The Variogram and Modelling

Abstract

Accurate estimates of variograms are needed for reliable prediction by kriging and subsequent mapping and for optimizing sampling schemes. Sample variograms are usually computed by the method of moments at a sequence of lags, and one or more ‘authorized’ functions are fitted to them. A variogram may be computed along transects or on grids at regular intervals or in bins from irregularly scattered data. Accuracy of the variogram depends on the size of sample, the number of lags at which it is estimated and the lag interval relative to the spatial scale of variation, the marginal distribution of the variable, anisotropy and trend. Robust estimators can deal with extreme values, outliers. Variograms may be bounded (for second-order stationary processes) or unbounded (intrinsically stationary only), and there are few simple authorized functions for modelling them. The parameters of the models summarize the spatial variation and are needed for subsequent kriging. Computing the variogram in at least three directions can identify anisotropy if it is present. Diagnostics including residual mean squares and the Akaike Information Criterion help in the selection of the best fitting model.