共查询到20条相似文献，搜索用时 468 毫秒
1.
Emmanouil A. Varouchakis Kostantinos Kolosionis George P. Karatzas 《Earth Science Informatics》2016,9(4):437-448
The spatial variability evaluation of the water table level of an aquifer provides useful information in water resources management plans. Three different approaches are applied to estimate the spatial variability of the water table in the study basin. All of them are based on the Kriging methodology. The first is the classical Ordinary Kriging approach, while the second involves information from a secondary variable (surface elevation) and the application of Residual Kriging. The third calculates the probability to lie below a certain groundwater level limit that could cause significant problems in groundwater resources availability. The latter is achieved by means of Indicator Kriging. A recently developed non-linear normalization method is used to transform both data and residuals closer to normal distribution for improved prediction results. In addition, the recently developed Spartan variogram model is applied to determine the spatial dependence of the measurements. The latter proves to be the optimal model, compared to a series of models tested, which provides in combination with the Kriging methodologies the most accurate cross validation estimations. The variogram form is explained with respect to the radius of influence of the pumping wells representing the spatial impact of the pumping activity. Groundwater level and probability maps are developed providing the ability to assess the spatial variability of the groundwater level in the basin and the risk that certain locations have in terms of a safe groundwater level limit that has been set for the sustainability of the groundwater resources of the basin. 相似文献
2.
Application and evaluation of universal kriging for optimal contouring of groundwater levels 总被引：4，自引：0，他引：4
B V N P KAMBHAMMETTU PRAVEENA ALLENA JAMES P KING 《Journal of Earth System Science》2011,120(3):413-422
This paper deals with the application of universal kriging to interpolate water table elevations from their measurements at
random locations. Geographic information system tools were used to generate the continuous surface of water table elevations
for the Carlsbad area alluvial aquifer located to the southeast of New Mexico, USA. Water table elevations in the 38 monitoring
wells that are common to 1996 and 2003 irrigation years follows normal distribution. A generalized MATLAB? code was developed to generate omni-directional and directional semi-variograms (at 22.5° intervals). Low-order polynomials
were used to model the trend as the water table profile exhibits a south-east gradient. Different theoretical semi-variogram
models were tried to select the base semi-variogram for performing geostatistical interpolation. The contour maps of water
table elevations exhibit significant decrease in the water table from 1996 to 2003. Statistical analysis performed on the
estimated contours revealed that the decrease in water table is between 0.6 and 4.5 m at 90% confidence. The estimation variance
contours show that the error in estimation was more than 8 m2 in the west and south-west portions of the aquifer due to the absence of monitoring wells. 相似文献
3.
Masoomeh Delbari 《Arabian Journal of Geosciences》2014,7(10):4221-4233
This paper presents the incorporation of a digital elevation model into the spatial prediction of water table elevation in Mazandaran province (Iran) using a range of interpolation techniques. The multivariate methods used are: linear regression (LR), cokriging (COK), kriging with an external drift (KED) and regression kriging (RK). The analysis is performed on 3 years (1987, 1997 and 2007) of water table elevation data from about 260 monitoring wells. Prediction performances of the different algorithms are compared with two univariate techniques, i.e. inverse distance weighting and ordinary kriging (OK), through cross validation and examination of the consistency of the generated maps with the natural phenomena. Significantly smaller prediction errors are obtained for four multivariate algorithms but, in particular, KED and RK outperform LR and COK for 3 years. The results show the potential for using elevation for a more precise mapping of water table elevation. 相似文献
4.
Kriging with imprecise (fuzzy) variograms. II: Application 总被引：2，自引：0，他引：2
The geostatistical analysis of soil liner permeability is based on 20 measurements and imprecise prior information on nugget effect, sill, and range of the unknown variogram. Using this information, membership functions for variogram parameters are assessed and the fuzzy variogram is constructed. Both kriging estimates and estimation variances are calculated as fuzzy numbers from the fuzzy variogram and data points. Contour maps are presented, indicating values of the kriged permeability and the estimation variance corresponding to selected membership values called levels. 相似文献
5.
