Extension of Spatial Information, Bayesian Kriging and Updating of Prior Variogram Parameters

Variograms are used to describe the spatial variability of environmental variables. In this study, the parameters that characterize the variogram are obtained from a variogram in a different but comparably polluted area. A procedure is presented for improving the variogram modelling when data become available from the area of interest. Interpolation is carried out by means of a Bayesian form of kriging, where prior distributions of the variogram parameters are used. This procedure differs from current procedures, since commonly applied least squares estimation for the variogram is avoided. The study is illustrated with data from a cadmium pollution in the Netherlands, where this form of extrapolation was compared with ordinary kriging. When sufficient data are available (more than 140), ordinary kriging gave the most precise predictions. When the number of data was small (i.e. less than 60), predictions obtained with Bayesian kriging were more precise as compared to those obtained with ordinary kriging. This leads to a considerable reduction of costs, without loss of information.