006, Mapping mean annual river discharges: Geostatistical developments for incorporating river network dependencies. Journal of Hydrology 331(1-2), 300-314.

Rainfall Observed Over Bangladesh 2000-2008: A Comparison of Spatial Interpolation Methods

NASA Astrophysics Data System (ADS)

Pervez, M.; Henebry, G. M.

2010-12-01

In preparation for a hydrometeorological study of freshwater resources in the greater Ganges-Brahmaputra region, we compared the results of four methods of spatial interpolation applied to point measurements of daily rainfall over Bangladesh during a seven year period (2000-2008). Two univariate (inverse distance weighted and spline-regularized and tension) and two multivariate geostatistical (ordinary kriging and kriging with external drift) methods were used to interpolate daily observations from a network of 221 rain gauges across Bangladesh spanning an area of 143,000 sq km. Elevation and topographic index were used as the covariates in the geostatistical methods. The validity of the interpolated maps was analyzed through cross-validation. The quality of the methods was assessed through the Pearson and Spearman correlations and root mean square error measurements of accuracy in cross-validation. Preliminary results indicated that the univariate methods performed better than the geostatistical methods at daily scales, likely due to the relatively dense sampled point measurements and a weak correlation between the rainfall and covariates at daily scales in this region. Inverse distance weighted produced the better results than the spline. For the days with extreme or high rainfall—spatially and quantitatively—the correlation between observed and interpolated estimates appeared to be high (r2 ~ 0.6 RMSE ~ 10mm), although for low rainfall days the correlations were poor (r2 ~ 0.1 RMSE ~ 3mm). The performance quality of these methods was influenced by the density of the sample point measurements, the quantity of the observed rainfall along with spatial extent, and an appropriate search radius defining the neighboring points. Results indicated that interpolated rainfall estimates at daily scales may introduce uncertainties in the successive hydrometeorological analysis. Interpolations at 5-day, 10-day, 15-day, and monthly time scales are currently under investigation.

Construction of Response Surface with Higher Order Continuity and Its Application to Reliability Engineering

NASA Technical Reports Server (NTRS)

Krishnamurthy, T.; Romero, V. J.

2002-01-01

The usefulness of piecewise polynomials with C1 and C2 derivative continuity for response surface construction method is examined. A Moving Least Squares (MLS) method is developed and compared with four other interpolation methods, including kriging. First the selected methods are applied and compared with one another in a two-design variables problem with a known theoretical response function. Next the methods are tested in a four-design variables problem from a reliability-based design application. In general the piecewise polynomial with higher order derivative continuity methods produce less error in the response prediction. The MLS method was found to be superior for response surface construction among the methods evaluated.

Optimization of a Coastal Environmental Monitoring Network Based on the Kriging Method: A Case Study of Quanzhou Bay, China

PubMed Central

Chen, Kai; Ni, Minjie; Wang, Jun; Huang, Dongren; Chen, Huorong; Wang, Xiao; Liu, Mengyang

2016-01-01

Environmental monitoring is fundamental in assessing environmental quality and to fulfill protection and management measures with permit conditions. However, coastal environmental monitoring work faces many problems and challenges, including the fact that monitoring information cannot be linked up with evaluation, monitoring data cannot well reflect the current coastal environmental condition, and monitoring activities are limited by cost constraints. For these reasons, protection and management measures cannot be developed and implemented well by policy makers who intend to solve this issue. In this paper, Quanzhou Bay in southeastern China was selected as a case study; and the Kriging method and a geographic information system were employed to evaluate and optimize the existing monitoring network in a semienclosed bay. This study used coastal environmental monitoring data from 15 sites (including COD, DIN, and PO4-P) to adequately analyze the water quality from 2009 to 2012 by applying the Trophic State Index. The monitoring network in Quanzhou Bay was evaluated and optimized, with the number of sites increased from 15 to 24, and the monitoring precision improved by 32.9%. The results demonstrated that the proposed advanced monitoring network optimization was appropriate for environmental monitoring in Quanzhou Bay. It might provide technical support for coastal management and pollutant reduction in similar areas. PMID:27777951

Optimization of a Coastal Environmental Monitoring Network Based on the Kriging Method: A Case Study of Quanzhou Bay, China.

PubMed

Chen, Kai; Ni, Minjie; Cai, Minggang; Wang, Jun; Huang, Dongren; Chen, Huorong; Wang, Xiao; Liu, Mengyang

2016-01-01

Environmental monitoring is fundamental in assessing environmental quality and to fulfill protection and management measures with permit conditions. However, coastal environmental monitoring work faces many problems and challenges, including the fact that monitoring information cannot be linked up with evaluation, monitoring data cannot well reflect the current coastal environmental condition, and monitoring activities are limited by cost constraints. For these reasons, protection and management measures cannot be developed and implemented well by policy makers who intend to solve this issue. In this paper, Quanzhou Bay in southeastern China was selected as a case study; and the Kriging method and a geographic information system were employed to evaluate and optimize the existing monitoring network in a semienclosed bay. This study used coastal environmental monitoring data from 15 sites (including COD, DIN, and PO 4 -P) to adequately analyze the water quality from 2009 to 2012 by applying the Trophic State Index. The monitoring network in Quanzhou Bay was evaluated and optimized, with the number of sites increased from 15 to 24, and the monitoring precision improved by 32.9%. The results demonstrated that the proposed advanced monitoring network optimization was appropriate for environmental monitoring in Quanzhou Bay. It might provide technical support for coastal management and pollutant reduction in similar areas.

Quantifying variabilty of the solar resource using the Kriging method

NASA Astrophysics Data System (ADS)

Monger, Samuel Haze

Energy consumption will steadily rise in coming years and if fossil fuels, particularly coal, continue to be the primary resource for electricity generation our planet is going to face many hardships. Solar energy is the most abundant resource available to humankind, and although solar generated power is still expensive, the technology is in a state of rapid development as governments strive to meet renewable energy goals as part of the effort to slow climate change and become less dependent on finite resources. However there are many valid concerns associated with integrating high levels of solar energy with the transmission grid due to the rapid changes in power output and voltage from photovoltaic generated electricity due to drops in the solar resource. Therefore, a study was conducted to address issues in this field of research by attempting to quantify the variability of solar irradiance at a specific area using a uniform grid of 45 irradiance sensors. Another goal of this study was to determine if fewer measurement stations could be used in the quantification of variability. This thesis addresses these issues by using the Sandia Variability Index and the dead band ramp algorithm in a statistical analysis on irradiance fluctuations in the regulation and sub-regulation time frames. A kriging method will be introduced which accurately predicts variability using only four stations.

Spatial uncertainty of a geoid undulation model in Guayaquil, Ecuador

NASA Astrophysics Data System (ADS)

Chicaiza, E. G.; Leiva, C. A.; Arranz, J. J.; Buenańo, X. E.

2017-06-01

Geostatistics is a discipline that deals with the statistical analysis of regionalized variables. In this case study, geostatistics is used to estimate geoid undulation in the rural area of Guayaquil town in Ecuador. The geostatistical approach was chosen because the estimation error of prediction map is getting. Open source statistical software R and mainly geoR, gstat and RGeostats libraries were used. Exploratory data analysis (EDA), trend and structural analysis were carried out. An automatic model fitting by Iterative Least Squares and other fitting procedures were employed to fit the variogram. Finally, Kriging using gravity anomaly of Bouguer as external drift and Universal Kriging were used to get a detailed map of geoid undulation. The estimation uncertainty was reached in the interval [-0.5; +0.5] m for errors and a maximum estimation standard deviation of 2 mm in relation with the method of interpolation applied. The error distribution of the geoid undulation map obtained in this study provides a better result than Earth gravitational models publicly available for the study area according the comparison with independent validation points. The main goal of this paper is to confirm the feasibility to use geoid undulations from Global Navigation Satellite Systems and leveling field measurements and geostatistical techniques methods in order to use them in high-accuracy engineering projects.

Wave height data assimilation using non-stationary kriging

NASA Astrophysics Data System (ADS)

Tolosana-Delgado, R.; Egozcue, J. J.; Sáchez-Arcilla, A.; Gómez, J.

2011-03-01

Data assimilation into numerical models should be both computationally fast and physically meaningful, in order to be applicable in online environmental surveillance. We present a way to improve assimilation for computationally intensive models, based on non-stationary kriging and a separable space-time covariance function. The method is illustrated with significant wave height data. The covariance function is expressed as a collection of fields: each one is obtained as the empirical covariance between the studied property (significant wave height in log-scale) at a pixel where a measurement is located (a wave-buoy is available) and the same parameter at every other pixel of the field. These covariances are computed from the available history of forecasts. The method provides a set of weights, that can be mapped for each measuring location, and that do not vary with time. Resulting weights may be used in a weighted average of the differences between the forecast and measured parameter. In the case presented, these weights may show long-range connection patterns, such as between the Catalan coast and the eastern coast of Sardinia, associated to common prevailing meteo-oceanographic conditions. When such patterns are considered as non-informative of the present situation, it is always possible to diminish their influence by relaxing the covariance maps.

Estimating the Depth of Stratigraphic Units from Marine Seismic Profiles Using Nonstationary Geostatistics

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

Chihi, Hayet; Galli, Alain; Ravenne, Christian

2000-03-15

The object of this study is to build a three-dimensional (3D) geometric model of the stratigraphic units of the margin of the Rhone River on the basis of geophysical investigations by a network of seismic profiles at sea. The geometry of these units is described by depth charts of each surface identified by seismic profiling, which is done by geostatistics. The modeling starts by a statistical analysis by which we determine the parameters that enable us to calculate the variograms of the identified surfaces. After having determined the statistical parameters, we calculate the variograms of the variable Depth. By analyzingmore » the behavior of the variogram we then can deduce whether the situation is stationary and if the variable has an anisotropic behavior. We tried the following two nonstationary methods to obtain our estimates: (a) The method of universal kriging if the underlying variogram was directly accessible. (b) The method of increments if the underlying variogram was not directly accessible. After having modeled the variograms of the increments and of the variable itself, we calculated the surfaces by kriging the variable Depth on a small-mesh estimation grid. The two methods then are compared and their respective advantages and disadvantages are discussed, as well as their fields of application. These methods are capable of being used widely in earth sciences for automatic mapping of geometric surfaces or for variables such as a piezometric surface or a concentration, which are not 'stationary,' that is, essentially, possess a gradient or a tendency to develop systematically in space.« less

Mapping Copper and Lead Concentrations at Abandoned Mine Areas Using Element Analysis Data from ICP–AES and Portable XRF Instruments: A Comparative Study

PubMed Central

Lee, Hyeongyu; Choi, Yosoon; Suh, Jangwon; Lee, Seung-Ho

2016-01-01

Understanding spatial variation of potentially toxic trace elements (PTEs) in soil is necessary to identify the proper measures for preventing soil contamination at both operating and abandoned mining areas. Many studies have been conducted worldwide to explore the spatial variation of PTEs and to create soil contamination maps using geostatistical methods. However, they generally depend only on inductively coupled plasma atomic emission spectrometry (ICP–AES) analysis data, therefore such studies are limited by insufficient input data owing to the disadvantages of ICP–AES analysis such as its costly operation and lengthy period required for analysis. To overcome this limitation, this study used both ICP–AES and portable X-ray fluorescence (PXRF) analysis data, with relatively low accuracy, for mapping copper and lead concentrations at a section of the Busan abandoned mine in Korea and compared the prediction performances of four different approaches: the application of ordinary kriging to ICP–AES analysis data, PXRF analysis data, both ICP–AES and transformed PXRF analysis data by considering the correlation between the ICP–AES and PXRF analysis data, and co-kriging to both the ICP–AES (primary variable) and PXRF analysis data (secondary variable). Their results were compared using an independent validation data set. The results obtained in this case study showed that the application of ordinary kriging to both ICP–AES and transformed PXRF analysis data is the most accurate approach when considers the spatial distribution of copper and lead contaminants in the soil and the estimation errors at 11 sampling points for validation. Therefore, when generating soil contamination maps for an abandoned mine, it is beneficial to use the proposed approach that incorporates the advantageous aspects of both ICP–AES and PXRF analysis data. PMID:27043594

A data fusion-based methodology for optimal redesign of groundwater monitoring networks

NASA Astrophysics Data System (ADS)

Hosseini, Marjan; Kerachian, Reza

2017-09-01

In this paper, a new data fusion-based methodology is presented for spatio-temporal (S-T) redesigning of Groundwater Level Monitoring Networks (GLMNs). The kriged maps of three different criteria (i.e. marginal entropy of water table levels, estimation error variances of mean values of water table levels, and estimation values of long-term changes in water level) are combined for determining monitoring sub-areas of high and low priorities in order to consider different spatial patterns for each sub-area. The best spatial sampling scheme is selected by applying a new method, in which a regular hexagonal gridding pattern and the Thiessen polygon approach are respectively utilized in sub-areas of high and low monitoring priorities. An Artificial Neural Network (ANN) and a S-T kriging models are used to simulate water level fluctuations. To improve the accuracy of the predictions, results of the ANN and S-T kriging models are combined using a data fusion technique. The concept of Value of Information (VOI) is utilized to determine two stations with maximum information values in both sub-areas with high and low monitoring priorities. The observed groundwater level data of these two stations are considered for the power of trend detection, estimating periodic fluctuations and mean values of the stationary components, which are used for determining non-uniform sampling frequencies for sub-areas. The proposed methodology is applied to the Dehgolan plain in northwestern Iran. The results show that a new sampling configuration with 35 and 7 monitoring stations and sampling intervals of 20 and 32 days, respectively in sub-areas with high and low monitoring priorities, leads to a more efficient monitoring network than the existing one containing 52 monitoring stations and monthly temporal sampling.

Learning Kriging by an instructive program.

NASA Astrophysics Data System (ADS)

Cuador, José

2016-04-01

There are three types of problem classification: the deterministic, the approximated and the stochastic problems. First, in the deterministic problems the law of the phenomenon and the data are known in the entire domain and for each instant of time. In the approximated problems, the law of the phenomenon behavior is unknown but the data can be known in the entire domain and for each instant of time. In the stochastic problems much of the law and the data are unknown in the domain, so in this case the spatial behavior of the data can only be explained with probabilistic laws. This is the most important reason why the students of geo-sciences careers and others related careers need to take courses in advance estimation methods. A good example of this situation is the estimation grades in ore mineral deposit for which the Geostatistics was formalized by G. Matheron in 1962 [6]. Geostatistics is defined as the application of the theory of Random Function to the recognition and estimation of natural phenomenon [4]. Nowadays, Geostatistics is widely used in several fields of earth sciences, for example: Mining, Oil exploration, Environment, Agricultural, Forest and others [3]. It provides a wide variety of tools for spatial data analysis and allows analysing models which are subjected to degrees of uncertainty with the rigor of mathematics and formal statistical analysis [9]. Adequate models for the Kriging interpolator has been developed according to the data behavior; however there are two key steps in applying this interpolator properly: the semivariogram determination and the Kriging neighborhood selection. The main objective of this paper is to present these two elements using an instructive program.

Mapping Copper and Lead Concentrations at Abandoned Mine Areas Using Element Analysis Data from ICP-AES and Portable XRF Instruments: A Comparative Study.

PubMed

Lee, Hyeongyu; Choi, Yosoon; Suh, Jangwon; Lee, Seung-Ho

2016-03-30

Understanding spatial variation of potentially toxic trace elements (PTEs) in soil is necessary to identify the proper measures for preventing soil contamination at both operating and abandoned mining areas. Many studies have been conducted worldwide to explore the spatial variation of PTEs and to create soil contamination maps using geostatistical methods. However, they generally depend only on inductively coupled plasma atomic emission spectrometry (ICP-AES) analysis data, therefore such studies are limited by insufficient input data owing to the disadvantages of ICP-AES analysis such as its costly operation and lengthy period required for analysis. To overcome this limitation, this study used both ICP-AES and portable X-ray fluorescence (PXRF) analysis data, with relatively low accuracy, for mapping copper and lead concentrations at a section of the Busan abandoned mine in Korea and compared the prediction performances of four different approaches: the application of ordinary kriging to ICP-AES analysis data, PXRF analysis data, both ICP-AES and transformed PXRF analysis data by considering the correlation between the ICP-AES and PXRF analysis data, and co-kriging to both the ICP-AES (primary variable) and PXRF analysis data (secondary variable). Their results were compared using an independent validation data set. The results obtained in this case study showed that the application of ordinary kriging to both ICP-AES and transformed PXRF analysis data is the most accurate approach when considers the spatial distribution of copper and lead contaminants in the soil and the estimation errors at 11 sampling points for validation. Therefore, when generating soil contamination maps for an abandoned mine, it is beneficial to use the proposed approach that incorporates the advantageous aspects of both ICP-AES and PXRF analysis data.

Spatial analysis of groundwater electrical conductivity using ordinary kriging and artificial intelligence methods (Case study: Maharlu-Bakhtegan and Tashk salt lakes basin, Iran)

NASA Astrophysics Data System (ADS)

Ghader, Fatemeh; Aljoumani, Basem; Tröger, Uwe

2017-04-01

The main resources of fresh water are the groundwater. In Iran, the quality and quantity of groundwater is affected significantly by rapid population growth and unsustainable water management in the agricultural and industrial sectors. in Maharlu-Bakhtegan and Tashk salt lakes basin, the overexploitation of groundwater for irrigation purpose caused the salt water intrusion from the lakes to the area's aquifers, moreover, the basin is located in south of Iran with semiarid climate, faces a significant decline in rainfall. All these reasons cause the degradation of ground water quality. For this study, geographical coordinates of 406 observation wells will be defined as inputs and groundwater electrical conductivities (EC) will be set as output. Ordinary kriging (OK) and artificial neural networks (ANN) will be investigated for modeling groundwater salinity. Eighty percent of data will be randomly selected to train and develop mentioned models and twenty percent of data will be used for testing and validating. Finally, the outputs of models will be compared with the corresponding measured values in observation wells.

Inference of Spatio-Temporal Functions Over Graphs via Multikernel Kriged Kalman Filtering

NASA Astrophysics Data System (ADS)

Ioannidis, Vassilis N.; Romero, Daniel; Giannakis, Georgios B.

2018-06-01

Inference of space-time varying signals on graphs emerges naturally in a plethora of network science related applications. A frequently encountered challenge pertains to reconstructing such dynamic processes, given their values over a subset of vertices and time instants. The present paper develops a graph-aware kernel-based kriged Kalman filter that accounts for the spatio-temporal variations, and offers efficient online reconstruction, even for dynamically evolving network topologies. The kernel-based learning framework bypasses the need for statistical information by capitalizing on the smoothness that graph signals exhibit with respect to the underlying graph. To address the challenge of selecting the appropriate kernel, the proposed filter is combined with a multi-kernel selection module. Such a data-driven method selects a kernel attuned to the signal dynamics on-the-fly within the linear span of a pre-selected dictionary. The novel multi-kernel learning algorithm exploits the eigenstructure of Laplacian kernel matrices to reduce computational complexity. Numerical tests with synthetic and real data demonstrate the superior reconstruction performance of the novel approach relative to state-of-the-art alternatives.

Applying Factor Analysis Combined with Kriging and Information Entropy Theory for Mapping and Evaluating the Stability of Groundwater Quality Variation in Taiwan

PubMed Central

Shyu, Guey-Shin; Cheng, Bai-You; Chiang, Chi-Ting; Yao, Pei-Hsuan; Chang, Tsun-Kuo

2011-01-01

In Taiwan many factors, whether geological parent materials, human activities, and climate change, can affect the groundwater quality and its stability. This work combines factor analysis and kriging with information entropy theory to interpret the stability of groundwater quality variation in Taiwan between 2005 and 2007. Groundwater quality demonstrated apparent differences between the northern and southern areas of Taiwan when divided by the Wu River. Approximately 52% of the monitoring wells in southern Taiwan suffered from progressing seawater intrusion, causing unstable groundwater quality. Industrial and livestock wastewaters also polluted 59.6% of the monitoring wells, resulting in elevated EC and TOC concentrations in the groundwater. In northern Taiwan, domestic wastewaters polluted city groundwater, resulting in higher NH3-N concentration and groundwater quality instability was apparent among 10.3% of the monitoring wells. The method proposed in this study for analyzing groundwater quality inspects common stability factors, identifies potential areas influenced by common factors, and assists in elevating and reinforcing information in support of an overall groundwater management strategy. PMID:21695030

Robust optimization of supersonic ORC nozzle guide vanes

NASA Astrophysics Data System (ADS)

Bufi, Elio A.; Cinnella, Paola

2017-03-01

An efficient Robust Optimization (RO) strategy is developed for the design of 2D supersonic Organic Rankine Cycle turbine expanders. The dense gas effects are not-negligible for this application and they are taken into account describing the thermodynamics by means of the Peng-Robinson-Stryjek-Vera equation of state. The design methodology combines an Uncertainty Quantification (UQ) loop based on a Bayesian kriging model of the system response to the uncertain parameters, used to approximate statistics (mean and variance) of the uncertain system output, a CFD solver, and a multi-objective non-dominated sorting algorithm (NSGA), also based on a Kriging surrogate of the multi-objective fitness function, along with an adaptive infill strategy for surrogate enrichment at each generation of the NSGA. The objective functions are the average and variance of the isentropic efficiency. The blade shape is parametrized by means of a Free Form Deformation (FFD) approach. The robust optimal blades are compared to the baseline design (based on the Method of Characteristics) and to a blade obtained by means of a deterministic CFD-based optimization.

Rtop - an R package for interpolation along the stream network

NASA Astrophysics Data System (ADS)

Skøien, J. O.

2009-04-01

Rtop - an R package for interpolation along the stream network Geostatistical methods have been used to a limited extent for estimation along stream networks, with a few exceptions(Gottschalk, 1993; Gottschalk, et al., 2006; Sauquet, et al., 2000; Skøien, et al., 2006). Interpolation of runoff characteristics are more complicated than the traditional random variables estimated by geostatistical methods, as the measurements have a more complicated support, and many catchments are nested. Skøien et al. (2006) presented the model Top-kriging which takes these effects into account for interpolation of stream flow characteristics (exemplified by the 100 year flood). The method has here been implemented as a package in the statistical environment R (R Development Core Team, 2004). Taking advantage of the existing methods in R for working with spatial objects, and the extensive possibilities for visualizing the result, this makes it considerably easier to apply the method on new data sets, in comparison to earlier implementation of the method. Gottschalk, L. 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., I. Krasovskaia, E. Leblois, and E. Sauquet. 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. R Development Core Team. 2004. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Sauquet, E., L. Gottschalk, and E. Leblois. 2000. Mapping average annual runoff: a hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J. O., R. Merz, and G. Blöschl. 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

Comparison of wildfire smoke estimation methods and associations with cardiopulmonary-related hospital admissions.

PubMed

Gan, Ryan W; Ford, Bonne; Lassman, William; Pfister, Gabriele; Vaidyanathan, Ambarish; Fischer, Emily; Volckens, John; Pierce, Jeffrey R; Magzamen, Sheryl

2017-03-01

Climate forecasts predict an increase in frequency and intensity of wildfires. Associations between health outcomes and population exposure to smoke from Washington 2012 wildfires were compared using surface monitors, chemical-weather models, and a novel method blending three exposure information sources. The association between smoke particulate matter ≤2.5 μm in diameter (PM 2.5 ) and cardiopulmonary hospital admissions occurring in Washington from 1 July to 31 October 2012 was evaluated using a time-stratified case-crossover design. Hospital admissions aggregated by ZIP code were linked with population-weighted daily average concentrations of smoke PM 2.5 estimated using three distinct methods: a simulation with the Weather Research and Forecasting with Chemistry (WRF-Chem) model, a kriged interpolation of PM 2.5 measurements from surface monitors, and a geographically weighted ridge regression (GWR) that blended inputs from WRF-Chem, satellite observations of aerosol optical depth, and kriged PM 2.5 . A 10 μg/m 3 increase in GWR smoke PM 2.5 was associated with an 8% increased risk in asthma-related hospital admissions (odds ratio (OR): 1.076, 95% confidence interval (CI): 1.019-1.136); other smoke estimation methods yielded similar results. However, point estimates for chronic obstructive pulmonary disease (COPD) differed by smoke PM 2.5 exposure method: a 10 μg/m 3 increase using GWR was significantly associated with increased risk of COPD (OR: 1.084, 95%CI: 1.026-1.145) and not significant using WRF-Chem (OR: 0.986, 95%CI: 0.931-1.045). The magnitude (OR) and uncertainty (95%CI) of associations between smoke PM 2.5 and hospital admissions were dependent on estimation method used and outcome evaluated. Choice of smoke exposure estimation method used can impact the overall conclusion of the study.

Space Weather Activities of IONOLAB Group: TEC Mapping

NASA Astrophysics Data System (ADS)

Arikan, F.; Yilmaz, A.; Arikan, O.; Sayin, I.; Gurun, M.; Akdogan, K. E.; Yildirim, S. A.

2009-04-01

Being a key player in Space Weather, ionospheric variability affects the performance of both communication and navigation systems. To improve the performance of these systems, ionosphere has to be monitored. Total Electron Content (TEC), line integral of the electron density along a ray path, is an important parameter to investigate the ionospheric variability. A cost-effective way of obtaining TEC is by using dual-frequency GPS receivers. Since these measurements are sparse in space, accurate and robust interpolation techniques are needed to interpolate (or map) the TEC distribution for a given region in space. However, the TEC data derived from GPS measurements contain measurement noise, model and computational errors. Thus, it is necessary to analyze the interpolation performance of the techniques on synthetic data sets that can represent various ionospheric states. By this way, interpolation performance of the techniques can be compared over many parameters that can be controlled to represent the desired ionospheric states. In this study, Multiquadrics, Inverse Distance Weighting (IDW), Cubic Splines, Ordinary and Universal Kriging, Random Field Priors (RFP), Multi-Layer Perceptron Neural Network (MLP-NN), and Radial Basis Function Neural Network (RBF-NN) are employed as the spatial interpolation algorithms. These mapping techniques are initially tried on synthetic TEC surfaces for parameter and coefficient optimization and determination of error bounds. Interpolation performance of these methods are compared on synthetic TEC surfaces over the parameters of sampling pattern, number of samples, the variability of the surface and the trend type in the TEC surfaces. By examining the performance of the interpolation methods, it is observed that both Kriging, RFP and NN have important advantages and possible disadvantages depending on the given constraints. It is also observed that the determining parameter in the error performance is the trend in the Ionosphere. Optimization of the algorithms in terms of their performance parameters (like the choice of the semivariogram function for Kriging algorithms and the hidden layer and neuron numbers for MLP-NN) mostly depend on the behavior of the ionosphere at that given time instant for the desired region. The sampling pattern and number of samples are the other important parameters that may contribute to the higher errors in reconstruction. For example, for all of the above listed algorithms, hexagonal regular sampling of the ionosphere provides the lowest reconstruction error and the performance significantly degrades as the samples in the region become sparse and clustered. The optimized models and coefficients are applied to regional GPS-TEC mapping using the IONOLAB-TEC data (www.ionolab.org). Both Kriging combined with Kalman Filter and dynamic modeling of NN are also implemented as first trials of TEC and space weather predictions.

Comparing ordinary kriging and inverse distance weighting for soil as pollution in Beijing.

PubMed

Qiao, Pengwei; Lei, Mei; Yang, Sucai; Yang, Jun; Guo, Guanghui; Zhou, Xiaoyong

2018-06-01

Spatial interpolation method is the basis of soil heavy metal pollution assessment and remediation. The existing evaluation index for interpolation accuracy did not combine with actual situation. The selection of interpolation methods needs to be based on specific research purposes and research object characteristics. In this paper, As pollution in soils of Beijing was taken as an example. The prediction accuracy of ordinary kriging (OK) and inverse distance weighted (IDW) were evaluated based on the cross validation results and spatial distribution characteristics of influencing factors. The results showed that, under the condition of specific spatial correlation, the cross validation results of OK and IDW for every soil point and the prediction accuracy of spatial distribution trend are similar. But the prediction accuracy of OK for the maximum and minimum is less than IDW, while the number of high pollution areas identified by OK are less than IDW. It is difficult to identify the high pollution areas fully by OK, which shows that the smoothing effect of OK is obvious. In addition, with increasing of the spatial correlation of As concentration, the cross validation error of OK and IDW decreases, and the high pollution area identified by OK is approaching the result of IDW, which can identify the high pollution areas more comprehensively. However, because the semivariogram constructed by OK interpolation method is more subjective and requires larger number of soil samples, IDW is more suitable for spatial prediction of heavy metal pollution in soils.

Geostatistics and spatial analysis in biological anthropology.

PubMed

Relethford, John H

2008-05-01

A variety of methods have been used to make evolutionary inferences based on the spatial distribution of biological data, including reconstructing population history and detection of the geographic pattern of natural selection. This article provides an examination of geostatistical analysis, a method used widely in geology but which has not often been applied in biological anthropology. Geostatistical analysis begins with the examination of a variogram, a plot showing the relationship between a biological distance measure and the geographic distance between data points and which provides information on the extent and pattern of spatial correlation. The results of variogram analysis are used for interpolating values of unknown data points in order to construct a contour map, a process known as kriging. The methods of geostatistical analysis and discussion of potential problems are applied to a large data set of anthropometric measures for 197 populations in Ireland. The geostatistical analysis reveals two major sources of spatial variation. One pattern, seen for overall body and craniofacial size, shows an east-west cline most likely reflecting the combined effects of past population dispersal and settlement. The second pattern is seen for craniofacial height and shows an isolation by distance pattern reflecting rapid spatial changes in the midlands region of Ireland, perhaps attributable to the genetic impact of the Vikings. The correspondence of these results with other analyses of these data and the additional insights generated from variogram analysis and kriging illustrate the potential utility of geostatistical analysis in biological anthropology. (c) 2008 Wiley-Liss, Inc.

Spatially distributed modeling of soil organic carbon across China with improved accuracy

NASA Astrophysics Data System (ADS)

Li, Qi-quan; Zhang, Hao; Jiang, Xin-ye; Luo, Youlin; Wang, Chang-quan; Yue, Tian-xiang; Li, Bing; Gao, Xue-song

2017-06-01

There is a need for more detailed spatial information on soil organic carbon (SOC) for the accurate estimation of SOC stock and earth system models. As it is effective to use environmental factors as auxiliary variables to improve the prediction accuracy of spatially distributed modeling, a combined method (HASM_EF) was developed to predict the spatial pattern of SOC across China using high accuracy surface modeling (HASM), artificial neural network (ANN), and principal component analysis (PCA) to introduce land uses, soil types, climatic factors, topographic attributes, and vegetation cover as predictors. The performance of HASM_EF was compared with ordinary kriging (OK), OK, and HASM combined, respectively, with land uses and soil types (OK_LS and HASM_LS), and regression kriging combined with land uses and soil types (RK_LS). Results showed that HASM_EF obtained the lowest prediction errors and the ratio of performance to deviation (RPD) presented the relative improvements of 89.91%, 63.77%, 55.86%, and 42.14%, respectively, compared to the other four methods. Furthermore, HASM_EF generated more details and more realistic spatial information on SOC. The improved performance of HASM_EF can be attributed to the introduction of more environmental factors, to explicit consideration of the multicollinearity of selected factors and the spatial nonstationarity and nonlinearity of relationships between SOC and selected factors, and to the performance of HASM and ANN. This method may play a useful tool in providing more precise spatial information on soil parameters for global modeling across large areas.

Gap-filling a spatially explicit plant trait database: comparing imputation methods and different levels of environmental information

NASA Astrophysics Data System (ADS)

Poyatos, Rafael; Sus, Oliver; Badiella, Llorenç; Mencuccini, Maurizio; Martínez-Vilalta, Jordi

2018-05-01

The ubiquity of missing data in plant trait databases may hinder trait-based analyses of ecological patterns and processes. Spatially explicit datasets with information on intraspecific trait variability are rare but offer great promise in improving our understanding of functional biogeography. At the same time, they offer specific challenges in terms of data imputation. Here we compare statistical imputation approaches, using varying levels of environmental information, for five plant traits (leaf biomass to sapwood area ratio, leaf nitrogen content, maximum tree height, leaf mass per area and wood density) in a spatially explicit plant trait dataset of temperate and Mediterranean tree species (Ecological and Forest Inventory of Catalonia, IEFC, dataset for Catalonia, north-east Iberian Peninsula, 31 900 km2). We simulated gaps at different missingness levels (10-80 %) in a complete trait matrix, and we used overall trait means, species means, k nearest neighbours (kNN), ordinary and regression kriging, and multivariate imputation using chained equations (MICE) to impute missing trait values. We assessed these methods in terms of their accuracy and of their ability to preserve trait distributions, multi-trait correlation structure and bivariate trait relationships. The relatively good performance of mean and species mean imputations in terms of accuracy masked a poor representation of trait distributions and multivariate trait structure. Species identity improved MICE imputations for all traits, whereas forest structure and topography improved imputations for some traits. No method performed best consistently for the five studied traits, but, considering all traits and performance metrics, MICE informed by relevant ecological variables gave the best results. However, at higher missingness (> 30 %), species mean imputations and regression kriging tended to outperform MICE for some traits. MICE informed by relevant ecological variables allowed us to fill the gaps in the IEFC incomplete dataset (5495 plots) and quantify imputation uncertainty. Resulting spatial patterns of the studied traits in Catalan forests were broadly similar when using species means, regression kriging or the best-performing MICE application, but some important discrepancies were observed at the local level. Our results highlight the need to assess imputation quality beyond just imputation accuracy and show that including environmental information in statistical imputation approaches yields more plausible imputations in spatially explicit plant trait datasets.

Interpolating Non-Parametric Distributions of Hourly Rainfall Intensities Using Random Mixing

NASA Astrophysics Data System (ADS)

Mosthaf, Tobias; Bárdossy, András; Hörning, Sebastian

2015-04-01

The correct spatial interpolation of hourly rainfall intensity distributions is of great importance for stochastical rainfall models. Poorly interpolated distributions may lead to over- or underestimation of rainfall and consequently to wrong estimates of following applications, like hydrological or hydraulic models. By analyzing the spatial relation of empirical rainfall distribution functions, a persistent order of the quantile values over a wide range of non-exceedance probabilities is observed. As the order remains similar, the interpolation weights of quantile values for one certain non-exceedance probability can be applied to the other probabilities. This assumption enables the use of kernel smoothed distribution functions for interpolation purposes. Comparing the order of hourly quantile values over different gauges with the order of their daily quantile values for equal probabilities, results in high correlations. The hourly quantile values also show high correlations with elevation. The incorporation of these two covariates into the interpolation is therefore tested. As only positive interpolation weights for the quantile values assure a monotonically increasing distribution function, the use of geostatistical methods like kriging is problematic. Employing kriging with external drift to incorporate secondary information is not applicable. Nonetheless, it would be fruitful to make use of covariates. To overcome this shortcoming, a new random mixing approach of spatial random fields is applied. Within the mixing process hourly quantile values are considered as equality constraints and correlations with elevation values are included as relationship constraints. To profit from the dependence of daily quantile values, distribution functions of daily gauges are used to set up lower equal and greater equal constraints at their locations. In this way the denser daily gauge network can be included in the interpolation of the hourly distribution functions. The applicability of this new interpolation procedure will be shown for around 250 hourly rainfall gauges in the German federal state of Baden-Württemberg. The performance of the random mixing technique within the interpolation is compared to applicable kriging methods. Additionally, the interpolation of kernel smoothed distribution functions is compared with the interpolation of fitted parametric distributions.

The Choice of Spatial Interpolation Method Affects Research Conclusions

NASA Astrophysics Data System (ADS)

Eludoyin, A. O.; Ijisesan, O. S.; Eludoyin, O. M.

2017-12-01

Studies from developing countries using spatial interpolations in geographical information systems (GIS) are few and recent. Many of the studies have adopted interpolation procedures including kriging, moving average or Inverse Weighted Average (IDW) and nearest point without the necessary recourse to their uncertainties. This study compared the results of modelled representations of popular interpolation procedures from two commonly used GIS software (ILWIS and ArcGIS) at the Obafemi Awolowo University, Ile-Ife, Nigeria. Data used were concentrations of selected biochemical variables (BOD5, COD, SO4, NO3, pH, suspended and dissolved solids) in Ere stream at Ayepe-Olode, in the southwest Nigeria. Water samples were collected using a depth-integrated grab sampling approach at three locations (upstream, downstream and along a palm oil effluent discharge point in the stream); four stations were sited along each location (Figure 1). Data were first subjected to examination of their spatial distributions and associated variogram variables (nugget, sill and range), using the PAleontological STatistics (PAST3), before the mean values were interpolated in selected GIS software for the variables using each of kriging (simple), moving average and nearest point approaches. Further, the determined variogram variables were substituted with the default values in the selected software, and their results were compared. The study showed that the different point interpolation methods did not produce similar results. For example, whereas the values of conductivity was interpolated to vary as 120.1 - 219.5 µScm-1 with kriging interpolation, it varied as 105.6 - 220.0 µScm-1 and 135.0 - 173.9µScm-1 with nearest point and moving average interpolations, respectively (Figure 2). It also showed that whereas the computed variogram model produced the best fit lines (with least associated error value, Sserror) with Gaussian model, the Spherical model was assumed default for all the distributions in the software, such that the value of nugget was assumed as 0.00, when it was rarely so (Figure 3). The study concluded that interpolation procedures may affect decisions and conclusions on modelling inferences.

Spatial assessment of soil organic carbon and physicochemical properties in a horticultural orchard at arid zone of India using geostatistical approaches.

PubMed

Singh, Akath; Santra, Priyabrata; Kumar, Mahesh; Panwar, Navraten; Meghwal, P R

2016-09-01

Soil organic carbon (SOC) is a major indicator of long-term sustenance of agricultural production system. Apart from sustaining productivity, SOC plays a crucial role in context of climate change. Keeping in mind these potentials, spatial variation of SOC contents of a fruit orchard comprising several arid fruit plantations located at arid region of India is assessed in this study through geostatistical approaches. For this purpose, surface and subsurface soil samples from 175 locations from a fruit orchard spreading over 14.33 ha area were collected along with geographical coordinates. SOC content and soil physicochemical properties of collected soil samples were determined followed by geostatistical analysis for mapping purposes. Average SOC stock density of the orchard was 14.48 Mg ha(-1) for 0- to 30-cm soil layer ranging from 9.01 Mg ha(-1) in Carissa carandas to 19.52 Mg ha(-1) in Prosopis cineraria block. Range of spatial variation of SOC content was found about 100 m, while two other soil physicochemical properties, e.g., pH and electrical conductivity (EC) also showed similar spatial trend. This indicated that minimum sampling distance for future SOC mapping programme may be kept lower than 100 m for better accuracy. Ordinary kriging technique satisfactorily predicted SOC contents (in percent) at unsampled locations with root-mean-squared residual (RMSR) of 0.35-0.37. Co-kriging approach was found slightly superior (RMSR = 0.26-0.28) than ordinary kriging for spatial prediction of SOC contents because of significant correlations of SOC contents with pH and EC. Uncertainty of SOC estimation was also presented in terms of 90 % confidence interval. Spatial estimates of SOC stock through ordinary kriging or co-kriging approach were also found with low uncertainty of estimation than non-spatial estimates, e.g., arithmetic averaging approach. Among different fruit block plantations of the orchard, the block with Prosopis cineraria ('khejri') has higher SOC stock density than others.

Geostatistical Modeling of Sediment Abundance in a Heterogeneous Basalt Aquifer at the Idaho National Laboratory, Idaho

USGS Publications Warehouse

Welhan, John A.; Farabaugh, Renee L.; Merrick, Melissa J.; Anderson, Steven R.

