A disjunctive kriging program for assessing point-support conditional distributions

Abstract

In geostatistical applications, the local distributions of the values of a regionalized attribute at unsampled locations can be assessed by nonlinear methods such as indicator or multigaussian kriging. Disjunctive kriging can also be applied in the framework of bivariate isofactorial models, for which there exists a complete family of functions (factors) with no spatial cross-correlations. This work focuses on the point-support models with polynomial factors and gives practical tips for the modeling of the univariate and bivariate distributions and for the implementation of disjunctive kriging, mainly in what refers to the convergence of the expansions into factors, the post-processing of the estimated statistics and the use of ordinary kriging. The tools and concepts are complemented by a set of computer programs and applied to two case studies. The first one consists of topsoil samples measuring the lead concentration at a smelter site in Dallas, Texas. A gamma isofactorial model is fitted to these data and disjunctive kriging is used to map the local probabilities that the actual concentrations exceed a toxic threshold and to divide the smelter site into a safe and a polluted area. The second case study concerns the infestation of field crops by a caterpillar. A negative binomial model is used to characterize the number of bored stalk internodes and to assess the risk that this number exceeds given values.