A review of spatial statistical approaches to modeling water quality

We review different regression models related to water quality that incorporate spatial aspects in their model. Spatial aspects refer to the location of different sites and are usually characterized by the distance between different points and directions by which they are related to each other. We focus on spatial lag and error, spatial eigenvector-based, geographically weighted regression, and spatial-stream-network-based models. We evaluated different studies using these methods based on how they dealt with clustering (spatial autocorrelation) of response variables, incorporated those clustering in the error (residual spatial autocorrelation), used multi-scale processes, and improved the model performance. The water-quality-based regression modeling approaches are shifting from straight-line distance-based spatial relations to upstream-downstream relations. Calculation of spatial autocorrelation and residual spatial autocorrelation was dependent upon the type of spatial regression used. The weights matrix is used as available in the software and most of the studies did not attempt to modify it. Different scale processes like certain distance from rivers versus consideration of entire watersheds are dealt with separately in most of the studies. Generally, the capacity of the predictor variables to predict the response variable significantly improves when spatial regressions are used. We identify new research directions in terms of spatial considerations, weights matrix construction, inclusion of multi-scale processes, and identification of predictor variables in such models.