Spatial prediction of groundwater level change based on the Third Law of Geography

Abstract Spatial prediction methods are an important means of predicting the spatial variation of groundwater level change. Existing methods extract spatial or statistical relationships from samples to represent the study area for inference and require a representative sample set that is usually in large quantity and is distributed across geographic or covariate space. However, samples for groundwater are usually sparsely and unevenly distributed. In this paper, an approach based on the Third Law of Geography is proposed to make predictions by comparing the similarity between each individual sample and unmeasured site. The approach requires no specific number or distribution of samples and provides individual uncertainty measures at each location. Experiments in three different watersheds across the U.S. show that the proposed methods outperform machine learning methods when available samples do not well represent the area. The provided uncertainty measures are indicative of prediction accuracy by location. The results of this study also show that the spatial prediction based on the Third Law of Geography can also be successfully applied to dynamic variables such as groundwater level change.