2007-01-01

The spatial distribution of sediment in the eastern Snake River Plain aquifer was evaluated and modeled to improve the parameterization of hydraulic conductivity (K) for a subregional-scale ground-water flow model being developed by the U.S. Geological Survey. The aquifer is hosted within a layered series of permeable basalts within which intercalated beds of fine-grained sediment constitute local confining units. These sediments have K values as much as six orders of magnitude lower than the most permeable basalt, and previous flow-model calibrations have shown that hydraulic conductivity is sensitive to the proportion of intercalated sediment. Stratigraphic data in the form of sediment thicknesses from 333 boreholes in and around the Idaho National Laboratory were evaluated as grouped subsets of lithologic units (composite units) corresponding to their relative time-stratigraphic position. The results indicate that median sediment abundances of the stratigraphic units below the water table are statistically invariant (stationary) in a spatial sense and provide evidence of stationarity across geologic time, as well. Based on these results, the borehole data were kriged as two-dimensional spatial data sets representing the sediment content of the layers that discretize the ground-water flow model in the uppermost 300 feet of the aquifer. Multiple indicator kriging (mIK) was used to model the geographic distribution of median sediment abundance within each layer by defining the local cumulative frequency distribution (CFD) of sediment via indicator variograms defined at multiple thresholds. The mIK approach is superior to ordinary kriging because it provides a statistically best estimate of sediment abundance (the local median) drawn from the distribution of local borehole data, independent of any assumption of normality. A methodology is proposed for delineating and constraining the assignment of hydraulic conductivity zones for parameter estimation, based on the locally estimated CFDs and relative kriging uncertainty. A kriging-based methodology improves the spatial resolution of hydraulic property zones that can be considered during parameter estimation and should improve calibration performance and sensitivity by more accurately reflecting the nuances of sediment distribution within the aquifer.

Interpolating of climate data using R

NASA Astrophysics Data System (ADS)

Reinhardt, Katja

2017-04-01

Interpolation methods are used in many different geoscientific areas, such as soil physics, climatology and meteorology. Thereby, unknown values are calculated by using statistical calculation approaches applied on known values. So far, the majority of climatologists have been using computer languages, such as FORTRAN or C++, but there is also an increasing number of climate scientists using R for data processing and visualization. Most of them, however, are still working with arrays and vector based data which is often associated with complex R code structures. For the presented study, I have decided to convert the climate data into geodata and to perform the whole data processing using the raster package, gstat and similar packages, providing a much more comfortable way for data handling. A central goal of my approach is to create an easy to use, powerful and fast R script, implementing the entire geodata processing and visualization into a single and fully automated R based procedure, which allows avoiding the necessity of using other software packages, such as ArcGIS or QGIS. Thus, large amount of data with recurrent process sequences can be processed. The aim of the presented study, which is located in western Central Asia, is to interpolate wind data based on the European reanalysis data Era-Interim, which are available as raster data with a resolution of 0.75˚ x 0.75˚ , to a finer grid. Therefore, various interpolation methods are used: inverse distance weighting, the geostatistical methods ordinary kriging and regression kriging, generalized additve model and the machine learning algorithms support vector machine and neural networks. Besides the first two mentioned methods, the methods are used with influencing factors, e.g. geopotential and topography.

Improving Estimations of Spatial Distribution of Soil Respiration Using the Bayesian Maximum Entropy Algorithm and Soil Temperature as Auxiliary Data.

PubMed

Hu, Junguo; Zhou, Jian; Zhou, Guomo; Luo, Yiqi; Xu, Xiaojun; Li, Pingheng; Liang, Junyi

2016-01-01

Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME) algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information) effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK) and Co-Kriging (Co-OK) methods. The results indicated that the root mean squared errors (RMSEs) and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193) were less than those for the OK method (1.146 and 1.539) when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points.

Improving Estimations of Spatial Distribution of Soil Respiration Using the Bayesian Maximum Entropy Algorithm and Soil Temperature as Auxiliary Data

PubMed Central

Hu, Junguo; Zhou, Jian; Zhou, Guomo; Luo, Yiqi; Xu, Xiaojun; Li, Pingheng; Liang, Junyi

2016-01-01

Soil respiration inherently shows strong spatial variability. It is difficult to obtain an accurate characterization of soil respiration with an insufficient number of monitoring points. However, it is expensive and cumbersome to deploy many sensors. To solve this problem, we proposed employing the Bayesian Maximum Entropy (BME) algorithm, using soil temperature as auxiliary information, to study the spatial distribution of soil respiration. The BME algorithm used the soft data (auxiliary information) effectively to improve the estimation accuracy of the spatiotemporal distribution of soil respiration. Based on the functional relationship between soil temperature and soil respiration, the BME algorithm satisfactorily integrated soil temperature data into said spatial distribution. As a means of comparison, we also applied the Ordinary Kriging (OK) and Co-Kriging (Co-OK) methods. The results indicated that the root mean squared errors (RMSEs) and absolute values of bias for both Day 1 and Day 2 were the lowest for the BME method, thus demonstrating its higher estimation accuracy. Further, we compared the performance of the BME algorithm coupled with auxiliary information, namely soil temperature data, and the OK method without auxiliary information in the same study area for 9, 21, and 37 sampled points. The results showed that the RMSEs for the BME algorithm (0.972 and 1.193) were less than those for the OK method (1.146 and 1.539) when the number of sampled points was 9 and 37, respectively. This indicates that the former method using auxiliary information could reduce the required number of sampling points for studying spatial distribution of soil respiration. Thus, the BME algorithm, coupled with soil temperature data, can not only improve the accuracy of soil respiration spatial interpolation but can also reduce the number of sampling points. PMID:26807579

A pseudo-penalized quasi-likelihood approach to the spatial misalignment problem with non-normal data.

PubMed

Lopiano, Kenneth K; Young, Linda J; Gotway, Carol A

2014-09-01

Spatially referenced datasets arising from multiple sources are routinely combined to assess relationships among various outcomes and covariates. The geographical units associated with the data, such as the geographical coordinates or areal-level administrative units, are often spatially misaligned, that is, observed at different locations or aggregated over different geographical units. As a result, the covariate is often predicted at the locations where the response is observed. The method used to align disparate datasets must be accounted for when subsequently modeling the aligned data. Here we consider the case where kriging is used to align datasets in point-to-point and point-to-areal misalignment problems when the response variable is non-normally distributed. If the relationship is modeled using generalized linear models, the additional uncertainty induced from using the kriging mean as a covariate introduces a Berkson error structure. In this article, we develop a pseudo-penalized quasi-likelihood algorithm to account for the additional uncertainty when estimating regression parameters and associated measures of uncertainty. The method is applied to a point-to-point example assessing the relationship between low-birth weights and PM2.5 levels after the onset of the largest wildfire in Florida history, the Bugaboo scrub fire. A point-to-areal misalignment problem is presented where the relationship between asthma events in Florida's counties and PM2.5 levels after the onset of the fire is assessed. Finally, the method is evaluated using a simulation study. Our results indicate the method performs well in terms of coverage for 95% confidence intervals and naive methods that ignore the additional uncertainty tend to underestimate the variability associated with parameter estimates. The underestimation is most profound in Poisson regression models. © 2014, The International Biometric Society.

Scramjet Fuel Injection Array Optimization Utilizing Mixed Variable Pattern Search With Kriging Surrogates

DTIC Science & Technology

2008-03-01

injector con- figurations for Scramjet applications.” International Journal of Heat and Mass Transfer 49: 3634–3644 (2006). 8. Anderson, C.D...Experimental Attainment of Optimal Conditions,” Journal of the Royal Statistical Society, B(13): 1–38, 1951. 19. Brewer, K.M. Exergy Methods for the Mission...second applies mvps to a new scramjet design in support of the Hypersonic International Flight Re- search Experimentation (hifire). The results

Regional prediction of basin-scale brown trout habitat suitability

NASA Astrophysics Data System (ADS)

Ceola, S.; Pugliese, A.

2014-09-01

In this study we propose a novel method for the estimation of ecological indices describing the habitat suitability of brown trout (Salmo trutta). Traditional hydrological tools are coupled with an innovative regional geostatistical technique, aiming at the prediction of the brown trout habitat suitability index where partial or totally ungauged conditions occur. Several methods for the assessment of ecological indices are already proposed in the scientific literature, but the possibility of exploiting a geostatistical prediction model, such as Topological Kriging, has never been investigated before. In order to develop a regional habitat suitability model we use the habitat suitability curve, obtained from measured data of brown trout adult individuals collected in several river basins across the USA. The Top-kriging prediction model is then employed to assess the spatial correlation between upstream and downstream habitat suitability indices. The study area is the Metauro River basin, located in the central part of Italy (Marche region), for which both water depth and streamflow data were collected. The present analysis focuses on discharge values corresponding to the 0.1-, 0.5-, 0.9-empirical quantiles derived from flow-duration curves available for seven gauging stations located within the study area, for which three different suitability indices (i.e. ψ10, ψ50 and ψ90) are evaluated. The results of this preliminary analysis are encouraging showing Nash-Sutcliffe efficiencies equal to 0.52, 0.65, and 0.69, respectively.

Robust optimization of a tandem grating solar thermal absorber

NASA Astrophysics Data System (ADS)

Choi, Jongin; Kim, Mingeon; Kang, Kyeonghwan; Lee, Ikjin; Lee, Bong Jae

2018-04-01

Ideal solar thermal absorbers need to have a high value of the spectral absorptance in the broad solar spectrum to utilize the solar radiation effectively. Majority of recent studies about solar thermal absorbers focus on achieving nearly perfect absorption using nanostructures, whose characteristic dimension is smaller than the wavelength of sunlight. However, precise fabrication of such nanostructures is not easy in reality; that is, unavoidable errors always occur to some extent in the dimension of fabricated nanostructures, causing an undesirable deviation of the absorption performance between the designed structure and the actually fabricated one. In order to minimize the variation in the solar absorptance due to the fabrication error, the robust optimization can be performed during the design process. However, the optimization of solar thermal absorber considering all design variables often requires tremendous computational costs to find an optimum combination of design variables with the robustness as well as the high performance. To achieve this goal, we apply the robust optimization using the Kriging method and the genetic algorithm for designing a tandem grating solar absorber. By constructing a surrogate model through the Kriging method, computational cost can be substantially reduced because exact calculation of the performance for every combination of variables is not necessary. Using the surrogate model and the genetic algorithm, we successfully design an effective solar thermal absorber exhibiting a low-level of performance degradation due to the fabrication uncertainty of design variables.

Identification of hydraulic conductivity structure in sand and gravel aquifers: Cape Cod data set

USGS Publications Warehouse

Eggleston, J.R.; Rojstaczer, S.A.; Peirce, J.J.

1996-01-01

This study evaluates commonly used geostatistical methods to assess reproduction of hydraulic conductivity (K) structure and sensitivity under limiting amounts of data. Extensive conductivity measurements from the Cape Cod sand and gravel aquifer are used to evaluate two geostatistical estimation methods, conditional mean as an estimate and ordinary kriging, and two stochastic simulation methods, simulated annealing and sequential Gaussian simulation. Our results indicate that for relatively homogeneous sand and gravel aquifers such as the Cape Cod aquifer, neither estimation methods nor stochastic simulation methods give highly accurate point predictions of hydraulic conductivity despite the high density of collected data. Although the stochastic simulation methods yielded higher errors than the estimation methods, the stochastic simulation methods yielded better reproduction of the measured In (K) distribution and better reproduction of local contrasts in In (K). The inability of kriging to reproduce high In (K) values, as reaffirmed by this study, provides a strong instigation for choosing stochastic simulation methods to generate conductivity fields when performing fine-scale contaminant transport modeling. Results also indicate that estimation error is relatively insensitive to the number of hydraulic conductivity measurements so long as more than a threshold number of data are used to condition the realizations. This threshold occurs for the Cape Cod site when there are approximately three conductivity measurements per integral volume. The lack of improvement with additional data suggests that although fine-scale hydraulic conductivity structure is evident in the variogram, it is not accurately reproduced by geostatistical estimation methods. If the Cape Cod aquifer spatial conductivity characteristics are indicative of other sand and gravel deposits, then the results on predictive error versus data collection obtained here have significant practical consequences for site characterization. Heavily sampled sand and gravel aquifers, such as Cape Cod and Borden, may have large amounts of redundant data, while in more common real world settings, our results suggest that denser data collection will likely improve understanding of permeability structure.

Hydrogeologic unit flow characterization using transition probability geostatistics.

PubMed

Jones, Norman L; Walker, Justin R; Carle, Steven F

2005-01-01

This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has some advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upward sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids and/or grids with nonuniform cell thicknesses.

Predictions of runoff signatures in ungauged basins: Austrian case study

NASA Astrophysics Data System (ADS)

Viglione, A.; Parajka, J.; Salinas, J.; Rogger, M.; Sivapalan, M.; Bloeschl, G.

2012-12-01

Runoff variability can be broken up into several components, each of them meaningful of a certain class of applications of societal relevance: annual runoff, seasonal runoff, flow duration curve, low flows, floods and hydrographs. We call them runoff signatures and we view them as a manifestation of catchment functioning at different time scales, as emergent properties of the complex systems that catchments are. Just as a medical doctor has many different options for studying the state and functioning of a patient, we can infer the state and functioning of a catchment observing its runoff signatures. But what can we do in the absence of runoff data? This study aims to understand how well one can predict runoff signatures in ungauged catchments. The comparison across signatures is based on one consistent data set (Austria) and one regionalisation method (Top-Kriging) in order to explore the relative performance of the predictions of each of the signatures. Results indicate that the performance, assessed by cross-validation, is best for annual and seasonal runoff, it degrades as one moves to low flows and floods and goes up again to high values for runoff hydrographs. Also, dedicated regionalisation methods, i.e. focusing on particular signatures and their characteristics, provide better predictions of the signatures than regionalisation of the entire hydrograph. These results suggest that the use of signatures in the calibration or assessment of process models can be valuable, in that this can lead to models predicting runoff correctly for the right reasons.

Electromagnet Weight Reduction in a Magnetic Levitation System for Contactless Delivery Applications

PubMed Central

Hong, Do-Kwan; Woo, Byung-Chul; Koo, Dae-Hyun; Lee, Ki-Chang

2010-01-01

This paper presents an optimum design of a lightweight vehicle levitation electromagnet, which also provides a passive guide force in a magnetic levitation system for contactless delivery applications. The split alignment of C-shaped electromagnets about C-shaped rails has a bad effect on the lateral deviation force, therefore, no-split positioning of electromagnets is better for lateral performance. This is verified by simulations and experiments. This paper presents a statistically optimized design with a high number of the design variables to reduce the weight of the electromagnet under the constraint of normal force using response surface methodology (RSM) and the kriging interpolation method. 2D and 3D magnetostatic analysis of the electromagnet are performed using ANSYS. The most effective design variables are extracted by a Pareto chart. The most desirable set is determined and the influence of each design variable on the objective function can be obtained. The generalized reduced gradient (GRG) algorithm is adopted in the kriging model. This paper’s procedure is validated by a comparison between experimental and calculation results, which shows that the predicted performance of the electromagnet designed by RSM is in good agreement with the simulation results. PMID:22163572

Horizontal and vertical variability of soil properties in a trace element contaminated area

NASA Astrophysics Data System (ADS)

Burgos, Pilar; Madejón, Engracia; Pérez-de-Mora, Alfredo; Cabrera, Francisco

2008-02-01

The spatial distribution of some soil chemical properties and trace element contents of a plot affected by the Aznalcóllar mine spill were investigated using statistical and geostatistical methods to assess the extent of soil contamination. Total and EDTA-extractable soil trace element concentrations and total S content showed great variability and high coefficients of variation in the three examined depths. Soil in the plot was found to be significantly contaminated by As, Cd, Cu, Pb and Zn within a wide range of pH. Total trace element concentrations at all depths (0-60 cm) were much higher than background values of non-affected soil, indicating that despite the clean-up operations, the concentration of trace elements in the experimental plot was still high. The spatial distribution of the different variables was estimated by kriging to design contour maps. These maps allowed the identification of specific zones with high metal concentrations and low pH values corresponding to spots of residual sludge. Moreover, kriged maps showed distinct spatial distribution and hence different behaviour for the elements considered. This information may be applied to optimise remediation strategies in highly and moderately contaminated areas.

Using Multivariate Geostatistics to Assess Patterns of Spatial Dependence of Apparent Soil Electrical Conductivity and Selected Soil Properties

PubMed Central

Siqueira, Glécio Machado; Dafonte, Jorge Dafonte; Valcárcel Armesto, Montserrat; Silva, Ênio Farias França e

2014-01-01

The apparent soil electrical conductivity (ECa) was continuously recorded in three successive dates using electromagnetic induction in horizontal (ECa-H) and vertical (ECa-V) dipole modes at a 6 ha plot located in Northwestern Spain. One of the ECa data sets was used to devise an optimized sampling scheme consisting of 40 points. Soil was sampled at the 0.0–0.3 m depth, in these 40 points, and analyzed for sand, silt, and clay content; gravimetric water content; and electrical conductivity of saturated soil paste. Coefficients of correlation between ECa and gravimetric soil water content (0.685 for ECa-V and 0.649 for ECa-H) were higher than those between ECa and clay content (ranging from 0.197 to 0.495, when different ECa recording dates were taken into account). Ordinary and universal kriging have been used to assess the patterns of spatial variability of the ECa data sets recorded at successive dates and the analyzed soil properties. Ordinary and universal cokriging methods have improved the estimation of gravimetric soil water content using the data of ECa as secondary variable with respect to the use of ordinary kriging. PMID:25614893

Using multivariate geostatistics to assess patterns of spatial dependence of apparent soil electrical conductivity and selected soil properties.

PubMed

Siqueira, Glécio Machado; Dafonte, Jorge Dafonte; Valcárcel Armesto, Montserrat; França e Silva, Ênio Farias

2014-01-01

The apparent soil electrical conductivity (ECa) was continuously recorded in three successive dates using electromagnetic induction in horizontal (ECa-H) and vertical (ECa-V) dipole modes at a 6 ha plot located in Northwestern Spain. One of the ECa data sets was used to devise an optimized sampling scheme consisting of 40 points. Soil was sampled at the 0.0-0.3 m depth, in these 40 points, and analyzed for sand, silt, and clay content; gravimetric water content; and electrical conductivity of saturated soil paste. Coefficients of correlation between ECa and gravimetric soil water content (0.685 for ECa-V and 0.649 for ECa-H) were higher than those between ECa and clay content (ranging from 0.197 to 0.495, when different ECa recording dates were taken into account). Ordinary and universal kriging have been used to assess the patterns of spatial variability of the ECa data sets recorded at successive dates and the analyzed soil properties. Ordinary and universal cokriging methods have improved the estimation of gravimetric soil water content using the data of ECa as secondary variable with respect to the use of ordinary kriging.

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

Thomas, J.M.; Callahan, C.A.; Cline, J.F.

Bioassays were used in a three-phase research project to assess the comparative sensitivity of test organisms to known chemicals, determine if the chemical components in field soil and water samples containing unknown contaminants could be inferred from our laboratory studies using known chemicals, and to investigate kriging (a relatively new statistical mapping technique) and bioassays as methods to define the areal extent of chemical contamination. The algal assay generally was most sensitive to samples of pure chemicals, soil elutriates and water from eight sites with known chemical contamination. Bioassays of nine samples of unknown chemical composition from the Rocky Mountainmore » Arsenal (RMA) site showed that a lettuce seed soil contact phytoassay was most sensitive. In general, our bioassays can be used to broadly identify toxic components of contaminated soil. Nearly pure compounds of insecticides and herbicides were less toxic in the sensitive bioassays than were the counterpart commercial formulations. This finding indicates that chemical analysis alone may fail to correctly rate the severity of environmental toxicity. Finally, we used the lettuce seed phytoassay and kriging techniques in a field study at RMA to demonstrate the feasibility of mapping contamination to aid in cleanup decisions. 25 references, 9 figures, 9 tables.« less

Detection of terrain indices related to soil salinity and mapping salt-affected soils using remote sensing and geostatistical techniques.

PubMed

Triki Fourati, Hela; Bouaziz, Moncef; Benzina, Mourad; Bouaziz, Samir

2017-04-01

Traditional surveying methods of soil properties over landscapes are dramatically cost and time-consuming. Thus, remote sensing is a proper choice for monitoring environmental problem. This research aims to study the effect of environmental factors on soil salinity and to map the spatial distribution of this salinity over the southern east part of Tunisia by means of remote sensing and geostatistical techniques. For this purpose, we used Advanced Spaceborne Thermal Emission and Reflection Radiometer data to depict geomorphological parameters: elevation, slope, plan curvature (PLC), profile curvature (PRC), and aspect. Pearson correlation between these parameters and soil electrical conductivity (EC soil ) showed that mainly slope and elevation affect the concentration of salt in soil. Moreover, spectral analysis illustrated the high potential of short-wave infrared (SWIR) bands to identify saline soils. To map soil salinity in southern Tunisia, ordinary kriging (OK), minimum distance (MD) classification, and simple regression (SR) were used. The findings showed that ordinary kriging technique provides the most reliable performances to identify and classify saline soils over the study area with a root mean square error of 1.83 and mean error of 0.018.

Robust Kriged Kalman Filtering

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

Baingana, Brian; Dall'Anese, Emiliano; Mateos, Gonzalo

2015-11-11

Although the kriged Kalman filter (KKF) has well-documented merits for prediction of spatial-temporal processes, its performance degrades in the presence of outliers due to anomalous events, or measurement equipment failures. This paper proposes a robust KKF model that explicitly accounts for presence of measurement outliers. Exploiting outlier sparsity, a novel l1-regularized estimator that jointly predicts the spatial-temporal process at unmonitored locations, while identifying measurement outliers is put forth. Numerical tests are conducted on a synthetic Internet protocol (IP) network, and real transformer load data. Test results corroborate the effectiveness of the novel estimator in joint spatial prediction and outlier identification.

Mapping wildfire effects on Ca2+ and Mg2+ released from ash. A microplot analisis.

NASA Astrophysics Data System (ADS)

Pereira, Paulo; Úbeda, Xavier; Martin, Deborah

2010-05-01

Wildland fires have important implications in ecosystems dynamic. Their effects depends on many biophysical components, mainly burned specie, ecosystem affected, amount and spatial distribution of the fuel, relative humidity, slope, aspect and time of residence. These parameters are heterogenic across the landscape, producing a complex mosaic of severities. Wildland fires have a heterogenic impact on ecosystems due their diverse biophysical features. It is widely known that fire impacts can change rapidly even in short distances, producing at microplot scale highly spatial variation. Also after a fire, the most visible thing is ash and his physical and chemical properties are of main importance because here reside the majority of the available nutrients available to the plants. Considering this idea, is of major importance, study their characteristics in order to observe the type and amount of elements available to plants. This study is focused on the study of the spatial variability of two nutrients essential to plant growth, Ca2+ and Mg2+, released from ash after a wildfire at microplot scale. The impacts of fire are highly variable even small distances. This creates many problems at the hour of map the effects of fire in the release of the studied elements. Hence is of major priority identify the less biased interpolation method in order to predict with great accuracy the variable in study. The aim of this study is map the effects of wildfire on the referred elements released from ash at microplot scale, testing several interpolation methods. 16 interpolation techniques were tested, Inverse Distance to a Weight (IDW), with the with the weights of 1,2, 3, 4 and 5, Local Polynomial, with the power of 1 (LP1) and 2 (LP2), Polynomial Regression (PR), Radial Basis Functions, especially, Spline With Tension (SPT), Completely Regularized Spline (CRS), Multiquadratic (MTQ), Inverse Multiquadratic (MTQ), and Thin Plate Spline (TPS). Also geostatistical methods were tested from Kriging family, mainly Ordinary Kriging (OK), Simple Kriging (SK) and Universal Kriging (UK). Interpolation techniques were assessed throughout the Mean Error (ME) and Root Mean Square (RMSE), obtained from the cross validation procedure calculated in all methods. The fire occurred in Portugal, near an urban area and inside the affected area we designed a grid with the dimensions of 9 x 27 m and we collected 40 samples. Before modelling data, we tested their normality with the Shapiro Wilk test. Since the distributions of Ca2+ and Mg2+ did not respect the gaussian distribution we transformed data logarithmically (Ln). With this transformation, data respect the normality and spatial distribution was modelled with the transformed data. On average in the entire plot the ash slurries contained 4371.01 mg/l of Ca2+, however with a higher coefficient of variation (CV%) of 54.05%. From all the tested methods LP1 was the less biased and hence the most accurate to interpolate this element. The most biased was LP2. In relation to Mg2+, considering the entire plot, the ash released in solution on average 1196.01 mg/l, with a CV% of 52.36%, similar to the identified in Ca2+. The best interpolator in this case was SK and the most biased was LP1 and TPS. Comparing all methods in both elements, the quality of the interpolations was higher in Ca2+. These results allowed us to conclude that to achieve the best prediction it is necessary test a wide range of interpolation methods. The best accuracy will permit us to understand with more precision where the studied elements are more available and accessible to plant growth and ecosystem recovers. This spatial pattern of both nutrients is related with ash pH and burned severity evaluated from ash colour and CaCO3 content. These aspects will be also discussed in the work.

Long-Term Quantitative Precipitation Estimates (QPE) at High Spatial and Temporal Resolution over CONUS: Bias-Adjustment of the Radar-Only National Mosaic and Multi-sensor QPE (NMQ/Q2) Precipitation Reanalysis (2001-2012)

NASA Astrophysics Data System (ADS)

Prat, Olivier; Nelson, Brian; Stevens, Scott; Seo, Dong-Jun; Kim, Beomgeun

2015-04-01

The processing of radar-only precipitation via the reanalysis from the National Mosaic and Multi-Sensor Quantitative (NMQ/Q2) based on the WSR-88D Next-generation Radar (NEXRAD) network over Continental United States (CONUS) is completed for the period covering from 2001 to 2012. This important milestone constitutes a unique opportunity to study precipitation processes at a 1-km spatial resolution for a 5-min temporal resolution. However, in order to be suitable for hydrological, meteorological and climatological applications, the radar-only product needs to be bias-adjusted and merged with in-situ rain gauge information. Several in-situ datasets are available to assess the biases of the radar-only product and to adjust for those biases to provide a multi-sensor QPE. The rain gauge networks that are used such as the Global Historical Climatology Network-Daily (GHCN-D), the Hydrometeorological Automated Data System (HADS), the Automated Surface Observing Systems (ASOS), and the Climate Reference Network (CRN), have different spatial density and temporal resolution. The challenges related to incorporating non-homogeneous networks over a vast area and for a long-term record are enormous. Among the challenges we are facing are the difficulties incorporating differing resolution and quality surface measurements to adjust gridded estimates of precipitation. Another challenge is the type of adjustment technique. The objective of this work is threefold. First, we investigate how the different in-situ networks can impact the precipitation estimates as a function of the spatial density, sensor type, and temporal resolution. Second, we assess conditional and un-conditional biases of the radar-only QPE for various time scales (daily, hourly, 5-min) using in-situ precipitation observations. Finally, after assessing the bias and applying reduction or elimination techniques, we are using a unique in-situ dataset merging the different RG networks (CRN, ASOS, HADS, GHCN-D) to adjust the radar-only QPE product via an Inverse Distance Weighting (IDW) approach. In addition, we also investigate alternate adjustment techniques such as the kriging method and its variants (Simple Kriging: SK; Ordinary Kriging: OK; Conditional Bias-Penalized Kriging: CBPK). From this approach, we also hope to generate estimates of uncertainty for the gridded bias-adjusted QPE. Further comparison with a suite of lower resolution QPEs derived from ground based radar measurements (Stage IV) and satellite products (TMPA, CMORPH, PERSIANN) is also provided in order to give a detailed picture of the improvements and remaining challenges.

Fusion of sensor geometry into additive strain fields measured with sensing skin

NASA Astrophysics Data System (ADS)

Downey, Austin; Sadoughi, Mohammadkazem; Laflamme, Simon; Hu, Chao

2018-07-01

Recently, numerous studies have been conducted on flexible skin-like membranes for the cost effective monitoring of large-scale structures. The authors have proposed a large-area electronic consisting of a soft elastomeric capacitor (SEC) that transduces a structure’s strain into a measurable change in capacitance. Arranged in a network configuration, SECs deployed onto the surface of a structure could be used to reconstruct strain maps. Several regression methods have been recently developed with the purpose of reconstructing such maps, but all these algorithms assumed that each SEC-measured strain located at its geometric center. This assumption may not be realistic since an SEC measures the average strain value of the whole area covered by the sensor. One solution is to reduce the size of each SEC, but this would also increase the number of required sensors needed to cover the large-scale structure, therefore increasing the need for the power and data acquisition capabilities. Instead, this study proposes an algorithm that accounts for the sensor’s strain averaging feature by adjusting the strain measurements and constructing a full-field strain map using the kriging interpolation method. The proposed algorithm fuses the geometry of an SEC sensor into the strain map reconstruction in order to adaptively adjust the average kriging-estimated strain of the area monitored by the sensor to the signal. Results show that by considering the sensor geometry, in addition to the sensor signal and location, the proposed strain map adjustment algorithm is capable of producing more accurate full-field strain maps than the traditional spatial interpolation method that considered only signal and location.

Comparison of particle swarm optimization and simulated annealing for locating additional boreholes considering combined variance minimization

NASA Astrophysics Data System (ADS)

Soltani-Mohammadi, Saeed; Safa, Mohammad; Mokhtari, Hadi

2016-10-01

One of the most important stages in complementary exploration is optimal designing the additional drilling pattern or defining the optimum number and location of additional boreholes. Quite a lot research has been carried out in this regard in which for most of the proposed algorithms, kriging variance minimization as a criterion for uncertainty assessment is defined as objective function and the problem could be solved through optimization methods. Although kriging variance implementation is known to have many advantages in objective function definition, it is not sensitive to local variability. As a result, the only factors evaluated for locating the additional boreholes are initial data configuration and variogram model parameters and the effects of local variability are omitted. In this paper, with the goal of considering the local variability in boundaries uncertainty assessment, the application of combined variance is investigated to define the objective function. Thus in order to verify the applicability of the proposed objective function, it is used to locate the additional boreholes in Esfordi phosphate mine through the implementation of metaheuristic optimization methods such as simulated annealing and particle swarm optimization. Comparison of results from the proposed objective function and conventional methods indicates that the new changes imposed on the objective function has caused the algorithm output to be sensitive to the variations of grade, domain's boundaries and the thickness of mineralization domain. The comparison between the results of different optimization algorithms proved that for the presented case the application of particle swarm optimization is more appropriate than simulated annealing.

Accounting for geophysical information in geostatistical characterization of unexploded ordnance (UXO) sites.

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

Saito, Hirotaka; Goovaerts, Pierre; McKenna, Sean Andrew

2003-06-01

Efficient and reliable unexploded ordnance (UXO) site characterization is needed for decisions regarding future land use. There are several types of data available at UXO sites and geophysical signal maps are one of the most valuable sources of information. Incorporation of such information into site characterization requires a flexible and reliable methodology. Geostatistics allows one to account for exhaustive secondary information (i.e.,, known at every location within the field) in many different ways. Kriging and logistic regression were combined to map the probability of occurrence of at least one geophysical anomaly of interest, such as UXO, from a limited numbermore » of indicator data. Logistic regression is used to derive the trend from a geophysical signal map, and kriged residuals are added to the trend to estimate the probabilities of the presence of UXO at unsampled locations (simple kriging with varying local means or SKlm). Each location is identified for further remedial action if the estimated probability is greater than a given threshold. The technique is illustrated using a hypothetical UXO site generated by a UXO simulator, and a corresponding geophysical signal map. Indicator data are collected along two transects located within the site. Classification performances are then assessed by computing proportions of correct classification, false positive, false negative, and Kappa statistics. Two common approaches, one of which does not take any secondary information into account (ordinary indicator kriging) and a variant of common cokriging (collocated cokriging), were used for comparison purposes. Results indicate that accounting for exhaustive secondary information improves the overall characterization of UXO sites if an appropriate methodology, SKlm in this case, is used.« less

Geostatistical Interpolation of Particle-Size Curves in Heterogeneous Aquifers

NASA Astrophysics Data System (ADS)

Guadagnini, A.; Menafoglio, A.; Secchi, P.

2013-12-01

We address the problem of predicting the spatial field of particle-size curves (PSCs) from measurements associated with soil samples collected at a discrete set of locations within an aquifer system. Proper estimates of the full PSC are relevant to applications related to groundwater hydrology, soil science and geochemistry and aimed at modeling physical and chemical processes occurring in heterogeneous earth systems. Hence, we focus on providing kriging estimates of the entire PSC at unsampled locations. To this end, we treat particle-size curves as cumulative distribution functions, model their densities as functional compositional data and analyze them by embedding these into the Hilbert space of compositional functions endowed with the Aitchison geometry. On this basis, we develop a new geostatistical methodology for the analysis of spatially dependent functional compositional data. Our functional compositional kriging (FCK) approach allows providing predictions at unsampled location of the entire particle-size curve, together with a quantification of the associated uncertainty, by fully exploiting both the functional form of the data and their compositional nature. This is a key advantage of our approach with respect to traditional methodologies, which treat only a set of selected features (e.g., quantiles) of PSCs. Embedding the full PSC into a geostatistical analysis enables one to provide a complete characterization of the spatial distribution of lithotypes in a reservoir, eventually leading to improved predictions of soil hydraulic attributes through pedotransfer functions as well as of soil geochemical parameters which are relevant in sorption/desorption and cation exchange processes. We test our new method on PSCs sampled along a borehole located within an alluvial aquifer near the city of Tuebingen, Germany. The quality of FCK predictions is assessed through leave-one-out cross-validation. A comparison between hydraulic conductivity estimates obtained via FCK approach and those predicted by classical kriging of effective particle diameters (i.e., quantiles of the PSCs) is finally performed.

Comparison of wildfire smoke estimation methods and associations with cardiopulmonary-related hospital admissions

PubMed Central

Gan, Ryan W.; Ford, Bonne; Lassman, William; Pfister, Gabriele; Vaidyanathan, Ambarish; Fischer, Emily; Volckens, John; Pierce, Jeffrey R.; Magzamen, Sheryl

2017-01-01

Climate forecasts predict an increase in frequency and intensity of wildfires. Associations between health outcomes and population exposure to smoke from Washington 2012 wildfires were compared using surface monitors, chemical-weather models, and a novel method blending three exposure information sources. The association between smoke particulate matter ≤2.5 μm in diameter (PM2.5) and cardiopulmonary hospital admissions occurring in Washington from 1 July to 31 October 2012 was evaluated using a time-stratified case-crossover design. Hospital admissions aggregated by ZIP code were linked with population-weighted daily average concentrations of smoke PM2.5 estimated using three distinct methods: a simulation with the Weather Research and Forecasting with Chemistry (WRF-Chem) model, a kriged interpolation of PM2.5 measurements from surface monitors, and a geographically weighted ridge regression (GWR) that blended inputs from WRF-Chem, satellite observations of aerosol optical depth, and kriged PM2.5. A 10 μg/m3 increase in GWR smoke PM2.5 was associated with an 8% increased risk in asthma-related hospital admissions (odds ratio (OR): 1.076, 95% confidence interval (CI): 1.019–1.136); other smoke estimation methods yielded similar results. However, point estimates for chronic obstructive pulmonary disease (COPD) differed by smoke PM2.5 exposure method: a 10 μg/m3 increase using GWR was significantly associated with increased risk of COPD (OR: 1.084, 95%CI: 1.026–1.145) and not significant using WRF-Chem (OR: 0.986, 95%CI: 0.931–1.045). The magnitude (OR) and uncertainty (95%CI) of associations between smoke PM2.5 and hospital admissions were dependent on estimation method used and outcome evaluated. Choice of smoke exposure estimation method used can impact the overall conclusion of the study. PMID:28868515

Snake River Plain Geothermal Play Fairway Analysis - Phase 1 Raster Files

DOE Data Explorer

John Shervais

2015-10-09

Snake River Plain Play Fairway Analysis - Phase 1 CRS Raster Files. This dataset contains raster files created in ArcGIS. These raster images depict Common Risk Segment (CRS) maps for HEAT, PERMEABILITY, AND SEAL, as well as selected maps of Evidence Layers. These evidence layers consist of either Bayesian krige functions or kernel density functions, and include: (1) HEAT: Heat flow (Bayesian krige map), Heat flow standard error on the krige function (data confidence), volcanic vent distribution as function of age and size, groundwater temperature (equivalue interval and natural breaks bins), and groundwater T standard error. (2) PERMEABILTY: Fault and lineament maps, both as mapped and as kernel density functions, processed for both dilational tendency (TD) and slip tendency (ST), along with data confidence maps for each data type. Data types include mapped surface faults from USGS and Idaho Geological Survey data bases, as well as unpublished mapping; lineations derived from maximum gradients in magnetic, deep gravity, and intermediate depth gravity anomalies. (3) SEAL: Seal maps based on presence and thickness of lacustrine sediments and base of SRP aquifer. Raster size is 2 km. All files generated in ArcGIS.

The geostatistical approach for structural and stratigraphic framework analysis of offshore NW Bonaparte Basin, Australia

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

Wahid, Ali, E-mail: ali.wahid@live.com; Salim, Ahmed Mohamed Ahmed, E-mail: mohamed.salim@petronas.com.my; Yusoff, Wan Ismail Wan, E-mail: wanismail-wanyusoff@petronas.com.my

2016-02-01

Geostatistics or statistical approach is based on the studies of temporal and spatial trend, which depend upon spatial relationships to model known information of variable(s) at unsampled locations. The statistical technique known as kriging was used for petrophycial and facies analysis, which help to assume spatial relationship to model the geological continuity between the known data and the unknown to produce a single best guess of the unknown. Kriging is also known as optimal interpolation technique, which facilitate to generate best linear unbiased estimation of each horizon. The idea is to construct a numerical model of the lithofacies and rockmore » properties that honor available data and further integrate with interpreting seismic sections, techtonostratigraphy chart with sea level curve (short term) and regional tectonics of the study area to find the structural and stratigraphic growth history of the NW Bonaparte Basin. By using kriging technique the models were built which help to estimate different parameters like horizons, facies, and porosities in the study area. The variograms were used to determine for identification of spatial relationship between data which help to find the depositional history of the North West (NW) Bonaparte Basin.« less

Eco-hydrological Wireless Sensor Network and upscaling method research in the Heihe River Basin, China

NASA Astrophysics Data System (ADS)

Jin, Rui; kang, Jian

2017-04-01

Wireless Sensor Networks are recognized as one of most important near-surface components of GEOSS (Global Earth Observation System of Systems), with flourish development of low-cost, robust and integrated data loggers and sensors. A nested eco-hydrological wireless sensor network (EHWSN) was installed in the up- and middle-reaches of the Heihe River Basin, operated to obtain multi-scale observation of soil moisture, soil temperature and land surface temperature from 2012 till now. The spatial distribution of EHWSN was optimally designed based on the geo-statistical theory, with the aim to capture the spatial variations and temporal dynamics of soil moisture and soil temperature, and to produce ground truth at grid scale for validating the related remote sensing products and model simulation in the heterogeneous land surface. In terms of upscaling research, we have developed a set of method to aggregate multi-point WSN observations to grid scale ( 1km), including regression kriging estimation to utilize multi-resource remote sensing auxiliary information, block kriging with homogeneous measurement errors, and bayesian-based upscaling algorithm that utilizes MODIS-derived apparent thermal inertia. All the EHWSN observation are organized as datasets to be freely published at http://westdc.westgis.ac.cn/hiwater. EHWSN integrates distributed observation nodes to achieve an automated, intelligent and remote-controllable network that provides superior integrated, standardized and automated observation capabilities for hydrological and ecological processes research at the basin scale.

Assessing the cost of groundwater pollution: the case of diffuse agricultural pollution in the Upper Rhine valley aquifer.

PubMed

Rinaudo, J-D; Arnal, C; Blanchin, R; Elsass, P; Meilhac, A; Loubier, S

2005-01-01

This paper presents an assessment of the costs of diffuse groundwater pollution by nitrates and pesticides for the industrial and the drinking water sectors in the Upper Rhine valley, France. Pollution costs which occurred between 1988 and 2002 are described and assessed using the avoidance cost method. Geo-statistical methods (kriging) are then used to construct three scenarios of nitrate concentration evolution. The economic consequences of each scenario are then assessed. The estimates obtained are compared with the results of a contingent valuation study carried out in the same study area ten years earlier.

