Area-to-point prediction under boundary conditions

Abstract

This article proposes a geostatistical solution for area-to-point spatial prediction(downscaling) taking into account boundary effects. Such effects are often poorly con-sidered in downscaling, even though they often have significant impact on the results.The geostatistical approach proposed in this article considers two types of boundaryconditions (BC), that is, a Dirichlet-type condition and a Neumann-type condition,while satisfying several critical issues in downscaling: the coherence of predictions,the explicit consideration of support differences, and the assessment of uncertaintyregarding the point predictions. An updating algorithm is used to reduce the compu-tational cost of area-to-point prediction under a given BC. In a case study, area-to-point prediction under a Dirichlet-type BC and a Neumann-type BC is illustratedusing simulated data, and the resulting predictions and error variances are comparedwith those obtained without considering such conditions.