Modelling complex soil properties as contaminated regionalized variables

Robust estimators of the variogram can be used to identify a random function that describes the background variation of a soil property with the minimum influence of contaminants from a quasi point process. A method is proposed to exploit this to identify data which are best treated as a realization of a quasi point process rather than of a continuous random function for purposes of spatial analysis. Having identified an appropriate robustly estimated variogram the cross-validation error of each datum is standardized by the kriging standard error to give the statistic εs(x). This and the standardized original variable, zs(x), are combined into a statistic, O(x), with a standard Gaussian distribution in the absence of data from a contaminant process. The O(x) statistic may then be used to identify data best regarded as realizations of the contaminating quasi point process. The technique is demonstrated using simulation and data on lead concentration in topsoil of the Swiss Jura.