Jorge Kazuo Yamamoto 《Mathematical Geology》2000,32(4):489-509
This paper presents an interpolation variance as an alternative to the measure of the reliability of ordinary kriging estimates. Contrary to the traditional kriging variance, the interpolation variance is data-values dependent, variogram dependent, and a measure of local accuracy. Natural phenomena are not homogeneous; therefore, local variability as expressed through data values must be recognized for a correct assessment of uncertainty. The interpolation variance is simply the weighted average of the squared differences between data values and the retained estimate. Ordinary kriging or simple kriging variances are the expected values of interpolation variances; therefore, these traditional homoscedastic estimation variances cannot properly measure local data dispersion. More precisely, the interpolation variance is an estimate of the local conditional variance, when the ordinary kriging weights are interpreted as conditional probabilities associated to the n neighboring data. This interpretation is valid if, and only if, all ordinary kriging weights are positive or constrained to be such. Extensive tests illustrate that the interpolation variance is a useful alternative to the traditional kriging variance. 相似文献
6.
Peter K. Kitanidis 《Mathematical Geology》1991,23(5):741-758
In linear geostatistics, models for the mean function (drift) and the variogram or generalized covariance function are selected on the basis of the modeler's understanding of the phenomenon studied as well as data. One can seldom be assured that the most appropriate model has been selected; however, analysis of residuals is helpful in diagnosing whether some important characteristic of the data has been neglected and, ultimately, in providing a reasonable degree of assurance that the selected model is consistent with the available information. The orthonormal residuals presented in this work are kriging errors constructed so that, when the correct model is used, they are uncorrelated and have zero mean and unit variance. It is suggested that testing of orthonormal residuals is a practical way for evaluating the agreement of the model with the data and for diagnosing model deficiencies. Their advantages over the usually employed standardized residuals are discussed. A set of tests are presented. Orthonormal residuals can also be useful in the estimation of the covariance (or variogram) parameters for a model that is considered correct. 相似文献
7.
The Second-Order Stationary Universal Kriging Model Revisited 总被引：3，自引：0，他引：3
Universal kriging originally was developed for problems of spatial interpolation if a drift seemed to be justified to model the experimental data. But its use has been questioned in relation to the bias of the estimated underlying variogram (variogram of the residuals), and furthermore universal kriging came to be considered an old-fashioned method after the theory of intrinsic random functions was developed. In this paper the model is reexamined together with methods for handling problems in the inference of parameters. The efficiency of the inference of covariance parameters is shown in terms of bias, variance, and mean square error of the sampling distribution obtained by Monte Carlo simulation for three different estimators (maximum likelihood, bias corrected maximum likelihood, and restricted maximum likelihood). It is shown that unbiased estimates for the covariance parameters may be obtained but if the number of samples is small there can be no guarantee of good estimates (estimates close to the true value) because the sampling variance usually is large. This problem is not specific to the universal kriging model but rather arises in any model where parameters are inferred from experimental data. The validity of the estimates may be evaluated statistically as a risk function as is shown in this paper. 相似文献
8.
Sample schemes used in geostatistical surveys must be suitable for both variogram estimation and kriging. Previously schemes
have been optimized for one of these steps in isolation. Ordinary kriging generally requires the sampling locations to be
evenly dispersed over the region. Variogram estimation requires a more irregular pattern of sampling locations since comparisons
must be made between measurements separated by all lags up to and beyond the range of spatial correlation. Previous studies
have not considered how to combine these optimized schemes into a single survey and how to decide what proportion of sampling
effort should be devoted to variogram estimation and what proportion devoted to kriging
An expression for the total error in a geostatistical survey accounting for uncertainty due to both ordinary kriging and variogram
uncertainty is derived. In the same manner as the kriging variance, this expression is a function of the variogram but not
of the sampled response data. If a particular variogram is assumed the total error in a geostatistical survey may be estimated
prior to sampling. We can therefore design an optimal sample scheme for the combined processes of variogram estimation and
ordinary kriging by minimizing this expression. The minimization is achieved by spatial simulated annealing. The resulting
sample schemes ensure that the region is fairly evenly covered but include some close pairs to analyse the spatial correlation
over short distances. The form of these optimal sample schemes is sensitive to the assumed variogram. Therefore a Bayesian
approach is adopted where, rather than assuming a single variogram, we minimize the expected total error over a distribution
of plausible variograms. This is computationally expensive so a strategy is suggested to reduce the number of computations
required 相似文献
9.
