Defining probability of saturation with indicator kriging on hard and soft data

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.     

Quantifying geological uncertainty for flow and transport modeling in multi-modal heterogeneous formations

In this work, we address the problem of characterizing the heterogeneity and uncertainty of hydraulic properties for complex geological settings. Hereby, we distinguish between two scales of heterogeneity, namely the hydrofacies structure and the intrafacies variability of the hydraulic properties. We employ multiple-point geostatistics to characterize the hydrofacies architecture. The multiple-point statistics are borrowed from a training image that is designed to reflect the prior geological conceptualization. The intrafacies variability of the hydraulic properties is represented using conventional two-point correlation methods, more precisely, spatial covariance models under a multi-Gaussian spatial law. We address the different levels and sources of uncertainty in characterizing the subsurface heterogeneity, and explore their effect on groundwater flow and transport predictions. Typically, uncertainty is assessed by way of many images, termed realizations, of a fixed statistical model. However, in many cases, sampling from a fixed stochastic model does not adequately represent the space of uncertainty. It neglects the uncertainty related to the selection of the stochastic model and the estimation of its input parameters. We acknowledge the uncertainty inherent in the definition of the prior conceptual model of aquifer architecture and in the estimation of global statistics, anisotropy, and correlation scales. Spatial bootstrap is used to assess the uncertainty of the unknown statistical parameters. As an illustrative example, we employ a synthetic field that represents a fluvial setting consisting of an interconnected network of channel sands embedded within finer-grained floodplain material. For this highly non-stationary setting we quantify the groundwater flow and transport model prediction uncertainty for various levels of hydrogeological uncertainty. Results indicate the importance of accurately describing the facies geometry, especially for transport predictions.     

Pilot points method incorporating prior information for solving the groundwater flow inverse problem

The pilot points method is often used in nonlinear geostatistical calibration. The method consists of estimating the values of the hydraulic properties at a set of arbitrary (pilot) points so as to best fit the aquifer response as measured by available indirect observations (i.e., heads or drawdowns). Though this method remains general and appealing, no prior information of the hydraulic properties is usually included in the optimization process, which constrains the number of pilot points to ensure stability. In this paper, we present a modification of the pilot points method, including prior information in the optimization process by adding a plausibility term to the objective function to be minimized. This results from formulating the inverse problem in a maximum likelihood framework. The performance of the method is tested on a synthetic example. Results show that including the plausibility term improves the identification of heterogeneity. Furthermore, this term makes the inverse problem more stable and allows the use of larger number of pilot points, thus improving the identification of the heterogeneity as well. Therefore, the use of the plausibility term is recommended.     

Geostatistical modelling of ground conditions to support the assessment of site contamination

The pattern of ground contamination across a site depends on the historical pattern of contaminant releases at the surface and the redistribution and the fate of contaminants below the surface. Using these concepts a new site assessment approach (assessment modelling) is proposed based on the development of three stochastic models: a model of the physical structure of the ground materials beneath the site; a model of the distribution of surface contaminant spills; and a model of the flow and transport of spilled material into the heterogeneous underlying ground to construct alternative, equally likely, present day contaminant distributions. Combining the models within a Monte Carlo framework can, in principle, improve the understanding of the potential for excess contamination across the site and improve decisions on remediation options and locations. A trial application has been undertaken in the UK using a particular site to assess the approach. The conditions at the site used for the trial and the first of the stochastic model developments, the geostatistical modelling of the soil heterogeneity, are presented in this paper. Non-parametric and parametric geostatistics have been employed to formulate the geostatistical models of the site soils using lithological information from 146 trial pits and boreholes. The approach to the soil modelling and the verification and validation of the results are described. The heterogeneity of the subsurface is complicated by the presence of made-ground, comprised of various inert building wastes, and the non-stationarity of the heterogeneity of the natural ground. This paper is the first of three describing the assessment modelling methodology and its trial application to the site.     