Comparison of different interpolation methods for spatial distribution of soil organic carbon and some soil properties in the Black Sea backward region of Turkey

NASA Astrophysics Data System (ADS)

Göl, Ceyhun; Bulut, Sinan; Bolat, Ferhat

2017-10-01

The purpose of this research is to compare the spatial variability of soil organic carbon (SOC) in four adjacent land uses including the cultivated area, the grassland area, the plantation area and the natural forest area in the semi - arid region of Black Sea backward region of Turkey. Some of the soil properties, including total nitrogen, SOC, soil organic matter, and bulk density were measured on a grid with a 50 m sampling distance on the top soil (0-15 cm depth). Accordingly, a total of 120 samples were taken from the four adjacent land uses. Data was analyzed using geostatistical methods. The methods used were: Block kriging (BK), co - kriging (CK) with organic matter, total nitrogen and bulk density as auxiliary variables and inverse distance weighting (IDW) methods with the power of 1, 2 and 4. The methods were compared using a performance criteria that included root mean square error (RMSE), mean absolute error (MAE) and the coefficient of correlation (r). The one - way ANOVA test showed that differences between the natural (0.6653 ± 0.2901) - plantation forest (0.7109 ± 0.2729) areas and the grassland (1.3964 ± 0.6828) - cultivated areas (1.5851 ± 0.5541) were statistically significant at 0.05 level (F = 28.462). The best model for describing spatially variation of SOC was CK with the lowest error criteria (RMSE = 0.3342, MAE = 0.2292) and the highest coefficient of correlation (r = 0.84). The spatial structure of SOC could be well described by the spherical model. The nugget effect indicated that SOC was moderately dependent on the study area. The error distributions of the model showed that the improved model was unbiased in predicting the spatial distribution of SOC. This study's results revealed that an explanatory variable linked SOC increased success of spatial interpolation methods. In subsequent studies, this case should be taken into account for reaching more accurate outputs.

Spatial structure and distribution of small pelagic fish in the northwestern Mediterranean Sea.

PubMed

Saraux, Claire; Fromentin, Jean-Marc; Bigot, Jean-Louis; Bourdeix, Jean-Hervé; Morfin, Marie; Roos, David; Van Beveren, Elisabeth; Bez, Nicolas

2014-01-01

Understanding the ecological and anthropogenic drivers of population dynamics requires detailed studies on habitat selection and spatial distribution. Although small pelagic fish aggregate in large shoals and usually exhibit important spatial structure, their dynamics in time and space remain unpredictable and challenging. In the Gulf of Lions (north-western Mediterranean), sardine and anchovy biomasses have declined over the past 5 years causing an important fishery crisis while sprat abundance rose. Applying geostatistical tools on scientific acoustic surveys conducted in the Gulf of Lions, we investigated anchovy, sardine and sprat spatial distributions and structures over 10 years. Our results show that sardines and sprats were more coastal than anchovies. The spatial structure of the three species was fairly stable over time according to variogram outputs, while year-to-year variations in kriged maps highlighted substantial changes in their location. Support for the McCall's basin hypothesis (covariation of both population density and presence area with biomass) was found only in sprats, the most variable of the three species. An innovative method to investigate species collocation at different scales revealed that globally the three species strongly overlap. Although species often co-occurred in terms of presence/absence, their biomass density differed at local scale, suggesting potential interspecific avoidance or different sensitivity to local environmental characteristics. Persistent favourable areas were finally detected, but their environmental characteristics remain to be determined.

High-resolution daily gridded data sets of air temperature and wind speed for Europe

NASA Astrophysics Data System (ADS)

Brinckmann, Sven; Krähenmann, Stefan; Bissolli, Peter

2016-10-01

New high-resolution data sets for near-surface daily air temperature (minimum, maximum and mean) and daily mean wind speed for Europe (the CORDEX domain) are provided for the period 2001-2010 for the purpose of regional model validation in the framework of DecReg, a sub-project of the German MiKlip project, which aims to develop decadal climate predictions. The main input data sources are SYNOP observations, partly supplemented by station data from the ECA&D data set (http://www.ecad.eu). These data are quality tested to eliminate erroneous data. By spatial interpolation of these station observations, grid data in a resolution of 0.044° (≈ 5km) on a rotated grid with virtual North Pole at 39.25° N, 162° W are derived. For temperature interpolation a modified version of a regression kriging method developed by Krähenmann et al.(2011) is used. At first, predictor fields of altitude, continentality and zonal mean temperature are used for a regression applied to monthly station data. The residuals of the monthly regression and the deviations of the daily data from the monthly averages are interpolated using simple kriging in a second and third step. For wind speed a new method based on the concept used for temperature was developed, involving predictor fields of exposure, roughness length, coastal distance and ERA-Interim reanalysis wind speed at 850 hPa. Interpolation uncertainty is estimated by means of the kriging variance and regression uncertainties. Furthermore, to assess the quality of the final daily grid data, cross validation is performed. Variance explained by the regression ranges from 70 to 90 % for monthly temperature and from 50 to 60 % for monthly wind speed. The resulting RMSE for the final daily grid data amounts to 1-2 K and 1-1.5 ms-1 (depending on season and parameter) for daily temperature parameters and daily mean wind speed, respectively. The data sets presented in this article are published at doi:10.5676/DWD_CDC/DECREG0110v2.

Optimization of water-level monitoring networks in the eastern Snake River Plain aquifer using a kriging-based genetic algorithm method

USGS Publications Warehouse

Fisher, Jason C.

2013-01-01

Long-term groundwater monitoring networks can provide essential information for the planning and management of water resources. Budget constraints in water resource management agencies often mean a reduction in the number of observation wells included in a monitoring network. A network design tool, distributed as an R package, was developed to determine which wells to exclude from a monitoring network because they add little or no beneficial information. A kriging-based genetic algorithm method was used to optimize the monitoring network. The algorithm was used to find the set of wells whose removal leads to the smallest increase in the weighted sum of the (1) mean standard error at all nodes in the kriging grid where the water table is estimated, (2) root-mean-squared-error between the measured and estimated water-level elevation at the removed sites, (3) mean standard deviation of measurements across time at the removed sites, and (4) mean measurement error of wells in the reduced network. The solution to the optimization problem (the best wells to retain in the monitoring network) depends on the total number of wells removed; this number is a management decision. The network design tool was applied to optimize two observation well networks monitoring the water table of the eastern Snake River Plain aquifer, Idaho; these networks include the 2008 Federal-State Cooperative water-level monitoring network (Co-op network) with 166 observation wells, and the 2008 U.S. Geological Survey-Idaho National Laboratory water-level monitoring network (USGS-INL network) with 171 wells. Each water-level monitoring network was optimized five times: by removing (1) 10, (2) 20, (3) 40, (4) 60, and (5) 80 observation wells from the original network. An examination of the trade-offs associated with changes in the number of wells to remove indicates that 20 wells can be removed from the Co-op network with a relatively small degradation of the estimated water table map, and 40 wells can be removed from the USGS-INL network before the water table map degradation accelerates. The optimal network designs indicate the robustness of the network design tool. Observation wells were removed from high well-density areas of the network while retaining the spatial pattern of the existing water-table map.

A Method of DTM Construction Based on Quadrangular Irregular Networks and Related Error Analysis

PubMed Central

Kang, Mengjun

2015-01-01

A new method of DTM construction based on quadrangular irregular networks (QINs) that considers all the original data points and has a topological matrix is presented. A numerical test and a real-world example are used to comparatively analyse the accuracy of QINs against classical interpolation methods and other DTM representation methods, including SPLINE, KRIGING and triangulated irregular networks (TINs). The numerical test finds that the QIN method is the second-most accurate of the four methods. In the real-world example, DTMs are constructed using QINs and the three classical interpolation methods. The results indicate that the QIN method is the most accurate method tested. The difference in accuracy rank seems to be caused by the locations of the data points sampled. Although the QIN method has drawbacks, it is an alternative method for DTM construction. PMID:25996691

APPLICATION OF BAYESIAN AND GEOSTATISTICAL MODELING TO THE ENVIRONMENTAL MONITORING OF CS-137 AT THE IDAHO NATIONAL LABORATORY

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

Kara G. Eby

2010-08-01

At the Idaho National Laboratory (INL) Cs-137 concentrations above the U.S. Environmental Protection Agency risk-based threshold of 0.23 pCi/g may increase the risk of human mortality due to cancer. As a leader in nuclear research, the INL has been conducting nuclear activities for decades. Elevated anthropogenic radionuclide levels including Cs-137 are a result of atmospheric weapons testing, the Chernobyl accident, and nuclear activities occurring at the INL site. Therefore environmental monitoring and long-term surveillance of Cs-137 is required to evaluate risk. However, due to the large land area involved, frequent and comprehensive monitoring is limited. Developing a spatial model thatmore » predicts Cs-137 concentrations at unsampled locations will enhance the spatial characterization of Cs-137 in surface soils, provide guidance for an efficient monitoring program, and pinpoint areas requiring mitigation strategies. The predictive model presented herein is based on applied geostatistics using a Bayesian analysis of environmental characteristics across the INL site, which provides kriging spatial maps of both Cs-137 estimates and prediction errors. Comparisons are presented of two different kriging methods, showing that the use of secondary information (i.e., environmental characteristics) can provide improved prediction performance in some areas of the INL site.« less

Quantitative assessment of mineral resources with an application to petroleum geology

USGS Publications Warehouse

Harff, Jan; Davis, J.C.; Olea, R.A.

1992-01-01

The probability of occurrence of natural resources, such as petroleum deposits, can be assessed by a combination of multivariate statistical and geostatistical techniques. The area of study is partitioned into regions that are as homogeneous as possible internally while simultaneously as distinct as possible. Fisher's discriminant criterion is used to select geological variables that best distinguish productive from nonproductive localities, based on a sample of previously drilled exploratory wells. On the basis of these geological variables, each wildcat well is assigned to the production class (dry or producer in the two-class case) for which the Mahalanobis' distance from the observation to the class centroid is a minimum. Universal kriging is used to interpolate values of the Mahalanobis' distances to all locations not yet drilled. The probability that an undrilled locality belongs to the productive class can be found, using the kriging estimation variances to assess the probability of misclassification. Finally, Bayes' relationship can be used to determine the probability that an undrilled location will be a discovery, regardless of the production class in which it is placed. The method is illustrated with a study of oil prospects in the Lansing/Kansas City interval of western Kansas, using geological variables derived from well logs. ?? 1992 Oxford University Press.

Heat Flow Contours and Well Data Around the Milford FORGE Site

DOE Data Explorer

Joe Moore

2016-03-09

This submission contains a shapefile of heat flow contour lines around the FORGE site located in Milford, Utah. The model was interpolated from data points in the Milford_wells shapefile. This heat flow model was interpolated from 66 data points using the kriging method in Geostatistical Analyst tool of ArcGIS. The resulting model was smoothed 100%. The well dataset contains 59 wells from various sources, with lat/long coordinates, temperature, quality, basement depth, and heat flow. This data was used to make models of the specific characteristics.

Surrogate Model Application to the Identification of Optimal Groundwater Exploitation Scheme Based on Regression Kriging Method—A Case Study of Western Jilin Province

PubMed Central

An, Yongkai; Lu, Wenxi; Cheng, Weiguo

2015-01-01

This paper introduces a surrogate model to identify an optimal exploitation scheme, while the western Jilin province was selected as the study area. A numerical simulation model of groundwater flow was established first, and four exploitation wells were set in the Tongyu county and Qian Gorlos county respectively so as to supply water to Daan county. Second, the Latin Hypercube Sampling (LHS) method was used to collect data in the feasible region for input variables. A surrogate model of the numerical simulation model of groundwater flow was developed using the regression kriging method. An optimization model was established to search an optimal groundwater exploitation scheme using the minimum average drawdown of groundwater table and the minimum cost of groundwater exploitation as multi-objective functions. Finally, the surrogate model was invoked by the optimization model in the process of solving the optimization problem. Results show that the relative error and root mean square error of the groundwater table drawdown between the simulation model and the surrogate model for 10 validation samples are both lower than 5%, which is a high approximation accuracy. The contrast between the surrogate-based simulation optimization model and the conventional simulation optimization model for solving the same optimization problem, shows the former only needs 5.5 hours, and the latter needs 25 days. The above results indicate that the surrogate model developed in this study could not only considerably reduce the computational burden of the simulation optimization process, but also maintain high computational accuracy. This can thus provide an effective method for identifying an optimal groundwater exploitation scheme quickly and accurately. PMID:26264008

Merging of rain gauge and radar data for urban hydrological modelling

NASA Astrophysics Data System (ADS)

Berndt, Christian; Haberlandt, Uwe

2015-04-01

Urban hydrological processes are generally characterised by short response times and therefore rainfall data with a high resolution in space and time are required for their modelling. In many smaller towns, no recordings of rainfall data exist within the urban catchment. Precipitation radar helps to provide extensive rainfall data with a temporal resolution of five minutes, but the rainfall amounts can be highly biased and hence the data should not be used directly as a model input. However, scientists proposed several methods for adjusting radar data to station measurements. This work tries to evaluate rainfall inputs for a hydrological model regarding the following two different applications: Dimensioning of urban drainage systems and analysis of single event flow. The input data used for this analysis can be divided into two groups: Methods, which rely on station data only (Nearest Neighbour Interpolation, Ordinary Kriging), and methods, which incorporate station as well as radar information (Conditional Merging, Bias correction of radar data based on quantile mapping with rain gauge recordings). Additionally, rainfall intensities that were directly obtained from radar reflectivities are used. A model of the urban catchment of the city of Brunswick (Lower Saxony, Germany) is utilised for the evaluation. First results show that radar data cannot help with the dimensioning task of sewer systems since rainfall amounts of convective events are often overestimated. Gauges in catchment proximity can provide more reliable rainfall extremes. Whether radar data can be helpful to simulate single event flow depends strongly on the data quality and thus on the selected event. Ordinary Kriging is often not suitable for the interpolation of rainfall data in urban hydrology. This technique induces a strong smoothing of rainfall fields and therefore a severe underestimation of rainfall intensities for convective events.

Applications of Geostatistics in Plant Nematology

PubMed Central

Wallace, M. K.; Hawkins, D. M.

1994-01-01

The application of geostatistics to plant nematology was made by evaluating soil and nematode data acquired from 200 soil samples collected from the Ap horizon of a reed canary-grass field in northern Minnesota. Geostatistical concepts relevant to nematology include semi-variogram modelling, kriging, and change of support calculations. Soil and nematode data generally followed a spherical semi-variogram model, with little random variability associated with soil data and large inherent variability for nematode data. Block kriging of soil and nematode data provided useful contour maps of the data. Change of snpport calculations indicated that most of the random variation in nematode data was due to short-range spatial variability in the nematode population densities. PMID:19279938

Applications of geostatistics in plant nematology.

PubMed

Wallace, M K; Hawkins, D M

1994-12-01

The application of geostatistics to plant nematology was made by evaluating soil and nematode data acquired from 200 soil samples collected from the A(p) horizon of a reed canary-grass field in northern Minnesota. Geostatistical concepts relevant to nematology include semi-variogram modelling, kriging, and change of support calculations. Soil and nematode data generally followed a spherical semi-variogram model, with little random variability associated with soil data and large inherent variability for nematode data. Block kriging of soil and nematode data provided useful contour maps of the data. Change of snpport calculations indicated that most of the random variation in nematode data was due to short-range spatial variability in the nematode population densities.

Dual-mode nested search method for categorical uncertain multi-objective optimization

NASA Astrophysics Data System (ADS)

Tang, Long; Wang, Hu

2016-10-01

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

Geostatistical uncertainty of assessing air quality using high-spatial-resolution lichen data: A health study in the urban area of Sines, Portugal.

PubMed

Ribeiro, Manuel C; Pinho, P; Branquinho, C; Llop, Esteve; Pereira, Maria J

2016-08-15

In most studies correlating health outcomes with air pollution, personal exposure assignments are based on measurements collected at air-quality monitoring stations not coinciding with health data locations. In such cases, interpolators are needed to predict air quality in unsampled locations and to assign personal exposures. Moreover, a measure of the spatial uncertainty of exposures should be incorporated, especially in urban areas where concentrations vary at short distances due to changes in land use and pollution intensity. These studies are limited by the lack of literature comparing exposure uncertainty derived from distinct spatial interpolators. Here, we addressed these issues with two interpolation methods: regression Kriging (RK) and ordinary Kriging (OK). These methods were used to generate air-quality simulations with a geostatistical algorithm. For each method, the geostatistical uncertainty was drawn from generalized linear model (GLM) analysis. We analyzed the association between air quality and birth weight. Personal health data (n=227) and exposure data were collected in Sines (Portugal) during 2007-2010. Because air-quality monitoring stations in the city do not offer high-spatial-resolution measurements (n=1), we used lichen data as an ecological indicator of air quality (n=83). We found no significant difference in the fit of GLMs with any of the geostatistical methods. With RK, however, the models tended to fit better more often and worse less often. Moreover, the geostatistical uncertainty results showed a marginally higher mean and precision with RK. Combined with lichen data and land-use data of high spatial resolution, RK is a more effective geostatistical method for relating health outcomes with air quality in urban areas. This is particularly important in small cities, which generally do not have expensive air-quality monitoring stations with high spatial resolution. Further, alternative ways of linking human activities with their environment are needed to improve human well-being. Copyright © 2016 Elsevier B.V. All rights reserved.

Measurement and modeling of particulate matter concentrations: Applying spatial analysis and regression techniques to assess air quality.

PubMed

Sajjadi, Seyed Ali; Zolfaghari, Ghasem; Adab, Hamed; Allahabadi, Ahmad; Delsouz, Mehri

2017-01-01

This paper presented the levels of PM 2.5 and PM 10 in different stations at the city of Sabzevar, Iran. Furthermore, this study was an attempt to evaluate spatial interpolation methods for determining the PM 2.5 and PM 10 concentrations in the city of Sabzevar. Particulate matters were measured by Haz-Dust EPAM at 48 stations. Then, four interpolating models, including Radial Basis Functions (RBF), Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Universal Kriging (UK) were used to investigate the status of air pollution in the city. Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) were employed to compare the four models. The results showed that the PM 2.5 concentrations in the stations were between 10 and 500 μg/m 3 . Furthermore, the PM 10 concentrations for all of 48 stations ranged from 20 to 1500 μg/m 3 . The concentrations obtained for the period of nine months were greater than the standard limits. There was difference in the values of MAPE, RMSE, MBE, and MAE. The results indicated that the MAPE in IDW method was lower than other methods: (41.05 for PM 2.5 and 25.89 for PM 10 ). The best interpolation method for the particulate matter (PM 2.5 and PM 10 ) seemed to be IDW method. •The PM 10 and PM 2.5 concentration measurements were performed in the period of warm and risky in terms of particulate matter at 2016.•Concentrations of PM 2.5 and PM 10 were measured by a monitoring device, environmental dust model Haz-Dust EPAM 5000.•Interpolation is used to convert data from observation points to continuous fields to compare spatial patterns sampled by these measurements with spatial patterns of other spatial entities.

Parametric geometric model and shape optimization of an underwater glider with blended-wing-body

NASA Astrophysics Data System (ADS)

Sun, Chunya; Song, Baowei; Wang, Peng

2015-11-01

Underwater glider, as a new kind of autonomous underwater vehicles, has many merits such as long-range, extended-duration and low costs. The shape of underwater glider is an important factor in determining the hydrodynamic efficiency. In this paper, a high lift to drag ratio configuration, the Blended-Wing-Body (BWB), is used to design a small civilian under water glider. In the parametric geometric model of the BWB underwater glider, the planform is defined with Bezier curve and linear line, and the section is defined with symmetrical airfoil NACA 0012. Computational investigations are carried out to study the hydrodynamic performance of the glider using the commercial Computational Fluid Dynamics (CFD) code Fluent. The Kriging-based genetic algorithm, called Efficient Global Optimization (EGO), is applied to hydrodynamic design optimization. The result demonstrates that the BWB underwater glider has excellent hydrodynamic performance, and the lift to drag ratio of initial design is increased by 7% in the EGO process.

Small-Scale Spatio-Temporal Distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) Using Probability Kriging.

PubMed

Wang, S Q; Zhang, H Y; Li, Z L

2016-10-01

Understanding spatio-temporal distribution of pest in orchards can provide important information that could be used to design monitoring schemes and establish better means for pest control. In this study, the spatial and temporal distribution of Bactrocera minax (Enderlein) (Diptera: Tephritidae) was assessed, and activity trends were evaluated by using probability kriging. Adults of B. minax were captured in two successive occurrences in a small-scale citrus orchard by using food bait traps, which were placed both inside and outside the orchard. The weekly spatial distribution of B. minax within the orchard and adjacent woods was examined using semivariogram parameters. The edge concentration was discovered during the most weeks in adult occurrence, and the population of the adults aggregated with high probability within a less-than-100-m-wide band on both of the sides of the orchard and the woods. The sequential probability kriged maps showed that the adults were estimated in the marginal zone with higher probability, especially in the early and peak stages. The feeding, ovipositing, and mating behaviors of B. minax are possible explanations for these spatio-temporal patterns. Therefore, spatial arrangement and distance to the forest edge of traps or spraying spot should be considered to enhance pest control on B. minax in small-scale orchards.

A Computer Program for Practical Semivariogram Modeling and Ordinary Kriging: A Case Study of Porosity Distribution in an Oil Field

NASA Astrophysics Data System (ADS)

Mert, Bayram Ali; Dag, Ahmet

2017-12-01

In this study, firstly, a practical and educational geostatistical program (JeoStat) was developed, and then example analysis of porosity parameter distribution, using oilfield data, was presented. With this program, two or three-dimensional variogram analysis can be performed by using normal, log-normal or indicator transformed data. In these analyses, JeoStat offers seven commonly used theoretical variogram models (Spherical, Gaussian, Exponential, Linear, Generalized Linear, Hole Effect and Paddington Mix) to the users. These theoretical models can be easily and quickly fitted to experimental models using a mouse. JeoStat uses ordinary kriging interpolation technique for computation of point or block estimate, and also uses cross-validation test techniques for validation of the fitted theoretical model. All the results obtained by the analysis as well as all the graphics such as histogram, variogram and kriging estimation maps can be saved to the hard drive, including digitised graphics and maps. As such, the numerical values of any point in the map can be monitored using a mouse and text boxes. This program is available to students, researchers, consultants and corporations of any size free of charge. The JeoStat software package and source codes available at: http://www.jeostat.com/JeoStat_2017.0.rar.

Temporal and Spatial prediction of groundwater levels using Artificial Neural Networks, Fuzzy logic and Kriging interpolation.

NASA Astrophysics Data System (ADS)

Tapoglou, Evdokia; Karatzas, George P.; Trichakis, Ioannis C.; Varouchakis, Emmanouil A.

2014-05-01

The purpose of this study is to examine the use of Artificial Neural Networks (ANN) combined with kriging interpolation method, in order to simulate the hydraulic head both spatially and temporally. Initially, ANNs are used for the temporal simulation of the hydraulic head change. The results of the most appropriate ANNs, determined through a fuzzy logic system, are used as an input for the kriging algorithm where the spatial simulation is conducted. The proposed algorithm is tested in an area located across Isar River in Bayern, Germany and covers an area of approximately 7800 km2. The available data extend to a time period from 1/11/2008 to 31/10/2012 (1460 days) and include the hydraulic head at 64 wells, temperature and rainfall at 7 weather stations and surface water elevation at 5 monitoring stations. One feedforward ANN was trained for each of the 64 wells, where hydraulic head data are available, using a backpropagation algorithm. The most appropriate input parameters for each wells' ANN are determined considering their proximity to the measuring station, as well as their statistical characteristics. For the rainfall, the data for two consecutive time lags for best correlated weather station, as well as a third and fourth input from the second best correlated weather station, are used as an input. The surface water monitoring stations with the three best correlations for each well are also used in every case. Finally, the temperature for the best correlated weather station is used. Two different architectures are considered and the one with the best results is used henceforward. The output of the ANNs corresponds to the hydraulic head change per time step. These predictions are used in the kriging interpolation algorithm. However, not all 64 simulated values should be used. The appropriate neighborhood for each prediction point is constructed based not only on the distance between known and prediction points, but also on the training and testing error of the ANN. Therefore, the neighborhood of each prediction point is the best available. Then, the appropriate variogram is determined, by fitting the experimental variogram to a theoretical variogram model. Three models are examined, the linear, the exponential and the power-law. Finally, the hydraulic head change is predicted for every grid cell and for every time step used. All the algorithms used were developed in Visual Basic .NET, while the visualization of the results was performed in MATLAB using the .NET COM Interoperability. The results are evaluated using leave one out cross-validation and various performance indicators. The best results were achieved by using ANNs with two hidden layers, consisting of 20 and 15 nodes respectively and by using power-law variogram with the fuzzy logic system.

Spatiotemporal stochastic models for earth science and engineering applications

NASA Astrophysics Data System (ADS)

Luo, Xiaochun

1998-12-01

Spatiotemporal processes occur in many areas of earth sciences and engineering. However, most of the available theoretical tools and techniques of space-time daft processing have been designed to operate exclusively in time or in space, and the importance of spatiotemporal variability was not fully appreciated until recently. To address this problem, a systematic framework of spatiotemporal random field (S/TRF) models for geoscience/engineering applications is presented and developed in this thesis. The space-tune continuity characterization is one of the most important aspects in S/TRF modelling, where the space-time continuity is displayed with experimental spatiotemporal variograms, summarized in terms of space-time continuity hypotheses, and modelled using spatiotemporal variogram functions. Permissible spatiotemporal covariance/variogram models are addressed through permissibility criteria appropriate to spatiotemporal processes. The estimation of spatiotemporal processes is developed in terms of spatiotemporal kriging techniques. Particular emphasis is given to the singularity analysis of spatiotemporal kriging systems. The impacts of covariance, functions, trend forms, and data configurations on the singularity of spatiotemporal kriging systems are discussed. In addition, the tensorial invariance of universal spatiotemporal kriging systems is investigated in terms of the space-time trend. The conditional simulation of spatiotemporal processes is proposed with the development of the sequential group Gaussian simulation techniques (SGGS), which is actually a series of sequential simulation algorithms associated with different group sizes. The simulation error is analyzed with different covariance models and simulation grids. The simulated annealing technique honoring experimental variograms, is also proposed, providing a way of conditional simulation without the covariance model fitting which is prerequisite for most simulation algorithms. The proposed techniques were first applied for modelling of the pressure system in a carbonate reservoir, and then applied for modelling of springwater contents in the Dyle watershed. The results of these case studies as well as the theory suggest that these techniques are realistic and feasible.

Use of ordinary kriging to interpolate observations of fire radiative heat flux sampled with airborne imagery

NASA Astrophysics Data System (ADS)

Klauberg Silva, C.; Hudak, A. T.; Bright, B. C.; Dickinson, M. B.; Kremens, R.; Paugam, R.; Mell, W.

2016-12-01

Biomass burning has impacts on air pollution at local to regional scales and contributes to greenhouse gases and affects carbon balance at the global scale. Therefore, is important to accurately estimate and manage carbon pools (fuels) and fluxes (gases and particulate emissions having public health implications) associated with wildland fires. Fire radiative energy (FRE) has been shown to be linearly correlated with biomass burned in small-scale experimental fires but not at the landscape level. Characterization of FRE density (FRED) flux in J m-2 from a landscape-level fire presents an undersampling problem. Specifically, airborne acquisitions of long-wave infrared radiation (LWIR) from a nadir-viewing LWIR camera mounted on board fixed-wing aircraft provide only samples of FRED from a landscape-level fire, because of the time required to turn the plane around between passes, and a fire extent that is broader than the camera field of view. This undersampling in time and space produces apparent firelines in an image of observed FRED, capturing the fire spread only whenever and wherever the scene happened to be imaged. We applied ordinary kriging to images of observed FRED from five prescribed burns collected in forested and non-forested management units burned at Eglin Air Force Base in Florida USA in 2011 and 2012. The three objectives were to: 1. more realistically map FRED, 2. more accurately estimate total FRED as predicted from fuel consumption measurements, and 3. compare the sampled and kriged FRED maps to modeled estimates of fire rate of spread (ROS). Observed FRED was integrated from LWIR images calibrated to units of fire radiative flux density (FRFD) in W m-2. Iterating the kriging analysis 2-10 times (depending on the burn unit) led to more accurate FRED estimates, both in map form and in terms of total FRED, as corroborated by independent estimates of fuel consumption and ROS.

The use of propagation path corrections to improve regional seismic event location in western China

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

Steck, L.K.; Cogbill, A.H.; Velasco, A.A.

1999-03-01

In an effort to improve the ability to locate seismic events in western China using only regional data, the authors have developed empirical propagation path corrections (PPCs) and applied such corrections using both traditional location routines as well as a nonlinear grid search method. Thus far, the authors have concentrated on corrections to observed P arrival times for shallow events using travel-time observations available from the USGS EDRs, the ISC catalogs, their own travel-tim picks from regional data, and data from other catalogs. They relocate events with the algorithm of Bratt and Bache (1988) from a region encompassing China. Formore » individual stations having sufficient data, they produce a map of the regional travel-time residuals from all well-located teleseismic events. From these maps, interpolated PPC surfaces have been constructed using both surface fitting under tension and modified Bayesian kriging. The latter method offers the advantage of providing well-behaved interpolants, but requires that the authors have adequate error estimates associated with the travel-time residuals. To improve error estimates for kriging and event location, they separate measurement error from modeling error. The modeling error is defined as the travel-time variance of a particular model as a function of distance, while the measurement error is defined as the picking error associated with each phase. They estimate measurement errors for arrivals from the EDRs based on roundoff or truncation, and use signal-to-noise for the travel-time picks from the waveform data set.« less

Optimization of Heat Exchangers with Dimpled Surfaces to Improve the Performance in Thermoelectric Generators Using a Kriging Model

NASA Astrophysics Data System (ADS)

Li, Shuai; Wang, Yiping; Wang, Tao; Yang, Xue; Deng, Yadong; Su, Chuqi

2017-05-01

Thermoelectric generators (TEGs) have become a topic of interest for vehicle exhaust energy recovery. Electrical power generation is deeply influenced by temperature differences, temperature uniformity and topological structures of TEGs. When the dimpled surfaces are adopted in heat exchangers, the heat transfer rates can be augmented with a minimal pressure drop. However, the temperature distribution shows a large gradient along the flow direction which has adverse effects on the power generation. In the current study, the heat exchanger performance was studied in a computational fluid dynamics (CFD) model. The dimple depth, dimple print diameter, and channel height were chosen as design variables. The objective function was defined as a combination of average temperature, temperature uniformity and pressure loss. The optimal Latin hypercube method was used to determine the experiment points as a method of design of the experiment in order to analyze the sensitivity of the design variables. A Kriging surrogate model was built and verified according to the database resulting from the CFD simulation. A multi-island genetic algorithm was used to optimize the structure in the heat exchanger based on the surrogate model. The results showed that the average temperature of the heat exchanger was most sensitive to the dimple depth. The pressure loss and temperature uniformity were most sensitive to the parameter of channel rear height, h 2. With an optimal design of channel structure, the temperature uniformity can be greatly improved compared with the initial exchanger, and the additional pressure loss also increased.

Sobol‧ sensitivity analysis of NAPL-contaminated aquifer remediation process based on multiple surrogates

NASA Astrophysics Data System (ADS)

Luo, Jiannan; Lu, Wenxi

2014-06-01

Sobol‧ sensitivity analyses based on different surrogates were performed on a trichloroethylene (TCE)-contaminated aquifer to assess the sensitivity of the design variables of remediation duration, surfactant concentration and injection rates at four wells to remediation efficiency First, the surrogate models of a multi-phase flow simulation model were constructed by applying radial basis function artificial neural network (RBFANN) and Kriging methods, and the two models were then compared. Based on the developed surrogate models, the Sobol‧ method was used to calculate the sensitivity indices of the design variables which affect the remediation efficiency. The coefficient of determination (R2) and the mean square error (MSE) of these two surrogate models demonstrated that both models had acceptable approximation accuracy, furthermore, the approximation accuracy of the Kriging model was slightly better than that of the RBFANN model. Sobol‧ sensitivity analysis results demonstrated that the remediation duration was the most important variable influencing remediation efficiency, followed by rates of injection at wells 1 and 3, while rates of injection at wells 2 and 4 and the surfactant concentration had negligible influence on remediation efficiency. In addition, high-order sensitivity indices were all smaller than 0.01, which indicates that interaction effects of these six factors were practically insignificant. The proposed Sobol‧ sensitivity analysis based on surrogate is an effective tool for calculating sensitivity indices, because it shows the relative contribution of the design variables (individuals and interactions) to the output performance variability with a limited number of runs of a computationally expensive simulation model. The sensitivity analysis results lay a foundation for the optimal groundwater remediation process optimization.

Dental implant customization using numerical optimization design and 3-dimensional printing fabrication of zirconia ceramic.

PubMed

Cheng, Yung-Chang; Lin, Deng-Huei; Jiang, Cho-Pei; Lin, Yuan-Min

2017-05-01

This study proposes a new methodology for dental implant customization consisting of numerical geometric optimization and 3-dimensional printing fabrication of zirconia ceramic. In the numerical modeling, exogenous factors for implant shape include the thread pitch, thread depth, maximal diameter of implant neck, and body size. Endogenous factors are bone density, cortical bone thickness, and non-osseointegration. An integration procedure, including uniform design method, Kriging interpolation and genetic algorithm, is applied to optimize the geometry of dental implants. The threshold of minimal micromotion for optimization evaluation was 100 μm. The optimized model is imported to the 3-dimensional slurry printer to fabricate the zirconia green body (powder is bonded by polymer weakly) of the implant. The sintered implant is obtained using a 2-stage sintering process. Twelve models are constructed according to uniform design method and simulated the micromotion behavior using finite element modeling. The result of uniform design models yields a set of exogenous factors that can provide the minimal micromotion (30.61 μm), as a suitable model. Kriging interpolation and genetic algorithm modified the exogenous factor of the suitable model, resulting in 27.11 μm as an optimization model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model, but the accuracy of sintered part still needs to be improved. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1 MPa. Copyright © 2016 John Wiley & Sons, Ltd.

Automated mapping of the ocean floor using the theory of intrinsic random functions of order k

USGS Publications Warehouse

David, M.; Crozel, D.; Robb, James M.

1986-01-01

High-quality contour maps can be computer drawn from single track echo-sounding data by combining Universal Kriging and the theory of intrinsic random function of order K (IRFK). These methods interpolate values among the closely spaced points that lie along relatively widely spaced lines. The technique provides a variance which can be contoured as a quantitative measure of map precision. The technique can be used to evaluate alternative survey trackline configurations and data collection intervals, and can be applied to other types of oceanographic data. ?? 1986 D. Reidel Publishing Company.

Spatial analysis of health risk assessment with arsenic intake of drinking water in the LanYang plain

NASA Astrophysics Data System (ADS)

Chen, C. F.; Liang, C. P.; Jang, C. S.; Chen, J. S.

2016-12-01

Groundwater is one of the most component water resources in Lanyang plain. The groundwater of the Lanyang Plain contains arsenic levels that exceed the current Taiwan Environmental Protection Administration (Taiwan EPA) limit of 10 μg/L. The arsenic of groundwater in some areas of the Lanyang Plain pose great menace for the safe use of groundwater resources. Therefore, poor water quality can adversely impact drinking water uses, leading to human health risks. This study analyzed the potential health risk associated with the ingestion of arsenic-affected groundwater in the arseniasis-endemic Lanyang plain. Geostatistical approach is widely used in spatial variability analysis and distributions of field data with uncertainty. The estimation of spatial distribution of the arsenic contaminant in groundwater is very important in the health risk assessment. This study used indicator kriging (IK) and ordinary kriging (OK) methods to explore the spatial variability of arsenic-polluted parameters. The estimated difference between IK and OK estimates was compared. The extent of arsenic pollution was spatially determined and the Target cancer risk (TR) and dose response were explored when the ingestion of arsenic in groundwater. Thus, a zonal management plan based on safe groundwater use is formulated. The research findings can provide a plan reference of regional water resources supplies for local government administrators and developing groundwater resources in the Lanyang Plain.

Spatio-temporal analysis of annual rainfall in Crete, Greece

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil A.; Corzo, Gerald A.; Karatzas, George P.; Kotsopoulou, Anastasia

2018-03-01

Analysis of rainfall data from the island of Crete, Greece was performed to identify key hydrological years and return periods as well as to analyze the inter-annual behavior of the rainfall variability during the period 1981-2014. The rainfall spatial distribution was also examined in detail to identify vulnerable areas of the island. Data analysis using statistical tools and spectral analysis were applied to investigate and interpret the temporal course of the available rainfall data set. In addition, spatial analysis techniques were applied and compared to determine the rainfall spatial distribution on the island of Crete. The analysis presented that in contrast to Regional Climate Model estimations, rainfall rates have not decreased, while return periods vary depending on seasonality and geographic location. A small but statistical significant increasing trend was detected in the inter-annual rainfall variations as well as a significant rainfall cycle almost every 8 years. In addition, statistically significant correlation of the island's rainfall variability with the North Atlantic Oscillation is identified for the examined period. On the other hand, regression kriging method combining surface elevation as secondary information improved the estimation of the annual rainfall spatial variability on the island of Crete by 70% compared to ordinary kriging. The rainfall spatial and temporal trends on the island of Crete have variable characteristics that depend on the geographical area and on the hydrological period.

A SPATIOTEMPORAL APPROACH FOR HIGH RESOLUTION TRAFFIC FLOW IMPUTATION

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

Han, Lee; Chin, Shih-Miao; Hwang, Ho-Ling

Along with the rapid development of Intelligent Transportation Systems (ITS), traffic data collection technologies have been evolving dramatically. The emergence of innovative data collection technologies such as Remote Traffic Microwave Sensor (RTMS), Bluetooth sensor, GPS-based Floating Car method, automated license plate recognition (ALPR) (1), etc., creates an explosion of traffic data, which brings transportation engineering into the new era of Big Data. However, despite the advance of technologies, the missing data issue is still inevitable and has posed great challenges for research such as traffic forecasting, real-time incident detection and management, dynamic route guidance, and massive evacuation optimization, because themore » degree of success of these endeavors depends on the timely availability of relatively complete and reasonably accurate traffic data. A thorough literature review suggests most current imputation models, if not all, focus largely on the temporal nature of the traffic data and fail to consider the fact that traffic stream characteristics at a certain location are closely related to those at neighboring locations and utilize these correlations for data imputation. To this end, this paper presents a Kriging based spatiotemporal data imputation approach that is able to fully utilize the spatiotemporal information underlying in traffic data. Imputation performance of the proposed approach was tested using simulated scenarios and achieved stable imputation accuracy. Moreover, the proposed Kriging imputation model is more flexible compared to current models.« less

Characterization and geostatistical mapping of water salinity: A case study of terminal complex in the Oued Righ Valley (southern Algeria)

NASA Astrophysics Data System (ADS)

Belkesier, Mohamed Saleh; Zeddouri, Aziez; Halassa, Younes; Kechiched, Rabah

2018-05-01

The region of Oued Righ contains large quantities of groundwater hosted by the three aquifers: the Terminal Complex (CT), the Continental Intercalary (CI) and the phreatic aquifer. The present study is focused on the water from CT aquifer in order to characterize their salinity using geostatistical tool for maping. Indeed, water in this aquifer show a high mineralization exceeding the OMS standards. The main hydro-chemical facies of this water is Chloride-Sodium and Sulfate-Sodium. The elementary statistics have been performed on the physico-chemical analysis from 97 wells whereas 766 wells were analyzed on salinity and are used for the geostatistical mapping. The obtained results show a spatial evolution of the salinity toward the direction South to the North. The salinity is locally strong in the central part of Oued Righ valley. The non-parametric geostatistic of indicator kriging was performed on the salinity data using a cut-off of 5230 mg/l which represents the average value in the studied area. The indicator Kriging allows the estimation of salinity probabilities I (5230 mg / l) in the water of the CT aquifer using bloc model (500 x 500 m). The automatic mapping is used to visualize the distribution of the kriged probabilities of salinity. These results can help to ensure a rational and a selective exploitation of groundwater according the salinity contents.

A framework for accelerated phototrophic bioprocess development: integration of parallelized microscale cultivation, laboratory automation and Kriging-assisted experimental design.

PubMed

Morschett, Holger; Freier, Lars; Rohde, Jannis; Wiechert, Wolfgang; von Lieres, Eric; Oldiges, Marco

2017-01-01

Even though microalgae-derived biodiesel has regained interest within the last decade, industrial production is still challenging for economic reasons. Besides reactor design, as well as value chain and strain engineering, laborious and slow early-stage parameter optimization represents a major drawback. The present study introduces a framework for the accelerated development of phototrophic bioprocesses. A state-of-the-art micro-photobioreactor supported by a liquid-handling robot for automated medium preparation and product quantification was used. To take full advantage of the technology's experimental capacity, Kriging-assisted experimental design was integrated to enable highly efficient execution of screening applications. The resulting platform was used for medium optimization of a lipid production process using Chlorella vulgaris toward maximum volumetric productivity. Within only four experimental rounds, lipid production was increased approximately threefold to 212 ± 11 mg L -1  d -1 . Besides nitrogen availability as a key parameter, magnesium, calcium and various trace elements were shown to be of crucial importance. Here, synergistic multi-parameter interactions as revealed by the experimental design introduced significant further optimization potential. The integration of parallelized microscale cultivation, laboratory automation and Kriging-assisted experimental design proved to be a fruitful tool for the accelerated development of phototrophic bioprocesses. By means of the proposed technology, the targeted optimization task was conducted in a very timely and material-efficient manner.

