Alternative Spatial Estimators for Ground‐Water and Soil Measurements

Abstract

AbstractDetail in mapping studies of spatial data results from spatial interpolation of field or laboratory measurements. The interpolation method used can markedly affect the interpolated estimates and thus the appearance of the resulting map. A popular method, oridinary kriging, is based on several assumptions, including normally distributed observations. For data containing outliers or “hotspots,” which are common in ground‐water monitoring, kriging may not be the most appropriate interpolation method. A robust, nonparametric alternative was developed, tested, and demonstrated using case‐study data from the San Luis Valley in Colorado. The method uses a robust measure of spatial correlation, called the medogram, as an inverse‐distance weight for estimates based on LAD (least‐absolute‐deviation) regression. For both synthetic and real case‐study data containing a few high values (outliers or “hotspots”), this LAD method showed improved performance over ordinary kriging. While performance of the LAD method is slightly better than kriging in terms of the mean squared interpolation error for the “contaminated” data sets studied, the significant advantage of the LAD approach is that it does not produce concentric contours around observations and thus provides more realistic maps.