A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These
transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study
presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured
transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity
maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and
ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated
data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates
to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother
than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even
natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic
information systems (GIS) as basic information for further groundwater study.
Received: 27 August 1999 · Accepted: 22 February 2000 相似文献
10.
Analysis of nonintrinsic spatial variability by residual kriging with application to regional groundwater levels 总被引：8，自引：0，他引：8
A method for obtaining pointwise or spatially averaged estimates of a nonintrinsic function is introduced based on residual kriging. The method relies on a stepwise iterative regression process for simultaneously estimating the global drift and residual semivariogram. Estimates of the function are then obtained by solving a modified set of simple kriging equations written for the residuals. The modification consists of replacing the true variogram in the kriging equations by the variogram of the residual estimates as obtained from the iterative regression process. The method is illustrated by considering groundwater levels in an Arizona aquifer. The results are compared with those obtained for the aquifer by the generalized covariance package BLUEPACK-3D. 相似文献
11.
Four variogram models for regional groundwater geochemical data are presented. These models were developed from an empirical study of the sample variograms for more than 10 elements in groundwaters from two geologic regions in the Plainview quandrangle, Texas. A procedure is given for the estimation of the variogram in the isotropic and anisotropic case. The variograms were found useful for quantifying the differences in spatial variability for elements within a geologic unit and for elements in different geologic units. Additionally, the variogram analysis enables assessment of the assumption of statistical independence of regional samples which is commonly used in many statistical procedures. The estimated variograms are used in computation of kriged estimates for the Plainview quadrangle data. The results indicate that an inverse distance weighting model was superior for prediction than simple kriging with the particular variograms used. 相似文献
12.
Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented. 相似文献
13.
Geostatistics provides a suite of methods, summarized as kriging, to analyze a finite data set to describe a continuous property of the Earth. Kriging methods consist of moving window optimum estimation techniques, which are based on a least-squares principle and use a spatial structure function, usually the variogram. Applications of kriging techniques have become increasingly wide-spread, with ordinary kriging and universal kriging being the most popular ones. The dependence of the final map or model on the input, however, is not generally understood. Herein we demonstrate how changes in the kriging parameters and the neighborhood search affect the cartographic result. Principles are illustrated through a glaciological study. The objective is to map ice thickness and subglacial topography of Storglaciären, Kebnekaise Massif, northern Sweden, from several sets of radio-echo soundings and hot water drillings. New maps are presented. 相似文献
14.
Robustness of variograms and conditioning of kriging matrices 总被引：1，自引：0，他引：1
Current ideas of robustness in geostatistics concentrate upon estimation of the experimental variogram. However, predictive algorithms can be very sensitive to small perturbations in data or in the variogram model as well. To quantify this notion of robustness, nearness of variogram models is defined. Closeness of two variogram models is reflected in the sensitivity of their corresponding kriging estimators. The condition number of kriging matrices is shown to play a central role. Various examples are given. The ideas are used to analyze more complex universal kriging systems.Research performed while on leave at Centre de Geóstatistique et de Morphologie Mathématique, Fontainebleau. 相似文献
15.
