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

AbstractSpatial 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.Keywords: Spatial predictionthe Third Law of Geographymachine learninggroundwater level change Disclosure statementNo potential conflict of interest was reported by the author(s).Data and codes availability statementThe data that support the findings of this study are available at https://doi.org/10.17605/OSF.IO/6ZU4T. These data were derived from the following resources available in the public domain: TerraClimate, a high-resolution global dataset of monthly climate and climatic water balance from 1958 to 2015 (https://www.climatologylab.org/terraclimate.html); ERA5: Fifth generation of ECMWF atmospheric reanalyses of the global climate (https://cds.climate.copernicus.eu/cdsapp#!/home); Data from: Soil Properties and Class 100 m Grids United States (https://doi.org/10.18113/S1KW2H); National Water Information System data available on the World Wide Web (http://waterdata.usgs.gov/nwis/); 1 Arc-second Digital Elevation Models (DEMs) (https://www.sciencebase.gov/catalog/item/4f70aa71e4b058caae3f8de1).Additional informationFundingThe work reported here was supported by grants from National Natural Science Foundation of China [41871300], the China Scholarship Council [201904910630], and the 111 Program of China [D19002]. Supports to A-Xing Zhu through the Vilas Associate Award, the Hammel Faculty Fellow Award, and the Manasse Chair Professorship from the University of Wisconsin-Madison are greatly appreciated.Notes on contributorsFang-He ZhaoFang-He Zhao is currently a PhD candidate at the Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences. Her research is focused on the spatial prediction of geographic variables and the intelligent realization of spatial prediction. She contributed to data collection, experiment design and conduction, and manuscript writing and revision of this paper.Jingyi HuangJingyi Huang is currently an Assistant Professor at the Department of Soil Science, University of Wisconsin-Madison. His research interests include remote sensing and proximal sensing of soil, digital soil mapping, soil physics, and soil-vegetation-atmosphere interaction. He contributed to the conceptualization, data collection, and manuscript writing of the paper.A-Xing ZhuA-Xing Zhu is a Professor at the Department of Geography, University of Wisconsin-Madison, and an adjunct professor at Nanjing Normal University. His current research interest is the development of the Third Law of Geography and its application in geographic analysis. In this study, he planned and supervised the project, and contributed to manuscript writing and revision.