Spatial multi-scale variability of soil nutrients in relation to environmental factors in a typical agricultural region, eastern China.

PubMed

Liu, Yang; Lv, Jianshu; Zhang, Bing; Bi, Jun

2013-04-15

Identifying the sources of spatial variability and deficiency risk of soil nutrients is a crucial issue for soil and agriculture management. A total of 1247 topsoil samples (0-20 cm) were collected at the nodes of a 2×2 km grid in Rizhao City and the contents of soil organic carbon (OC), total nitrogen (TN), and total phosphorus (TP) were determined. Factorial kriging analysis (FKA), stepwise multiple regression, and indicator kriging (IK) were appled to investigate the scale dependent correlations among soil nutrients, identify the sources of spatial variability at each spatial scale, and delineate the potential risk of soil nutrient deficiency. Linear model of co-regionalization (LMC) fitting indicated that the presence of multi-scale variation was comprised of nugget effect, an exponential structure with a range of 12 km (local scale), and a spherical structure with a range of 84 km (regional scale). The short-range variation of OC and TN was mainly dominated by land use types, and TP was controlled by terrain. At long-range scale, spatial variation of OC, TN, and TP was dominated by parent material. Indicator kriging maps depicted the probability of soil nutrient deficiency compared with the background values in eastern Shandong province. The high deficiency risk area of all nutrient integration was mainly located in eastern and northwestern parts. Copyright © 2013 Elsevier B.V. All rights reserved.

Assessing groundwater quality in Greece based on spatial and temporal analysis.

PubMed

Dokou, Zoi; Kourgialas, Nektarios N; Karatzas, George P

2015-12-01

The recent industrial growth together with the urban expansion and intensive agriculture in Greece has increased groundwater contamination in many regions of the country. In order to design successful remediation strategies and protect public health, it is very important to identify those areas that are most vulnerable to groundwater contamination. In this work, an extensive contamination database from monitoring wells that cover the entire Greek territory during the last decade (2000-2008) was used in order to study the temporal and spatial distribution of groundwater contamination for the most common and serious anionic and cationic trace element pollutants (heavy metals). Spatial and temporal patterns and trends in the occurrence of groundwater contamination were also identified highlighting the regions where the higher groundwater contamination rates have been detected across the country. As a next step, representative contaminated aquifers in Greece, which were identified by the above analysis, were selected in order to analyze the specific contamination problem in more detail. To this end, geostatistical techniques (various types of kriging, co-kriging, and indicator kriging) were employed in order to map the contaminant values and the probability of exceeding critical thresholds (set as the parametric values of the contaminant of interest in each case). The resulting groundwater contamination maps could be used as a useful tool for water policy makers and water managers in order to assist the decision-making process.

Comparison of Highly Resolved Model-Based Exposure ...

EPA Pesticide Factsheets

Human exposure to air pollution in many studies is represented by ambient concentrations from space-time kriging of observed values. Space-time kriging techniques based on a limited number of ambient monitors may fail to capture the concentration from local sources. Further, because people spend more time indoors, using ambient concentration to represent exposure may cause error. To quantify the associated exposure error, we computed a series of six different hourly-based exposure metrics at 16,095 Census blocks of three Counties in North Carolina for CO, NOx, PM2.5, and elemental carbon (EC) during 2012. These metrics include ambient background concentration from space-time ordinary kriging (STOK), ambient on-road concentration from the Research LINE source dispersion model (R-LINE), a hybrid concentration combining STOK and R-LINE, and their associated indoor concentrations from an indoor infiltration mass balance model. Using a hybrid-based indoor concentration as the standard, the comparison showed that outdoor STOK metrics yielded large error at both population (67% to 93%) and individual level (average bias between −10% to 95%). For pollutants with significant contribution from on-road emission (EC and NOx), the on-road based indoor metric performs the best at the population level (error less than 52%). At the individual level, however, the STOK-based indoor concentration performs the best (average bias below 30%). For PM2.5, due to the relatively low co

Comparative soil CO2 flux measurements and geostatistical estimation methods on Masaya volcano, Nicaragua

USGS Publications Warehouse

Lewicki, Jennifer L.; Bergfeld, Deborah; Cardellini, Carlo; Chiodini, Giovanni; Granieri, Domenico; Varley, Nick; Werner, Cynthia A.

2005-01-01

We present a comparative study of soil CO2 flux (FCO2">FCO2) measured by five groups (Groups 1–5) at the IAVCEI-CCVG Eighth Workshop on Volcanic Gases on Masaya volcano, Nicaragua. Groups 1–5 measured FCO2 using the accumulation chamber method at 5-m spacing within a 900 m2 grid during a morning (AM) period. These measurements were repeated by Groups 1–3 during an afternoon (PM) period. Measured FCO2 ranged from 218 to 14,719 g m−2 day−1. The variability of the five measurements made at each grid point ranged from ±5 to 167%. However, the arithmetic means of fluxes measured over the entire grid and associated total CO2 emission rate estimates varied between groups by only ±22%. All three groups that made PM measurements reported an 8–19% increase in total emissions over the AM results. Based on a comparison of measurements made during AM and PM times, we argue that this change is due in large part to natural temporal variability of gas flow, rather than to measurement error. In order to estimate the mean and associated CO2 emission rate of one data set and to map the spatial FCO2 distribution, we compared six geostatistical methods: arithmetic and minimum variance unbiased estimator means of uninterpolated data, and arithmetic means of data interpolated by the multiquadric radial basis function, ordinary kriging, multi-Gaussian kriging, and sequential Gaussian simulation methods. While the total CO2 emission rates estimated using the different techniques only varied by ±4.4%, the FCO2 maps showed important differences. We suggest that the sequential Gaussian simulation method yields the most realistic representation of the spatial distribution of FCO2, but a variety of geostatistical methods are appropriate to estimate the total CO2 emission rate from a study area, which is a primary goal in volcano monitoring research.

The total probabilities from high-resolution ensemble forecasting of floods

NASA Astrophysics Data System (ADS)

Olav Skøien, Jon; Bogner, Konrad; Salamon, Peter; Smith, Paul; Pappenberger, Florian

2015-04-01

Ensemble forecasting has for a long time been used in meteorological modelling, to give an indication of the uncertainty of the forecasts. As meteorological ensemble forecasts often show some bias and dispersion errors, there is a need for calibration and post-processing of the ensembles. Typical methods for this are Bayesian Model Averaging (Raftery et al., 2005) and Ensemble Model Output Statistics (EMOS) (Gneiting et al., 2005). There are also methods for regionalizing these methods (Berrocal et al., 2007) and for incorporating the correlation between lead times (Hemri et al., 2013). To make optimal predictions of floods along the stream network in hydrology, we can easily use the ensemble members as input to the hydrological models. However, some of the post-processing methods will need modifications when regionalizing the forecasts outside the calibration locations, as done by Hemri et al. (2013). We present a method for spatial regionalization of the post-processed forecasts based on EMOS and top-kriging (Skøien et al., 2006). We will also look into different methods for handling the non-normality of runoff and the effect on forecasts skills in general and for floods in particular. Berrocal, V. J., Raftery, A. E. and Gneiting, T.: Combining Spatial Statistical and Ensemble Information in Probabilistic Weather Forecasts, Mon. Weather Rev., 135(4), 1386-1402, doi:10.1175/MWR3341.1, 2007. Gneiting, T., Raftery, A. E., Westveld, A. H. and Goldman, T.: Calibrated Probabilistic Forecasting Using Ensemble Model Output Statistics and Minimum CRPS Estimation, Mon. Weather Rev., 133(5), 1098-1118, doi:10.1175/MWR2904.1, 2005. Hemri, S., Fundel, F. and Zappa, M.: Simultaneous calibration of ensemble river flow predictions over an entire range of lead times, Water Resour. Res., 49(10), 6744-6755, doi:10.1002/wrcr.20542, 2013. Raftery, A. E., Gneiting, T., Balabdaoui, F. and Polakowski, M.: Using Bayesian Model Averaging to Calibrate Forecast Ensembles, Mon. Weather Rev., 133(5), 1155-1174, doi:10.1175/MWR2906.1, 2005. Skøien, J. O., Merz, R. and Blöschl, G.: Top-kriging - Geostatistics on stream networks, Hydrol. Earth Syst. Sci., 10(2), 277-287, 2006.

Hydrogeologic Unit Flow Characterization Using Transition Probability Geostatistics

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

Jones, N L; Walker, J R; Carle, S F

2003-11-21

This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has several advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upwards sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow (HUF) package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids. An application of themore » technique involving probabilistic capture zone delineation for the Aberjona Aquifer in Woburn, Ma. is included.« less

Geostatistical applications in ground-water modeling in south-central Kansas

USGS Publications Warehouse

Ma, T.-S.; Sophocleous, M.; Yu, Y.-S.

1999-01-01

This paper emphasizes the supportive role of geostatistics in applying ground-water models. Field data of 1994 ground-water level, bedrock, and saltwater-freshwater interface elevations in south-central Kansas were collected and analyzed using the geostatistical approach. Ordinary kriging was adopted to estimate initial conditions for ground-water levels and topography of the Permian bedrock at the nodes of a finite difference grid used in a three-dimensional numerical model. Cokriging was used to estimate initial conditions for the saltwater-freshwater interface. An assessment of uncertainties in the estimated data is presented. The kriged and cokriged estimation variances were analyzed to evaluate the adequacy of data employed in the modeling. Although water levels and bedrock elevations are well described by spherical semivariogram models, additional data are required for better cokriging estimation of the interface data. The geostatistically analyzed data were employed in a numerical model of the Siefkes site in the project area. Results indicate that the computed chloride concentrations and ground-water drawdowns reproduced the observed data satisfactorily.This paper emphasizes the supportive role of geostatistics in applying ground-water models. Field data of 1994 ground-water level, bedrock, and saltwater-freshwater interface elevations in south-central Kansas were collected and analyzed using the geostatistical approach. Ordinary kriging was adopted to estimate initial conditions for ground-water levels and topography of the Permian bedrock at the nodes of a finite difference grid used in a three-dimensional numerical model. Cokriging was used to estimate initial conditions for the saltwater-freshwater interface. An assessment of uncertainties in the estimated data is presented. The kriged and cokriged estimation variances were analyzed to evaluate the adequacy of data employed in the modeling. Although water levels and bedrock elevations are well described by spherical semivariogram models, additional data are required for better cokriging estimation of the interface data. The geostatistically analyzed data were employed in a numerical model of the Siefkes site in the project area. Results indicate that the computed chloride concentrations and ground-water drawdowns reproduced the observed data satisfactorily.

Pyrogenic carbon distribution in mineral topsoils of the northeastern United States

USGS Publications Warehouse

Jauss, Verena; Sullivan, Patrick J.; Sanderman, Jonathan; Smith, David; Lehmann, Johannes

2017-01-01

Due to its slow turnover rates in soil, pyrogenic carbon (PyC) is considered an important C pool and relevant to climate change processes. Therefore, the amounts of soil PyC were compared to environmental covariates over an area of 327,757 km2 in the northeastern United States in order to understand the controls on PyC distribution over large areas. Topsoil (defined as the soil A horizon, after removal of any organic horizons) samples were collected at 165 field sites in a generalised random tessellation stratified design that corresponded to approximately 1 site per 1600 km2 and PyC was estimated from diffuse reflectance mid-infrared spectroscopy measurements using a partial least-squares regression analysis in conjunction with a large database of PyC measurements based on a solid-state 13C nuclear magnetic resonance spectroscopy technique. Three spatial models were applied to the data in order to relate critical environmental covariates to the changes in spatial density of PyC over the landscape. Regional mean density estimates of PyC were 11.0 g kg− 1 (0.84 Gg km− 2) for Ordinary Kriging, 25.8 g kg− 1(12.2 Gg km− 2) for Multivariate Linear Regression, and 26.1 g kg− 1 (12.4 Gg km− 2) for Bayesian Regression Kriging. Akaike Information Criterion (AIC) indicated that the Multivariate Linear Regression model performed best (AIC = 842.6; n = 165) compared to Ordinary Kriging (AIC = 982.4) and Bayesian Regression Kriging (AIC = 979.2). Soil PyC concentrations correlated well with total soil sulphur (P < 0.001; n = 165), plant tissue lignin (P = 0.003), and drainage class (P = 0.008). This suggests the opportunity of including related environmental parameters in the spatial assessment of PyC in soils. Better estimates of the contribution of PyC to the global carbon cycle will thus also require more accurate assessments of these covariates.

Application of Poisson kriging to the mapping of cholera and dysentery incidence in an endemic area of Bangladesh.

PubMed

Ali, Mohammad; Goovaerts, Pierre; Nazia, Nushrat; Haq, M Zahirul; Yunus, Mohammad; Emch, Michael

2006-10-13

Disease maps can serve to display incidence rates geographically, to inform on public health provision about the success or failure of interventions, and to make hypothesis or to provide evidences concerning disease etiology. Poisson kriging was recently introduced to filter the noise attached to rates recorded over sparsely populated administrative units. Its benefit over simple population-weighted averages and empirical Bayesian smoothers was demonstrated by simulation studies using county-level cancer mortality rates. This paper presents the first application of Poisson kriging to the spatial interpolation of local disease rates, resulting in continuous maps of disease rate estimates and the associated prediction variance. The methodology is illustrated using cholera and dysentery data collected in a cholera endemic area (Matlab) of Bangladesh. The spatial analysis was confined to patrilineally-related clusters of households, known as baris, located within 9 kilometers from the Matlab hospital to avoid underestimating the risk of disease incidence, since patients far away from the medical facilities are less likely to travel. Semivariogram models reveal a range of autocorrelation of 1.1 km for dysentery and 0.37 km for cholera. This result translates into a cholera risk map that is patchier than the dysentery map that shows a large zone of high incidence in the south-central part of the study area, which is quasi-urban. On both maps, lower risk values are found in the Northern part of the study area, which is also the most distant from the Matlab hospital. The weaker spatial continuity of cholera versus dysentery incidence rates resulted in larger kriging variance across the study area. The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of incidence rates into the mapping of risk values and the quantification of the associated uncertainty. Differences in spatial patterns, in particular the range of spatial autocorrelation, reflect differences in the mode of transmission of cholera and dysentery. Our risk maps for cholera and dysentery incidences should help identifying putative factors of increased disease incidence, leading to more effective prevention and remedial actions in endemic areas.

Application of Poisson kriging to the mapping of cholera and dysentery incidence in an endemic area of Bangladesh

PubMed Central

Ali, Mohammad; Goovaerts, Pierre; Nazia, Nushrat; Haq, M Zahirul; Yunus, Mohammad; Emch, Michael

2006-01-01

Background Disease maps can serve to display incidence rates geographically, to inform on public health provision about the success or failure of interventions, and to make hypothesis or to provide evidences concerning disease etiology. Poisson kriging was recently introduced to filter the noise attached to rates recorded over sparsely populated administrative units. Its benefit over simple population-weighted averages and empirical Bayesian smoothers was demonstrated by simulation studies using county-level cancer mortality rates. This paper presents the first application of Poisson kriging to the spatial interpolation of local disease rates, resulting in continuous maps of disease rate estimates and the associated prediction variance. The methodology is illustrated using cholera and dysentery data collected in a cholera endemic area (Matlab) of Bangladesh. Results The spatial analysis was confined to patrilineally-related clusters of households, known as baris, located within 9 kilometers from the Matlab hospital to avoid underestimating the risk of disease incidence, since patients far away from the medical facilities are less likely to travel. Semivariogram models reveal a range of autocorrelation of 1.1 km for dysentery and 0.37 km for cholera. This result translates into a cholera risk map that is patchier than the dysentery map that shows a large zone of high incidence in the south-central part of the study area, which is quasi-urban. On both maps, lower risk values are found in the Northern part of the study area, which is also the most distant from the Matlab hospital. The weaker spatial continuity of cholera versus dysentery incidence rates resulted in larger kriging variance across the study area. Conclusion The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of incidence rates into the mapping of risk values and the quantification of the associated uncertainty. Differences in spatial patterns, in particular the range of spatial autocorrelation, reflect differences in the mode of transmission of cholera and dysentery. Our risk maps for cholera and dysentery incidences should help identifying putative factors of increased disease incidence, leading to more effective prevention and remedial actions in endemic areas. PMID:17038192

Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations

NASA Astrophysics Data System (ADS)

Bogusz, Janusz; Kłos, Anna; Grzempowski, Piotr; Kontny, Bernard

2014-06-01

The paper presents the results of testing the various methods of permanent stations' velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT ( The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities' values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors' opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.

Metamodel-based inverse method for parameter identification: elastic-plastic damage model

NASA Astrophysics Data System (ADS)

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

The Association of Ambient Air Pollution and Physical Inactivity in the United States

PubMed Central

Roberts, Jennifer D.; Voss, Jameson D.; Knight, Brandon

2014-01-01

Background Physical inactivity, ambient air pollution and obesity are modifiable risk factors for non-communicable diseases, with the first accounting for 10% of premature deaths worldwide. Although community level interventions may target each simultaneously, research on the relationship between these risk factors is lacking. Objectives After comparing spatial interpolation methods to determine the best predictor for particulate matter (PM2.5; PM10) and ozone (O3) exposures throughout the U.S., we evaluated the cross-sectional association of ambient air pollution with leisure-time physical inactivity among adults. Methods In this cross-sectional study, we assessed leisure-time physical inactivity using individual self-reported survey data from the Centers for Disease Control and Prevention's 2011 Behavioral Risk Factor Surveillance System. These data were combined with county-level U.S. Environmental Protection Agency air pollution exposure estimates using two interpolation methods (Inverse Distance Weighting and Empirical Bayesian Kriging). Finally, we evaluated whether those exposed to higher levels of air pollution were less active by performing logistic regression, adjusting for demographic and behavioral risk factors, and after stratifying by body weight category. Results With Empirical Bayesian Kriging air pollution values, we estimated a statistically significant 16–35% relative increase in the odds of leisure-time physical inactivity per exposure class increase of PM2.5 in the fully adjusted model across the normal weight respondents (p-value<0.0001). Evidence suggested a relationship between the increasing dose of PM2.5 exposure and the increasing odds of physical inactivity. Conclusions In a nationally representative, cross-sectional sample, increased community level air pollution is associated with reduced leisure-time physical activity particularly among the normal weight. Although our design precludes a causal inference, these results provide additional evidence that air pollution should be investigated as an environmental determinant of inactivity. PMID:24598907

Mapping soil texture classes and optimization of the result by accuracy assessment

NASA Astrophysics Data System (ADS)

Laborczi, Annamária; Takács, Katalin; Bakacsi, Zsófia; Szabó, József; Pásztor, László

2014-05-01

There are increasing demands nowadays on spatial soil information in order to support environmental related and land use management decisions. The GlobalSoilMap.net (GSM) project aims to make a new digital soil map of the world using state-of-the-art and emerging technologies for soil mapping and predicting soil properties at fine resolution. Sand, silt and clay are among the mandatory GSM soil properties. Furthermore, soil texture class information is input data of significant agro-meteorological and hydrological models. Our present work aims to compare and evaluate different digital soil mapping methods and variables for producing the most accurate spatial prediction of texture classes in Hungary. In addition to the Hungarian Soil Information and Monitoring System as our basic data, digital elevation model and its derived components, geological database, and physical property maps of the Digital Kreybig Soil Information System have been applied as auxiliary elements. Two approaches have been applied for the mapping process. At first the sand, silt and clay rasters have been computed independently using regression kriging (RK). From these rasters, according to the USDA categories, we have compiled the texture class map. Different combinations of reference and training soil data and auxiliary covariables have resulted several different maps. However, these results consequentially include the uncertainty factor of the three kriged rasters. Therefore we have suited data mining methods as the other approach of digital soil mapping. By working out of classification trees and random forests we have got directly the texture class maps. In this way the various results can be compared to the RK maps. The performance of the different methods and data has been examined by testing the accuracy of the geostatistically computed and the directly classified results. We have used the GSM methodology to assess the most predictive and accurate way for getting the best among the several result maps. Acknowledgement: Our work was supported by the Hungarian National Scientific Research Foundation (OTKA, Grant No. K105167).

Using Predictions Based on Geostatistics to Monitor Trends in Aspergillus flavus Strain Composition.

PubMed

Orum, T V; Bigelow, D M; Cotty, P J; Nelson, M R

1999-09-01

ABSTRACT Aspergillus flavus is a soil-inhabiting fungus that frequently produces aflatoxins, potent carcinogens, in cottonseed and other seed crops. A. flavus S strain isolates, characterized on the basis of sclerotial morphology, are highly toxigenic. Spatial and temporal characteristics of the percentage of the A. flavus isolates that are S strain (S strain incidence) were used to predict patterns across areas of more than 30 km(2). Spatial autocorrelation in S strain incidence in Yuma County, AZ, was shown to extend beyond field boundaries to adjacent fields. Variograms revealed both short-range (2 to 6 km) and long-range (20 to 30 km) spatial structure in S strain incidence. S strain incidence at 36 locations sampled in July 1997 was predicted with a high correlation between expected and observed values (R = 0.85, P = 0.0001) by kriging data from July 1995 and July 1996. S strain incidence at locations sampled in October 1997 and March 1998 was markedly less than predicted by kriging data from the same months in prior years. Temporal analysis of four locations repeatedly sampled from April 1995 through July 1998 also indicated a major reduction in S strain incidence in the Texas Hill area after July 1997. Surface maps generated by kriging point data indicated a similarity in the spatial pattern of S strain incidence among all sampling dates despite temporal changes in the overall S strain incidence. Geostatistics provided useful descriptions of variability in S strain incidence over space and time.

Analysis of field-scale spatial correlations and variations of soil nutrients using geostatistics.

PubMed

Liu, Ruimin; Xu, Fei; Yu, Wenwen; Shi, Jianhan; Zhang, Peipei; Shen, Zhenyao

2016-02-01

Spatial correlations and soil nutrient variations are important for soil nutrient management. They help to reduce the negative impacts of agricultural nonpoint source pollution. Based on the sampled available nitrogen (AN), available phosphorus (AP), and available potassium (AK), soil nutrient data from 2010, the spatial correlation, was analyzed, and the probabilities of the nutrient's abundance or deficiency were discussed. This paper presents a statistical approach to spatial analysis, the spatial correlation analysis (SCA), which was originally developed for describing heterogeneity in the presence of correlated variation and based on ordinary kriging (OK) results. Indicator kriging (IK) was used to assess the susceptibility of excess of soil nutrients based on crop needs. The kriged results showed there was a distinct spatial variability in the concentration of all three soil nutrients. High concentrations of these three soil nutrients were found near Anzhou. As the distance from the center of town increased, the concentration of the soil nutrients gradually decreased. Spatially, the relationship between AN and AP was negative, and the relationship between AP and AK was not clear. The IK results showed that there were few areas with a risk of AN and AP overabundance. However, almost the entire study region was at risk of AK overabundance. Based on the soil nutrient distribution results, it is clear that the spatial variability of the soil nutrients differed throughout the study region. This spatial soil nutrient variability might be caused by different fertilizer types and different fertilizing practices.

Remote sensing data with the conditional latin hypercube sampling and geostatistical approach to delineate landscape changes induced by large chronological physical disturbances.

PubMed

Lin, Yu-Pin; Chu, Hone-Jay; Wang, Cheng-Long; Yu, Hsiao-Hsuan; Wang, Yung-Chieh

2009-01-01

This study applies variogram analyses of normalized difference vegetation index (NDVI) images derived from SPOT HRV images obtained before and after the ChiChi earthquake in the Chenyulan watershed, Taiwan, as well as images after four large typhoons, to delineate the spatial patterns, spatial structures and spatial variability of landscapes caused by these large disturbances. The conditional Latin hypercube sampling approach was applied to select samples from multiple NDVI images. Kriging and sequential Gaussian simulation with sufficient samples were then used to generate maps of NDVI images. The variography of NDVI image results demonstrate that spatial patterns of disturbed landscapes were successfully delineated by variogram analysis in study areas. The high-magnitude Chi-Chi earthquake created spatial landscape variations in the study area. After the earthquake, the cumulative impacts of typhoons on landscape patterns depended on the magnitudes and paths of typhoons, but were not always evident in the spatiotemporal variability of landscapes in the study area. The statistics and spatial structures of multiple NDVI images were captured by 3,000 samples from 62,500 grids in the NDVI images. Kriging and sequential Gaussian simulation with the 3,000 samples effectively reproduced spatial patterns of NDVI images. However, the proposed approach, which integrates the conditional Latin hypercube sampling approach, variogram, kriging and sequential Gaussian simulation in remotely sensed images, efficiently monitors, samples and maps the effects of large chronological disturbances on spatial characteristics of landscape changes including spatial variability and heterogeneity.

Merging Radar Quantitative Precipitation Estimates (QPEs) from the High-resolution NEXRAD Reanalysis over CONUS with Rain-gauge Observations

NASA Astrophysics Data System (ADS)

Prat, O. P.; Nelson, B. R.; Stevens, S. E.; Nickl, E.; Seo, D. J.; Kim, B.; Zhang, J.; Qi, Y.

2015-12-01

The processing of radar-only precipitation via the reanalysis from the National Mosaic and Multi-Sensor Quantitative (NMQ/Q2) based on the WSR-88D Next-generation Radar (Nexrad) network over the Continental United States (CONUS) is completed for the period covering from 2002 to 2011. While this constitutes a unique opportunity to study precipitation processes at higher resolution than conventionally possible (1-km, 5-min), the long-term radar-only product needs to be merged with in-situ information in order to be suitable for hydrological, meteorological and climatological applications. The radar-gauge merging is performed by using rain gauge information at daily (Global Historical Climatology Network-Daily: GHCN-D), hourly (Hydrometeorological Automated Data System: HADS), and 5-min (Automated Surface Observing Systems: ASOS; Climate Reference Network: CRN) resolution. The challenges related to incorporating differing resolution and quality networks to generate long-term large-scale gridded estimates of precipitation are enormous. In that perspective, we are implementing techniques for merging the rain gauge datasets and the radar-only estimates such as Inverse Distance Weighting (IDW), Simple Kriging (SK), Ordinary Kriging (OK), and Conditional Bias-Penalized Kriging (CBPK). An evaluation of the different radar-gauge merging techniques is presented and we provide an estimate of uncertainty for the gridded estimates. In addition, comparisons with a suite of lower resolution QPEs derived from ground based radar measurements (Stage IV) are provided in order to give a detailed picture of the improvements and remaining challenges.

Metamodels for Computer-Based Engineering Design: Survey and Recommendations

NASA Technical Reports Server (NTRS)

Simpson, Timothy W.; Peplinski, Jesse; Koch, Patrick N.; Allen, Janet K.

1997-01-01

The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of todays engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper we review several of these techniques including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning, and kriging. We survey their existing application in engineering design and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations and how common pitfalls can be avoided.

A path-level exact parallelization strategy for sequential simulation

NASA Astrophysics Data System (ADS)

Peredo, Oscar F.; Baeza, Daniel; Ortiz, Julián M.; Herrero, José R.

2018-01-01

Sequential Simulation is a well known method in geostatistical modelling. Following the Bayesian approach for simulation of conditionally dependent random events, Sequential Indicator Simulation (SIS) method draws simulated values for K categories (categorical case) or classes defined by K different thresholds (continuous case). Similarly, Sequential Gaussian Simulation (SGS) method draws simulated values from a multivariate Gaussian field. In this work, a path-level approach to parallelize SIS and SGS methods is presented. A first stage of re-arrangement of the simulation path is performed, followed by a second stage of parallel simulation for non-conflicting nodes. A key advantage of the proposed parallelization method is to generate identical realizations as with the original non-parallelized methods. Case studies are presented using two sequential simulation codes from GSLIB: SISIM and SGSIM. Execution time and speedup results are shown for large-scale domains, with many categories and maximum kriging neighbours in each case, achieving high speedup results in the best scenarios using 16 threads of execution in a single machine.

Spatially resolved hazard and exposure assessments: an example of lead in soil at Lavrion, Greece.

PubMed

Tristán, E; Demetriades, A; Ramsey, M H; Rosenbaum, M S; Stavrakis, P; Thornton, I; Vassiliades, E; Vergou, K

2000-01-01

Spatially resolved hazard assessment (SRHA) and spatially resolved exposure assessment (SREA) are methodologies that have been devised for assessing child exposure to soil containing environmental pollutants. These are based on either a quantitative or a semiquantitative approach. The feasibility of the methodologies has been demonstrated in a study assessing child exposure to Pb accessible in soil at the town of Lavrion in Greece. Using a quantitative approach, both measured and kriged concentrations of Pb in soil are compared with an "established" statutory threshold value. The probabilistic approach gives a refined classification of the contaminated land, since it takes into consideration the uncertainty in both the actual measurement and estimated kriged values. Two exposure assessment models (i.e., IEUBK and HESP) are used as the basis of the quantitative SREA methodologies. The significant correlation between the blood-Pb predictions, using the IEUBK model, and measured concentrations provides a partial validation of the method, because it allows for the uncertainty in the measurements and the lack of some site-specific measurements. The semiquantitative applications of SRHA and SREA incorporate both qualitative information (e.g., land use and dustiness of waste) and quantitative information (e.g., distance from wastes and distance from industry). The significant correlation between the results of these assessments and the measured blood-Pb levels confirms the robust nature of this approach. Successful application of these methodologies could reduce the cost of the assessment and allow areas to be prioritized for further investigation, remediation, or risk management.

Nine martian years of dust optical depth observations: A reference dataset

NASA Astrophysics Data System (ADS)

Montabone, Luca; Forget, Francois; Kleinboehl, Armin; Kass, David; Wilson, R. John; Millour, Ehouarn; Smith, Michael; Lewis, Stephen; Cantor, Bruce; Lemmon, Mark; Wolff, Michael

2016-07-01

We present a multi-annual reference dataset of the horizontal distribution of airborne dust from martian year 24 to 32 using observations of the martian atmosphere from April 1999 to June 2015 made by the Thermal Emission Spectrometer (TES) aboard Mars Global Surveyor, the Thermal Emission Imaging System (THEMIS) aboard Mars Odyssey, and the Mars Climate Sounder (MCS) aboard Mars Reconnaissance Orbiter (MRO). Our methodology to build the dataset works by gridding the available retrievals of column dust optical depth (CDOD) from TES and THEMIS nadir observations, as well as the estimates of this quantity from MCS limb observations. The resulting (irregularly) gridded maps (one per sol) were validated with independent observations of CDOD by PanCam cameras and Mini-TES spectrometers aboard the Mars Exploration Rovers "Spirit" and "Opportunity", by the Surface Stereo Imager aboard the Phoenix lander, and by the Compact Reconnaissance Imaging Spectrometer for Mars aboard MRO. Finally, regular maps of CDOD are produced by spatially interpolating the irregularly gridded maps using a kriging method. These latter maps are used as dust scenarios in the Mars Climate Database (MCD) version 5, and are useful in many modelling applications. The two datasets (daily irregularly gridded maps and regularly kriged maps) for the nine available martian years are publicly available as NetCDF files and can be downloaded from the MCD website at the URL: http://www-mars.lmd.jussieu.fr/mars/dust_climatology/index.html

Average variograms to guide soil sampling

NASA Astrophysics Data System (ADS)

Kerry, R.; Oliver, M. A.

2004-10-01

To manage land in a site-specific way for agriculture requires detailed maps of the variation in the soil properties of interest. To predict accurately for mapping, the interval at which the soil is sampled should relate to the scale of spatial variation. A variogram can be used to guide sampling in two ways. A sampling interval of less than half the range of spatial dependence can be used, or the variogram can be used with the kriging equations to determine an optimal sampling interval to achieve a given tolerable error. A variogram might not be available for the site, but if the variograms of several soil properties were available on a similar parent material and or particular topographic positions an average variogram could be calculated from these. Averages of the variogram ranges and standardized average variograms from four different parent materials in southern England were used to suggest suitable sampling intervals for future surveys in similar pedological settings based on half the variogram range. The standardized average variograms were also used to determine optimal sampling intervals using the kriging equations. Similar sampling intervals were suggested by each method and the maps of predictions based on data at different grid spacings were evaluated for the different parent materials. Variograms of loss on ignition (LOI) taken from the literature for other sites in southern England with similar parent materials had ranges close to the average for a given parent material showing the possible wider application of such averages to guide sampling.

An assessment of air pollutant exposure methods in Mexico City, Mexico.

PubMed

Rivera-González, Luis O; Zhang, Zhenzhen; Sánchez, Brisa N; Zhang, Kai; Brown, Daniel G; Rojas-Bracho, Leonora; Osornio-Vargas, Alvaro; Vadillo-Ortega, Felipe; O'Neill, Marie S

2015-05-01

Geostatistical interpolation methods to estimate individual exposure to outdoor air pollutants can be used in pregnancy cohorts where personal exposure data are not collected. Our objectives were to a) develop four assessment methods (citywide average (CWA); nearest monitor (NM); inverse distance weighting (IDW); and ordinary Kriging (OK)), and b) compare daily metrics and cross-validations of interpolation models. We obtained 2008 hourly data from Mexico City's outdoor air monitoring network for PM10, PM2.5, O3, CO, NO2, and SO2 and constructed daily exposure metrics for 1,000 simulated individual locations across five populated geographic zones. Descriptive statistics from all methods were calculated for dry and wet seasons, and by zone. We also evaluated IDW and OK methods' ability to predict measured concentrations at monitors using cross validation and a coefficient of variation (COV). All methods were performed using SAS 9.3, except ordinary Kriging which was modeled using R's gstat package. Overall, mean concentrations and standard deviations were similar among the different methods for each pollutant. Correlations between methods were generally high (r=0.77 to 0.99). However, ranges of estimated concentrations determined by NM, IDW, and OK were wider than the ranges for CWA. Root mean square errors for OK were consistently equal to or lower than for the IDW method. OK standard errors varied considerably between pollutants and the computed COVs ranged from 0.46 (least error) for SO2 and PM10 to 3.91 (most error) for PM2.5. OK predicted concentrations measured at the monitors better than IDW and NM. Given the similarity in results for the exposure methods, OK is preferred because this method alone provides predicted standard errors which can be incorporated in statistical models. The daily estimated exposures calculated using these different exposure methods provide flexibility to evaluate multiple windows of exposure during pregnancy, not just trimester or pregnancy-long exposures. Many studies evaluating associations between outdoor air pollution and adverse pregnancy outcomes rely on outdoor air pollution monitoring data linked to information gathered from large birth registries, and often lack residence location information needed to estimate individual exposure. This study simulated 1,000 residential locations to evaluate four air pollution exposure assessment methods, and describes possible exposure misclassification from using spatial averaging versus geostatistical interpolation models. An implication of this work is that policies to reduce air pollution and exposure among pregnant women based on epidemiologic literature should take into account possible error in estimates of effect when spatial averages alone are evaluated.

Creating a monthly time series of the potentiometric surface in the Upper Floridan aquifer, Northern Tampa Bay area, Florida, January 2000-December 2009

USGS Publications Warehouse

Lee, Terrie M.; Fouad, Geoffrey G.

2014-01-01

In Florida’s karst terrain, where groundwater and surface waters interact, a mapping time series of the potentiometric surface in the Upper Floridan aquifer offers a versatile metric for assessing the hydrologic condition of both the aquifer and overlying streams and wetlands. Long-term groundwater monitoring data were used to generate a monthly time series of potentiometric surfaces in the Upper Floridan aquifer over a 573-square-mile area of west-central Florida between January 2000 and December 2009. Recorded groundwater elevations were collated for 260 groundwater monitoring wells in the Northern Tampa Bay area, and a continuous time series of daily observations was created for 197 of the wells by estimating missing daily values through regression relations with other monitoring wells. Kriging was used to interpolate the monthly average potentiometric-surface elevation in the Upper Floridan aquifer over a decade. The mapping time series gives spatial and temporal coherence to groundwater monitoring data collected continuously over the decade by three different organizations, but at various frequencies. Further, the mapping time series describes the potentiometric surface beneath parts of six regionally important stream watersheds and 11 municipal well fields that collectively withdraw about 90 million gallons per day from the Upper Floridan aquifer. Monthly semivariogram models were developed using monthly average groundwater levels at wells. Kriging was used to interpolate the monthly average potentiometric-surface elevations and to quantify the uncertainty in the interpolated elevations. Drawdown of the potentiometric surface within well fields was likely the cause of a characteristic decrease and then increase in the observed semivariance with increasing lag distance. This characteristic made use of the hole effect model appropriate for describing the monthly semivariograms and the interpolated surfaces. Spatial variance reflected in the monthly semivariograms decreased markedly between 2002 and 2003, timing that coincided with decreases in well-field pumping. Cross-validation results suggest that the kriging interpolation may smooth over the drawdown of the potentiometric surface near production wells. The groundwater monitoring network of 197 wells yielded an average kriging error in the potentiometric-surface elevations of 2 feet or less over approximately 70 percent of the map area. Additional data collection within the existing monitoring network of 260 wells and near selected well fields could reduce the error in individual months. Reducing the kriging error in other areas would require adding new monitoring wells. Potentiometric-surface elevations fluctuated by as much as 30 feet over the study period, and the spatially averaged elevation for the entire surface rose by about 2 feet over the decade. Monthly potentiometric-surface elevations describe the lateral groundwater flow patterns in the aquifer and are usable at a variety of spatial scales to describe vertical groundwater recharge and discharge conditions for overlying surface-water features.

Methods for developing time-series climate surfaces to drive topographically distributed energy- and water-balance models

USGS Publications Warehouse

Susong, D.; Marks, D.; Garen, D.

1999-01-01

Topographically distributed energy- and water-balance models can accurately simulate both the development and melting of a seasonal snowcover in the mountain basins. To do this they require time-series climate surfaces of air temperature, humidity, wind speed, precipitation, and solar and thermal radiation. If data are available, these parameters can be adequately estimated at time steps of one to three hours. Unfortunately, climate monitoring in mountain basins is very limited, and the full range of elevations and exposures that affect climate conditions, snow deposition, and melt is seldom sampled. Detailed time-series climate surfaces have been successfully developed using limited data and relatively simple methods. We present a synopsis of the tools and methods used to combine limited data with simple corrections for the topographic controls to generate high temporal resolution time-series images of these climate parameters. Methods used include simulations, elevational gradients, and detrended kriging. The generated climate surfaces are evaluated at points and spatially to determine if they are reasonable approximations of actual conditions. Recommendations are made for the addition of critical parameters and measurement sites into routine monitoring systems in mountain basins.Topographically distributed energy- and water-balance models can accurately simulate both the development and melting of a seasonal snowcover in the mountain basins. To do this they require time-series climate surfaces of air temperature, humidity, wind speed, precipitation, and solar and thermal radiation. If data are available, these parameters can be adequately estimated at time steps of one to three hours. Unfortunately, climate monitoring in mountain basins is very limited, and the full range of elevations and exposures that affect climate conditions, snow deposition, and melt is seldom sampled. Detailed time-series climate surfaces have been successfully developed using limited data and relatively simple methods. We present a synopsis of the tools and methods used to combine limited data with simple corrections for the topographic controls to generate high temporal resolution time-series images of these climate parameters. Methods used include simulations, elevational gradients, and detrended kriging. The generated climate surfaces are evaluated at points and spatially to determine if they are reasonable approximations of actual conditions. Recommendations are made for the addition of critical parameters and measurement sites into routine monitoring systems in mountain basins.

Spatiotemporal Interpolation for Environmental Modelling

PubMed Central

Susanto, Ferry; de Souza, Paulo; He, Jing

2016-01-01

A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications. PMID:27509497

Outlier identification in urban soils and its implications for identification of potential contaminated land

NASA Astrophysics Data System (ADS)

Zhang, Chaosheng

2010-05-01

Outliers in urban soil geochemical databases may imply potential contaminated land. Different methodologies which can be easily implemented for the identification of global and spatial outliers were applied for Pb concentrations in urban soils of Galway City in Ireland. Due to its strongly skewed probability feature, a Box-Cox transformation was performed prior to further analyses. The graphic methods of histogram and box-and-whisker plot were effective in identification of global outliers at the original scale of the dataset. Spatial outliers could be identified by a local indicator of spatial association of local Moran's I, cross-validation of kriging, and a geographically weighted regression. The spatial locations of outliers were visualised using a geographical information system. Different methods showed generally consistent results, but differences existed. It is suggested that outliers identified by statistical methods should be confirmed and justified using scientific knowledge before they are properly dealt with.