R. J. Yao J. S. Yang P. Gao H. B. Shao G. M. Liu S. P. Yu 《Environmental Earth Sciences》2014,71(1):233-243
Soil salinity has been known to be problematic to land productivity and environment in the lower Yellow River Delta due to the presence of a shallow, saline water table and marine sediments. Spatial information on soil salinity has gained increasing importance for the demand of management and sustainable utilization of arable land in this area. Apparent electrical conductivity, as measured by electromagnetic induction instrument in a fairly quick manner, has succeeded in mapping soil salinity and many other soil physical and chemical properties from field to regional scales. This was done based on the correlation that existed between apparent electrical conductivity and many other soil properties. In this paper, four spatial prediction methods, i.e., local polynomial, inverse distance weighed, ordinary kriging and universal kriging, were employed to estimate field-scale apparent electrical conductivity with the aid of an electromagnetic induction instrument (type EM38). The spatial patterns estimated by the four methods using EM38 survey datasets of various sample sizes were compared with those generated by each method using the entire sample size. Spatial similarity was evaluated using difference index (DI) between the maps created using various sample sizes (i.e., target maps) and the maps generated with the entire sample size (i.e., the reference map). The results indicated that universal kriging had the best performance owing to the inclusion of residuals and spatial detrending in the kriging system. DI showed that spatial similarity between the target and reference maps of apparent electrical conductivity decreased with the reduction in sample size for each prediction method. Under the same reduction in sample size, the method retaining the most spatial similarity was universal kriging, followed by ordinary kriging, inverse distance weighed, and local polynomial. Approximately, 70 % of total survey data essentially met the need for retaining 90 % details of the reference map for universal kriging and ordinary kriging methods. This conclusion was that OK and UK were two most appropriate methods for spatial estimation of apparent electrical conductivity as they were robust with the reduction in sample size. 相似文献
16.
Shavkat Rakhmatullaev Antoine Marache Frédéric Huneau Philippe Le Coustumer Masharif Bakiev Mikael Motelica-Heino 《Environmental Earth Sciences》2011,63(3):447-460
The paper presents the results of a new geostatistical approach to generate bathymetric surface models from point measurement
converted into continuous contour surfaces of reservoir bottoms in Uzbekistan. Sedimentation of reservoirs raises engineering,
environmental and economical issues for the communities around the world in areas affected by a strong water deficit. Because
of Uzbekistan’s arid climatic conditions, and uneven spatial and temporal water resources distribution, responsive and innovative
water availability assessment surveys of all major water reservoirs are required. Bathymetric surveying is a traditional method
that is carried out for the estimation of reservoir volumes and surface areas of the corresponding reservoir stages in order
to assess the water availability. Volume and surface area differences derived from multiple surveys of a reservoir provide
storage loss estimates over time due to sedimentation. However, two main factors, such as intensive field data measurement
and post data-processing, often limit the frequency of these surveys. Alternatively, innovative depth measurement technologies
coupled with contouring and surface mapping programs provide automated reservoir volume and surface area calculations. This
significantly reduces time, workload and financial burdens for reservoir sedimentation projects. This research proposes the
use of geostatistical approach to assess the reservoir sedimentation in the Akdarya reservoir of Uzbekistan. The geostatistical
approach includes (semi-) variogram analysis and interpolation (kriging and simulations—turning bands) techniques predicting
values at unsampled locations for generating digital bathymetric surface models of reservoir bottom conditions in order to
calculate the volume and surface area at a given water elevation. The simulation enables to have range of reservoir volumes
and surface areas with the same probability, in comparison to the kriging and traditional methods. This gives a real estimation
of the resource availability for water operators to manage natural resources and hydraulic infrastructure in a sustainable
manner. 相似文献
17.
Pierre Petitgas Mathieu Woillez Mathieu Doray Jacques Rivoirard 《Mathematical Geosciences》2018,50(2):187-208
Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided. 相似文献
18.
Imprecise (fuzzy) information in geostatistics 总被引：2，自引：0，他引：2
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 (Journel, 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 a 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.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987. 相似文献
19.
Comparison of kriging techniques in a space-time context 总被引：1，自引：0，他引：1
Patrick Bogaert 《Mathematical Geology》1996,28(1):73-86
Space-time processes constitute a particular class, requiring suitable tools in order to predict values in time and space, such as a space-time variogram or covariance function. The space-time co-variance function is defined and linked to the Linear Model of Coregionalization under second-order space-time stationarity. Simple and ordinary space-time kriging systems are compared to simple and ordinary cokriging and their differences for unbiasedness conditions are underlined. The ordinary space-time kriging estimation then is applied to simulated data. Prediction variances and prediction errors are compared with those for ordinary kriging and cokriging under different unbiasedness conditions using a cross-validation. The results show that space-time kriging tend to produce lower prediction variances and prediction errors that kriging and cokriging. 相似文献
20.
The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging. 相似文献