共查询到20条相似文献，搜索用时 15 毫秒
1.
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. 相似文献
2.
Steve W. Lyon Arthur J. Lembo Jr. M. Todd Walter Tammo S. Steenhuis 《Advances in water resources》2006
In humid, well-vegetated areas, such as in the northeastern US, runoff is most commonly generated from relatively small portions of the landscape becoming completely saturated, however, little is known about the spatial and temporal behavior of these saturated regions. Indicator kriging provides a way to use traditional water table data to quantify probability of saturation to evaluate predicted spatial distributions of runoff generation risk, especially for the new generation of water quality models incorporating saturation excess runoff theory. When spatial measurements of a variable are transformed to binary indicators (i.e., 1 if above a given threshold value and 0 if below) and the resulting indicator semivariogram is modeled, indicator kriging produces the probability of the measured variable to exceed the threshold value. Indicator kriging gives quantified probability of saturation or, consistent with saturation excess runoff theory, runoff generation risk with depth to water table as the variable and the threshold set near the soil surface. The probability of saturation for a 120 m × 180 m hillslope based upon 43 measurements of depth to water table is investigated with indicator semivariograms for six storm events. The indicator semivariograms show high spatial structure in saturated regions with large antecedent rainfall conditions. The temporal structure of the data is used to generate interpolated (soft) data to supplement measured (hard) data. This improved the spatial structure of the indicator semivariograms for lower antecedent rainfall conditions. Probability of saturation was evaluated through indicator kriging incorporating soft data showing, based on this preliminary study, highly connected regions of saturation as expected for the wet season (April through May) in the Catskill Mountain region of New York State. Supplementation of hard data with soft data incorporates physical hydrology of the hillslope to capture significant patterns not available when using hard data alone for indicator kriging. With the need for water quality models incorporating appropriate runoff generation risk estimates on the rise, this manner of data will lay the groundwork for future model evaluation and development. 相似文献
3.
Ryan M. Pollyea Jerry P. Fairley Robert K. Podgorney Travis L. McLing 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(7):1735-1740
The stochastic continuum (SC) representation is one common approach for simulating the effects of fracture heterogeneity in groundwater flow and transport models. These SC reservoir models are generally developed using geostatistical methods (e.g., kriging or sequential simulation) that rely on the model semivariogram to describe the spatial variability of each continuum. Although a number of strategies for sampling spatial distributions have been published in the literature, little attention has been paid to the optimization of sampling in resource- or access-limited environments. Here we present a strategy for estimating the minimum sample spacing needed to define the spatial distribution of fractures on a vertical outcrop of basalt, located in the Box Canyon, east Snake River Plain, Idaho. We used fracture maps of similar basalts from the published literature to test experimentally the effects of different sample spacings on the resulting semivariogram model. Our final field sampling strategy was based on the lowest sample density that reproduced the semivariogram of the exhaustively sampled fracture map. Application of the derived sampling strategy to an outcrop in our field area gave excellent results, and illustrates the utility of this type of sample optimization. The method will work for developing a sampling plan for any intensive property, provided prior information for a similar domain is available; for example, fracture maps or ortho-rectified photographs from analogous rock types could be used to plan for sampling of a fractured rock outcrop. 相似文献
4.
Bayesian model averaging assessment on groundwater management under model structure uncertainty 总被引：1，自引：1，他引：0
This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the “1,500-foot” sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used. 相似文献
5.
《水文科学杂志》2013,58(5):1038-1050
Abstract Universal kriging is applied to the command area of a set of canal irrigation projects in north-western India to show its applicability for optimal contour mapping of groundwater levels. This command area faces the problem of a rising groundwater table and manifestation of waterlogging over the years at many places. With the use of measured elevations of the water table in September 1990 at 143 observation sites in an area of 4500 km2, an omni-directional experimental semivariogram was constructed. The concave upward shape of omni-directional experimental semivariogram indicated the non-stationarity of the data and so the need for universal kriging. Directional semivariograms were calculated to find out the direction along which there is least drift. This directional semivariogram was considered as the underlying semivariogram and various theoretical semivariogram models were fitted to it. The drift order was estimated from the cross-validation procedure. The model and drift order finally selected were used to estimate the groundwater levels and corresponding estimation variances at the nodes of a square grid of 2 km × 2 km, and to develop the corresponding contour map. 相似文献
6.
