Kriging with Categorical External Drift: Use of Thematic Maps in Spatial Prediction and Application to Local Climate Interpolation for Agriculture

Abstract

The method of kriging with external drift is revisited when the external drift variable has a categorical nature. When the domain of interest is partitioned in a certain number, say p, of spatial classes supposed to be homogenous, and when this partition influences the quantitative variable to be interpolated, we propose a new kriging approach which filters the class effects without estimating them. The random function Z(x) is decomposed into a deterministic unknown drift, depending on the classes, and a residual random function R(x). Kriging equations are derived using a variogram model of the residual random function, estimated through all intra-class pairs of sample points. The unbiasedness condition adds p conditions on the weights (as many as classes) in place of the usual unit sum weights. An application in climatology is presented. The purpose is to interpolate daily maximum temperatures at a small agricultural scale in SE of France, using environmental classes defined by land use around the point of interest and determined everywhere from high resolution satellite imaging. Comparison with ordinary kriging is performed.