Geostatistical Study of the Scale-dependent and Spatially Varying Impact of Geology on Arsenic in Groundwater of Southeast Michigan

Geostatistical analysis of arsenic concentrations in groundwater of Southeast Michigan confirmed the intense spatial non-homogeneity of As concentration, resulting in samples that greatly vary even when located a few meters apart. These results stressed the need for incorporating in the prediction any auxiliary information that is more densely sampled and could inform on the variability of arsenic concentrations. Regression analysis indicated that secondary information, such as proximity to Marshall Sandstone, helped only the prediction at a regional scale (i.e. beyond 15 kms), leaving the short-range variability largely unexplained. This global or "aspatial" regression is, however, based on the implicit assumption that the relationship between variables is constant across the study area. This assumption is likely unrealistic for large areas that display substantial geographic variation in landscape, geology and land uses. In such cases, the geographic variation in the set of variables is too complex to be captured by a single set of correlation or regression coefficients. Spatial changes in the correlation between arsenic concentrations and several secondary variables (type of bedrock and unconsolidated deposits, and proximity of well to the Marshall Sandstone subcrop, where the highest concentrations of arsenic were found) were investigated using geographically weighted regression that performs the regression within local windows. Within each window, the observations are weighted according to their proximity to the centre of the window. Local regression coefficients and associated statistics (i.e. proportion of variance explained, correlation coefficients) were mapped to visualize how the explanatory power of secondary variables changes spatially. These maps highlighted regions of interest where the local pattern of correlation departs from the global one. This local correlation analysis also reduced the mean square error of predictions, leading to residuals of smaller magnitude but less correlated in space than results of aspatial regression.