G. C. Poole J. A. Stanford S. W. Running C. A. Frissell W. W. Woessner B. K. Ellis 《地球表面变化过程与地形》2004,29(10):1259-1274
Geomorphology interacts with surface‐ and ground‐water hydrology across multiple spatial scales. Nonetheless, hydrologic and hydrogeologic models are most commonly implemented at a single spatial scale. Using an existing hydrogeologic computer model, we implemented a simple hierarchical approach to modeling surface‐ and ground‐water hydrology in a complex geomorphic setting. We parameterized the model to simulate ground‐ and surface‐water ?ow patterns through a hierarchical, three‐dimensional, quantitative representation of an anabranched montane alluvial ?ood plain (the Nyack Flood Plain, Middle Fork Flathead River, Montana, USA). Comparison of model results to ?eld data showed that the model provided reasonable representations of spatial patterns of aquifer recharge and discharge, temporal patterns of ?ood‐water storage on the ?ood plain, and rates of ground‐water movement from the main river channel into a large lateral spring channel on the ?ood plain, and water table elevation in the alluvial aquifer. These results suggest that a hierarchical approach to modeling ground‐ and surface‐water hydrology can reproduce realistic patterns of surface‐ and ground‐water ?ux on alluvial ?ood plains, and therefore should provide an excellent ‘quantitative laboratory’ for studying complex interactions between geomorphology and hydrology at and across multiple spatial scales. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
7.
Abstract The present research study investigates the application of nonlinear normalizing data transformations in conjunction with ordinary kriging (OK) for the accurate prediction of groundwater level spatial variability in a sparsely-gauged basin. We investigate three established normalizing methods, Gaussian anamorphosis, trans-Gaussian kriging and the Box-Cox method to improve the estimation accuracy. The first two are applied for the first time to groundwater level data. All three methods improve the mean absolute prediction error compared to the application of OK to the non-transformed data. In addition, a modified Box-Cox transformation is proposed and applied to normalize the hydraulic heads. The modified Box-Cox transformation in conjunction with OK is found to be the optimal spatial model based on leave-one-out cross-validation. The recently established Spartan semivariogram family provides the optimal model fit to the transformed data. Finally, we present maps of the groundwater level and the kriging variance based on the optimal spatial model. Editor D. Koutsoyiannis; Associate editor A. Montanari Citation Varouchakis, E.A., Hristopoulos, D.T., and Karatzas, G.P., 2012. Improving kriging of groundwater level data using nonlinear normalizing transformations—a field application. Hydrological Sciences Journal, 57 (7), 1404–1419. 相似文献
8.
A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps. 相似文献
9.
by Husam Baalousha 《Ground water》2009,47(5):709-713
Uncertainty in ground water hydrology originates from different sources. Neglecting uncertainty in ground water problems can lead to incorrect results and misleading output. Several approaches have been developed to cope with uncertainty in ground water problems. The most widely used methods in uncertainty analysis are Monte Carlo simulation (MCS) and Latin hypercube sampling (LHS), developed from MCS. Despite the simplicity of MCS, many runs are required to achieve a reliable result. This paper presents orthogonal array (OA) sampling as a means to cope with uncertainty in ground water problems. The method was applied to an analytical stream depletion problem. To examine the convergence rate of the OA sampling, the results were compared to MCS and LHS. This study shows that OA can be applied to ground water problems. Results reveal that the convergence rate of the OA sampling is faster than MCS and LHS, with a smaller error of estimate when applied to a stream depletion problem. 相似文献
10.
Gómez-Hernández J. J. Wen X. -H. 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(1):19-55
A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps. 相似文献
11.
Spatiotemporal estimation of snow depth using point data from snow stakes,digital terrain models,and satellite data 
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下载免费PDF全文 Antonio‐Juan Collados‐Lara Eulogio Pardo‐Igúzquiza David Pulido‐Velazquez 《水文研究》2017,31(10):1966-1982
Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources. 相似文献
12.
