Robust Measures of Spatial Continuity

Abstract

The variogram often suffers in practice from the effects of heteroscedasticity and clustering. “Relative” variograms have enjoyed practical success despite their uncertain theoretical pedigree. These relative variograms achieve their robustness by scaling the traditional variogram by a function of the mean. The mean which determines the scaling factor can be chosen in several different ways, giving rise to several different relative variograms. Other practically successful alternatives to the variogram include the covariance, which achieves its robustness by accounting for the lag means, and the correlogram, which incorporates the lag variances. A simulated data set is used to explore the performance of the traditional variogram and four alternatives. The results of these studies lead to the conclusion that the traditional variogram should not be used to describe spatial continuity in the presence of skewed distributions which have been preferentially sampled.