Optimal selection of number and location of rainfall gauges for areal rainfall estimation using geostatistics and simulated annealing

This paper presents a method for establishing an optimal network design for the estimation of areal averages of rainfall events. The problem consists of minimising an objective function which includes both the accuracy of the areal mean estimation (as expressed by the kriging variance of estimation) and the economic cost of the data collection. The well known geostatistical variance-reduction method is used in combination with simulated annealing as an algorithm of minimisation. This methodology has several advantages which will be demonstrated in this paper. Several synthetic examples are shown in order to illustrate the performance of the methodology in two different optimisation problems: the optimal selection of a subset from a set of stations that already exist and the optimal augmentation of a previously existing network.     

全球变化中土壤信息系统的研究进展

地理信息系统（GIS）支持下的土壤信息系统（SIS）在评价土地生产能力、土地退化的现状、速率和风险以及全球变化研究中具有重要意义。简述了国内外SIS的研究进展,包括FAO世界土壤图的出版和修正、数字化世界土壤资源数据库（SDB）的建立、土壤—土地数字化数据库（SOTER）在全世界的进展、世界土壤排放清单（WISE）的发展以及美国和我国的SIS进展情况。在此基础上简介了土壤属性空间变异性的研究方法———地形分析和地质统计学,并指出地质统计学与GIS的结合将是未来的发展趋势。     

Geostatistics of near-surface moisture in bare cultivated organic soils

The aim of this study was to characterise fine scale patterns of organic soil moisture content in the top 5 cm by means of semi-variogram modelling. Soil moisture content was observed along a transect on 2 occasions, early in the 1999 growing season to avoid any influences originating from vegetation and cultural practices. Soil moisture values were found to be normally distributed and were not significantly correlated with the soil organic matter content. Many similarities were depicted between the exponential semi-variograms characteristics of this study and another one in mineral soils, reported in the literature, except for the much higher sills associated with organic soils. Of particular interest were similar correlation lengths, indicating that a correlation range of the order of 100 m should be expected for mineral soils and for the level of moisture and organic matter contents found in this study.     

A stability analysis of the geostatistical approach to aquifer transmissivity identification

In recent years, geostatistical concepts have been applied to the inverse problem of transmissivity estimation from piezometric head data. It has been claimed that such methods overcome various difficulties encountered in other approaches. However, the reconstruction of transmissivity from head measurements is ill-posed as it depends on derivatives of the head field. Consequently, any accurate method for its solution is likely to encounter numerically ill-conditioned systems. This paper reviews the geostatistical approach, and uses the stability analyses of linear algebra to show that, as the amount of available data increases and the discretization of the system is refined, both a numerically ill-conditioned parameter estimation problem and ill-conditioned cokriging equations may appear. Therefore, while the geostatistical approach does have conceptual appeal, it does not avoid the fundamental difficulties arising out of the ill-posed nature of transmissivity identification. Instead, the method is likely to be quite sensitive to these difficulties, so care must be taken in its formulation to minimize their effects. A means to stabilize the geostatistical method is suggested and numerical experiments that highlight key points of our analysis are given.     

A treatise on the use of geostatistics for the characterization of nonrenewable resources

Five decades of geostatistical development are reviewed to summarize the state of the art for spatial interpolation vis-à-vis kriging or a form thereof. Although a search of the literature reveals a variety of kriging methods, there are but two infrastructures for geostatistical interpolation: simple cokriging, for estimating a single variable using two variables, and generalized cokriging, for estimating one or more variables using the same number of variables that are estimated. The many forms of kriging are varieties of these two interpolation infrastructures. This notion is emphasized to aid the selection of an appropriate interpolation model for a nonrenewable resource. These models are discussed, and literature for the models and for applicable software is cited. Additionally, all aspects of spatial interpolation are discussed, including the adequacy of spatial sampling, distribution characteristics of spatial samples, semivariograms, search parameters, and selection of interpolation models in conformance with spatial data characteristics. Finally, the relationship between interpolation and raster-based geographic information systems is emphasized.     

用人工神经网络进行变差图的最优拟合

本文提出变差图最优拟合的人工神经网络方法,并选取几个实例作为研究对象,其拟合最大相对误差不超过2％,计算机CPU时间不超过80秒。结果表明,该方法性能良好,在地质统计学上有广泛的应用前景。