Estimating threshold-exceeding probability maps of environmental variables with Markov chain random fields 总被引：2，自引：2，他引：0
Weidong Li Chuanrong Zhang Dipak K. Dey Shanqin Wang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(8):1113-1126
Estimating and mapping spatial uncertainty of environmental variables is crucial for environmental evaluation and decision
making. For a continuous spatial variable, estimation of spatial uncertainty may be conducted in the form of estimating the
probability of (not) exceeding a threshold value. In this paper, we introduced a Markov chain geostatistical approach for
estimating threshold-exceeding probabilities. The differences of this approach compared to the conventional indicator approach
lie with its nonlinear estimators—Markov chain random field models and its incorporation of interclass dependencies through
transiograms. We estimated threshold-exceeding probability maps of clay layer thickness through simulation (i.e., using a
number of realizations simulated by Markov chain sequential simulation) and interpolation (i.e., direct conditional probability
estimation using only the indicator values of sample data), respectively. To evaluate the approach, we also estimated those
probability maps using sequential indicator simulation and indicator kriging interpolation. Our results show that (i) the
Markov chain approach provides an effective alternative for spatial uncertainty assessment of environmental spatial variables
and the probability maps from this approach are more reasonable than those from conventional indicator geostatistics, and
(ii) the probability maps estimated through sequential simulation are more realistic than those through interpolation because
the latter display some uneven transitions caused by spatial structures of the sample data. 相似文献
13.
There is a significant body of work demonstrating the importance of hydrologic control on land energy feedbacks. Yet, quantitative data on aquifer conductivity can be difficult to assemble. Furthermore, how subsurface uncertainty propagates into land-surface processes is not well understood. This study analyzes the impact of aquifer characterization on land energy fluxes, using a coupled hydrology–land-surface model. Four gridded subsurface conductivity fields are developed for the Upper Klamath basin using two data sources and different levels of imposed heterogeneity. Each model is forced with the same transient, observed meteorology for 3 years prior to the final year presented here. Results are analyzed to quantify the impact of subsurface heterogeneity on groundwater surface water interactions and spatial patterns in hydrologic variables. Analysis shows that heterogeneity does not fundamentally alter the connection between groundwater and land surface processes. However, differences between scenarios impact the extent and location of the critical zone. 相似文献
14.
A method is presented for quantifying the uncertainty of the semivariogram of transmissivity and determining the required number of measurements. In this method, the estimated semivariogram and its 95% confidence limits are first determined from a finite number of measurements. The uncertainty of the estimated semivariogram is then quantified using the random field simulation technique. For a given value of the quantitative index of uncertainty, the required number of measured data can finally be obtained. Actual transmissivity data of an existing groundwater monitoring network are used in the application of the proposed method. The required numbers of measurements of transmissivity for four different values of the quantitative index of uncertainty are provided, from which reliable semivariograms of the transmissivity can be obtained. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
Spatial interpolation methods for nonstationary plume data 总被引：1，自引：0，他引：1
Plume interpolation consists of estimating contaminant concentrations at unsampled locations using the available contaminant data surrounding those locations. The goal of ground water plume interpolation is to maximize the accuracy in estimating the spatial distribution of the contaminant plume given the data limitations associated with sparse monitoring networks with irregular geometries. Beyond data limitations, contaminant plume interpolation is a difficult task because contaminant concentration fields are highly heterogeneous, anisotropic, and nonstationary phenomena. This study provides a comprehensive performance analysis of six interpolation methods for scatter-point concentration data, ranging in complexity from intrinsic kriging based on intrinsic random function theory to a traditional implementation of inverse-distance weighting. High resolution simulation data of perchloroethylene (PCE) contamination in a highly heterogeneous alluvial aquifer were used to generate three test cases, which vary in the size and complexity of their contaminant plumes as well as the number of data available to support interpolation. Overall, the variability of PCE samples and preferential sampling controlled how well each of the interpolation schemes performed. Quantile kriging was the most robust of the interpolation methods, showing the least bias from both of these factors. This study provides guidance to practitioners balancing opposing theoretical perspectives, ease-of-implementation, and effectiveness when choosing a plume interpolation method. 相似文献
16.
