Geostatistical modelling of uncertainty in soil science

This paper addresses the issue of modelling the uncertainty about the value of continuous soil Ž . attributes, at any particular unsampled location local uncertainty as well as jointly over several Ž . locations multiple-point or spatial uncertainty . Two approaches are presented: kriging-based and Ž . simulation-based techniques that can be implemented within a parametric e.g. multi-Gaussian or Ž . 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 Ž . several advantages over kriging: 1 it provides a model of spatial uncertainty, e.g. the probability Ž . that a given threshold is exceeded jointly at several locations can be readily computed, 2 Ž . conditional cumulative distribution function ccdf for supports larger than the measurement Ž . 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 Ž . 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 AgoodnessB of uncertainty models. Two new Ž 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 Ž . indicator kriging for the hydraulic conductivity HC data set. However, looking at the distribution Ž . of flow simulator responses, sequential indicator simulation sis yields better results than Ž . sequential Gaussian simulation sGs that does not allow for significant correlation of extreme Ž . values destructuration effect . q 2001 Elsevier Science B.V. All rights reserved.