Multi-fidelity machine learning models for accurate bandgap predictions of solids

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

Pilania, Ghanshyam; Gubernatis, James E.; Lookman, Turab

Here, we present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. Additionally, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. In using a set of 600 elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of fidelities, we demonstrate the excellent learning performance of the method against actual high fidelitymore » quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.« less

Multi-fidelity machine learning models for accurate bandgap predictions of solids

DOE PAGES

Pilania, Ghanshyam; Gubernatis, James E.; Lookman, Turab

2016-12-28

Here, we present a multi-fidelity co-kriging statistical learning framework that combines variable-fidelity quantum mechanical calculations of bandgaps to generate a machine-learned model that enables low-cost accurate predictions of the bandgaps at the highest fidelity level. Additionally, the adopted Gaussian process regression formulation allows us to predict the underlying uncertainties as a measure of our confidence in the predictions. In using a set of 600 elpasolite compounds as an example dataset and using semi-local and hybrid exchange correlation functionals within density functional theory as two levels of fidelities, we demonstrate the excellent learning performance of the method against actual high fidelitymore » quantum mechanical calculations of the bandgaps. The presented statistical learning method is not restricted to bandgaps or electronic structure methods and extends the utility of high throughput property predictions in a significant way.« less

Efficient prediction designs for random fields.

PubMed

Müller, Werner G; Pronzato, Luc; Rendas, Joao; Waldl, Helmut

2015-03-01

For estimation and predictions of random fields, it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging (EK) are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the EK variance when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, whereas the second uses the surrogate criteria as local heuristic to choose the points at which the (costly) true EK variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset. © 2014 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.

Use of geostatistics to predict virus decay rates for determination of septic tank setback distances.

PubMed Central

Yates, M V; Yates, S R; Warrick, A W; Gerba, C P

1986-01-01

Water samples were collected from 71 public drinking-water supply wells in the Tucson, Ariz., basin. Virus decay rates in the water samples were determined with MS-2 coliphage as a model virus. The correlations between the virus decay rates and the sample locations were shown by fitting a spherical model to the experimental semivariogram. Kriging, a geostatistical technique, was used to calculate virus decay rates at unsampled locations by using the known values at nearby wells. Based on the regional characteristics of groundwater flow and the kriged estimates of virus decay rates, a contour map of the area was constructed. The map shows the variation in separation distances that would have to be maintained between wells and sources of contamination to afford similar degrees of protection from viral contamination of the drinking water in wells throughout the basin. PMID:3532954

Analysis of ICESat Data Using Kalman Filter and Kriging to Study Height Changes in East Antarctica

NASA Technical Reports Server (NTRS)

Herring, Thomas A.

2005-01-01

We analyze ICESat derived heights collected between Feb. 03-Nov. 04 using a kriging/Kalman filtering approach to investigate height changes in East Antarctica. The model's parameters are height change to an a priori static digital height model, seasonal signal expressed as an amplitude Beta and phase Theta, and height-change rate dh/dt for each (100 km)(exp 2) block. From the Kalman filter results, dh/dt has a mean of -0.06 m/yr in the flat interior of East Antarctica. Spatially correlated pointing errors in the current data releases give uncertainties in the range 0.06 m/yr, making height change detection unreliable at this time. Our test shows that when using all available data with pointing knowledge equivalent to that of Laser 2a, height change detection with an accuracy level 0.02 m/yr can be achieved over flat terrains in East Antarctica.

Lognormal kriging for the assessment of reliability in groundwater quality control observation networks

USGS Publications Warehouse

Candela, L.; Olea, R.A.; Custodio, E.

1988-01-01

Groundwater quality observation networks are examples of discontinuous sampling on variables presenting spatial continuity and highly skewed frequency distributions. Anywhere in the aquifer, lognormal kriging provides estimates of the variable being sampled and a standard error of the estimate. The average and the maximum standard error within the network can be used to dynamically improve the network sampling efficiency or find a design able to assure a given reliability level. The approach does not require the formulation of any physical model for the aquifer or any actual sampling of hypothetical configurations. A case study is presented using the network monitoring salty water intrusion into the Llobregat delta confined aquifer, Barcelona, Spain. The variable chloride concentration used to trace the intrusion exhibits sudden changes within short distances which make the standard error fairly invariable to changes in sampling pattern and to substantial fluctuations in the number of wells. ?? 1988.

Optimization and comparison of three spatial interpolation methods for electromagnetic levels in the AM band within an urban area.

PubMed

Rufo, Montaña; Antolín, Alicia; Paniagua, Jesús M; Jiménez, Antonio

2018-04-01

A comparative study was made of three methods of interpolation - inverse distance weighting (IDW), spline and ordinary kriging - after optimization of their characteristic parameters. These interpolation methods were used to represent the electric field levels for three emission frequencies (774kHz, 900kHz, and 1107kHz) and for the electrical stimulation quotient, Q E , characteristic of complex electromagnetic environments. Measurements were made with a spectrum analyser in a village in the vicinity of medium-wave radio broadcasting antennas. The accuracy of the models was quantified by comparing their predictions with levels measured at the control points not used to generate the models. The results showed that optimizing the characteristic parameters of each interpolation method allows any of them to be used. However, the best results in terms of the regression coefficient between each model's predictions and the actual control point field measurements were for the IDW method. Copyright © 2018 Elsevier Inc. All rights reserved.

Precipitation estimation in mountainous terrain using multivariate geostatistics. Part II: isohyetal maps

USGS Publications Warehouse

Hevesi, Joseph A.; Flint, Alan L.; Istok, Jonathan D.

1992-01-01

Values of average annual precipitation (AAP) may be important for hydrologic characterization of a potential high-level nuclear-waste repository site at Yucca Mountain, Nevada. Reliable measurements of AAP are sparse in the vicinity of Yucca Mountain, and estimates of AAP were needed for an isohyetal mapping over a 2600-square-mile watershed containing Yucca Mountain. Estimates were obtained with a multivariate geostatistical model developed using AAP and elevation data from a network of 42 precipitation stations in southern Nevada and southeastern California. An additional 1531 elevations were obtained to improve estimation accuracy. Isohyets representing estimates obtained using univariate geostatistics (kriging) defined a smooth and continuous surface. Isohyets representing estimates obtained using multivariate geostatistics (cokriging) defined an irregular surface that more accurately represented expected local orographic influences on AAP. Cokriging results included a maximum estimate within the study area of 335 mm at an elevation of 7400 ft, an average estimate of 157 mm for the study area, and an average estimate of 172 mm at eight locations in the vicinity of the potential repository site. Kriging estimates tended to be lower in comparison because the increased AAP expected for remote mountainous topography was not adequately represented by the available sample. Regression results between cokriging estimates and elevation were similar to regression results between measured AAP and elevation. The position of the cokriging 250-mm isohyet relative to the boundaries of pinyon pine and juniper woodlands provided indirect evidence of improved estimation accuracy because the cokriging result agreed well with investigations by others concerning the relationship between elevation, vegetation, and climate in the Great Basin. Calculated estimation variances were also mapped and compared to evaluate improvements in estimation accuracy. Cokriging estimation variances were reduced by an average of 54% relative to kriging variances within the study area. Cokriging reduced estimation variances at the potential repository site by 55% relative to kriging. The usefulness of an existing network of stations for measuring AAP within the study area was evaluated using cokriging variances, and twenty additional stations were located for the purpose of improving the accuracy of future isohyetal mappings. Using the expanded network of stations, the maximum cokriging estimation variance within the study area was reduced by 78% relative to the existing network, and the average estimation variance was reduced by 52%.

The Research on Elevation Change of Antarctic Ice Sheet Based on CRYOSAT-2 Alimeter

NASA Astrophysics Data System (ADS)

Sun, Q.; Wan, J.; Liu, S.; Li, Y.

2018-04-01

In this paper, the Cryosat-2 altimeter data distributed by the ESA, and these data are processed to extract the information of the elevation change of the Antarctic ice sheet from 2010 to 2017. Firstly, the main pretreatment preprocessing for Cryosat-2 altimetry data is crossover adjustment and elimination of rough difference. Then the grid DEM of the Antarctic ice sheet was constructed by using the kriging interpolation method,and analyzed the spatial characteristic time characteristics of the Antarctic ice sheet. The latitude-weighted elevation can be obtained by using the elevation data of each cycle, and then the general trend of the Antarctic ice sheet elevation variation can be seen roughly.

Cross-comparison and evaluation of air pollution field estimation methods

NASA Astrophysics Data System (ADS)

Yu, Haofei; Russell, Armistead; Mulholland, James; Odman, Talat; Hu, Yongtao; Chang, Howard H.; Kumar, Naresh

2018-04-01

Accurate estimates of human exposure is critical for air pollution health studies and a variety of methods are currently being used to assign pollutant concentrations to populations. Results from these methods may differ substantially, which can affect the outcomes of health impact assessments. Here, we applied 14 methods for developing spatiotemporal air pollutant concentration fields of eight pollutants to the Atlanta, Georgia region. These methods include eight methods relying mostly on air quality observations (CM: central monitor; SA: spatial average; IDW: inverse distance weighting; KRIG: kriging; TESS-D: discontinuous tessellation; TESS-NN: natural neighbor tessellation with interpolation; LUR: land use regression; AOD: downscaled satellite-derived aerosol optical depth), one using the RLINE dispersion model, and five methods using a chemical transport model (CMAQ), with and without using observational data to constrain results. The derived fields were evaluated and compared. Overall, all methods generally perform better at urban than rural area, and for secondary than primary pollutants. We found the CM and SA methods may be appropriate only for small domains, and for secondary pollutants, though the SA method lead to large negative spatial correlations when using data withholding for PM2.5 (spatial correlation coefficient R = -0.81). The TESS-D method was found to have major limitations. Results of the IDW, KRIG and TESS-NN methods are similar. They are found to be better suited for secondary pollutants because of their satisfactory temporal performance (e.g. average temporal R2 > 0.85 for PM2.5 but less than 0.35 for primary pollutant NO2). In addition, they are suitable for areas with relatively dense monitoring networks due to their inability to capture spatial concentration variabilities, as indicated by the negative spatial R (lower than -0.2 for PM2.5 when assessed using data withholding). The performance of LUR and AOD methods were similar to kriging. Using RLINE and CMAQ fields without fusing observational data led to substantial errors and biases, though the CMAQ model captured spatial gradients reasonably well (spatial R = 0.45 for PM2.5). Two unique tests conducted here included quantifying autocorrelation of method biases (which can be important in time series analyses) and how well the methods capture the observed interspecies correlations (which would be of particular importance in multipollutant health assessments). Autocorrelation of method biases lasted longest and interspecies correlations of primary pollutants was higher than observations when air quality models were used without data fusing. Use of hybrid methods that combine air quality model outputs with observational data overcome some of these limitations and is better suited for health studies. Results from this study contribute to better understanding the strengths and weaknesses of different methods for estimating human exposures.

POLLUTION MONITORING OF PUGET SOUND WITH HONEY BEES

EPA Science Inventory

To show that honey bees are effective biological monitors of environmental contaminants over large geographic areas, beekeepers of Puget Sound, Washington, collected pollen and bees for chemical analysis. From these data, kriging maps of arsenic, cadmium, and fluoride were genera...

Uncertainty quantification-based robust aerodynamic optimization of laminar flow nacelle

NASA Astrophysics Data System (ADS)

Xiong, Neng; Tao, Yang; Liu, Zhiyong; Lin, Jun

2018-05-01

The aerodynamic performance of laminar flow nacelle is highly sensitive to uncertain working conditions, especially the surface roughness. An efficient robust aerodynamic optimization method on the basis of non-deterministic computational fluid dynamic (CFD) simulation and Efficient Global Optimization (EGO)algorithm was employed. A non-intrusive polynomial chaos method is used in conjunction with an existing well-verified CFD module to quantify the uncertainty propagation in the flow field. This paper investigates the roughness modeling behavior with the γ-Ret shear stress transport model including modeling flow transition and surface roughness effects. The roughness effects are modeled to simulate sand grain roughness. A Class-Shape Transformation-based parametrical description of the nacelle contour as part of an automatic design evaluation process is presented. A Design-of-Experiments (DoE) was performed and surrogate model by Kriging method was built. The new design nacelle process demonstrates that significant improvements of both mean and variance of the efficiency are achieved and the proposed method can be applied to laminar flow nacelle design successfully.

Prediction of conformationally dependent atomic multipole moments in carbohydrates

PubMed Central

Cardamone, Salvatore

2015-01-01

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol−1 for open chains and just over 90% an error of maximum 4 kJ mol−1 for rings. © 2015 Wiley Periodicals, Inc. PMID:26547500

Prediction of conformationally dependent atomic multipole moments in carbohydrates.

PubMed

Cardamone, Salvatore; Popelier, Paul L A

2015-12-15

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an "atom in a molecule," thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol(-1) for open chains and just over 90% an error of maximum 4 kJ mol(-1) for rings. © 2015 Wiley Periodicals, Inc.

Factorial Kriging analysis and sources of heavy metals in soils of different land-use types in the Yangtze River Delta of Eastern China.

PubMed

Zhou, Jie; Feng, Ke; Li, Yinju; Zhou, Yang

2016-08-01

The objectives of this study are to analyse the pollution status and spatial correlation of soil heavy metals and identify natural and anthropogenic sources of these heavy metals at different spatial scales. Two hundred and twenty-four soil samples (0-20 cm) were collected and analysed for eight heavy metals (Cd, Hg, As, Cu, Pb, Cr, Zn and Ni) in soils of different land-use types in the Yangtze River Delta of Eastern China. The multivariate methods and factorial Kriging analysis were used to achieve the research objectives. The results indicated that the human and natural effects of different land-use types on the contents of soil heavy metals were different. The Cd, Hg, Cu, Pb and Zn in soils of industrial area were affected by human activities, and the pollution level of these heavy metals in this area was moderate. The Pb in soils of traffic area was affected by human activities, and eight heavy metals in soils of residential area and farmland area were affected by natural factor. The ecological risk status of eight heavy metals in soils of the whole study area was light. The heavy metals in soils showed three spatial scales (nugget effect, short range and long range). At the nugget effect and short range scales, the Cd, Hg, Cu, Pb and Zn in soils were affected by human and natural factors. At three spatial scales, the As, Cr and Ni in soils were affected by soil parent materials.

Assessment of spatial distribution of fallout radionuclides through geostatistics concept.

PubMed

Mabit, L; Bernard, C

2007-01-01

After introducing geostatistics concept and its utility in environmental science and especially in Fallout Radionuclide (FRN) spatialisation, a case study for cesium-137 ((137)Cs) redistribution at the field scale using geostatistics is presented. On a Canadian agricultural field, geostatistics coupled with a Geographic Information System (GIS) was used to test three different techniques of interpolation [Ordinary Kriging (OK), Inverse Distance Weighting power one (IDW1) and two (IDW2)] to create a (137)Cs map and to establish a radioisotope budget. Following the optimization of variographic parameters, an experimental semivariogram was developed to determine the spatial dependence of (137)Cs. It was adjusted to a spherical isotropic model with a range of 30 m and a very small nugget effect. This (137)Cs semivariogram showed a good autocorrelation (R(2)=0.91) and was well structured ('nugget-to-sill' ratio of 4%). It also revealed that the sampling strategy was adequate to reveal the spatial correlation of (137)Cs. The spatial redistribution of (137)Cs was estimated by Ordinary Kriging and IDW to produce contour maps. A radioisotope budget was established for the 2.16 ha agricultural field under investigation. It was estimated that around 2 x 10(7)Bq of (137)Cs were missing (around 30% of the total initial fallout) and were exported by physical processes (runoff and erosion processes) from the area under investigation. The cross-validation analysis showed that in the case of spatially structured data, OK is a better interpolation method than IDW1 or IDW2 for the assessment of potential radioactive contamination and/or pollution.

Heavy Metal Pollution Delineation Based on Uncertainty in a Coastal Industrial City in the Yangtze River Delta, China

PubMed Central

Zhao, Ruiying; Chen, Songchao; Zhou, Yue; Jin, Bin; Li, Yan

2018-01-01

Assessing heavy metal pollution and delineating pollution are the bases for evaluating pollution and determining a cost-effective remediation plan. Most existing studies are based on the spatial distribution of pollutants but ignore related uncertainty. In this study, eight heavy-metal concentrations (Cr, Pb, Cd, Hg, Zn, Cu, Ni, and Zn) were collected at 1040 sampling sites in a coastal industrial city in the Yangtze River Delta, China. The single pollution index (PI) and Nemerow integrated pollution index (NIPI) were calculated for every surface sample (0–20 cm) to assess the degree of heavy metal pollution. Ordinary kriging (OK) was used to map the spatial distribution of heavy metals content and NIPI. Then, we delineated composite heavy metal contamination based on the uncertainty produced by indicator kriging (IK). The results showed that mean values of all PIs and NIPIs were at safe levels. Heavy metals were most accumulated in the central portion of the study area. Based on IK, the spatial probability of composite heavy metal pollution was computed. The probability of composite contamination in the central core urban area was highest. A probability of 0.6 was found as the optimum probability threshold to delineate polluted areas from unpolluted areas for integrative heavy metal contamination. Results of pollution delineation based on uncertainty showed the proportion of false negative error areas was 6.34%, while the proportion of false positive error areas was 0.86%. The accuracy of the classification was 92.80%. This indicated the method we developed is a valuable tool for delineating heavy metal pollution. PMID:29642623

A new strategy for developing Vs30 maps

USGS Publications Warehouse

Wald, David J.; McWhirter, Leslie; Thompson, Eric; Hering, Amanda S.

2011-01-01

Despite obvious limitations as a proxy for site amplification, the use of time-averaged shear-wave velocity over the top 30m (Vs30) is useful and widely practiced, most notably through its use as an explanatory variable in ground motion prediction equations (and thus hazard maps and ShakeMaps, among other applications). Local, regional, and global Vs30 maps thus have diverse and fundamental uses in earthquake and engineering seismology. As such, we are developing an improved strategy for producing Vs30 maps given the common observational constraints available in any region for various spatial scales. We investigate a hierarchical approach to mapping Vs30, where the baseline model is derived from topographic slope because it is available globally, but geological maps and Vs30 observations contribute, where available. Using the abundant measured Vs30 values in Taiwan as an example, we analyze Vs30 versus slope per geologic unit and observe minor trends that indicate potential interaction of geologic and slope terms. We then regress Vs30 for the geologic Vs30 medians, topographic-slope, and cross-term coefficients for a hybrid model. The residuals of this hybrid model still exhibit a strong spatial correlation structure, so we use the kriging-with-a-trend method (the trend is the hybrid model) to further refine the Vs30 map so as to honor the Vs30 observations. Unlike the geology or slope models alone, this strategytakes advantage of the predictive capabilities of the two models, yet effectively defaults to ordinary kriging in the vicinity of the observed data, thereby achieving consistency with the observed data.

Heavy Metal Pollution Delineation Based on Uncertainty in a Coastal Industrial City in the Yangtze River Delta, China.

PubMed

Hu, Bifeng; Zhao, Ruiying; Chen, Songchao; Zhou, Yue; Jin, Bin; Li, Yan; Shi, Zhou

2018-04-10

Assessing heavy metal pollution and delineating pollution are the bases for evaluating pollution and determining a cost-effective remediation plan. Most existing studies are based on the spatial distribution of pollutants but ignore related uncertainty. In this study, eight heavy-metal concentrations (Cr, Pb, Cd, Hg, Zn, Cu, Ni, and Zn) were collected at 1040 sampling sites in a coastal industrial city in the Yangtze River Delta, China. The single pollution index (PI) and Nemerow integrated pollution index (NIPI) were calculated for every surface sample (0-20 cm) to assess the degree of heavy metal pollution. Ordinary kriging (OK) was used to map the spatial distribution of heavy metals content and NIPI. Then, we delineated composite heavy metal contamination based on the uncertainty produced by indicator kriging (IK). The results showed that mean values of all PIs and NIPIs were at safe levels. Heavy metals were most accumulated in the central portion of the study area. Based on IK, the spatial probability of composite heavy metal pollution was computed. The probability of composite contamination in the central core urban area was highest. A probability of 0.6 was found as the optimum probability threshold to delineate polluted areas from unpolluted areas for integrative heavy metal contamination. Results of pollution delineation based on uncertainty showed the proportion of false negative error areas was 6.34%, while the proportion of false positive error areas was 0.86%. The accuracy of the classification was 92.80%. This indicated the method we developed is a valuable tool for delineating heavy metal pollution.

A practical primer on geostatistics

USGS Publications Warehouse

Olea, Ricardo A.

2009-01-01

The Challenge—Most geological phenomena are extraordinarily complex in their interrelationships and vast in their geographical extension. Ordinarily, engineers and geoscientists are faced with corporate or scientific requirements to properly prepare geological models with measurements involving a small fraction of the entire area or volume of interest. Exact description of a system such as an oil reservoir is neither feasible nor economically possible. The results are necessarily uncertain. Note that the uncertainty is not an intrinsic property of the systems; it is the result of incomplete knowledge by the observer.The Aim of Geostatistics—The main objective of geostatistics is the characterization of spatial systems that are incompletely known, systems that are common in geology. A key difference from classical statistics is that geostatistics uses the sampling location of every measurement. Unless the measurements show spatial correlation, the application of geostatistics is pointless. Ordinarily the need for additional knowledge goes beyond a few points, which explains the display of results graphically as fishnet plots, block diagrams, and maps.Geostatistical Methods—Geostatistics is a collection of numerical techniques for the characterization of spatial attributes using primarily two tools: probabilistic models, which are used for spatial data in a manner similar to the way in which time-series analysis characterizes temporal data, or pattern recognition techniques. The probabilistic models are used as a way to handle uncertainty in results away from sampling locations, making a radical departure from alternative approaches like inverse distance estimation methods.Differences with Time Series—On dealing with time-series analysis, users frequently concentrate their attention on extrapolations for making forecasts. Although users of geostatistics may be interested in extrapolation, the methods work at their best interpolating. This simple difference has significant methodological implications.Historical Remarks—As a discipline, geostatistics was firmly established in the 1960s by the French engineer Georges Matheron, who was interested in the appraisal of ore reserves in mining. Geostatistics did not develop overnight. Like other disciplines, it has built on previous results, many of which were formulated with different objectives in various fields.Pioneers—Seminal ideas conceptually related to what today we call geostatistics or spatial statistics are found in the work of several pioneers, including: 1940s: A.N. Kolmogorov in turbulent flow and N. Wiener in stochastic processing; 1950s: D. Krige in mining; 1960s: B. Mathern in forestry and L.S. Gandin in meteorologyCalculations—Serious applications of geostatistics require the use of digital computers. Although for most geostatistical techniques rudimentary implementation from scratch is fairly straightforward, coding programs from scratch is recommended only as part of a practice that may help users to gain a better grasp of the formulations.Software—For professional work, the reader should employ software packages that have been thoroughly tested to handle any sampling scheme, that run as efficiently as possible, and that offer graphic capabilities for the analysis and display of results. This primer employs primarily the package Stanford Geomodeling Software (SGeMS) - recently developed at the Energy Resources Engineering Department at Stanford University - as a way to show how to obtain results practically. This applied side of the primer should not be interpreted as the notes being a manual for the use of SGeMS. The main objective of the primer is to help the reader gain an understanding of the fundamental concepts and tools in geostatistics.Organization of the Primer—The chapters of greatest importance are those covering kriging and simulation. All other materials are peripheral and are included for better comprehension of these main geostatistical modeling tools. The choice of kriging versus simulation is often a big puzzle to the uninitiated, let alone the different variants of both of them. Chapters 14, 18, and 19 are intended to shed light on those subjects. The critical aspect of assessing and modeling spatial correlation is covered in chapter 7. Chapters 2 and 3 review relevant concepts in classical statistics.Course Objectives—This course offers stochastic solutions to common problems in the characterization of complex geological systems. At the end of the course, participants should have: an understanding of the theoretical foundations of geostatistics; a good grasp of its possibilities and limitations; and reasonable familiarity with the SGeMS software, thus opening the possibility of practically applying geostatistics.

Multivariate Analysis and Modeling of Sediment Pollution Using Neural Network Models and Geostatistics

NASA Astrophysics Data System (ADS)

Golay, Jean; Kanevski, Mikhaïl

2013-04-01

The present research deals with the exploration and modeling of a complex dataset of 200 measurement points of sediment pollution by heavy metals in Lake Geneva. The fundamental idea was to use multivariate Artificial Neural Networks (ANN) along with geostatistical models and tools in order to improve the accuracy and the interpretability of data modeling. The results obtained with ANN were compared to those of traditional geostatistical algorithms like ordinary (co)kriging and (co)kriging with an external drift. Exploratory data analysis highlighted a great variety of relationships (i.e. linear, non-linear, independence) between the 11 variables of the dataset (i.e. Cadmium, Mercury, Zinc, Copper, Titanium, Chromium, Vanadium and Nickel as well as the spatial coordinates of the measurement points and their depth). Then, exploratory spatial data analysis (i.e. anisotropic variography, local spatial correlations and moving window statistics) was carried out. It was shown that the different phenomena to be modeled were characterized by high spatial anisotropies, complex spatial correlation structures and heteroscedasticity. A feature selection procedure based on General Regression Neural Networks (GRNN) was also applied to create subsets of variables enabling to improve the predictions during the modeling phase. The basic modeling was conducted using a Multilayer Perceptron (MLP) which is a workhorse of ANN. MLP models are robust and highly flexible tools which can incorporate in a nonlinear manner different kind of high-dimensional information. In the present research, the input layer was made of either two (spatial coordinates) or three neurons (when depth as auxiliary information could possibly capture an underlying trend) and the output layer was composed of one (univariate MLP) to eight neurons corresponding to the heavy metals of the dataset (multivariate MLP). MLP models with three input neurons can be referred to as Artificial Neural Networks with EXternal drift (ANNEX). Moreover, the exact number of output neurons and the selection of the corresponding variables were based on the subsets created during the exploratory phase. Concerning hidden layers, no restriction were made and multiple architectures were tested. For each MLP model, the quality of the modeling procedure was assessed by variograms: if the variogram of the residuals demonstrates pure nugget effect and if the level of the nugget exactly corresponds to the nugget value of the theoretical variogram of the corresponding variable, all the structured information has been correctly extracted without overfitting. Finally, it is worth mentioning that simple MLP models are not always able to remove all the spatial correlation structure from the data. In that case, Neural Network Residual Kriging (NNRK) can be carried out and risk assessment can be conducted with Neural Network Residual Simulations (NNRS). Finally, the results of the ANNEX models were compared to those of ordinary (co)kriging and (co)kriging with an external drift. It was shown that the ANNEX models performed better than traditional geostatistical algorithms when the relationship between the variable of interest and the auxiliary predictor was not linear. References Kanevski, M. and Maignan, M. (2004). Analysis and Modelling of Spatial Environmental Data. Lausanne: EPFL Press.

Tradespace Exploration for the Engineering of Resilient Systems

DTIC Science & Technology

2015-05-01

world scenarios. The types of tools within the SAE set include visualization, decision analysis, and M&S, so it is difficult to categorize this toolset... overpopulated , or questionable. ERS Tradespace Workshop Create predictive models using multiple techniques (e.g., regression, Kriging, neural nets

A new Hessian - based approach for segmentation of CT porous media images

NASA Astrophysics Data System (ADS)

Timofey, Sizonenko; Marina, Karsanina; Dina, Gilyazetdinova; Kirill, Gerke

2017-04-01

Hessian matrix based methods are widely used in image analysis for features detection, e.g., detection of blobs, corners and edges. Hessian matrix of the imageis the matrix of 2nd order derivate around selected voxel. Most significant features give highest values of Hessian transform and lowest values are located at smoother parts of the image. Majority of conventional segmentation techniques can segment out cracks, fractures and other inhomogeneities in soils and rocks only if the rest of the image is significantly "oversigmented". To avoid this disadvantage, we propose to enhance greyscale values of voxels belonging to such specific inhomogeneities on X-ray microtomography scans. We have developed and implemented in code a two-step approach to attack the aforementioned problem. During the first step we apply a filter that enhances the image and makes outstanding features more sharply defined. During the second step we apply Hessian filter based segmentation. The values of voxels on the image to be segmented are calculated in conjunction with the values of other voxels within prescribed region. Contribution from each voxel within such region is computed by weighting according to the local Hessian matrix value. We call this approach as Hessian windowed segmentation. Hessian windowed segmentation has been tested on different porous media X-ray microtomography images, including soil, sandstones, carbonates and shales. We also compared this new method against others widely used methods such as kriging, Markov random field, converging active contours and region grow. We show that our approach is more accurate in regions containing special features such as small cracks, fractures, elongated inhomogeneities and other features with low contrast related to the background solid phase. Moreover, Hessian windowed segmentation outperforms some of these methods in computational efficiency. We further test our segmentation technique by computing permeability of segmented images and comparing them against laboratory based measurements. This work was partially supported by RFBR grant 15-34-20989 (X-ray tomography and image fusion) and RSF grant 14-17-00658 (image segmentation and pore-scale modelling).

Combined Estimation of Hydrogeologic Conceptual Model and Parameter Uncertainty

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

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

2004-03-01

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

Assessment of outdoor radiofrequency electromagnetic field exposure through hotspot localization using kriging-based sequential sampling.

PubMed

Aerts, Sam; Deschrijver, Dirk; Verloock, Leen; Dhaene, Tom; Martens, Luc; Joseph, Wout

2013-10-01

In this study, a novel methodology is proposed to create heat maps that accurately pinpoint the outdoor locations with elevated exposure to radiofrequency electromagnetic fields (RF-EMF) in an extensive urban region (or, hotspots), and that would allow local authorities and epidemiologists to efficiently assess the locations and spectral composition of these hotspots, while at the same time developing a global picture of the exposure in the area. Moreover, no prior knowledge about the presence of radiofrequency radiation sources (e.g., base station parameters) is required. After building a surrogate model from the available data using kriging, the proposed method makes use of an iterative sampling strategy that selects new measurement locations at spots which are deemed to contain the most valuable information-inside hotspots or in search of them-based on the prediction uncertainty of the model. The method was tested and validated in an urban subarea of Ghent, Belgium with a size of approximately 1 km2. In total, 600 input and 50 validation measurements were performed using a broadband probe. Five hotspots were discovered and assessed, with maximum total electric-field strengths ranging from 1.3 to 3.1 V/m, satisfying the reference levels issued by the International Commission on Non-Ionizing Radiation Protection for exposure of the general public to RF-EMF. Spectrum analyzer measurements in these hotspots revealed five radiofrequency signals with a relevant contribution to the exposure. The radiofrequency radiation emitted by 900 MHz Global System for Mobile Communications (GSM) base stations was always dominant, with contributions ranging from 45% to 100%. Finally, validation of the subsequent surrogate models shows high prediction accuracy, with the final model featuring an average relative error of less than 2dB (factor 1.26 in electric-field strength), a correlation coefficient of 0.7, and a specificity of 0.96. Copyright © 2013 Elsevier Inc. All rights reserved.

Spatial analysis of soil organic carbon in Zhifanggou catchment of the Loess Plateau.

PubMed

Li, Mingming; Zhang, Xingchang; Zhen, Qing; Han, Fengpeng

2013-01-01

Soil organic carbon (SOC) reflects soil quality and plays a critical role in soil protection, food safety, and global climate changes. This study involved grid sampling at different depths (6 layers) between 0 and 100 cm in a catchment. A total of 1282 soil samples were collected from 215 plots over 8.27 km(2). A combination of conventional analytical methods and geostatistical methods were used to analyze the data for spatial variability and soil carbon content patterns. The mean SOC content in the 1282 samples from the study field was 3.08 g · kg(-1). The SOC content of each layer decreased with increasing soil depth by a power function relationship. The SOC content of each layer was moderately variable and followed a lognormal distribution. The semi-variograms of the SOC contents of the six different layers were fit with the following models: exponential, spherical, exponential, Gaussian, exponential, and exponential, respectively. A moderate spatial dependence was observed in the 0-10 and 10-20 cm layers, which resulted from stochastic and structural factors. The spatial distribution of SOC content in the four layers between 20 and 100 cm exhibit were mainly restricted by structural factors. Correlations within each layer were observed between 234 and 562 m. A classical Kriging interpolation was used to directly visualize the spatial distribution of SOC in the catchment. The variability in spatial distribution was related to topography, land use type, and human activity. Finally, the vertical distribution of SOC decreased. Our results suggest that the ordinary Kriging interpolation can directly reveal the spatial distribution of SOC and the sample distance about this study is sufficient for interpolation or plotting. More research is needed, however, to clarify the spatial variability on the bigger scale and better understand the factors controlling spatial variability of soil carbon in the Loess Plateau region.

Optimizing a Sensor Network with Data from Hazard Mapping Demonstrated in a Heavy-Vehicle Manufacturing Facility.

PubMed

Berman, Jesse D; Peters, Thomas M; Koehler, Kirsten A

2018-05-28

To design a method that uses preliminary hazard mapping data to optimize the number and location of sensors within a network for a long-term assessment of occupational concentrations, while preserving temporal variability, accuracy, and precision of predicted hazards. Particle number concentrations (PNCs) and respirable mass concentrations (RMCs) were measured with direct-reading instruments in a large heavy-vehicle manufacturing facility at 80-82 locations during 7 mapping events, stratified by day and season. Using kriged hazard mapping, a statistical approach identified optimal orders for removing locations to capture temporal variability and high prediction precision of PNC and RMC concentrations. We compared optimal-removal, random-removal, and least-optimal-removal orders to bound prediction performance. The temporal variability of PNC was found to be higher than RMC with low correlation between the two particulate metrics (ρ = 0.30). Optimal-removal orders resulted in more accurate PNC kriged estimates (root mean square error [RMSE] = 49.2) at sample locations compared with random-removal order (RMSE = 55.7). For estimates at locations having concentrations in the upper 10th percentile, the optimal-removal order preserved average estimated concentrations better than random- or least-optimal-removal orders (P < 0.01). However, estimated average concentrations using an optimal-removal were not statistically different than random-removal when averaged over the entire facility. No statistical difference was observed for optimal- and random-removal methods for RMCs that were less variable in time and space than PNCs. Optimized removal performed better than random-removal in preserving high temporal variability and accuracy of hazard map for PNC, but not for the more spatially homogeneous RMC. These results can be used to reduce the number of locations used in a network of static sensors for long-term monitoring of hazards in the workplace, without sacrificing prediction performance.

Mathematical modelling of ionospheric TEC from Turkish permanent GNSS Network (TPGN) observables during 2009-2017 and predictability of NeQuick and Kriging models

NASA Astrophysics Data System (ADS)

Ansari, Kutubuddin; Panda, Sampad Kumar; Corumluoglu, Ozsen

2018-03-01

The present study examines the ionospheric Total Electron Content (TEC) variations in the lower mid-latitude Turkish region from the Turkish permanent GNSS network (TPGN) and International GNSS Services (IGS) observations during the years 2009 to 2017. The corresponding vertical TEC (VTEC) predicted by Kriging and NeQuick-2 models are evaluated to realize their efficacy over the country. We studied the diurnal, seasonal and spatial pattern of VTEC variation and tried to estimate by a new mathematical model using the long term of 9 years VTEC data. The diurnal variation of VTEC demonstrates a normal trend with its gradual enhancement from dawn to attain a peak around 09:00-14.00 UT and reaching the minimum level after 22.00 UT. The seasonal behavior of VTEC indicates a strong semi-annual variation of VTEC with maxima in September equinox followed by March equinox and minima in June solstice followed by December solstice. Also, the spatial variation in VTEC depicts a meaningful longitudinal/latitudinal pattern altering with seasons. It decreases longitudinally from the west to the east during March equinox and June solstice increases with latitude. The comparative analysis among the GNSS-VTEC, Kriging, NeQuick and the proposed mathematical model are evaluated with the help one way ANOVA test. The analysis shows that the null hypothesis of the models during storm and quiet days are accepted and suggesting that all models are statistically significantly equivalent from each other. We believe the outcomes from this study would complement towards a relatively better understanding of the lower mid-latitude VTEC variation over the Turkish region and analogous latitudes over the globe.

Comparing Approaches to Deal With Non-Gaussianity of Rainfall Data in Kriging-Based Radar-Gauge Rainfall Merging

NASA Astrophysics Data System (ADS)

Cecinati, F.; Wani, O.; Rico-Ramirez, M. A.

2017-11-01

Merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of Kriging with External Drift (KED) is a very effective radar-rain gauge rainfall merging technique. However, kriging interpolations assume Gaussianity of the process. Rainfall has a strongly skewed, positive, probability distribution, characterized by a discontinuity due to intermittency. In KED rainfall residuals are used, implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates. Rainfall residuals are non-Gaussian as well. The aim of this work is to evaluate the impact of applying KED to non-Gaussian rainfall residuals, and to assess the best techniques to improve Gaussianity. We compare Box-Cox transformations with λ parameters equal to 0.5, 0.25, and 0.1, Box-Cox with time-variant optimization of λ, normal score transformation, and a singularity analysis technique. The results suggest that Box-Cox with λ = 0.1 and the singularity analysis is not suitable for KED. Normal score transformation and Box-Cox with optimized λ, or λ = 0.25 produce satisfactory results in terms of Gaussianity of the residuals, probability distribution of the merged rainfall products, and rainfall estimate quality, when validated through cross-validation. However, it is observed that Box-Cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity. Overall, applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific data set are used.

On the use of posterior predictive probabilities and prediction uncertainty to tailor informative sampling for parasitological surveillance in livestock.

PubMed

Musella, Vincenzo; Rinaldi, Laura; Lagazio, Corrado; Cringoli, Giuseppe; Biggeri, Annibale; Catelan, Dolores

2014-09-15

Model-based geostatistics and Bayesian approaches are appropriate in the context of Veterinary Epidemiology when point data have been collected by valid study designs. The aim is to predict a continuous infection risk surface. Little work has been done on the use of predictive infection probabilities at farm unit level. In this paper we show how to use predictive infection probability and related uncertainty from a Bayesian kriging model to draw a informative samples from the 8794 geo-referenced sheep farms of the Campania region (southern Italy). Parasitological data come from a first cross-sectional survey carried out to study the spatial distribution of selected helminths in sheep farms. A grid sampling was performed to select the farms for coprological examinations. Faecal samples were collected for 121 sheep farms and the presence of 21 different helminths were investigated using the FLOTAC technique. The 21 responses are very different in terms of geographical distribution and prevalence of infection. The observed prevalence range is from 0.83% to 96.69%. The distributions of the posterior predictive probabilities for all the 21 parasites are very heterogeneous. We show how the results of the Bayesian kriging model can be used to plan a second wave survey. Several alternatives can be chosen depending on the purposes of the second survey: weight by posterior predictive probabilities, their uncertainty or combining both information. The proposed Bayesian kriging model is simple, and the proposed samping strategy represents a useful tool to address targeted infection control treatments and surbveillance campaigns. It is easily extendable to other fields of research. Copyright © 2014 Elsevier B.V. All rights reserved.

Rtop - an R package for interpolation along the stream network

NASA Astrophysics Data System (ADS)

Skøien, J. O.; Laaha, G.; Koffler, D.; Blöschl, G.; Pebesma, E.; Parajka, J.; Viglione, A.

