Geostatistical modelling of uncertainty in soil science

This paper addresses the issue of modelling the uncertainty about the value of continuous soil attributes, at any particular unsampled location (local uncertainty) as well as jointly over several locations (multiple-point or spatial uncertainty). Two approaches are presented: kriging-based and simulation-based techniques that can be implemented within a parametric (e.g. multi-Gaussian) or non-parametric (indicator) frameworks. As expected in theory and illustrated by case studies, the two approaches yield similar models of local uncertainty, yet the simulation-based approach has several advantages over kriging: (1) it provides a model of spatial uncertainty, e.g. the probability that a given threshold is exceeded jointly at several locations can be readily computed, (2) conditional cumulative distribution function (ccdf) for supports larger than the measurement support (e.g. remediation units or flow simulator cells) can be numerically approximated by the cumulative distribution of block simulated values that are obtained by averaging values simulated within the block, and (3) the set of realizations allows one to study the propagation of uncertainty through global GIS operations or complex transfer functions, such as flow simulators that consider many locations simultaneously rather than one at a time. The other issue is the evaluation of the quality or "goodness" of uncertainty models. Two new criteria (exceedence probability plot and narrowness of probability intervals that include the true values) are presented to assess the accuracy and precision of local uncertainty models using cross-validation. According to the second criterion, multi-Gaussian kriging performs better than indicator kriging for the hydraulic conductivity (HC) data set. However, looking at the distribution of flow simulator responses, sequential indicator simulation (sis) yields better results than sequential Gaussian simulation (sGs) that does not allow for significant correlation of extreme values (destructuration effect). (C) 2001 Elsevier Science B.V. All rights reserved.