Identification of field attribute error under different models of spatial variation

Abstract

Recent developments in theory and computer software mean that it is now relatively straightforward to evaluate how attribute errors are propagated through quantitative spatial models in GIS. A major problem, however, is to estimate the errors associated with the inputs to these spatial models. A first approach is to use the root mean square error, but in many cases it is better to estimate the errors from the degree of spatial variation and the method used for mapping. It is essential to decide at an early stage whether one should use a discrete model of spatial variation (DMSV—homogeneous areas, abrupt boundaries), a continuous model (CMSV—a continuously varying regionalized variable field) or a mixture of both (MMSV—mixed model of spatial variation). Maps of predictions and prediction error standard deviations are different in all three cases, and it is crucial for error estimation which model of spatial variation is used. The choice of model has been insufficiently studied in depth, but can be based on prior information about the kinds of spatial processes and patterns that are present, or on validation results. When undetermined it is sensible to adopt the MMSV in order to bypass the rigidity of the DMSV and CMSV. These issues are explored and illustrated using data on the mean highest groundwater level in a polder area in the Netherlands.