2012-04-01

Geostatistical methods have a long tradition within analysis of data that can be conceptualized as simple point data, such as soil properties, or for regular blocks, such as mining data. However, these methods have been used to a limited extent for estimation along stream networks. A few exceptions are given by (Gottschalk 1993, Sauquet et al. 2000, Gottschalk et al. 2006, Skøien et al. 2006), and an overview by Laaha and Blöschl (2011). Interpolation of runoff characteristics are more complicated than the traditional random variables estimated by geostatistical methods, as the measurements have a more complicated support, and many catchments are nested. Skøien et al. (2006) presented the model Top-kriging which takes these effects into account for interpolation of stream flow characteristics (exemplified by the 100 year flood). The method has here been implemented as a package in the open source statistical environment R (R Development Core Team 2011). Taking advantage of the existing methods in R for working with spatial objects, and the extensive possibilities for visualizing the result, this makes it considerably easier to apply the method on new data sets, in comparison to earlier implementation of the method. In addition to user feedback, the package has also been tested by colleagues whose only responsibility has been to search for bugs, inconsistencies and shortcomings of the documentation. The last part is often the part that gets the least attention in small open source projects, and we have solved this by acknowledging their effects as co-authors. The model will soon be uploaded to CRAN, but is in the meantime also available from R-forge and can be installed by: > install.packages("rtop", repos="http://R-Forge.R-project.org") Gottschalk, L., 1993. Interpolation of runoff applying objective methods. Stochastic Hydrology and Hydraulics, 7, 269-281. Gottschalk, L., Krasovskaia, I., Leblois, E. & Sauquet, E., 2006. Mapping mean and variance of runoff in a river basin. Hydrology and Earth System Sciences, 10, 469-484. Laaha, G. & Blöschl, G. 2011. Geostatistics on river networks - a reviewed. EGU General Assembly, Vienna, Austria. R Development Core Team, 2011. R: A language and environment for statistical computing. Vienna, Austria, ISBN 3-900051-07-0. Sauquet, E., Gottschalk, L. & Leblois, E., 2000. Mapping average annual runoff: A hierarchical approach applying a stochastic interpolation scheme. Hydrological Sciences Journal, 45 (6), 799-815. Skøien, J.O., Merz, R. & Blöschl, G., 2006. Top-kriging - geostatistics on stream networks. Hydrology and Earth System Sciences, 10, 277-287.

Hazardous air pollutants and childhood lymphohematopoietic cancer in Southeast Texas, 1995--2004

NASA Astrophysics Data System (ADS)

Whitworth, Kristina Walker

Southeast Texas, including Houston, has a large presence of industrial facilities and has been documented to have poorer air quality and significantly higher cancer rates than the remainder of Texas. Given citizens' concerns in this 4th largest city in the U.S., Mayor Bill White recently partnered with the UT School of Public Health to determine methods to evaluate the health risks of hazardous air pollutants (HAPs). Sexton et al. (2007) published a report that strongly encouraged analytic studies linking these pollutants with health outcomes. In response, we set out to complete the following aims: 1. determine the optimal exposure assessment strategy to assess the association between childhood cancer rates and increased ambient levels of benzene and 1,3-butadiene (in an ecologic setting) and 2. evaluate whether census tracts with the highest levels of benzene or 1,3-butadiene have higher incidence of childhood lymphohematopoietic cancer compared with census tracts with the lowest levels of benzene or 1,3-butadiene, using Poisson regression. The first aim was achieved by evaluating the usefulness of four data sources: geographic information systems (GIS) to identify proximity to point sources of industrial air pollution, industrial emission data from the U.S. EPA's Toxic Release Inventory (TRI), routine monitoring data from the U.S. EPA Air Quality System (AQS) from 1999-2000 and modeled ambient air levels from the U.S. EPA's 1999 National Air Toxic Assessment Project (NATA) ASPEN model. Further, once these four data sources were evaluated, we narrowed them down to two: the routine monitoring data from the AQS for the years 1998-2000 and the 1999 U.S. EPA NATA ASPEN modeled data. We applied kriging (spatial interpolation) methodology to the monitoring data and compared the kriged values to the ASPEN modeled data. Our results indicated poor agreement between the two methods. Relative to the U.S. EPA ASPEN modeled estimates, relying on kriging to classify census tracts into exposure groups would have caused a great deal of misclassification. To address the second aim, we additionally obtained childhood lymphohematopoietic cancer data for 1995-2004 from the Texas Cancer Registry. The U.S. EPA ASPEN modeled data were used to estimate ambient levels of benzene and 1,3-butadiene in separate Poisson regression analyses. All data were analyzed at the census tract level. We found that census tracts with the highest benzene levels had elevated rates of all leukemia (rate ratio (RR) = 1.37; 95% confidence interval (CI), 1.05-1.78). Among census tracts with the highest 1,3-butadiene levels, we observed RRs of 1.40 (95% CI, 1.07-1.81) for all leukemia. We detected no associations between benzene or 1,3-butadiene levels and childhood lymphoma incidence. This study is the first to examine this association in Harris and surrounding counties in Texas and is among the first to correlate monitored levels of HAPs with childhood lymphohematopoietic cancer incidence, evaluating several analytic methods in an effort to determine the most appropriate approach to test this association. Despite recognized weakness of ecologic analyses, our analysis suggests an association between childhood leukemia and hazardous air pollution.

Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results

NASA Astrophysics Data System (ADS)

Chebbi, A.; Bargaoui, Z. K.; da Conceição Cunha, M.

2012-12-01

Based on rainfall intensity-duration-frequency (IDF) curves, a robust optimization approach is proposed to identify the best locations to install new rain gauges. The advantage of robust optimization is that the resulting design solutions yield networks which behave acceptably under hydrological variability. Robust optimisation can overcome the problem of selecting representative rainfall events when building the optimization process. This paper reports an original approach based on Montana IDF model parameters. The latter are assumed to be geostatistical variables and their spatial interdependence is taken into account through the adoption of cross-variograms in the kriging process. The problem of optimally locating a fixed number of new monitoring stations based on an existing rain gauge network is addressed. The objective function is based on the mean spatial kriging variance and rainfall variogram structure using a variance-reduction method. Hydrological variability was taken into account by considering and implementing several return periods to define the robust objective function. Variance minimization is performed using a simulated annealing algorithm. In addition, knowledge of the time horizon is needed for the computation of the robust objective function. A short and a long term horizon were studied, and optimal networks are identified for each. The method developed is applied to north Tunisia (area = 21 000 km2). Data inputs for the variogram analysis were IDF curves provided by the hydrological bureau and available for 14 tipping bucket type rain gauges. The recording period was from 1962 to 2001, depending on the station. The study concerns an imaginary network augmentation based on the network configuration in 1973, which is a very significant year in Tunisia because there was an exceptional regional flood event in March 1973. This network consisted of 13 stations and did not meet World Meteorological Organization (WMO) recommendations for the minimum spatial density. So, it is proposed to virtually augment it by 25, 50, 100 and 160% which is the rate that would meet WMO requirements. Results suggest that for a given augmentation robust networks remain stable overall for the two time horizons.

Development of a method of robust rain gauge network optimization based on intensity-duration-frequency results

NASA Astrophysics Data System (ADS)

Chebbi, A.; Bargaoui, Z. K.; da Conceição Cunha, M.

2013-10-01

Based on rainfall intensity-duration-frequency (IDF) curves, fitted in several locations of a given area, a robust optimization approach is proposed to identify the best locations to install new rain gauges. The advantage of robust optimization is that the resulting design solutions yield networks which behave acceptably under hydrological variability. Robust optimization can overcome the problem of selecting representative rainfall events when building the optimization process. This paper reports an original approach based on Montana IDF model parameters. The latter are assumed to be geostatistical variables, and their spatial interdependence is taken into account through the adoption of cross-variograms in the kriging process. The problem of optimally locating a fixed number of new monitoring stations based on an existing rain gauge network is addressed. The objective function is based on the mean spatial kriging variance and rainfall variogram structure using a variance-reduction method. Hydrological variability was taken into account by considering and implementing several return periods to define the robust objective function. Variance minimization is performed using a simulated annealing algorithm. In addition, knowledge of the time horizon is needed for the computation of the robust objective function. A short- and a long-term horizon were studied, and optimal networks are identified for each. The method developed is applied to north Tunisia (area = 21 000 km2). Data inputs for the variogram analysis were IDF curves provided by the hydrological bureau and available for 14 tipping bucket type rain gauges. The recording period was from 1962 to 2001, depending on the station. The study concerns an imaginary network augmentation based on the network configuration in 1973, which is a very significant year in Tunisia because there was an exceptional regional flood event in March 1973. This network consisted of 13 stations and did not meet World Meteorological Organization (WMO) recommendations for the minimum spatial density. Therefore, it is proposed to augment it by 25, 50, 100 and 160% virtually, which is the rate that would meet WMO requirements. Results suggest that for a given augmentation robust networks remain stable overall for the two time horizons.

Spatial distribution and risk assessment of radionuclides in soils around a coal-fired power plant: A case study from the city of Baoji, China

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

Dai Lijun; Wei Haiyan; Wang Lingqing

2007-06-15

Coal burning may enhance human exposure to the natural radionuclides that occur around coal-fired power plants (CFPP). In this study, the spatial distribution and hazard assessment of radionuclides found in soils around a CFPP were investigated using statistics, geostatistics, and geographic information system (GIS) techniques. The concentrations of {sup 226}Ra, {sup 232}Th, and {sup 40}K in soils range from 12.54 to 40.18, 38.02 to 72.55, and 498.02 to 1126.98 Bq kg{sup -1}, respectively. Ordinary kriging was carried out to map the spatial patterns of radionuclides, and disjunctive kriging was used to quantify the probability of radium equivalent activity (Ra{sub eq})more » higher than the threshold. The maps show that the spatial variability of the natural radionuclide concentrations in soils was apparent. The results of this study could provide valuable information for risk assessment of environmental pollution and decision support.« less

Spatial distribution and risk assessment of radionuclides in soils around a coal-fired power plant: A case study from the city of Baoji, China

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

Dai, L.J.; Wei, H.Y.; Wang, L.Q.

2007-06-15

Coal burning may enhance human exposure to the natural radionuclides that occur around coal-fired power plants (CFPP). In this study, the spatial distribution and hazard assessment of radionuclides found in soils around a CFPP were investigated using statistics, geostatistics, and geographic information system (GIS) techniques. The concentrations of Ra-226, Th-232, and K-40 in soils range from 12.54 to 40.18, 38.02 to 72.55, and 498.02 to 1126.98 Bq kg{sup -1}, respectively. Ordinary kriging was carried out to map the spatial patterns of radionuclides, and disjunctive kriging was used to quantify the probability of radium equivalent activity (Ra{sub eq}) higher than themore » threshold. The maps show that the spatial variability of the natural radionuclide concentrations in soils was apparent. The results of this study could provide valuable information for risk assessment of environmental pollution and decision support.« less

Statistical comparison of various interpolation algorithms for reconstructing regional grid ionospheric maps over China

NASA Astrophysics Data System (ADS)

Li, Min; Yuan, Yunbin; Wang, Ningbo; Li, Zishen; Liu, Xifeng; Zhang, Xiao

2018-07-01

This paper presents a quantitative comparison of several widely used interpolation algorithms, i.e., Ordinary Kriging (OrK), Universal Kriging (UnK), planar fit and Inverse Distance Weighting (IDW), based on a grid-based single-shell ionosphere model over China. The experimental data were collected from the Crustal Movement Observation Network of China (CMONOC) and the International GNSS Service (IGS), covering the days of year 60-90 in 2015. The quality of these interpolation algorithms was assessed by cross-validation in terms of both the ionospheric correction performance and Single-Frequency (SF) Precise Point Positioning (PPP) accuracy on an epoch-by-epoch basis. The results indicate that the interpolation models perform better at mid-latitudes than low latitudes. For the China region, the performance of OrK and UnK is relatively better than the planar fit and IDW model for estimating ionospheric delay and positioning. In addition, the computational efficiencies of the IDW and planar fit models are better than those of OrK and UnK.

Geostatistical Investigations of Displacements on the Basis of Data from the Geodetic Monitoring of a Hydrotechnical Object

NASA Astrophysics Data System (ADS)

Namysłowska-Wilczyńska, Barbara; Wynalek, Janusz

2017-12-01

Geostatistical methods make the analysis of measurement data possible. This article presents the problems directed towards the use of geostatistics in spatial analysis of displacements based on geodetic monitoring. Using methods of applied (spatial) statistics, the research deals with interesting and current issues connected to space-time analysis, modeling displacements and deformations, as applied to any large-area objects on which geodetic monitoring is conducted (e.g., water dams, urban areas in the vicinity of deep excavations, areas at a macro-regional scale subject to anthropogenic influences caused by mining, etc.). These problems are very crucial, especially for safety assessment of important hydrotechnical constructions, as well as for modeling and estimating mining damage. Based on the geodetic monitoring data, a substantial basic empirical material was created, comprising many years of research results concerning displacements of controlled points situated on the crown and foreland of an exemplary earth dam, and used to assess the behaviour and safety of the object during its whole operating period. A research method at a macro-regional scale was applied to investigate some phenomena connected with the operation of the analysed big hydrotechnical construction. Applying a semivariogram function enabled the spatial variability analysis of displacements. Isotropic empirical semivariograms were calculated and then, theoretical parameters of analytical functions were determined, which approximated the courses of the mentioned empirical variability measure. Using ordinary (block) kriging at the grid nodes of an elementary spatial grid covering the analysed object, the values of the Z* estimated means of displacements were calculated together with the accompanying assessment of uncertainty estimation - a standard deviation of estimation σk. Raster maps of the distribution of estimated averages Z* and raster maps of deviations of estimation σk (in perspective) were obtained for selected years (1995 and 2007), taking the ground height 136 m a.s.l. into calculation. To calculate raster maps of Z* interpolated values, methods of quick interpolation were also used, such as the technique of the inverse distance squares, a linear model of kriging, a spline kriging, which made the recognition of the general background of displacements possible, without the accuracy assessment of Z* value estimation, i.e., the value of σk. These maps are also related to 1995 and 2007 and the elevation. As a result of applying these techniques, clear boundaries of subsiding areas, upthrusting and also horizontal displacements on the examined hydrotechnical object were marked out, which can be interpreted as areas of local deformations of the object, important for the safety of the construction. The effect of geostatistical research conducted, including the structural analysis, semivariograms modeling, estimating the displacements of the hydrotechnical object, are rich cartographic characteristic (semivariograms, raster maps, block diagrams), which present the spatial visualization of the conducted various analyses of the monitored displacements. The prepared geostatistical model (3D) of displacement variability (analysed within the area of the dam, during its operating period and including its height) will be useful not only in the correct assessment of displacements and deformations, but it will also make it possible to forecast these phenomena, which is crucial when the operating safety of such constructions is taken into account.

A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling

NASA Astrophysics Data System (ADS)

Cao, G.

2015-12-01

All types of spatiotemporal measurements are subject to uncertainty. With spatiotemporal data becomes increasingly involved in scientific research and decision making, it is important to appropriately model the impact of uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, is a challenging problem considering the complex dependence and dataheterogeneities.State-space models provide a unifying and intuitive framework for dynamic systems modeling. In this paper, we aim to extend the conventional state-space models for uncertainty modeling in space-time contexts while accounting for spatiotemporal effects and data heterogeneities. Gaussian Markov Random Field (GMRF) models, also known as conditional autoregressive models, are arguably the most commonly used methods for modeling of spatially dependent data. GMRF models basically assume that a geo-referenced variable primarily depends on its neighborhood (Markov property), and the spatial dependence structure is described via a precision matrix. Recent study has shown that GMRFs are efficient approximation to the commonly used Gaussian fields (e.g., Kriging), and compared with Gaussian fields, GMRFs enjoy a series of appealing features, such as fast computation and easily accounting for heterogeneities in spatial data (e.g, point and areal). This paper represents each spatial dataset as a GMRF and integrates them into a state-space form to statistically model the temporal dynamics. Different types of spatial measurements (e.g., categorical, count or continuous), can be accounted for by according link functions. A fast alternative to MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), was adopted for model inference.Preliminary case studies will be conducted to showcase the advantages of the described framework. In the first case, we apply the proposed method for modeling the water table elevation of Ogallala aquifer over the past decades. In the second case, we analyze the drought impacts in Texas counties in the past years, where the spatiotemporal dynamics are represented in areal data.

Structural Optimization of a Knuckle with Consideration of Stiffness and Durability Requirements

PubMed Central

Kim, Geun-Yeon

2014-01-01

The automobile's knuckle is connected to the parts of the steering system and the suspension system and it is used for adjusting the direction of a rotation through its attachment to the wheel. This study changes the existing material made of GCD45 to Al6082M and recommends the lightweight design of the knuckle as the optimal design technique to be installed in small cars. Six shape design variables were selected for the optimization of the knuckle and the criteria relevant to stiffness and durability were considered as the design requirements during the optimization process. The metamodel-based optimization method that uses the kriging interpolation method as the optimization technique was applied. The result shows that all constraints for stiffness and durability are satisfied using A16082M, while reducing the weight of the knuckle by 60% compared to that of the existing GCD450. PMID:24995359

Geostatistics and GIS: tools for characterizing environmental contamination.

PubMed

Henshaw, Shannon L; Curriero, Frank C; Shields, Timothy M; Glass, Gregory E; Strickland, Paul T; Breysse, Patrick N

2004-08-01

Geostatistics is a set of statistical techniques used in the analysis of georeferenced data that can be applied to environmental contamination and remediation studies. In this study, the 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) contamination at a Superfund site in western Maryland is evaluated. Concern about the site and its future clean up has triggered interest within the community because residential development surrounds the area. Spatial statistical methods, of which geostatistics is a subset, are becoming increasingly popular, in part due to the availability of geographic information system (GIS) software in a variety of application packages. In this article, the joint use of ArcGIS software and the R statistical computing environment are demonstrated as an approach for comprehensive geostatistical analyses. The spatial regression method, kriging, is used to provide predictions of DDE levels at unsampled locations both within the site and the surrounding areas where residential development is ongoing.

The FORBIO Climate data set for climate analyses

NASA Astrophysics Data System (ADS)

Delvaux, C.; Journée, M.; Bertrand, C.

2015-06-01

In the framework of the interdisciplinary FORBIO Climate research project, the Royal Meteorological Institute of Belgium is in charge of providing high resolution gridded past climate data (i.e. temperature and precipitation). This climate data set will be linked to the measurements on seedlings, saplings and mature trees to assess the effects of climate variation on tree performance. This paper explains how the gridded daily temperature (minimum and maximum) data set was generated from a consistent station network between 1980 and 2013. After station selection, data quality control procedures were developed and applied to the station records to ensure that only valid measurements will be involved in the gridding process. Thereafter, the set of unevenly distributed validated temperature data was interpolated on a 4 km × 4 km regular grid over Belgium. The performance of different interpolation methods has been assessed. The method of kriging with external drift using correlation between temperature and altitude gave the most relevant results.

“Estimating Regional Background Air Quality using Space/Time Ordinary Kriging to Support Exposure Studies”

EPA Science Inventory

Local-scale dispersion models are increasingly being used to perform exposure assessments. These types of models, while able to characterize local-scale air quality at increasing spatial scale, however, lack the ability to include background concentration in their overall estimat...

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

Roehm, Dominic; Pavel, Robert S.; Barros, Kipton

We present an adaptive sampling method supplemented by a distributed database and a prediction method for multiscale simulations using the Heterogeneous Multiscale Method. A finite-volume scheme integrates the macro-scale conservation laws for elastodynamics, which are closed by momentum and energy fluxes evaluated at the micro-scale. In the original approach, molecular dynamics (MD) simulations are launched for every macro-scale volume element. Our adaptive sampling scheme replaces a large fraction of costly micro-scale MD simulations with fast table lookup and prediction. The cloud database Redis provides the plain table lookup, and with locality aware hashing we gather input data for our predictionmore » scheme. For the latter we use kriging, which estimates an unknown value and its uncertainty (error) at a specific location in parameter space by using weighted averages of the neighboring points. We find that our adaptive scheme significantly improves simulation performance by a factor of 2.5 to 25, while retaining high accuracy for various choices of the algorithm parameters.« less

Assessment of pollutant mean concentrations in the Yangtze estuary based on MSN theory.

PubMed

Ren, Jing; Gao, Bing-Bo; Fan, Hai-Mei; Zhang, Zhi-Hong; Zhang, Yao; Wang, Jin-Feng

2016-12-15

Reliable assessment of water quality is a critical issue for estuaries. Nutrient concentrations show significant spatial distinctions between areas under the influence of fresh-sea water interaction and anthropogenic effects. For this situation, given the limitations of general mean estimation approaches, a new method for surfaces with non-homogeneity (MSN) was applied to obtain optimized linear unbiased estimations of the mean nutrient concentrations in the study area in the Yangtze estuary from 2011 to 2013. Other mean estimation methods, including block Kriging (BK), simple random sampling (SS) and stratified sampling (ST) inference, were applied simultaneously for comparison. Their performance was evaluated by estimation error. The results show that MSN had the highest accuracy, while SS had the highest estimation error. ST and BK were intermediate in terms of their performance. Thus, MSN is an appropriate method that can be adopted to reduce the uncertainty of mean pollutant estimation in estuaries. Copyright © 2016 Elsevier Ltd. All rights reserved.

High-performance parallel approaches for three-dimensional light detection and ranging point clouds gridding

NASA Astrophysics Data System (ADS)

Rizki, Permata Nur Miftahur; Lee, Heezin; Lee, Minsu; Oh, Sangyoon

2017-01-01

With the rapid advance of remote sensing technology, the amount of three-dimensional point-cloud data has increased extraordinarily, requiring faster processing in the construction of digital elevation models. There have been several attempts to accelerate the computation using parallel methods; however, little attention has been given to investigating different approaches for selecting the most suited parallel programming model for a given computing environment. We present our findings and insights identified by implementing three popular high-performance parallel approaches (message passing interface, MapReduce, and GPGPU) on time demanding but accurate kriging interpolation. The performances of the approaches are compared by varying the size of the grid and input data. In our empirical experiment, we demonstrate the significant acceleration by all three approaches compared to a C-implemented sequential-processing method. In addition, we also discuss the pros and cons of each method in terms of usability, complexity infrastructure, and platform limitation to give readers a better understanding of utilizing those parallel approaches for gridding purposes.

Outlier identification and visualization for Pb concentrations in urban soils and its implications for identification of potential contaminated land.

PubMed

Zhang, Chaosheng; Tang, Ya; Luo, Lin; Xu, Weilin

2009-11-01

Outliers in urban soil geochemical databases may imply potential contaminated land. Different methodologies which can be easily implemented for the identification of global and spatial outliers were applied for Pb concentrations in urban soils of Galway City in Ireland. Due to its strongly skewed probability feature, a Box-Cox transformation was performed prior to further analyses. The graphic methods of histogram and box-and-whisker plot were effective in identification of global outliers at the original scale of the dataset. Spatial outliers could be identified by a local indicator of spatial association of local Moran's I, cross-validation of kriging, and a geographically weighted regression. The spatial locations of outliers were visualised using a geographical information system. Different methods showed generally consistent results, but differences existed. It is suggested that outliers identified by statistical methods should be confirmed and justified using scientific knowledge before they are properly dealt with.

Two-dimensional fracture analysis of piezoelectric material based on the scaled boundary node method

NASA Astrophysics Data System (ADS)

Shen-Shen, Chen; Juan, Wang; Qing-Hua, Li

2016-04-01

A scaled boundary node method (SBNM) is developed for two-dimensional fracture analysis of piezoelectric material, which allows the stress and electric displacement intensity factors to be calculated directly and accurately. As a boundary-type meshless method, the SBNM employs the moving Kriging (MK) interpolation technique to an approximate unknown field in the circumferential direction and therefore only a set of scattered nodes are required to discretize the boundary. As the shape functions satisfy Kronecker delta property, no special techniques are required to impose the essential boundary conditions. In the radial direction, the SBNM seeks analytical solutions by making use of analytical techniques available to solve ordinary differential equations. Numerical examples are investigated and satisfactory solutions are obtained, which validates the accuracy and simplicity of the proposed approach. Project supported by the National Natural Science Foundation of China (Grant Nos. 11462006 and 21466012), the Foundation of Jiangxi Provincial Educational Committee, China (Grant No. KJLD14041), and the Foundation of East China Jiaotong University, China (Grant No. 09130020).

Three-Dimensional Mapping of Soil Chemical Characteristics at Micrometric Scale by Combining 2D SEM-EDX Data and 3D X-Ray CT Images.

PubMed

Hapca, Simona; Baveye, Philippe C; Wilson, Clare; Lark, Richard Murray; Otten, Wilfred

2015-01-01

There is currently a significant need to improve our understanding of the factors that control a number of critical soil processes by integrating physical, chemical and biological measurements on soils at microscopic scales to help produce 3D maps of the related properties. Because of technological limitations, most chemical and biological measurements can be carried out only on exposed soil surfaces or 2-dimensional cuts through soil samples. Methods need to be developed to produce 3D maps of soil properties based on spatial sequences of 2D maps. In this general context, the objective of the research described here was to develop a method to generate 3D maps of soil chemical properties at the microscale by combining 2D SEM-EDX data with 3D X-ray computed tomography images. A statistical approach using the regression tree method and ordinary kriging applied to the residuals was developed and applied to predict the 3D spatial distribution of carbon, silicon, iron, and oxygen at the microscale. The spatial correlation between the X-ray grayscale intensities and the chemical maps made it possible to use a regression-tree model as an initial step to predict the 3D chemical composition. For chemical elements, e.g., iron, that are sparsely distributed in a soil sample, the regression-tree model provides a good prediction, explaining as much as 90% of the variability in some of the data. However, for chemical elements that are more homogenously distributed, such as carbon, silicon, or oxygen, the additional kriging of the regression tree residuals improved significantly the prediction with an increase in the R2 value from 0.221 to 0.324 for carbon, 0.312 to 0.423 for silicon, and 0.218 to 0.374 for oxygen, respectively. The present research develops for the first time an integrated experimental and theoretical framework, which combines geostatistical methods with imaging techniques to unveil the 3-D chemical structure of soil at very fine scales. The methodology presented in this study can be easily adapted and applied to other types of data such as bacterial or fungal population densities for the 3D characterization of microbial distribution.

Three-Dimensional Mapping of Soil Chemical Characteristics at Micrometric Scale by Combining 2D SEM-EDX Data and 3D X-Ray CT Images

PubMed Central

Hapca, Simona; Baveye, Philippe C.; Wilson, Clare; Lark, Richard Murray; Otten, Wilfred

2015-01-01

There is currently a significant need to improve our understanding of the factors that control a number of critical soil processes by integrating physical, chemical and biological measurements on soils at microscopic scales to help produce 3D maps of the related properties. Because of technological limitations, most chemical and biological measurements can be carried out only on exposed soil surfaces or 2-dimensional cuts through soil samples. Methods need to be developed to produce 3D maps of soil properties based on spatial sequences of 2D maps. In this general context, the objective of the research described here was to develop a method to generate 3D maps of soil chemical properties at the microscale by combining 2D SEM-EDX data with 3D X-ray computed tomography images. A statistical approach using the regression tree method and ordinary kriging applied to the residuals was developed and applied to predict the 3D spatial distribution of carbon, silicon, iron, and oxygen at the microscale. The spatial correlation between the X-ray grayscale intensities and the chemical maps made it possible to use a regression-tree model as an initial step to predict the 3D chemical composition. For chemical elements, e.g., iron, that are sparsely distributed in a soil sample, the regression-tree model provides a good prediction, explaining as much as 90% of the variability in some of the data. However, for chemical elements that are more homogenously distributed, such as carbon, silicon, or oxygen, the additional kriging of the regression tree residuals improved significantly the prediction with an increase in the R2 value from 0.221 to 0.324 for carbon, 0.312 to 0.423 for silicon, and 0.218 to 0.374 for oxygen, respectively. The present research develops for the first time an integrated experimental and theoretical framework, which combines geostatistical methods with imaging techniques to unveil the 3-D chemical structure of soil at very fine scales. The methodology presented in this study can be easily adapted and applied to other types of data such as bacterial or fungal population densities for the 3D characterization of microbial distribution. PMID:26372473

Air pollution and gastrointestinal diseases in Utah

NASA Astrophysics Data System (ADS)

Maestas, Melissa May

The valleys of northern Utah, where most of Utah's population resides, experience episodic air pollution events well in excess of the National Ambient Air Quality Standards. Most of the events are due to an accumulation of particulate matter during persistent cold air pools in winter from both direct emissions and secondary chemical reactions in the atmosphere. High wintertime ozone concentrations are occasionally observed in the Uintah Basin, in addition to particulate matter. At other times of the year, blowing dust, wildland fires, fireworks, and summertime ozone formation contribute to local air pollution. The objective of this dissertation is to investigate one facet of the health effects of Utah's air pollution on its residents: the acute impacts of air pollution on gastrointestinal (GI) disease. To study the health effects of these episodic pollution events, some measure of air pollution exposure must be matched to the health data. Time and place are used to link the health data for a person with the pollution data. This dissertation describes the method of kriging data from the sparse pollution monitoring network to estimate personal air pollution history based on the zip code of residence. This dissertation then describes the application of these exposure estimates to a health study on GI disease. The purpose of the GI study is to retrospectively look at two groups of patients during 2000-2014: those with autoimmune disease of the GI tract (inflammatory bowel disease, IBD) and those with allergic disease of the GI tract (eosinophilic esophagitis, EoE) to determine whether disease exacerbations occur more commonly during and following periods of poor air quality compared to periods of good air quality. The primary analysis method is case crossover design. In addition to using the kriged air pollution estimates, the analysis was repeated using simpler empirical estimation methods to assess whether the odds ratios are sensitive to the air pollution estimation method. The data suggests an association between particulate matter smaller than 2.5 microns and prednisone prescriptions, gastrointestinal infections in general, clostridium difficile infections specifically, and hospitalizations among people who have at least five entries of IBD diagnosis codes in their medical records. EoE exacerbations appear to be associated with high concentrations of particulate matter as well as ozone.

Assessment of groundwater level estimation uncertainty using sequential Gaussian simulation and Bayesian bootstrapping

NASA Astrophysics Data System (ADS)

Varouchakis, Emmanouil; Hristopulos, Dionissios

2015-04-01

Space-time geostatistical approaches can improve the reliability of dynamic groundwater level models in areas with limited spatial and temporal data. Space-time residual Kriging (STRK) is a reliable method for spatiotemporal interpolation that can incorporate auxiliary information. The method usually leads to an underestimation of the prediction uncertainty. The uncertainty of spatiotemporal models is usually estimated by determining the space-time Kriging variance or by means of cross validation analysis. For de-trended data the former is not usually applied when complex spatiotemporal trend functions are assigned. A Bayesian approach based on the bootstrap idea and sequential Gaussian simulation are employed to determine the uncertainty of the spatiotemporal model (trend and covariance) parameters. These stochastic modelling approaches produce multiple realizations, rank the prediction results on the basis of specified criteria and capture the range of the uncertainty. The correlation of the spatiotemporal residuals is modeled using a non-separable space-time variogram based on the Spartan covariance family (Hristopulos and Elogne 2007, Varouchakis and Hristopulos 2013). We apply these simulation methods to investigate the uncertainty of groundwater level variations. The available dataset consists of bi-annual (dry and wet hydrological period) groundwater level measurements in 15 monitoring locations for the time period 1981 to 2010. The space-time trend function is approximated using a physical law that governs the groundwater flow in the aquifer in the presence of pumping. The main objective of this research is to compare the performance of two simulation methods for prediction uncertainty estimation. In addition, we investigate the performance of the Spartan spatiotemporal covariance function for spatiotemporal geostatistical analysis. Hristopulos, D.T. and Elogne, S.N. 2007. Analytic properties and covariance functions for a new class of generalized Gibbs random fields. IΕΕΕ Transactions on Information Theory, 53:4667-4467. Varouchakis, E.A. and Hristopulos, D.T. 2013. Improvement of groundwater level prediction in sparsely gauged basins using physical laws and local geographic features as auxiliary variables. Advances in Water Resources, 52:34-49. Research supported by the project SPARTA 1591: "Development of Space-Time Random Fields based on Local Interaction Models and Applications in the Processing of Spatiotemporal Datasets". "SPARTA" is implemented under the "ARISTEIA" Action of the operational programme Education and Lifelong Learning and is co-funded by the European Social Fund (ESF) and National Resources.

COMPARISON OF ANOVA AND KRIGING IN DETECTING ANT RESPONSES TO ENVIRONMENTAL STRESSORS

EPA Science Inventory

In an ecosystems, ants effect ecosystem functions such as water infiltration, soil nutrient distribution and composition of the soil seed bank. Ants have also been used as indicators of ecosystems health. In a study, we hypothesized that some ant species would respond to changes ...

IDENTIFYING DISCHARGE ZONES OF ARSENIC IN THE GOOSE RIVER BASIN, MAINE

EPA Science Inventory

Groundwater discharge areas are simulated from water balance modeling and kriging of oxygen isotopes in groundwater within the Goose River basin. Groundwater fluxes of discharge range from -10 cm yr-1 to < -25 cm yr-1 and are associated with areas of elevated arsenic in wells. De...

Regression-kriged soil organic carbon stock changes in manured corn silage-alfalfa production systems

USDA-ARS?s Scientific Manuscript database

Accurately measuring soil organic C (SOC) stock changes over time is essential for verifying agronomic management effects on C sequestration. This study quantified the spatial and temporal changes in SOC stocks on adjacent 65-ha corn silage-alfalfa production fields receiving liquid dairy manure in...

Uncertainty Analysis of Radar and Gauge Rainfall Estimates in the Russian River Basin

NASA Astrophysics Data System (ADS)

Cifelli, R.; Chen, H.; Willie, D.; Reynolds, D.; Campbell, C.; Sukovich, E.

2013-12-01

Radar Quantitative Precipitation Estimation (QPE) has been a very important application of weather radar since it was introduced and made widely available after World War II. Although great progress has been made over the last two decades, it is still a challenging process especially in regions of complex terrain such as the western U.S. It is also extremely difficult to make direct use of radar precipitation data in quantitative hydrologic forecasting models. To improve the understanding of rainfall estimation and distributions in the NOAA Hydrometeorology Testbed in northern California (HMT-West), extensive evaluation of radar and gauge QPE products has been performed using a set of independent rain gauge data. This study focuses on the rainfall evaluation in the Russian River Basin. The statistical properties of the different gridded QPE products will be compared quantitatively. The main emphasis of this study will be on the analysis of uncertainties of the radar and gauge rainfall products that are subject to various sources of error. The spatial variation analysis of the radar estimates is performed by measuring the statistical distribution of the radar base data such as reflectivity and by the comparison with a rain gauge cluster. The application of mean field bias values to the radar rainfall data will also be described. The uncertainty analysis of the gauge rainfall will be focused on the comparison of traditional kriging and conditional bias penalized kriging (Seo 2012) methods. This comparison is performed with the retrospective Multisensor Precipitation Estimator (MPE) system installed at the NOAA Earth System Research Laboratory. The independent gauge set will again be used as the verification tool for the newly generated rainfall products.

Assessing soil carbon vulnerability in the Western USA by geospatial modeling of pyrogenic and particulate carbon stocks

NASA Astrophysics Data System (ADS)

Ahmed, Zia U.; Woodbury, Peter B.; Sanderman, Jonathan; Hawke, Bruce; Jauss, Verena; Solomon, Dawit; Lehmann, Johannes

2017-02-01

To predict how land management practices and climate change will affect soil carbon cycling, improved understanding of factors controlling soil organic carbon fractions at large spatial scales is needed. We analyzed total soil organic (SOC) as well as pyrogenic (PyC), particulate (POC), and other soil organic carbon (OOC) fractions in surface layers from 650 stratified-sampling locations throughout Colorado, Kansas, New Mexico, and Wyoming. PyC varied from 0.29 to 18.0 mg C g-1 soil with a mean of 4.05 mg C g-1 soil. The mean PyC was 34.6% of the SOC and ranged from 11.8 to 96.6%. Both POC and PyC were highest in forests and canyon bottoms. In the best random forest regression model, normalized vegetation index (NDVI), mean annual precipitation (MAP), mean annual temperature (MAT), and elevation were ranked as the top four important variables determining PyC and POC variability. Random forests regression kriging (RFK) with environmental covariables improved predictions over ordinary kriging by 20 and 7% for PyC and POC, respectively. Based on RFK, 8% of the study area was dominated (≥50% of SOC) by PyC and less than 1% was dominated by POC. Furthermore, based on spatial analysis of the ratio of POC to PyC, we estimated that about 16% of the study area is medium to highly vulnerable to SOC mineralization in surface soil. These are the first results to characterize PyC and POC stocks geospatially using stratified sampling scheme at the scale of 1,000,000 km2, and the methods are scalable to other regions.

Visualizing geographic and temporal trends in rotavirus activity in the United States, 1991 to 1996. National Respiratory and Enteric Virus Surveillance System Collaborating Laboratories.

PubMed

Török, T J; Kilgore, P E; Clarke, M J; Holman, R C; Bresee, J S; Glass, R I

1997-10-01

Rotavirus is the leading cause of severe pediatric gastroenteritis worldwide. A vaccine may soon be licensed for use in the United States to prevent this disease. To characterize US geographic and temporal trends in rotavirus activity, we made contour maps showing the timing of peak rotavirus activity. From July, 1991, through June, 1996, 79 laboratories participating in the National Respiratory and Enteric Virus Surveillance System reported on a weekly basis the number of stool specimens that tested positive for rotavirus. The peak weeks in rotavirus detections from each laboratory were mapped using kriging, a modeling technique originally developed for geostatistics. During the 5-year period 118,716 fecal specimens were examined, of which 27,616 (23%) were positive for rotavirus. Timing of rotavirus activity varied by geographic location in a characteristic pattern in which peak activity occurred first in the Southwest from October through December and last in the Northeast in April or May. The Northwest exhibited considerable year-to-year variability (range, December to May) in the timing of peak activity, whereas the temporal pattern in the remainder of the contiguous 48 states was relatively constant. Kriging is a useful method for visualizing geographic and temporal trends in rotavirus activity in the United States. This analysis confirmed trends reported in previous years, and it also identified unexpected variability in the timing of peak rotavirus activity in the Northwest. The causes of the seasonal differences in rotavirus activity by region are unknown. Tracking of laboratory detections of rotavirus may provide an effective surveillance tool to assess the impact of a rotavirus vaccination campaign in the United States.

Categorical Indicator Kriging for assessing the risk of groundwater nitrate pollution: the case of Vega de Granada aquifer (SE Spain).

PubMed

Chica-Olmo, Mario; Luque-Espinar, Juan Antonio; Rodriguez-Galiano, Victor; Pardo-Igúzquiza, Eulogio; Chica-Rivas, Lucía

2014-02-01

Groundwater nitrate pollution associated with agricultural activity is an important environmental problem in the management of this natural resource, as acknowledged by the European Water Framework Directive. Therefore, specific measures aimed to control the risk of water pollution by nitrates must be implemented to minimise its impact on the environment and potential risk to human health. The spatial probability distribution of nitrate contents exceeding a threshold or limit value, established within the quality standard, will be helpful to managers and decision-makers. A methodology based on non-parametric and non-linear methods of Indicator Kriging was used in the elaboration of a nitrate pollution categorical map for the aquifer of Vega de Granada (SE Spain). The map has been obtained from the local estimation of the probability that a nitrate content in an unsampled location belongs to one of the three categories established by the European Water Framework Directive: CL. 1 good quality [Min - 37.5 ppm], CL. 2 intermediate quality [37.5-50 ppm] and CL. 3 poor quality [50 ppm - Max]. The obtained results show that the areas exceeding nitrate concentrations of 50 ppm, poor quality waters, occupy more than 50% of the aquifer area. A great proportion of the area's municipalities are located in these poor quality water areas. The intermediate quality and good quality areas correspond to 21% and 28%, respectively, but with the highest population density. These results are coherent with the experimental data, which show an average nitrate concentration value of 72 ppm, significantly higher than the quality standard limit of 50 ppm. Consequently, the results suggest the importance of planning actions in order to control and monitor aquifer nitrate pollution. © 2013.

S-Genius, a universal software platform with versatile inverse problem resolution for scatterometry

NASA Astrophysics Data System (ADS)

Fuard, David; Troscompt, Nicolas; El Kalyoubi, Ismael; Soulan, Sébastien; Besacier, Maxime

2013-05-01

S-Genius is a new universal scatterometry platform, which gathers all the LTM-CNRS know-how regarding the rigorous electromagnetic computation and several inverse problem solver solutions. This software platform is built to be a userfriendly, light, swift, accurate, user-oriented scatterometry tool, compatible with any ellipsometric measurements to fit and any types of pattern. It aims to combine a set of inverse problem solver capabilities — via adapted Levenberg- Marquard optimization, Kriging, Neural Network solutions — that greatly improve the reliability and the velocity of the solution determination. Furthermore, as the model solution is mainly vulnerable to materials optical properties, S-Genius may be coupled with an innovative material refractive indices determination. This paper will a little bit more focuses on the modified Levenberg-Marquardt optimization, one of the indirect method solver built up in parallel with the total SGenius software coding by yours truly. This modified Levenberg-Marquardt optimization corresponds to a Newton algorithm with an adapted damping parameter regarding the definition domains of the optimized parameters. Currently, S-Genius is technically ready for scientific collaboration, python-powered, multi-platform (windows/linux/macOS), multi-core, ready for 2D- (infinite features along the direction perpendicular to the incident plane), conical, and 3D-features computation, compatible with all kinds of input data from any possible ellipsometers (angle or wavelength resolved) or reflectometers, and widely used in our laboratory for resist trimming studies, etching features characterization (such as complex stack) or nano-imprint lithography measurements for instance. The work about kriging solver, neural network solver and material refractive indices determination is done (or about to) by other LTM members and about to be integrated on S-Genius platform.