17.
Assessing hydrological model predictive uncertainty using stochastically generated geological models 下载免费PDF全文
下载免费PDF全文 In distributed and coupled surface water–groundwater modelling, the uncertainty from the geological structure is unaccounted for if only one deterministic geological model is used. In the present study, the geological structural uncertainty is represented by multiple, stochastically generated geological models, which are used to develop hydrological model ensembles for the Norsminde catchment in Denmark. The geological models have been constructed using two types of field data, airborne geophysical data and borehole well log data. The use of airborne geophysical data in constructing stochastic geological models and followed by the application of such models to assess hydrological simulation uncertainty for both surface water and groundwater have not been previously studied. The results show that the hydrological ensemble based on geophysical data has a lower level of simulation uncertainty, but the ensemble based on borehole data is able to encapsulate more observation points for stream discharge simulation. The groundwater simulations are in general more sensitive to the changes in the geological structure than the stream discharge simulations, and in the deeper groundwater layers, there are larger variations between simulations within an ensemble than in the upper layers. The relationship between hydrological prediction uncertainties measured as the spread within the hydrological ensembles and the spatial aggregation scale of simulation results has been analysed using a representative elementary scale concept. The results show a clear increase of prediction uncertainty as the spatial scale decreases. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
18.
《Journal of Hydrology》1989,110(3-4):295-314
Aquifers in sedimentary basins provide a regional domain for the spatial variabilities in geologic, hydrologic, geomorphologic and hydrochemical phenomena. Their study should account for this spatial variability within the study area prior to any formal modelling. A cumulative semivariogram scheme is adopted in this paper for the spatial variability, which is then incorporated with the kriging technique to provide maps of regional variation concerning variables such as storativity, transmissivity, piezometric levels, total dissolved solids and groundwater flow velocity. It is shown that the classical semivariogram models are not capable of accounting for the spatial variability of the Wasia aquifer. Comparison between the cumulative and classical semivariograms are given on the basis of hydrogeologic variables observed in the field. It is concluded, in general, that the cumulative semivariogram modelling of the spatial variability is more effective and yields realistic regional variables. 相似文献
19.
In this study, uncertainty in model input data (precipitation) and parameters is propagated through a physically based, spatially distributed hydrological model based on the MIKE SHE code. Precipitation uncertainty is accounted for using an ensemble of daily rainfall fields that incorporate four different sources of uncertainty, whereas parameter uncertainty is considered using Latin hypercube sampling. Model predictive uncertainty is assessed for multiple simulated hydrological variables (discharge, groundwater head, evapotranspiration, and soil moisture). Utilizing an extensive set of observational data, effective observational uncertainties for each hydrological variable are assessed. Considering not only model predictive uncertainty but also effective observational uncertainty leads to a notable increase in the number of instances, for which model simulation and observations are in good agreement (e.g., 47% vs. 91% for discharge and 0% vs. 98% for soil moisture). Effective observational uncertainty is in several cases larger than model predictive uncertainty. We conclude that the use of precipitation uncertainty with a realistic spatio‐temporal correlation structure, analyses of multiple variables with different spatial support, and the consideration of observational uncertainty are crucial for adequately evaluating the performance of physically based, spatially distributed hydrological models. 相似文献
20.
We present a methodology for global optimal design of ground water quality monitoring networks using a linear mixed-integer formulation. The proposed methodology incorporates ordinary kriging (OK) within the decision model formulation for spatial estimation of contaminant concentration values. Different monitoring network design models incorporating concentration estimation error, variance estimation error, mass estimation error, error in locating plume centroid, and spatial coverage of the designed network are developed. A big-M technique is used for reformulating the monitoring network design model to a linear decision model while incorporating different objectives and OK equations. Global optimality of the solutions obtained for the monitoring network design can be ensured due to the linear mixed-integer programming formulations proposed. Performances of the proposed models are evaluated for both field and hypothetical illustrative systems. Evaluation results indicate that the proposed methodology performs satisfactorily. These performance evaluation results demonstrate the potential applicability of the proposed methodology for optimal ground water contaminant monitoring network design. 相似文献