Geostatistical Methods for Incorporating Auxiliary Information in the Prediction of Spatial Variables

Abstract

Universal kriging is one method used for the prediction of nonstationary spatial functions. This article shows how the universal kriging approach may be used to incorporate explanatory variables in the mapping of a spatial process. Such an approach is often called "kriging with external drift" in the geostatistical literature. Both of these techniques require knowledge of the semivariogram of the residual process, and they have often been criticized for difficulties in obtaining this semivariogram. However, with regard to estimation of the parameters of the underlying semivariogram model, both universal kriging and kriging with external drift are special cases of a statistical regression model with spatially correlated errors. In this article, restricted maximum likelihood is used to obtain estimates of the parameters of the residual process, and an approximate F test that incorporates the spatial correlation in testing the significance of the trend or explanatory relationship is given. The external drift approach is contrasted with a different method, known as cokriging, for incorporating the same auxiliary information. Some of the fundamental ideas inherent in the cokriging approach are summarized and discussed. The use of a linear model of coregionalization in obtaining valid semivariogram models for cokriging is demonstrated. Both approaches are illustrated using a data set obtained from a variable-rate farming experiment in Adams County, Nebraska.