Combining Minimum Error Variance and Spatial Variability in the Mapping of Environmental Variables

This paper presents an algorithm for generating realizations of the spatial distribution of an environmental variable; these realizations must minimize the local error variance in addition to the traditional constraints of reproduction of histogram and semivariogram. The optimization technique is performed by simulated annealing and requires a prior determination of the conditional probability distribution functions of the attribute value at each grid node. The approach is illustrated using an environmental data set related to soil contamination by zinc. Imposing the constraint of minimum error variance reduces diierences between realizations, hence reduces the space of uncertainty. A validation set shows the proposed approach to reduce the risk of classifying wrongly a contaminated location as safe as compared with decision-making based on locally accurate but smooth estimated maps or unsmooth but inaccurate simulated maps.