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.     

地统计学方法研究与应用——以甘肃省为例

以甘肃省53个气象台站多年平均降水量和蒸发量为研究对象,运用地统计学分析方法,通过比较分析,分别采用指数模型和球状模型对降水量和蒸发量的半变异函数进行了拟合,并且应用克立格插值生成了年降水量与蒸发量的空间分布图,直观分析了研究对象的空间变异规律。     

Assigning land use to supply wells for the statistical characterization of regional groundwater quality: Correlating urban land use and VOC occurrence

Many national and regional groundwater studies have correlated land use “near” a well, often using a 500 m radius circle, with water quality. However, the use of a 500 m circle may seem counterintuitive given that contributing areas are expected to extend up-gradient from wells, and not be circular in shape. The objective of this study was to evaluate if a 500 m circle is adequate for assigning land use to a well for the statistical correlation between urban land use and the occurrence of volatile organic compounds (VOCs). Land use and VOC data came from 277 supply wells in four study areas in California. Land use was computed using ten different-sized circles and wedges (250 m to 10 km in radius), and three different-sized “searchlights” (1–2 km in length). We define these shapes as contributing area surrogates (CASs), recognizing that a simple shape is at best a surrogate for the actual contributing area. The presence or absence of correlation between land use and the occurrence of VOCs was evaluated using Kendall’s tau (τ). Values of τ were within 10% of one another for wedges and circles ranging in size from 500 m to 2 km, with correlations remaining statistically significant (p < 0.05) for all CAS sizes and shapes, suggesting that a 500 m circular CAS is adequate for assigning land use to a well. Additional evaluation indicated that urban land use is autocorrelated at distances ranging from 8 to 36 km. Thus, urban land use in a 500 m CAS is likely to be predictive of urban land use in the actual contributing area.     

Geostatistical inversing for large-contrast transmissivity fields

The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements. The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance of the quasilinear approach when applied to strongly heterogeneous (or “high-contrast”) transmissivity fields and, when needed, to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss–Newton iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation, we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis–Hastings algorithm. Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear approach but at a considerably higher computational cost.     

Distance-gradient-based variogram and Kriging to evaluate cobalt-rich crust deposits on seamounts

The spatial distribution of cobalt-rich crust thicknesses on seamounts is partly controlled by water depth and slope gradients. Conventional distance–direction-based variogram have not effectively expressed the spatial self-correlation or anisotropy of the thicknesses of cobalt-rich crusts. To estimate resources in cobalt-rich crusts on seamounts using geostatistics, we constructed a new variogram model to adapt to the spatial distribution of the thicknesses of the cobalt-rich crusts. In this model, we defined the data related to cobalt-rich crusts on seamounts as three-dimensional surface random variables, presented an experimental variogram process based on the distance–gradient or distance–“relative water depth,” and provided a theoretical variogram model that follows this process. This method was demonstrated by the spatial estimation of the thicknesses of cobalt-rich crusts on a seamount, and the results indicated that the new variogram model reflects the spatial self-correlation of the thicknesses of cobalt-rich crusts well. Substituted into the Kriging equation, the new variogram model successfully estimated the spatial thickness distribution of these cobalt-rich crusts.     

Comparative soil CO2 flux measurements and geostatistical estimation methods on Masaya volcano, Nicaragua

We present a comparative study of soil CO₂ flux () measured by five groups (Groups 1–5) at the IAVCEI-CCVG Eighth Workshop on Volcanic Gases on Masaya volcano, Nicaragua. Groups 1–5 measured 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 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 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 maps showed important differences. We suggest that the sequential Gaussian simulation method yields the most realistic representation of the spatial distribution of , 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.Editorial responsibility: H Shinohara