Kriging: a method of interpolation for geographical information systems

TLDR

Geographical information systems can be enhanced by incorporating geostatistical spatial analysis, as traditional interpolation relies on deterministic models while spatial data exhibit stochastic behavior that regionalized variable theory, and specifically Kriging, addresses through variogram-based prediction error minimization. The study aims to describe procedures for linking geostatistical interpolation methods using standard operating systems. These procedures are illustrated through case studies mapping soil salinity in Israel’s Jordan Valley and herbaceous cover in Botswana via aerial photography.

Abstract

Geographical information systems could be improved by adding procedures for geostatistical spatial analysis to existing facilities. Most traditional methods of interpolation are based on mathematical as distinct from stochastic models of spatial variation. Spatially distributed data behave more like random variables, however, and regionalized variable theory provides a set of stochastic methods for analysing them. Kriging is the method of interpolation deriving from regionalized variable theory. It depends on expressing spatial variation of the property in terms of the variogram, and it minimizes the prediction errors which are themselves estimated. We describe the procedures and the way we link them using standard operating systems. We illustrate them using examples from case studies, one involving the mapping and control of soil salinity in the Jordan Valley of Israel, the other in semi-arid Botswana where the herbaceous cover was estimated and mapped from aerial photographic survey.