Greedy Sampling and Incremental Surrogate Model-Based Tailoring of Aeroservoelastic Model Database for Flexible Aircraft

NASA Technical Reports Server (NTRS)

Wang, Yi; Pant, Kapil; Brenner, Martin J.; Ouellette, Jeffrey A.

2018-01-01

This paper presents a data analysis and modeling framework to tailor and develop linear parameter-varying (LPV) aeroservoelastic (ASE) model database for flexible aircrafts in broad 2D flight parameter space. The Kriging surrogate model is constructed using ASE models at a fraction of grid points within the original model database, and then the ASE model at any flight condition can be obtained simply through surrogate model interpolation. The greedy sampling algorithm is developed to select the next sample point that carries the worst relative error between the surrogate model prediction and the benchmark model in the frequency domain among all input-output channels. The process is iterated to incrementally improve surrogate model accuracy till a pre-determined tolerance or iteration budget is met. The methodology is applied to the ASE model database of a flexible aircraft currently being tested at NASA/AFRC for flutter suppression and gust load alleviation. Our studies indicate that the proposed method can reduce the number of models in the original database by 67%. Even so the ASE models obtained through Kriging interpolation match the model in the original database constructed directly from the physics-based tool with the worst relative error far below 1%. The interpolated ASE model exhibits continuously-varying gains along a set of prescribed flight conditions. More importantly, the selected grid points are distributed non-uniformly in the parameter space, a) capturing the distinctly different dynamic behavior and its dependence on flight parameters, and b) reiterating the need and utility for adaptive space sampling techniques for ASE model database compaction. The present framework is directly extendible to high-dimensional flight parameter space, and can be used to guide the ASE model development, model order reduction, robust control synthesis and novel vehicle design of flexible aircraft.

Geospatial Predictive Modelling for Climate Mapping of Selected Severe Weather Phenomena Over Poland: A Methodological Approach

NASA Astrophysics Data System (ADS)

Walawender, Ewelina; Walawender, Jakub P.; Ustrnul, Zbigniew

2017-02-01

The main purpose of the study is to introduce methods for mapping the spatial distribution of the occurrence of selected atmospheric phenomena (thunderstorms, fog, glaze and rime) over Poland from 1966 to 2010 (45 years). Limited in situ observations as well the discontinuous and location-dependent nature of these phenomena make traditional interpolation inappropriate. Spatially continuous maps were created with the use of geospatial predictive modelling techniques. For each given phenomenon, an algorithm identifying its favourable meteorological and environmental conditions was created on the basis of observations recorded at 61 weather stations in Poland. Annual frequency maps presenting the probability of a day with a thunderstorm, fog, glaze or rime were created with the use of a modelled, gridded dataset by implementing predefined algorithms. Relevant explanatory variables were derived from NCEP/NCAR reanalysis and downscaled with the use of a Regional Climate Model. The resulting maps of favourable meteorological conditions were found to be valuable and representative on the country scale but at different correlation ( r) strength against in situ data (from r = 0.84 for thunderstorms to r = 0.15 for fog). A weak correlation between gridded estimates of fog occurrence and observations data indicated the very local nature of this phenomenon. For this reason, additional environmental predictors of fog occurrence were also examined. Topographic parameters derived from the SRTM elevation model and reclassified CORINE Land Cover data were used as the external, explanatory variables for the multiple linear regression kriging used to obtain the final map. The regression model explained 89 % of annual frequency of fog variability in the study area. Regression residuals were interpolated via simple kriging.

Sampling design optimisation for rainfall prediction using a non-stationary geostatistical model

NASA Astrophysics Data System (ADS)

Wadoux, Alexandre M. J.-C.; Brus, Dick J.; Rico-Ramirez, Miguel A.; Heuvelink, Gerard B. M.

2017-09-01

The accuracy of spatial predictions of rainfall by merging rain-gauge and radar data is partly determined by the sampling design of the rain-gauge network. Optimising the locations of the rain-gauges may increase the accuracy of the predictions. Existing spatial sampling design optimisation methods are based on minimisation of the spatially averaged prediction error variance under the assumption of intrinsic stationarity. Over the past years, substantial progress has been made to deal with non-stationary spatial processes in kriging. Various well-documented geostatistical models relax the assumption of stationarity in the mean, while recent studies show the importance of considering non-stationarity in the variance for environmental processes occurring in complex landscapes. We optimised the sampling locations of rain-gauges using an extension of the Kriging with External Drift (KED) model for prediction of rainfall fields. The model incorporates both non-stationarity in the mean and in the variance, which are modelled as functions of external covariates such as radar imagery, distance to radar station and radar beam blockage. Spatial predictions are made repeatedly over time, each time recalibrating the model. The space-time averaged KED variance was minimised by Spatial Simulated Annealing (SSA). The methodology was tested using a case study predicting daily rainfall in the north of England for a one-year period. Results show that (i) the proposed non-stationary variance model outperforms the stationary variance model, and (ii) a small but significant decrease of the rainfall prediction error variance is obtained with the optimised rain-gauge network. In particular, it pays off to place rain-gauges at locations where the radar imagery is inaccurate, while keeping the distribution over the study area sufficiently uniform.

The contribution of hydroxylamine content to spatial variability of N2O formation in soil of a Norway spruce forest

NASA Astrophysics Data System (ADS)

Liu, Shurong; Herbst, Michael; Bol, Roland; Gottselig, Nina; Pütz, Thomas; Weymann, Daniel; Wiekenkamp, Inge; Vereecken, Harry; Brüggemann, Nicolas

2016-04-01

Hydroxylamine (NH2OH), a reactive intermediate of several microbial nitrogen turnover processes, is a potential precursor of nitrous oxide (N2O) formation in the soil. However, the contribution of soil NH2OH to soil N2O emission rates in natural ecosystems is unclear. Here, we determined the spatial variability of NH2OH content and potential N2O emission rates of organic (Oh) and mineral (Ah) soil layers of a Norway spruce forest, using a recently developed analytical method for the determination of soil NH2OH content, combined with a geostatistical Kriging approach. Potential soil N2O emission rates were determined by laboratory incubations under oxic conditions, followed by gas chromatographic analysis and complemented by ancillary measurements of soil characteristics. Stepwise multiple regressions demonstrated that the potential N2O emission rates, NH2OH and nitrate (NO3-) content were spatially highly correlated, with hotspots for all three parameters observed in the headwater of a small creek flowing through the sampling area. In contrast, soil ammonium (NH4+) was only weakly correlated with potential N2O emission rates, and was excluded from the multiple regression models. While soil NH2OH content explained the potential soil N2O emission rates best for both layers, also NO3- and Mn content turned out to be significant parameters explaining N2O formation in both soil layers. The Kriging approach was improved markedly by the addition of the co-variable information of soil NH2OH and NO3- content. The results indicate that determination of soil NH2OH content could provide crucial information for the prediction of the spatial variability of soil N2O emissions.

Large-extent digital soil mapping approaches for total soil depth

NASA Astrophysics Data System (ADS)

Mulder, Titia; Lacoste, Marine; Saby, Nicolas P. A.; Arrouays, Dominique

2015-04-01

Total soil depth (SDt) plays a key role in supporting various ecosystem services and properties, including plant growth, water availability and carbon stocks. Therefore, predictive mapping of SDt has been included as one of the deliverables within the GlobalSoilMap project. In this work SDt was predicted for France following the directions of GlobalSoilMap, which requires modelling at 90m resolution. This first method, further referred to as DM, consisted of modelling the deterministic trend in SDt using data mining, followed by a bias correction and ordinary kriging of the residuals. Considering the total surface area of France, being about 540K km2, employed methods may need to be able dealing with large data sets. Therefore, a second method, multi-resolution kriging (MrK) for large datasets, was implemented. This method consisted of modelling the deterministic trend by a linear model, followed by interpolation of the residuals. For the two methods, the general trend was assumed to be explained by the biotic and abiotic environmental conditions, as described by the Soil-Landscape paradigm. The mapping accuracy was evaluated by an internal validation and its concordance with previous soil maps. In addition, the prediction interval for DM and the confidence interval for MrK were determined. Finally, the opportunities and limitations of both approaches were evaluated. The results showed consistency in mapped spatial patterns and a good prediction of the mean values. DM was better capable in predicting extreme values due to the bias correction. Also, DM was more powerful in capturing the deterministic trend than the linear model of the MrK approach. However, MrK was found to be more straightforward and flexible in delivering spatial explicit uncertainty measures. The validation indicated that DM was more accurate than MrK. Improvements for DM may be expected by predicting soil depth classes. MrK shows potential for modelling beyond the country level, at high resolution. Large-extent digital soil mapping approaches for SDt may be improved by (1) taking into account SDt observations which are censored and (2) using high-resolution biotic and abiotic environmental data. The latter may improve modelling the soil-landscape interactions influencing soil pedogenesis. Concluding, this work provided a robust and reproducible method (DM) for high-resolution soil property modelling, in accordance with the GlobalSoilMap requirements and an efficient alternative for large-extent digital soil mapping (MrK).

Spatial Estimation of Sub-Hour Global Horizontal Irradiance Based on Official Observations and Remote Sensors

PubMed Central

Gutierrez-Corea, Federico-Vladimir; Manso-Callejo, Miguel-Angel; Moreno-Regidor, María-Pilar; Velasco-Gómez, Jesús

2014-01-01

This study was motivated by the need to improve densification of Global Horizontal Irradiance (GHI) observations, increasing the number of surface weather stations that observe it, using sensors with a sub-hour periodicity and examining the methods of spatial GHI estimation (by interpolation) with that periodicity in other locations. The aim of the present research project is to analyze the goodness of 15-minute GHI spatial estimations for five methods in the territory of Spain (three geo-statistical interpolation methods, one deterministic method and the HelioSat2 method, which is based on satellite images). The research concludes that, when the work area has adequate station density, the best method for estimating GHI every 15 min is Regression Kriging interpolation using GHI estimated from satellite images as one of the input variables. On the contrary, when station density is low, the best method is estimating GHI directly from satellite images. A comparison between the GHI observed by volunteer stations and the estimation model applied concludes that 67% of the volunteer stations analyzed present values within the margin of error (average of ±2 standard deviations). PMID:24732102

Spatial estimation of sub-hour Global Horizontal Irradiance based on official observations and remote sensors.

PubMed

Gutierrez-Corea, Federico-Vladimir; Manso-Callejo, Miguel-Angel; Moreno-Regidor, María-Pilar; Velasco-Gómez, Jesús

2014-04-11

This study was motivated by the need to improve densification of Global Horizontal Irradiance (GHI) observations, increasing the number of surface weather stations that observe it, using sensors with a sub-hour periodicity and examining the methods of spatial GHI estimation (by interpolation) with that periodicity in other locations. The aim of the present research project is to analyze the goodness of 15-minute GHI spatial estimations for five methods in the territory of Spain (three geo-statistical interpolation methods, one deterministic method and the HelioSat2 method, which is based on satellite images). The research concludes that, when the work area has adequate station density, the best method for estimating GHI every 15 min is Regression Kriging interpolation using GHI estimated from satellite images as one of the input variables. On the contrary, when station density is low, the best method is estimating GHI directly from satellite images. A comparison between the GHI observed by volunteer stations and the estimation model applied concludes that 67% of the volunteer stations analyzed present values within the margin of error (average of ±2 standard deviations).

Determining the area of influence of depression cone in the vicinity of lignite mine by means of triangle method and LANDSAT TM/ETM+ satellite images.

PubMed

Zawadzki, Jarosław; Przeździecki, Karol; Miatkowski, Zygmunt

2016-01-15

Problems with lowering of water table are common all over the world. Intensive pumping of water from aquifers for consumption, irrigation, industrial or mining purposes often causes groundwater depletion and results in the formation of cone of depression. This can severely decrease water pressure, even over vast areas, and can create severe problems such as degradation of agriculture or natural environment sometimes depriving people and animals of water supply. In this paper, the authors present a method for determining the area of influence of a groundwater depression cone resulting from prolonged drainage, by means of satellite images in optical, near infrared and thermal infrared bands from TM sensor (Thematic Mapper) and ETM+ sensor (Enhanced Thematic Mapper +) placed on Landsat 5 and Landsat 7 satellites. The research area was Szczercowska Valley (Pol. Kotlina Szczercowska), Central Poland, located within a range of influence of a groundwater drainage system of the lignite coal mine in Belchatow. It is the biggest lignite coal mine in Poland and one of the largest in Europe exerting an enormous impact on the environment. The main method of satellite data analysis for determining soil moisture, was the so-called triangle method. This method, based on TVDI (Temperature Vegetation Dryness Index) was supported by additional spatial analysis including ordinary kriging used in order to combine fragmentary information obtained from areas covered by meadows. The results obtained are encouraging and confirm the usefulness of the triangle method not only for soil moisture determination but also for assessment of the temporal and spatial changes in the area influenced by the groundwater depression cone. The range of impact of the groundwater depression cone determined by means of above-described remote sensing analysis shows good agreement with that determined by ground measurements. The developed satellite method is much faster and cheaper than in-situ measurements, and allows for systematic monitoring of the vast area in the vicinity of Belchatow lignite mine. Besides, this method could be useful as a helper in in-situ measurement allowing a significant reduction of the number of in-situ measurements by performing them only within problematic areas. Hence, the triangle method can be used as an effective supplement to field measurements. Although the research area is located in Poland, in the vicinity of lignite mine, the method of observation of depression cones provided in this study is universal and effective, and therefore could also be useful to an international audience. Copyright © 2015 Elsevier Ltd. All rights reserved.

Uncertainty assessment of PM2.5 contamination mapping using spatiotemporal sequential indicator simulations and multi-temporal monitoring data.

PubMed

Yang, Yong; Christakos, George; Huang, Wei; Lin, Chengda; Fu, Peihong; Mei, Yang

2016-04-12

Because of the rapid economic growth in China, many regions are subjected to severe particulate matter pollution. Thus, improving the methods of determining the spatiotemporal distribution and uncertainty of air pollution can provide considerable benefits when developing risk assessments and environmental policies. The uncertainty assessment methods currently in use include the sequential indicator simulation (SIS) and indicator kriging techniques. However, these methods cannot be employed to assess multi-temporal data. In this work, a spatiotemporal sequential indicator simulation (STSIS) based on a non-separable spatiotemporal semivariogram model was used to assimilate multi-temporal data in the mapping and uncertainty assessment of PM2.5 distributions in a contaminated atmosphere. PM2.5 concentrations recorded throughout 2014 in Shandong Province, China were used as the experimental dataset. Based on the number of STSIS procedures, we assessed various types of mapping uncertainties, including single-location uncertainties over one day and multiple days and multi-location uncertainties over one day and multiple days. A comparison of the STSIS technique with the SIS technique indicate that a better performance was obtained with the STSIS method.

Uncertainty assessment of PM2.5 contamination mapping using spatiotemporal sequential indicator simulations and multi-temporal monitoring data

NASA Astrophysics Data System (ADS)

Yang, Yong; Christakos, George; Huang, Wei; Lin, Chengda; Fu, Peihong; Mei, Yang

2016-04-01

Because of the rapid economic growth in China, many regions are subjected to severe particulate matter pollution. Thus, improving the methods of determining the spatiotemporal distribution and uncertainty of air pollution can provide considerable benefits when developing risk assessments and environmental policies. The uncertainty assessment methods currently in use include the sequential indicator simulation (SIS) and indicator kriging techniques. However, these methods cannot be employed to assess multi-temporal data. In this work, a spatiotemporal sequential indicator simulation (STSIS) based on a non-separable spatiotemporal semivariogram model was used to assimilate multi-temporal data in the mapping and uncertainty assessment of PM2.5 distributions in a contaminated atmosphere. PM2.5 concentrations recorded throughout 2014 in Shandong Province, China were used as the experimental dataset. Based on the number of STSIS procedures, we assessed various types of mapping uncertainties, including single-location uncertainties over one day and multiple days and multi-location uncertainties over one day and multiple days. A comparison of the STSIS technique with the SIS technique indicate that a better performance was obtained with the STSIS method.

The application of the pilot points in groundwater numerical inversion model

NASA Astrophysics Data System (ADS)

Hu, Bin; Teng, Yanguo; Cheng, Lirong

2015-04-01

Numerical inversion simulation of groundwater has been widely applied in groundwater. Compared to traditional forward modeling, inversion model has more space to study. Zones and inversing modeling cell by cell are conventional methods. Pilot points is a method between them. The traditional inverse modeling method often uses software dividing the model into several zones with a few parameters needed to be inversed. However, distribution is usually too simple for modeler and result of simulation deviation. Inverse cell by cell will get the most actual parameter distribution in theory, but it need computational complexity greatly and quantity of survey data for geological statistical simulation areas. Compared to those methods, pilot points distribute a set of points throughout the different model domains for parameter estimation. Property values are assigned to model cells by Kriging to ensure geological units within the parameters of heterogeneity. It will reduce requirements of simulation area geological statistics and offset the gap between above methods. Pilot points can not only save calculation time, increase fitting degree, but also reduce instability of numerical model caused by numbers of parameters and other advantages. In this paper, we use pilot point in a field which structure formation heterogeneity and hydraulics parameter was unknown. We compare inversion modeling results of zones and pilot point methods. With the method of comparative analysis, we explore the characteristic of pilot point in groundwater inversion model. First, modeler generates an initial spatially correlated field given a geostatistical model by the description of the case site with the software named Groundwater Vistas 6. Defining Kriging to obtain the value of the field functions over the model domain on the basis of their values at measurement and pilot point locations (hydraulic conductivity), then we assign pilot points to the interpolated field which have been divided into 4 zones. And add range of disturbance values to inversion targets to calculate the value of hydraulic conductivity. Third, after inversion calculation (PEST), the interpolated field will minimize an objective function measuring the misfit between calculated and measured data. It's an optimization problem to find the optimum value of parameters. After the inversion modeling, the following major conclusion can be found out: (1) In a field structure formation is heterogeneity, the results of pilot point method is more real: better fitting result of parameters, more stable calculation of numerical simulation (stable residual distribution). Compared to zones, it is better of reflecting the heterogeneity of study field. (2) Pilot point method ensures that each parameter is sensitive and not entirely dependent on other parameters. Thus it guarantees the relative independence and authenticity of parameters evaluation results. However, it costs more time to calculate than zones. Key words: groundwater; pilot point; inverse model; heterogeneity; hydraulic conductivity

Estimation of a Historic Mercury Load Function for Lake Michigan using Dated Sediment Cores

EPA Science Inventory

Box cores collected between 1994 and 1996 were used to estimate historic mercury loads to Lake Michigan. Based on a kriging spatial interpolation of 54 Pb-210 dated cores, 228 metric tons of mercury are stored in the lake’s sediments (excluding Green Bay). To estimate the time ...

Mechanical Characterization of Polysilicon MEMS: A Hybrid TMCMC/POD-Kriging Approach.

PubMed

Mirzazadeh, Ramin; Eftekhar Azam, Saeed; Mariani, Stefano

2018-04-17

Microscale uncertainties related to the geometry and morphology of polycrystalline silicon films, constituting the movable structures of micro electro-mechanical systems (MEMS), were investigated through a joint numerical/experimental approach. An on-chip testing device was designed and fabricated to deform a compliant polysilicon beam. In previous studies, we showed that the scattering in the input–output characteristics of the device can be properly described only if statistical features related to the morphology of the columnar polysilicon film and to the etching process adopted to release the movable structure are taken into account. In this work, a high fidelity finite element model of the device was used to feed a transitional Markov chain Monte Carlo (TMCMC) algorithm for the estimation of the unknown parameters governing the aforementioned statistical features. To reduce the computational cost of the stochastic analysis, a synergy of proper orthogonal decomposition (POD) and kriging interpolation was adopted. Results are reported for a batch of nominally identical tested devices, in terms of measurement error-affected probability distributions of the overall Young’s modulus of the polysilicon film and of the overetch depth.

Modeling of surface dust concentrations using neural networks and kriging

NASA Astrophysics Data System (ADS)

Buevich, Alexander G.; Medvedev, Alexander N.; Sergeev, Alexander P.; Tarasov, Dmitry A.; Shichkin, Andrey V.; Sergeeva, Marina V.; Atanasova, T. B.

2016-12-01

Creating models which are able to accurately predict the distribution of pollutants based on a limited set of input data is an important task in environmental studies. In the paper two neural approaches: (multilayer perceptron (MLP)) and generalized regression neural network (GRNN)), and two geostatistical approaches: (kriging and cokriging), are using for modeling and forecasting of dust concentrations in snow cover. The area of study is under the influence of dust emissions from a copper quarry and a several industrial companies. The comparison of two mentioned approaches is conducted. Three indices are used as the indicators of the models accuracy: the mean absolute error (MAE), root mean square error (RMSE) and relative root mean square error (RRMSE). Models based on artificial neural networks (ANN) have shown better accuracy. When considering all indices, the most precision model was the GRNN, which uses as input parameters for modeling the coordinates of sampling points and the distance to the probable emissions source. The results of work confirm that trained ANN may be more suitable tool for modeling of dust concentrations in snow cover.

A climate trend analysis of Kenya-August 2010

USGS Publications Warehouse

Funk, Christopher C.

2010-01-01

Introduction This brief report draws from a multi-year effort by the United States Agency for International Development's Famine Early Warning System Network (FEWS NET) to monitor and map rainfall and temperature trends over the last 50 years (1960-2009) in Kenya. Observations from seventy rainfall gauges and seventeen air temperature stations were analyzed for the long rains period, corresponding to March through June (MAMJ). The data were quality controlled, converted into 1960-2009 trend estimates, and interpolated using a rigorous geo-statistical technique (kriging). Kriging produces standard error estimates, and these can be used to assess the relative spatial accuracy of the identified trends. Dividing the trends by the associated errors allows us to identify the relative certainty of our estimates (Funk and others, 2005; Verdin and others, 2005; Brown and Funk, 2008; Funk and Verdin, 2009). Assuming that the same observed trends persist, regardless of whether or not these changes are due to anthropogenic or natural cyclical causes, these results can be extended to 2025, providing critical, and heretofore missing information about the types and locations of adaptation efforts that may be required to improve food security.

Determination of Time Dependent Virus Inactivation Rates

NASA Astrophysics Data System (ADS)

Chrysikopoulos, C. V.; Vogler, E. T.

2003-12-01

A methodology is developed for estimating temporally variable virus inactivation rate coefficients from experimental virus inactivation data. The methodology consists of a technique for slope estimation of normalized virus inactivation data in conjunction with a resampling parameter estimation procedure. The slope estimation technique is based on a relatively flexible geostatistical method known as universal kriging. Drift coefficients are obtained by nonlinear fitting of bootstrap samples and the corresponding confidence intervals are obtained by bootstrap percentiles. The proposed methodology yields more accurate time dependent virus inactivation rate coefficients than those estimated by fitting virus inactivation data to a first-order inactivation model. The methodology is successfully applied to a set of poliovirus batch inactivation data. Furthermore, the importance of accurate inactivation rate coefficient determination on virus transport in water saturated porous media is demonstrated with model simulations.

Spatio-temporal prediction of daily temperatures using time-series of MODIS LST images

NASA Astrophysics Data System (ADS)

Hengl, Tomislav; Heuvelink, Gerard B. M.; Perčec Tadić, Melita; Pebesma, Edzer J.

2012-01-01

A computational framework to generate daily temperature maps using time-series of publicly available MODIS MOD11A2 product Land Surface Temperature (LST) images (1 km resolution; 8-day composites) is illustrated using temperature measurements from the national network of meteorological stations (159) in Croatia. The input data set contains 57,282 ground measurements of daily temperature for the year 2008. Temperature was modeled as a function of latitude, longitude, distance from the sea, elevation, time, insolation, and the MODIS LST images. The original rasters were first converted to principal components to reduce noise and filter missing pixels in the LST images. The residual were next analyzed for spatio-temporal auto-correlation; sum-metric separable variograms were fitted to account for zonal and geometric space-time anisotropy. The final predictions were generated for time-slices of a 3D space-time cube, constructed in the R environment for statistical computing. The results show that the space-time regression model can explain a significant part of the variation in station-data (84%). MODIS LST 8-day (cloud-free) images are unbiased estimator of the daily temperature, but with relatively low precision (±4.1°C); however their added value is that they systematically improve detection of local changes in land surface temperature due to local meteorological conditions and/or active heat sources (urban areas, land cover classes). The results of 10-fold cross-validation show that use of spatio-temporal regression-kriging and incorporation of time-series of remote sensing images leads to significantly more accurate maps of temperature than if plain spatial techniques were used. The average (global) accuracy of mapping temperature was ±2.4°C. The regression-kriging explained 91% of variability in daily temperatures, compared to 44% for ordinary kriging. Further software advancement—interactive space-time variogram exploration and automated retrieval, resampling and filtering of MODIS images—are anticipated.

Using rainfall radar data to improve interpolated maps of dose rate in the Netherlands.

PubMed

Hiemstra, Paul H; Pebesma, Edzer J; Heuvelink, Gerard B M; Twenhöfel, Chris J W

2010-12-01

The radiation monitoring network in the Netherlands is designed to detect and track increased radiation levels, dose rate more specifically, in 10-minute intervals. The network consists of 153 monitoring stations. Washout of radon progeny by rainfall is the most important cause of natural variations in dose rate. The increase in dose rate at a given time is a function of the amount of progeny decaying, which in turn is a balance between deposition of progeny by rainfall and radioactive decay. The increase in progeny is closely related to average rainfall intensity over the last 2.5h. We included decay of progeny by using weighted averaged rainfall intensity, where the weight decreases back in time. The decrease in weight is related to the half-life of radon progeny. In this paper we show for a rainstorm on the 20th of July 2007 that weighted averaged rainfall intensity estimated from rainfall radar images, collected every 5min, performs much better as a predictor of increases in dose rate than using the non-averaged rainfall intensity. In addition, we show through cross-validation that including weighted averaged rainfall intensity in an interpolated map using universal kriging (UK) does not necessarily lead to a more accurate map. This might be attributed to the high density of monitoring stations in comparison to the spatial extent of a typical rain event. Reducing the network density improved the accuracy of the map when universal kriging was used instead of ordinary kriging (no trend). Consequently, in a less dense network the positive influence of including a trend is likely to increase. Furthermore, we suspect that UK better reproduces the sharp boundaries present in rainfall maps, but that the lack of short-distance monitoring station pairs prevents cross-validation from revealing this effect. Copyright © 2010 Elsevier B.V. All rights reserved.

Spatial Statistical Data Fusion (SSDF)

NASA Technical Reports Server (NTRS)

Braverman, Amy J.; Nguyen, Hai M.; Cressie, Noel

2013-01-01

As remote sensing for scientific purposes has transitioned from an experimental technology to an operational one, the selection of instruments has become more coordinated, so that the scientific community can exploit complementary measurements. However, tech nological and scientific heterogeneity across devices means that the statistical characteristics of the data they collect are different. The challenge addressed here is how to combine heterogeneous remote sensing data sets in a way that yields optimal statistical estimates of the underlying geophysical field, and provides rigorous uncertainty measures for those estimates. Different remote sensing data sets may have different spatial resolutions, different measurement error biases and variances, and other disparate characteristics. A state-of-the-art spatial statistical model was used to relate the true, but not directly observed, geophysical field to noisy, spatial aggregates observed by remote sensing instruments. The spatial covariances of the true field and the covariances of the true field with the observations were modeled. The observations are spatial averages of the true field values, over pixels, with different measurement noise superimposed. A kriging framework is used to infer optimal (minimum mean squared error and unbiased) estimates of the true field at point locations from pixel-level, noisy observations. A key feature of the spatial statistical model is the spatial mixed effects model that underlies it. The approach models the spatial covariance function of the underlying field using linear combinations of basis functions of fixed size. Approaches based on kriging require the inversion of very large spatial covariance matrices, and this is usually done by making simplifying assumptions about spatial covariance structure that simply do not hold for geophysical variables. In contrast, this method does not require these assumptions, and is also computationally much faster. This method is fundamentally different than other approaches to data fusion for remote sensing data because it is inferential rather than merely descriptive. All approaches combine data in a way that minimizes some specified loss function. Most of these are more or less ad hoc criteria based on what looks good to the eye, or some criteria that relate only to the data at hand.

Geostatistics and petroleum geology

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

Hohn, M.E.

1988-01-01

The book reviewed is designed as a practical guide to geostatistics or kriging for the petroleum geologists. The author's aim in the book is to explain geostatistics as a working tool for petroleum geologists through extensive use of case-study material mostly drawn from his own research in gas potential evaluation in West Virginia. Theory and mathematics are pared down to immediate needs.

DMSP F11 SSM/T-2 Calibration and Validation

DTIC Science & Technology

1992-10-29

throughput and memory allocations . I We express our respect for those visionaries of the past who conceived of the idea of an SSM/`T-2 and worked to...82 pp. Kriging, D.P., 1973, Analyse Objective du geopotential et du vent geostrophique par Krigeage universel , LaMetoiQ"i , V-25. Lindzen, R. S

Estimating Small-area Populations by Age and Sex Using Spatial Interpolation and Statistical Inference Methods

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

Qai, Qiang; Rushton, Gerald; Bhaduri, Budhendra L

The objective of this research is to compute population estimates by age and sex for small areas whose boundaries are different from those for which the population counts were made. In our approach, population surfaces and age-sex proportion surfaces are separately estimated. Age-sex population estimates for small areas and their confidence intervals are then computed using a binomial model with the two surfaces as inputs. The approach was implemented for Iowa using a 90 m resolution population grid (LandScan USA) and U.S. Census 2000 population. Three spatial interpolation methods, the areal weighting (AW) method, the ordinary kriging (OK) method, andmore » a modification of the pycnophylactic method, were used on Census Tract populations to estimate the age-sex proportion surfaces. To verify the model, age-sex population estimates were computed for paired Block Groups that straddled Census Tracts and therefore were spatially misaligned with them. The pycnophylactic method and the OK method were more accurate than the AW method. The approach is general and can be used to estimate subgroup-count types of variables from information in existing administrative areas for custom-defined areas used as the spatial basis of support in other applications.« less

Application of validation data for assessing spatial interpolation methods for 8-h ozone or other sparsely monitored constituents.

PubMed

Joseph, John; Sharif, Hatim O; Sunil, Thankam; Alamgir, Hasanat

2013-07-01

The adverse health effects of high concentrations of ground-level ozone are well-known, but estimating exposure is difficult due to the sparseness of urban monitoring networks. This sparseness discourages the reservation of a portion of the monitoring stations for validation of interpolation techniques precisely when the risk of overfitting is greatest. In this study, we test a variety of simple spatial interpolation techniques for 8-h ozone with thousands of randomly selected subsets of data from two urban areas with monitoring stations sufficiently numerous to allow for true validation. Results indicate that ordinary kriging with only the range parameter calibrated in an exponential variogram is the generally superior method, and yields reliable confidence intervals. Sparse data sets may contain sufficient information for calibration of the range parameter even if the Moran I p-value is close to unity. R script is made available to apply the methodology to other sparsely monitored constituents. Copyright © 2013 Elsevier Ltd. All rights reserved.

Impact of Drainage Networks on Cholera Outbreaks in Lusaka, Zambia

PubMed Central

Suzuki, Hiroshi; Fujino, Yasuyuki; Kimura, Yoshinari; Cheelo, Meetwell

2009-01-01

Objectives. We investigated the association between precipitation patterns and cholera outbreaks and the preventative roles of drainage networks against outbreaks in Lusaka, Zambia. Methods. We collected data on 6542 registered cholera patients in the 2003–2004 outbreak season and on 6045 cholera patients in the 2005–2006 season. Correlations between monthly cholera incidences and amount of precipitation were examined. The distribution pattern of the disease was analyzed by a kriging spatial analysis method. We analyzed cholera case distribution and spatiotemporal cluster by using 2590 cholera cases traced with a global positioning system in the 2005–2006 season. The association between drainage networks and cholera cases was analyzed with regression analysis. Results. Increased precipitation was associated with the occurrence of cholera outbreaks, and insufficient drainage networks were statistically associated with cholera incidences. Conclusions. Insufficient coverage of drainage networks elevated the risk of cholera outbreaks. Integrated development is required to upgrade high-risk areas with sufficient infrastructure for a long-term cholera prevention strategy. PMID:19762668

A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models

NASA Technical Reports Server (NTRS)

Giunta, Anthony A.; Watson, Layne T.

1998-01-01

Two methods of creating approximation models are compared through the calculation of the modeling accuracy on test problems involving one, five, and ten independent variables. Here, the test problems are representative of the modeling challenges typically encountered in realistic engineering optimization problems. The first approximation model is a quadratic polynomial created using the method of least squares. This type of polynomial model has seen considerable use in recent engineering optimization studies due to its computational simplicity and ease of use. However, quadratic polynomial models may be of limited accuracy when the response data to be modeled have multiple local extrema. The second approximation model employs an interpolation scheme known as kriging developed in the fields of spatial statistics and geostatistics. This class of interpolating model has the flexibility to model response data with multiple local extrema. However, this flexibility is obtained at an increase in computational expense and a decrease in ease of use. The intent of this study is to provide an initial exploration of the accuracy and modeling capabilities of these two approximation methods.

Testing geostatistical methods to combine radar and rain gauges for precipitation mapping in a mountainous region

NASA Astrophysics Data System (ADS)

Erdin, R.; Frei, C.; Sideris, I.; Kuensch, H.-R.

2010-09-01

There is an increasing demand for accurate mapping of precipitation at a spatial resolution of kilometers. Radar and rain gauges - the two main precipitation measurement systems - exhibit complementary strengths and weaknesses. Radar offers high spatial and temporal resolution but lacks accuracy of absolute values, whereas rain gauges provide accurate values at their specific point location but suffer from poor spatial representativeness. Methods of geostatistical mapping have been proposed to combine radar and rain gauge data for quantitative precipitation estimation (QPE). The aim is to combine the respective strengths and compensate for the respective weaknesses of the two observation platforms. Several studies have demonstrated the potential of these methods over topography of moderate complexity, but their performance remains unclear for high-mountain regions where rainfall patterns are complex, the representativeness of rain gauge measurements is limited and radar observations are obstructed. In this study we examine the potential and limitations of two frequently used geostatistical mapping methods for the territory of Switzerland, where the mountain chain of the Alps poses particular challenges to QPE. The two geostatistical methods explored are kriging with external drift (KED) using radar as drift variable and ordinary kriging of radar errors (OKRE). The radar data is a composite from three C-band radars using a constant Z-R relationship, advanced correction processings for visibility, ground clutter and beam shielding and a climatological bias adjustment. The rain gauge data originates from an automatic network with a typical inter-station distance of 25 km. Both combination methods are applied to a set of case examples representing typical rainfall situations in the Alps with their inherent challenges at daily and hourly time resolution. The quality of precipitation estimates is assessed by several skill scores calculated from cross validation errors at gauge locations. These scores assess different characteristics such as bias, distinction between dry and wet areas (HK, SLEEPS), accuracy of values at wet locations (SCATTER) and overall performance (RMSE, MAD). Special attention is paid to the subject of appropriate case-dependent transformation of variables in order to fulfill model assumptions. Our analyses show that geostatistical merging techniques can provide significant added value compared to pure radar and pure rain gauge data - also in mountainous terrain. Yet, the high a-priori quality of the radar product may have been essential for the good performance of methods. The comparison between the two combination methods shows better results in general for KED, the more flexible of the two methods. However, there are features, such as the differentiation between wet and dry areas (HK), and situations, such as small isolated convective cells, where OKRE outperforms KED. Our discussion conveys interesting insights into the potential and limitations of the two analyzed methods and leads to suggestions for further improvements of combination techniques.

New spatial upscaling methods for multi-point measurements: From normal to p-normal

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Xin

2017-12-01

Careful attention must be given to determining whether the geophysical variables of interest are normally distributed, since the assumption of a normal distribution may not accurately reflect the probability distribution of some variables. As a generalization of the normal distribution, the p-normal distribution and its corresponding maximum likelihood estimation (the least power estimation, LPE) were introduced in upscaling methods for multi-point measurements. Six methods, including three normal-based methods, i.e., arithmetic average, least square estimation, block kriging, and three p-normal-based methods, i.e., LPE, geostatistics LPE and inverse distance weighted LPE are compared in two types of experiments: a synthetic experiment to evaluate the performance of the upscaling methods in terms of accuracy, stability and robustness, and a real-world experiment to produce real-world upscaling estimates using soil moisture data obtained from multi-scale observations. The results show that the p-normal-based methods produced lower mean absolute errors and outperformed the other techniques due to their universality and robustness. We conclude that introducing appropriate statistical parameters into an upscaling strategy can substantially improve the estimation, especially if the raw measurements are disorganized; however, further investigation is required to determine which parameter is the most effective among variance, spatial correlation information and parameter p.

Mapping Urban Environmental Noise Using Smartphones.

PubMed

Zuo, Jinbo; Xia, Hao; Liu, Shuo; Qiao, Yanyou

2016-10-13

Noise mapping is an effective method of visualizing and accessing noise pollution. In this paper, a noise-mapping method based on smartphones to effectively and easily measure environmental noise is proposed. By using this method, a noise map of an entire area can be created using limited measurement data. To achieve the measurement with certain precision, a set of methods was designed to calibrate the smartphones. Measuring noise with mobile phones is different from the traditional static observations. The users may be moving at any time. Therefore, a method of attaching an additional microphone with a windscreen is proposed to reduce the wind effect. However, covering an entire area is impossible. Therefore, an interpolation method is needed to achieve full coverage of the area. To reduce the influence of spatial heterogeneity and improve the precision of noise mapping, a region-based noise-mapping method is proposed in this paper, which is based on the distribution of noise in different region types tagged by volunteers, to interpolate and combine them to create a noise map. To validate the effect of the method, a comparison of the interpolation results was made to analyse our method and the ordinary Kriging method. The result shows that our method is more accurate in reflecting the local distribution of noise and has better interpolation precision. We believe that the proposed noise-mapping method is a feasible and low-cost noise-mapping solution.

Mapping Urban Environmental Noise Using Smartphones

PubMed Central

Zuo, Jinbo; Xia, Hao; Liu, Shuo; Qiao, Yanyou

2016-01-01

Noise mapping is an effective method of visualizing and accessing noise pollution. In this paper, a noise-mapping method based on smartphones to effectively and easily measure environmental noise is proposed. By using this method, a noise map of an entire area can be created using limited measurement data. To achieve the measurement with certain precision, a set of methods was designed to calibrate the smartphones. Measuring noise with mobile phones is different from the traditional static observations. The users may be moving at any time. Therefore, a method of attaching an additional microphone with a windscreen is proposed to reduce the wind effect. However, covering an entire area is impossible. Therefore, an interpolation method is needed to achieve full coverage of the area. To reduce the influence of spatial heterogeneity and improve the precision of noise mapping, a region-based noise-mapping method is proposed in this paper, which is based on the distribution of noise in different region types tagged by volunteers, to interpolate and combine them to create a noise map. To validate the effect of the method, a comparison of the interpolation results was made to analyse our method and the ordinary Kriging method. The result shows that our method is more accurate in reflecting the local distribution of noise and has better interpolation precision. We believe that the proposed noise-mapping method is a feasible and low-cost noise-mapping solution. PMID:27754359

Mapping pyrophilic percentages across the northeastern United States using witness trees, with focus on four national forests

Treesearch

Melissa A. Thomas-Van Gundy; Gregory J. Nowacki; Charles V. Cogbill

2015-01-01

Witness trees provide information fundamental for restoration ecology, often serving as baselines for forest composition and structure. Furthermore, when categorized by fire relations, witness trees can shed light on past disturbance regimes. Kriging was applied to witness-tree point data to form a contiguous surface of pyrophilic percentage for four national forests...

