Using rank-order geostatistics for spatial interpolation of highly skewed data in a heavy-metal contaminated site

The spatial distribution of a pollutant in contaminated soils is usually hi ghly skewed. As a result, the sample variogram often differs considerably f rom its regional counterpart and the geostatistical interpolation is hinder ed. In this study, rank-order geostatistics with standardized rank transfor mation was used for the spatial interpolation of pollutants with a highly s kewed distribution in contaminated soils when commonly used nonlinear metho ds, such as logarithmic and normal-scored transformations, are not suitable . A real data set of soil Cd concentrations with great variation and high s kewness in a contaminated site of Taiwan was used for illustration. The spa tial dependence of ranks transformed from Cd concentrations was identified and kriging estimation was readily performed in the standardized-rank space . The estimated standardized rank was back-transformed into the concentrati on space using the middle point model within a standardized-rank interval o f the empirical distribution function (EDF). The spatial distribution of Cd concentrations was then obtained. The probability of Cd concentration bein g higher than a given cutoff value also can be estimated by using the estim ated distribution of standardized ranks. The contour maps of Cd concentrati ons and the probabilities of Cd concentrations being higher than the cutoff value can be simultaneously used for delineation of hazardous areas of con taminated soils.