A crustal seismic velocity model for the UK, Ireland and surrounding seas

USGS Publications Warehouse

Kelly, A.; England, R.W.; Maguire, Peter K.H.

2007-01-01

A regional model of the 3-D variation in seismic P-wave velocity structure in the crust of NW Europe has been compiled from wide-angle reflection/refraction profiles. Along each 2-D profile a velocity-depth function has been digitised at 5 km intervals. These 1-D velocity functions were mapped into three dimensions using ordinary kriging with weights determined to minimise the difference between digitised and interpolated values. An analysis of variograms of the digitised data suggested a radial isotropic weighting scheme was most appropriate. Horizontal dimensions of the model cells are optimised at 40 ?? 40 km and the vertical dimension at 1 km. The resulting model provides a higher resolution image of the 3-D variation in seismic velocity structure of the UK, Ireland and surrounding areas than existing models. The construction of the model through kriging allows the uncertainty in the velocity structure to be assessed. This uncertainty indicates the high density of data required to confidently interpolate the crustal velocity structure, and shows that for this region the velocity is poorly constrained for large areas away from the input data. ?? 2007 The Authors Journal compilation ?? 2007 RAS.

Spatial analysis of hazardous waste data using geostatistics

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

Zirschky, J.H.

1984-01-01

The objective of this investigation was to determine if geostatistics could be a useful tool for evaluating hazardous waste sites. Three sites contaminated by dioxin (2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD)) were investigated. The first site evaluated was a creek into which TCDD-contaminated soil had eroded. The second site was a town in which TCDD-contaminated wastes had been sprayed onto the streets. Finally, the third site was a highway of which the shoulders were contaminated by dust deposition from a nearby hazardous waste site. The distribution of TCDD at the first and third sites were investigated using kriging, an optimal estimation technique. By usingmore » kriging, the areas of both sites requiring cleanup were successfully identified. At the second site, the town, satisfactory results were not obtained. The distribution of contamination in this town is believed to be very heterogeneous; thus, reasonable estimates could not be obtained. Additional sampling was therefore recommended at this site. Based upon this research, geostatistics appears to be a very useful tool for evaluating a hazardous waste site if the distribution of contaminants at the site is homogeneous, or can be divided into homogeneous areas.« less

Using direct current resistivity sounding and geostatistics to aid in hydrogeological studies in the Choshuichi alluvial fan, Taiwan.

PubMed

Yang, Chieh-Hou; Lee, Wei-Feng

2002-01-01

Ground water reservoirs in the Choshuichi alluvial fan, central western Taiwan, were investigated using direct-current (DC) resistivity soundings at 190 locations, combined with hydrogeological measurements from 37 wells. In addition, attempts were made to calculate aquifer transmissivity from both surface DC resistivity measurements and geostatistically derived predictions of aquifer properties. DC resistivity sounding data are highly correlated to the hydraulic parameters in the Choshuichi alluvial fan. By estimating the spatial distribution of hydraulic conductivity from the kriged well data and the cokriged thickness of the correlative aquifer from both resistivity sounding data and well information, the transmissivity of the aquifer at each location can be obtained from the product of kriged hydraulic conductivity and computed thickness of the geoelectric layer. Thus, the spatial variation of the transmissivities in the study area is obtained. Our work is more comparable to Ahmed et al. (1988) than to the work of Niwas and Singhal (1981). The first "constraint" from Niwas and Singhal's work is a result of their use of linear regression. The geostatistical approach taken here (and by Ahmed et al. [1988]) is a natural improvement on the linear regression approach.

An ArcGIS approach to include tectonic structures in point data regionalization.

PubMed

Darsow, Andreas; Schafmeister, Maria-Theresia; Hofmann, Thilo

2009-01-01

Point data derived from drilling logs must often be regionalized. However, aquifers may show discontinuous surface structures, such as the offset of an aquitard caused by tectonic faults. One main challenge has been to incorporate these structures into the regionalization process of point data. We combined ordinary kriging and inverse distance weighted (IDW) interpolation to account for neotectonic structures in the regionalization process. The study area chosen to test this approach is the largest porous aquifer in Austria. It consists of three basins formed by neotectonic events and delimited by steep faults with a vertical offset of the aquitard up to 70 m within very short distances. First, ordinary kriging was used to incorporate the characteristic spatial variability of the aquitard location by means of a variogram. The tectonic faults could be included into the regionalization process by using breaklines with buffer zones. All data points inside the buffer were deleted. Last, IDW was performed, resulting in an aquitard map representing the discontinuous surface structures. This approach enables one to account for such surfaces using the standard software package ArcGIS; therefore, it could be adopted in many practical applications.

Indonesian Geomagnetic Maps for Epoch 2015.0 to cover of Indonesian Regions

NASA Astrophysics Data System (ADS)

Syirojudin, M.; Murjaya, J.; Zubaidah, S.; Hasanudin; Ahadi, S.; Efendi, N.; Suroyo, T.

2018-03-01

In compliance with the resolutions of IAGA (International Association of Geomagnetism and Aeronomy), Since 1960’s, every five years BMKG or Meteorology, Climatology and Geophysics Agency of Indonesia made geomagnetic field maps based on actual measurements in 53 repeat stations. It’s the map for more accurate result of Geomagnetic maps Epoch 2015.0, the number of repeat stations has been increased to 68 locations. Analysis data was conducted by spatial analyses using collocated co-kriging and kriging with external drift to map the observation data in five components, such as Declination (D), Inclination (I), Vertical (Z), Horizontal (H), and Total Geomagnetic Field (F). The data reduction used one permanent observatory i.e., Kupang Geophysical Observatory, as a reference standard. The results of this Geomagnetic Maps, that the contour lines of Indonesian geomagnetic declination in range -1 to 4.5 degree, Inclination component are -5 to -37 degree, Vertical component are -4000 to -28000 nT, Horizontal component are 36000 to 42000 nT, and Total Geomagnetic Field are 39000 to 46000 nT. In conclusion, Indonesian Geomagnetic Maps for Epoch 2015.0 can be used to compute geomagnetic data around Indonesian regions until next 5 years.

Uncertainty quantification of resonant ultrasound spectroscopy for material property and single crystal orientation estimation on a complex part

NASA Astrophysics Data System (ADS)

Aldrin, John C.; Mayes, Alexander; Jauriqui, Leanne; Biedermann, Eric; Heffernan, Julieanne; Livings, Richard; Goodlet, Brent; Mazdiyasni, Siamack

2018-04-01

A case study is presented evaluating uncertainty in Resonance Ultrasound Spectroscopy (RUS) inversion for a single crystal (SX) Ni-based superalloy Mar-M247 cylindrical dog-bone specimens. A number of surrogate models were developed with FEM model solutions, using different sampling schemes (regular grid, Monte Carlo sampling, Latin Hyper-cube sampling) and model approaches, N-dimensional cubic spline interpolation and Kriging. Repeated studies were used to quantify the well-posedness of the inversion problem, and the uncertainty was assessed in material property and crystallographic orientation estimates given typical geometric dimension variability in aerospace components. Surrogate model quality was found to be an important factor in inversion results when the model more closely represents the test data. One important discovery was when the model matches well with test data, a Kriging surrogate model using un-sorted Latin Hypercube sampled data performed as well as the best results from an N-dimensional interpolation model using sorted data. However, both surrogate model quality and mode sorting were found to be less critical when inverting properties from either experimental data or simulated test cases with uncontrolled geometric variation.

Developing GIS-based eastern equine encephalitis vector-host models in Tuskegee, Alabama.

PubMed

Jacob, Benjamin G; Burkett-Cadena, Nathan D; Luvall, Jeffrey C; Parcak, Sarah H; McClure, Christopher J W; Estep, Laura K; Hill, Geoffrey E; Cupp, Eddie W; Novak, Robert J; Unnasch, Thomas R

2010-02-24

A site near Tuskegee, Alabama was examined for vector-host activities of eastern equine encephalomyelitis virus (EEEV). Land cover maps of the study site were created in ArcInfo 9.2 from QuickBird data encompassing visible and near-infrared (NIR) band information (0.45 to 0.72 microm) acquired July 15, 2008. Georeferenced mosquito and bird sampling sites, and their associated land cover attributes from the study site, were overlaid onto the satellite data. SAS 9.1.4 was used to explore univariate statistics and to generate regression models using the field and remote-sampled mosquito and bird data. Regression models indicated that Culex erracticus and Northern Cardinals were the most abundant mosquito and bird species, respectively. Spatial linear prediction models were then generated in Geostatistical Analyst Extension of ArcGIS 9.2. Additionally, a model of the study site was generated, based on a Digital Elevation Model (DEM), using ArcScene extension of ArcGIS 9.2. For total mosquito count data, a first-order trend ordinary kriging process was fitted to the semivariogram at a partial sill of 5.041 km, nugget of 6.325 km, lag size of 7.076 km, and range of 31.43 km, using 12 lags. For total adult Cx. erracticus count, a first-order trend ordinary kriging process was fitted to the semivariogram at a partial sill of 5.764 km, nugget of 6.114 km, lag size of 7.472 km, and range of 32.62 km, using 12 lags. For the total bird count data, a first-order trend ordinary kriging process was fitted to the semivariogram at a partial sill of 4.998 km, nugget of 5.413 km, lag size of 7.549 km and range of 35.27 km, using 12 lags. For the Northern Cardinal count data, a first-order trend ordinary kriging process was fitted to the semivariogram at a partial sill of 6.387 km, nugget of 5.935 km, lag size of 8.549 km and a range of 41.38 km, using 12 lags. Results of the DEM analyses indicated a statistically significant inverse linear relationship between total sampled mosquito data and elevation (R2 = -.4262; p < .0001), with a standard deviation (SD) of 10.46, and total sampled bird data and elevation (R2 = -.5111; p < .0001), with a SD of 22.97. DEM statistics also indicated a significant inverse linear relationship between total sampled Cx. erracticus data and elevation (R2 = -.4711; p < .0001), with a SD of 11.16, and the total sampled Northern Cardinal data and elevation (R2 = -.5831; p < .0001), SD of 11.42. These data demonstrate that GIS/remote sensing models and spatial statistics can capture space-varying functional relationships between field-sampled mosquito and bird parameters for determining risk for EEEV transmission.

The concurrent multiplicative-additive approach for gauge-radar/satellite multisensor precipitation estimates

NASA Astrophysics Data System (ADS)

Garcia-Pintado, J.; Barberá, G. G.; Erena Arrabal, M.; Castillo, V. M.

2010-12-01

Objective analysis schemes (OAS), also called ``succesive correction methods'' or ``observation nudging'', have been proposed for multisensor precipitation estimation combining remote sensing data (meteorological radar or satellite) with data from ground-based raingauge networks. However, opposite to the more complex geostatistical approaches, the OAS techniques for this use are not optimized. On the other hand, geostatistical techniques ideally require, at the least, modelling the covariance from the rain gauge data at every time step evaluated, which commonly cannot be soundly done. Here, we propose a new procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) for operational rainfall estimation using rain gauges and meteorological radar, which does not require explicit modelling of spatial covariances. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on the OAS, whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The approach considers radar estimates as background a priori information (first guess), so that nudging to observations (gauges) may be relaxed smoothly to the first guess, and the relaxation shape is obtained from the sequential optimization. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, an OAS spatially variable adjustment with multiplicative factors, ordinary cokriging, and kriging with external drift. In theory, it could be equally applicable to gauge-satellite estimates and other hydrometeorological variables.

Evaluating and Mapping of Spatial Air Ion Quality Patterns in a Residential Garden Using a Geostatistic Method

PubMed Central

Wu, Chen-Fa; Lai, Chun-Hsien; Chu, Hone-Jay; Lin, Wen-Huang

2011-01-01

Negative air ions (NAI) produce biochemical reactions that increase the levels of the mood chemical serotonin in the environment. Moreover, they benefit both the psychological well being and the human body’s physiological condition. The aim of this research was to estimate and measure the spatial distributions of negative and positive air ions in a residential garden in central Taiwan. Negative and positive air ions were measured at thirty monitoring locations in the study garden from July 2009 to June 2010. Moreover, Kriging was applied to estimate the spatial distribution of negative and positive air ions, as well as the air ion index in the study area. The measurement results showed that the numbers of NAI and PAI differed greatly during the four seasons, the highest and the lowest negative and positive air ion concentrations were found in the summer and winter, respectively. Moreover, temperature was positively affected negative air ions concentration. No matter what temperature is, the ranges of variogram in NAI/PAI were similar during four seasons. It indicated that spatial patterns of NAI/PAI were independent of the seasons and depended on garden elements and configuration, thus the NAP/PAI was a good estimate of the air quality regarding air ions. Kriging maps depicted that the highest negative and positive air ion concentration was next to the waterfall, whereas the lowest air ions areas were next to the exits of the garden. The results reveal that waterscapes are a source of negative and positive air ions, and that plants and green space are a minor source of negative air ions in the study garden. Moreover, temperature and humidity are positively and negatively affected negative air ions concentration, respectively. The proposed monitoring and mapping approach provides a way to effectively assess the patterns of negative and positive air ions in future landscape design projects. PMID:21776231

Irrigation salinity hazard assessment and risk mapping in the lower Macintyre Valley, Australia.

PubMed

Huang, Jingyi; Prochazka, Melissa J; Triantafilis, John

2016-05-01

In the Murray-Darling Basin of Australia, secondary soil salinization occurs due to excessive deep drainage and the presence of shallow saline water tables. In order to understand the cause and best management, soil and vadose zone information is necessary. This type of information has been generated in the Toobeah district but owing to the state border an inconsistent methodology was used. This has led to much confusion from stakeholders who are unable to understand the ambiguity of the results in terms of final overall risk of salinization. In this research, a digital soil mapping method that employs various ancillary data is presented. Firstly, an electromagnetic induction survey using a Geonics EM34 and EM38 was used to characterise soil and vadose zone stratigraphy. From the apparent electrical conductivity (ECa) collected, soil sampling locations were selected and with laboratory analysis carried out to determine average (2-12m) clay and EC of a saturated soil-paste extract (ECe). EM34 ECa, land surface parameters derived from a digital elevation model and measured soil data were used to establish multiple linear regression models, which allowed for mapping of various hazard factors, including clay and ECe. EM38 ECa data were calibrated to deep drainage obtained from Salt and Leaching Fraction (SaLF) modelling of soil data. Expert knowledge and indicator kriging were used to determine critical values where the salinity hazard factors were likely to contribute to a shallow saline water table (i.e., clay ≤35%; ECe>2.5dS/m, and deep drainage >100mm/year). This information was combined to produce an overall salinity risk map for the Toobeah district using indicator kriging. The risk map shows potential salinization areas and where detailed information is required and where targeted research can be conducted to monitor soil conditions and water table heights and determine best management strategies. Copyright © 2016 Elsevier B.V. All rights reserved.

Surface emission determination of volatile organic compounds (VOC) from a closed industrial waste landfill using a self-designed static flux chamber.

PubMed

Gallego, E; Perales, J F; Roca, F J; Guardino, X

2014-02-01

Closed landfills can be a source of VOC and odorous nuisances to their atmospheric surroundings. A self-designed cylindrical air flux chamber was used to measure VOC surface emissions in a closed industrial landfill located in Cerdanyola del Vallès, Catalonia, Spain. The two main objectives of the study were the evaluation of the performance of the chamber setup in typical measurement conditions and the determination of the emission rates of 60 different VOC from that industrial landfill, generating a valuable database that can be useful in future studies related to industrial landfill management. Triplicate samples were taken in five selected sampling points. VOC were sampled dynamically using multi-sorbent bed tubes (Carbotrap, Carbopack X, Carboxen 569) connected to SKC AirCheck 2000 pumps. The analysis was performed by automatic thermal desorption coupled with a capillary gas chromatograph/mass spectrometry detector. The emission rates of sixty VOC were calculated for each sampling point in an effort to characterize surface emissions. To calculate average, minimum and maximum emission values for each VOC, the results were analyzed by three different methods: Global, Kriging and Tributary area. Global and Tributary area methodologies presented similar values, with total VOC emissions of 237 ± 48 and 222 ± 46 g day(-1), respectively; however, Kriging values were lower, 77 ± 17 gd ay(-1). The main contributors to the total emission rate were aldehydes (nonanal and decanal), acetic acid, ketones (acetone), aromatic hydrocarbons and alcohols. Most aromatic hydrocarbon (except benzene, naphthalene and methylnaphthalenes) and aldehyde emission rates exhibited strong correlations with the rest of VOC of their family, indicating a possible common source of these compounds. B:T ratio obtained from the emission rates of the studied landfill suggested that the factors that regulate aromatic hydrocarbon distributions in the landfill emissions are different from the ones from urban areas. Environmental conditions (atmospheric pressure, temperature and relative humidity) did not alter the pollutant emission fluxes. © 2013.

Multi objective decision making in hybrid energy system design

NASA Astrophysics Data System (ADS)

Merino, Gabriel Guillermo

The design of grid-connected photovoltaic wind generator system supplying a farmstead in Nebraska has been undertaken in this dissertation. The design process took into account competing criteria that motivate the use of different sources of energy for electric generation. The criteria considered were 'Financial', 'Environmental', and 'User/System compatibility'. A distance based multi-objective decision making methodology was developed to rank design alternatives. The method is based upon a precedence order imposed upon the design objectives and a distance metric describing the performance of each alternative. This methodology advances previous work by combining ambiguous information about the alternatives with a decision-maker imposed precedence order in the objectives. Design alternatives, defined by the photovoltaic array and wind generator installed capacities, were analyzed using the multi-objective decision making approach. The performance of the design alternatives was determined by simulating the system using hourly data for an electric load for a farmstead and hourly averages of solar irradiation, temperature and wind speed from eight wind-solar energy monitoring sites in Nebraska. The spatial variability of the solar energy resource within the region was assessed by determining semivariogram models to krige hourly and daily solar radiation data. No significant difference was found in the predicted performance of the system when using kriged solar radiation data, with the models generated vs. using actual data. The spatial variability of the combined wind and solar energy resources was included in the design analysis by using fuzzy numbers and arithmetic. The best alternative was dependent upon the precedence order assumed for the main criteria. Alternatives with no PV array or wind generator dominated when the 'Financial' criteria preceded the others. In contrast, alternatives with a nil component of PV array but a high wind generator component, dominated when the 'Environment' objective or the 'User/System compatibility' objectives were more important than the 'Financial' objectives and they also dominated when the three criteria were considered equally important.

Evaluating and mapping of spatial air ion quality patterns in a residential garden using a geostatistic method.

PubMed

Wu, Chen-Fa; Lai, Chun-Hsien; Chu, Hone-Jay; Lin, Wen-Huang

2011-06-01

Negative air ions (NAI) produce biochemical reactions that increase the levels of the mood chemical serotonin in the environment. Moreover, they benefit both the psychological well being and the human body's physiological condition. The aim of this research was to estimate and measure the spatial distributions of negative and positive air ions in a residential garden in central Taiwan. Negative and positive air ions were measured at thirty monitoring locations in the study garden from July 2009 to June 2010. Moreover, Kriging was applied to estimate the spatial distribution of negative and positive air ions, as well as the air ion index in the study area. The measurement results showed that the numbers of NAI and PAI differed greatly during the four seasons, the highest and the lowest negative and positive air ion concentrations were found in the summer and winter, respectively. Moreover, temperature was positively affected negative air ions concentration. No matter what temperature is, the ranges of variogram in NAI/PAI were similar during four seasons. It indicated that spatial patterns of NAI/PAI were independent of the seasons and depended on garden elements and configuration, thus the NAP/PAI was a good estimate of the air quality regarding air ions. Kriging maps depicted that the highest negative and positive air ion concentration was next to the waterfall, whereas the lowest air ions areas were next to the exits of the garden. The results reveal that waterscapes are a source of negative and positive air ions, and that plants and green space are a minor source of negative air ions in the study garden. Moreover, temperature and humidity are positively and negatively affected negative air ions concentration, respectively. The proposed monitoring and mapping approach provides a way to effectively assess the patterns of negative and positive air ions in future landscape design projects.

A Study of the Groundwater Level Spatial Variability in the Messara Valley of Crete

NASA Astrophysics Data System (ADS)

Varouchakis, E. A.; Hristopulos, D. T.; Karatzas, G. P.

2009-04-01

The island of Crete (Greece) has a dry sub-humid climate and marginal groundwater resources, which are extensively used for agricultural activities and human consumption. The Messara valley is located in the south of the Heraklion prefecture, it covers an area of 398 km2, and it is the largest and most productive valley of the island. Over-exploitation during the past thirty (30) years has led to a dramatic decrease of thirty five (35) meters in the groundwater level. Possible future climatic changes in the Mediterranean region, potential desertification, population increase, and extensive agricultural activity generate concern over the sustainability of the water resources of the area. The accurate estimation of the water table depth is important for an integrated groundwater resource management plan. This study focuses on the Mires basin of the Messara valley for reasons of hydro-geological data availability and geological homogeneity. The research goal is to model and map the spatial variability of the basin's groundwater level accurately. The data used in this study consist of seventy (70) piezometric head measurements for the hydrological year 2001-2002. These are unevenly distributed and mostly concentrated along a temporary river that crosses the basin. The range of piezometric heads varies from an extreme low value of 9.4 meters above sea level (masl) to 62 masl, for the wet period of the year (October to April). An initial goal of the study is to develop spatial models for the accurate generation of static maps of groundwater level. At a second stage, these maps should extend the models to dynamic (space-time) situations for the prediction of future water levels. Preliminary data analysis shows that the piezometric head variations are not normally distributed. Several methods including Box-Cox transformation and a modified version of it, transgaussian Kriging, and Gaussian anamorphosis have been used to obtain a spatial model for the piezometric head. A trend model was constructed that accounted for the distance of the wells from the river bed. The spatial dependence of the fluctuations was studied by fitting isotropic and anisotropic empirical variograms with classical models, the Matérn model and the Spartan variogram family (Hristopulos, 2003; Hristopoulos and Elogne, 2007). The most accurate results, mean absolute prediction error of 4.57 masl, were obtained using the modified Box-Cox transform of the original data. The exponential and the isotropic Spartan variograms provided the best fits to the experimental variogram. Using Ordinary Kriging with either variogram function gave a mean absolute estimation error of 4.57 masl based on leave-one-out cross validation. The bias error of the predictions was calculated equal to -0.38 masl and the correlation coefficient of the predictions with respect of the original data equal to 0.8. The estimates located on the borders of the study domain presented a higher prediction error that varies from 8 to 14 masl due to the limited number of neighbor data. The maximum estimation error, observed at the extreme low value calculation, was 23 masl. The method of locally weighted regression (LWR), (NIST/SEMATECH 2009) was also investigated as an alternative approach for spatial modeling. The trend calculated from a second order LWR method showed a remarkable fit to the original data marked by a mean absolute estimation error of 4.4 masl. The bias prediction error was calculated equal to -0.16 masl and the correlation coefficient between predicted and original data equal to 0.88 masl. Higher estimation errors were found at the same locations and vary within the same range. The extreme low value calculation error has improved to 21 masl. Plans for future research include the incorporation of spatial anisotropy in the kriging algorithm, the investigation of kernel functions other than the tricube in LWR, as well as the use of locally adapted bandwidth values. Furthermore, pumping rates for fifty eight (58) of the seventy (70) wells are available display a correlation coefficient of -0.6 with the respective ground water levels. A Digital Elevation Model (DEM) of the area will provide additional information about the unsampled locations of the basin. The pumping rates and the DEM will be used as secondary information in a co-kriging approach, leading to more accurate estimation of the basin's water table. NIST/SEMATECH e-Handbook of Statitical Methods, http://www.itl.nist.gov/div898/handbook/, 12/01/09. D.T. Hristopulos, "Spartan Gibbs random field models for geostatistical applications," SIAM J. Scient. Comput., vol. 24, no. 6, pp. 2125-2162, 2003 D.T. Hristopulos and S. Elogne, "Analytic properties and covariance functions for a new class of generalized Gibbs random fields," IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 53, no 12, pp. 4667-4679, 2007

Surface modeling of soil antibiotics.

PubMed

Shi, Wen-jiao; Yue, Tian-xiang; Du, Zheng-ping; Wang, Zong; Li, Xue-wen

2016-02-01

Large numbers of livestock and poultry feces are continuously applied into soils in intensive vegetable cultivation areas, and then some veterinary antibiotics are persistent existed in soils and cause health risk. For the spatial heterogeneity of antibiotic residues, developing a suitable technique to interpolate soil antibiotic residues is still a challenge. In this study, we developed an effective interpolator, high accuracy surface modeling (HASM) combined vegetable types, to predict the spatial patterns of soil antibiotics, using 100 surface soil samples collected from an intensive vegetable cultivation area located in east of China, and the fluoroquinolones (FQs), including ciprofloxacin (CFX), enrofloxacin (EFX) and norfloxacin (NFX), were analyzed as the target antibiotics. The results show that vegetable type is an effective factor to be combined to improve the interpolator performance. HASM achieves less mean absolute errors (MAEs) and root mean square errors (RMSEs) for total FQs (NFX+CFX+EFX), NFX, CFX and EFX than kriging with external drift (KED), stratified kriging (StK), ordinary kriging (OK) and inverse distance weighting (IDW). The MAE of HASM for FQs is 55.1 μg/kg, and the MAEs of KED, StK, OK and IDW are 99.0 μg/kg, 102.8 μg/kg, 106.3 μg/kg and 108.7 μg/kg, respectively. Further, RMSE simulated by HASM for FQs (CFX, EFX and NFX) are 106.2 μg/kg (88.6 μg/kg, 20.4 μg/kg and 39.2 μg/kg), and less 30% (27%, 22% and 36%), 33% (27%, 27% and 43%), 38% (34%, 23% and 41%) and 42% (32%, 35% and 51%) than the ones by KED, StK, OK and IDW, respectively. HASM also provides better maps with more details and more consistent maximum and minimum values of soil antibiotics compared with the measured data. The better performance can be concluded that HASM takes the vegetable type information as global approximate information, and takes local sampling data as its optimum control constraints. Copyright © 2015 Elsevier B.V. All rights reserved.

Spatial variability of soil available phosphorous and potassium at three different soils located in Pannonian Croatia

NASA Astrophysics Data System (ADS)

Bogunović, Igor; Pereira, Paulo; Đurđević, Boris

2017-04-01

Information on spatial distribution of soil nutrients in agroecosystems is critical for improving productivity and reducing environmental pressures in intensive farmed soils. In this context, spatial prediction of soil properties should be accurate. In this study we analyse 704 data of soil available phosphorus (AP) and potassium (AK); the data derive from soil samples collected across three arable fields in Baranja region (Croatia) in correspondence of different soil types: Cambisols (169 samples), Chernozems (131 samples) and Gleysoils (404 samples). The samples are collected in a regular sampling grid (distance 225 x 225 m). Several geostatistical techniques (Inverse Distance to a Weight (IDW) with the power of 1, 2 and 3; Radial Basis Functions (RBF) - Inverse Multiquadratic (IMT), Multiquadratic (MTQ), Completely Regularized Spline (CRS), Spline with Tension (SPT) and Thin Plate Spline (TPS); and Local Polynomial (LP) with the power of 1 and 2; two geostatistical techniques -Ordinary Kriging - OK and Simple Kriging - SK) were tested in order to evaluate the most accurate spatial variability maps using criteria of lowest RMSE during cross validation technique. Soil parameters varied considerably throughout the studied fields and their coefficient of variations ranged from 31.4% to 37.7% and from 19.3% to 27.1% for soil AP and AK, respectively. The experimental variograms indicate a moderate spatial dependence for AP and strong spatial dependence for all three locations. The best spatial predictor for AP at Chernozem field was Simple kriging (RMSE=61.711), and for AK inverse multiquadratic (RMSE=44.689). The least accurate technique was Thin plate spline (AP) and Inverse distance to a weight with a power of 1 (AK). Radial basis function models (Spline with Tension for AP at Gleysoil and Cambisol and Completely Regularized Spline for AK at Gleysol) were the best predictors, while Thin Plate Spline models were the least accurate in all three cases. The best interpolator for AK at Cambisol was the local polynomial with the power of 2 (RMSE=33.943), while the least accurate was Thin Plate Spline (RMSE=39.572).

Geometry control of long-span continuous girder concrete bridge during construction through finite element model updating

NASA Astrophysics Data System (ADS)

Wu, Jie; Yan, Quan-sheng; Li, Jian; Hu, Min-yi

2016-04-01

In bridge construction, geometry control is critical to ensure that the final constructed bridge has the consistent shape as design. A common method is by predicting the deflections of the bridge during each construction phase through the associated finite element models. Therefore, the cambers of the bridge during different construction phases can be determined beforehand. These finite element models are mostly based on the design drawings and nominal material properties. However, the accuracy of these bridge models can be large due to significant uncertainties of the actual properties of the materials used in construction. Therefore, the predicted cambers may not be accurate to ensure agreement of bridge geometry with design, especially for long-span bridges. In this paper, an improved geometry control method is described, which incorporates finite element (FE) model updating during the construction process based on measured bridge deflections. A method based on the Kriging model and Latin hypercube sampling is proposed to perform the FE model updating due to its simplicity and efficiency. The proposed method has been applied to a long-span continuous girder concrete bridge during its construction. Results show that the method is effective in reducing construction error and ensuring the accuracy of the geometry of the final constructed bridge.

Design of A Cyclone Separator Using Approximation Method

NASA Astrophysics Data System (ADS)

Sin, Bong-Su; Choi, Ji-Won; Lee, Kwon-Hee

2017-12-01

A Separator is a device installed in industrial applications to separate mixed objects. The separator of interest in this research is a cyclone type, which is used to separate a steam-brine mixture in a geothermal plant. The most important performance of the cyclone separator is the collection efficiency. The collection efficiency in this study is predicted by performing the CFD (Computational Fluid Dynamics) analysis. This research defines six shape design variables to maximize the collection efficiency. Thus, the collection efficiency is set up as the objective function in optimization process. Since the CFD analysis requires a lot of calculation time, it is impossible to obtain the optimal solution by linking the gradient-based optimization algorithm. Thus, two approximation methods are introduced to obtain an optimum design. In this process, an L18 orthogonal array is adopted as a DOE method, and kriging interpolation method is adopted to generate the metamodel for the collection efficiency. Based on the 18 analysis results, the relative importance of each variable to the collection efficiency is obtained through the ANOVA (analysis of variance). The final design is suggested considering the results obtained from two optimization methods. The fluid flow analysis of the cyclone separator is conducted by using the commercial CFD software, ANSYS-CFX.

Detecting spatial patterns of rivermouth processes using a geostatistical framework for near-real-time analysis

USGS Publications Warehouse

Xu, Wenzhao; Collingsworth, Paris D.; Bailey, Barbara; Carlson Mazur, Martha L.; Schaeffer, Jeff; Minsker, Barbara

2017-01-01

This paper proposes a geospatial analysis framework and software to interpret water-quality sampling data from towed undulating vehicles in near-real time. The framework includes data quality assurance and quality control processes, automated kriging interpolation along undulating paths, and local hotspot and cluster analyses. These methods are implemented in an interactive Web application developed using the Shiny package in the R programming environment to support near-real time analysis along with 2- and 3-D visualizations. The approach is demonstrated using historical sampling data from an undulating vehicle deployed at three rivermouth sites in Lake Michigan during 2011. The normalized root-mean-square error (NRMSE) of the interpolation averages approximately 10% in 3-fold cross validation. The results show that the framework can be used to track river plume dynamics and provide insights on mixing, which could be related to wind and seiche events.

Optimal weighted combinatorial forecasting model of QT dispersion of ECGs in Chinese adults.

PubMed

Wen, Zhang; Miao, Ge; Xinlei, Liu; Minyi, Cen

2016-07-01

This study aims to provide a scientific basis for unifying the reference value standard of QT dispersion of ECGs in Chinese adults. Three predictive models including regression model, principal component model, and artificial neural network model are combined to establish the optimal weighted combination model. The optimal weighted combination model and single model are verified and compared. Optimal weighted combinatorial model can reduce predicting risk of single model and improve the predicting precision. The reference value of geographical distribution of Chinese adults' QT dispersion was precisely made by using kriging methods. When geographical factors of a particular area are obtained, the reference value of QT dispersion of Chinese adults in this area can be estimated by using optimal weighted combinatorial model and reference value of the QT dispersion of Chinese adults anywhere in China can be obtained by using geographical distribution figure as well.

On-line estimation of nonlinear physical systems

USGS Publications Warehouse

Christakos, G.

1988-01-01

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared. ?? 1988 International Association for Mathematical Geology.

Spatial vulnerability assessments by regression kriging

NASA Astrophysics Data System (ADS)

Pásztor, László; Laborczi, Annamária; Takács, Katalin; Szatmári, Gábor

2016-04-01

Two fairly different complex environmental phenomena, causing natural hazard were mapped based on a combined spatial inference approach. The behaviour is related to various environmental factors and the applied approach enables the inclusion of several, spatially exhaustive auxiliary variables that are available for mapping. Inland excess water (IEW) is an interrelated natural and human induced phenomenon causes several problems in the flat-land regions of Hungary, which cover nearly half of the country. The term 'inland excess water' refers to the occurrence of inundations outside the flood levee that originate from sources differing from flood overflow, it is surplus surface water forming due to the lack of runoff, insufficient absorption capability of soil or the upwelling of groundwater. There is a multiplicity of definitions, which indicate the complexity of processes that govern this phenomenon. Most of the definitions have a common part, namely, that inland excess water is temporary water inundation that occurs in flat-lands due to both precipitation and groundwater emerging on the surface as substantial sources. Radon gas is produced in the radioactive decay chain of uranium, which is an element that is naturally present in soils. Radon is transported mainly by diffusion and convection mechanisms through the soil depending mainly on soil physical and meteorological parameters and can enter and accumulate in the buildings. Health risk originating from indoor radon concentration attributed to natural factors is characterized by geogenic radon potential (GRP). In addition to geology and meteorology, physical soil properties play significant role in the determination of GRP. Identification of areas with high risk requires spatial modelling, that is mapping of specific natural hazards. In both cases external environmental factors determine the behaviour of the target process (occurrence/frequncy of IEW and grade of GRP respectively). Spatial auxiliary information representing IEW or GRP forming environmental factors were taken into account to support the spatial inference of the locally experienced IEW frequency and measured GRP values respectively. An efficient spatial prediction methodology was applied to construct reliable maps, namely regression kriging (RK) using spatially exhaustive auxiliary data on soil, geology, topography, land use and climate. RK divides the spatial inference into two parts. Firstly the deterministic component of the target variable is determined by a regression model. The residuals of the multiple linear regression analysis represent the spatially varying but dependent stochastic component, which are interpolated by kriging. The final map is the sum of the two component predictions. Application of RK also provides the possibility of inherent accuracy assessment. The resulting maps are characterized by global and local measures of its accuracy. Additionally the method enables interval estimation for spatial extension of the areas of predefined risk categories. All of these outputs provide useful contribution to spatial planning, action planning and decision making. Acknowledgement: Our work was partly supported by the Hungarian National Scientific Research Foundation (OTKA, Grant No. K105167).

Modelling prehistoric terrain Models using LiDAR-data: a geomorphological approach

NASA Astrophysics Data System (ADS)

Höfler, Veit; Wessollek, Christine; Karrasch, Pierre

2015-10-01

Terrain surfaces conserve human activities in terms of textures and structures. With reference to archaeological questions, the geological archive is investigated by means of models regarding anthropogenic traces. In doing so, the high-resolution digital terrain model is of inestimable value for the decoding of the archive. The evaluation of these terrain models and the reconstruction of historical surfaces is still a challenging issue. Due to the data collection by means of LiDAR systems (light detection and ranging) and despite their subsequent pre-processing and filtering, recently anthropogenic artefacts are still present in the digital terrain model. Analysis have shown that elements, such as contour lines and channels, can well be extracted from a high-resolution digital terrain model. This way, channels in settlement areas show a clear anthropogenic character. This fact can also be observed for contour lines. Some contour lines representing a possibly natural ground surface and avoid anthropogenic artefacts. Comparable to channels, noticeable patterns of contour lines become visible in areas with anthropogenic artefacts. The presented workflow uses functionalities of ArcGIS and the programming language R.1 The method starts with the extraction of contour lines from the digital terrain model. Through macroscopic analyses based on geomorphological expert knowledge, contour lines are selected representing the natural geomorphological character of the surface. In a first step, points are determined along each contour line in regular intervals. This points and the corresponding height information which is taken from an original digital terrain model is saved as a point cloud. Using the programme library gstat, a variographic analysis and the use of a Kriging-procedure based on this follow.2-4 The result is a digital terrain model filtered considering geomorphological expert knowledge showing no human degradation in terms of artefacts, preserving the landscape-genetic character and can be called a prehistoric terrain model.

Simultaneous Genotype Calling and Haplotype Phasing Improves Genotype Accuracy and Reduces False-Positive Associations for Genome-wide Association Studies

PubMed Central

Browning, Brian L.; Yu, Zhaoxia

2009-01-01

We present a novel method for simultaneous genotype calling and haplotype-phase inference. Our method employs the computationally efficient BEAGLE haplotype-frequency model, which can be applied to large-scale studies with millions of markers and thousands of samples. We compare genotype calls made with our method to genotype calls made with the BIRDSEED, CHIAMO, GenCall, and ILLUMINUS genotype-calling methods, using genotype data from the Illumina 550K and Affymetrix 500K arrays. We show that our method has higher genotype-call accuracy and yields fewer uncalled genotypes than competing methods. We perform single-marker analysis of data from the Wellcome Trust Case Control Consortium bipolar disorder and type 2 diabetes studies. For bipolar disorder, the genotype calls in the original study yield 25 markers with apparent false-positive association with bipolar disorder at a p < 10−7 significance level, whereas genotype calls made with our method yield no associated markers at this significance threshold. Conversely, for markers with replicated association with type 2 diabetes, there is good concordance between genotype calls used in the original study and calls made by our method. Results from single-marker and haplotypic analysis of our method's genotype calls for the bipolar disorder study indicate that our method is highly effective at eliminating genotyping artifacts that cause false-positive associations in genome-wide association studies. Our new genotype-calling methods are implemented in the BEAGLE and BEAGLECALL software packages. PMID:19931040

Analysis and simulation of wireless signal propagation applying geostatistical interpolation techniques

NASA Astrophysics Data System (ADS)

Kolyaie, S.; Yaghooti, M.; Majidi, G.

2011-12-01

This paper is a part of an ongoing research to examine the capability of geostatistical analysis for mobile networks coverage prediction, simulation and tuning. Mobile network coverage predictions are used to find network coverage gaps and areas with poor serviceability. They are essential data for engineering and management in order to make better decision regarding rollout, planning and optimisation of mobile networks.The objective of this research is to evaluate different interpolation techniques in coverage prediction. In method presented here, raw data collected from drive testing a sample of roads in study area is analysed and various continuous surfaces are created using different interpolation methods. Two general interpolation methods are used in this paper with different variables; first, Inverse Distance Weighting (IDW) with various powers and number of neighbours and second, ordinary kriging with Gaussian, spherical, circular and exponential semivariogram models with different number of neighbours. For the result comparison, we have used check points coming from the same drive test data. Prediction values for check points are extracted from each surface and the differences with actual value are computed. The output of this research helps finding an optimised and accurate model for coverage prediction.

Holes in the ocean: Filling voids in bathymetric lidar data

NASA Astrophysics Data System (ADS)

Coleman, John B.; Yao, Xiaobai; Jordan, Thomas R.; Madden, Marguertie

2011-04-01

The mapping of coral reefs may be efficiently accomplished by the use of airborne laser bathymetry. However, there are often data holes within the bathymetry data which must be filled in order to produce a complete representation of the coral habitat. This study presents a method to fill these data holes through data merging and interpolation. The method first merges ancillary digital sounding data with airborne laser bathymetry data in order to populate data points in all areas but particularly those of data holes. What follows is to generate an elevation surface by spatial interpolation based on the merged data points obtained in the first step. We conduct a case study of the Dry Tortugas National Park in Florida and produced an enhanced digital elevation model in the ocean with this method. Four interpolation techniques, including Kriging, natural neighbor, spline, and inverse distance weighted, are implemented and evaluated on their ability to accurately and realistically represent the shallow-water bathymetry of the study area. The natural neighbor technique is found to be the most effective. Finally, this enhanced digital elevation model is used in conjunction with Ikonos imagery to produce a complete, three-dimensional visualization of the study area.