ACCOUNTING FOR SPATIAL AUTOCORRELATION IN MODELING THE DISTRIBUTION OF WATER QUALITY VARIABLES

Several studies in hydrology have reported differences in outcomes between models in which spatial autocorrelation (SAC) is accounted for and those in which SAC is not. However, the capacity to predict the magnitude of such differences is still ambiguous. In this thesis, I hypothesized that SAC, inherently possessed by a response variable, influences spatial modeling outcomes. I selected ten watersheds in the USA and analyzed them to determine whether water quality variables with higher Moran’s I values undergo greater increases in the coefficient of determination (R²) and greater decreases in residual SAC (rSAC) after spatial modeling. I compared non-spatial ordinary least squares to two spatial regression approaches, namely, spatial lag and error models. The predictors were the principal components of topographic, land cover, and soil group variables. The results revealed that water quality variables with higher inherent SAC showed more substantial increases in R² and decreases in rSAC after performing spatial regressions. In this study, I found a generally linear relationship between the spatial model outcomes (R² and rSAC) and the degree of SAC in each water quality variable. I suggest that the inherent level of SAC in response variables can predict improvements in models before spatial regression is performed. The benefits of this study go beyond modeling selection and performance, it has the potential to uncover hydrologic connectivity patterns that can serve as insights to water quality managers and policy makers

Accounting for and Predicting the Influence of Spatial Autocorrelation in Water Quality Modeling

Several studies in the hydrology field have reported differences in outcomes between models in which spatial autocorrelation (SAC) is accounted for and those in which SAC is not. However, the capacity to predict the magnitude of such differences is still ambiguous. In this study, we hypothesized that SAC, inherently possessed by a response variable, influences spatial modeling outcomes. We selected ten watersheds in the USA and analyzed if water quality variables with higher Moran’s I values undergo greater increases in the coefficient of determination (R2) and greater decreases in residual SAC (rSAC). We compared non-spatial ordinary least squares to two spatial regression approaches, namely, spatial lag and error models. The predictors were the principal components of topographic, land cover, and soil group variables. The results revealed that water quality variables with higher inherent SAC showed more substantial increases in R2 and decreases in rSAC after performing spatial regressions. In this study, we found a generally linear relationship between the spatial model outcomes (R2 and rSAC) and the degree of SAC in each water quality variable. We suggest that the inherent level of SAC in response variables can predict improvements in models before spatial regression is performed

Consequences of spatial structure in soil–geomorphic data on the results of machine learning models

In this paper, we examined the degree to which inherent spatial structure in soil properties influences the outcomes of machine learning (ML) approaches to predicting soil spatial variability. We compared the performances of four ML algorithms (support vector machine, artificial neural network, random forest, and random forest for spatial data) against two non-ML algorithms (ordinary least squares regression and spatial filtering regression). None of the ML algorithms produced residuals that had lower mean values or were less autocorrelated over space compared with the non-ML approaches. We recommend the use of random forest when a soil variable of interest is weakly autocorrelated (Moran’s I  0.4). Overall, this work opens the door to a more consistent selection of model algorithms through the establishment of threshold criteria for spatial autocorrelation of input variables

Consequences of Spatial Structure in Soil–Geomorphic Data on the Results of Machine Learning Models

In this paper, we examined the degree to which inherent spatial structure in soil properties influences the outcomes of machine learning (ML) approaches to predicting soil spatial variability. We compared the performances of four ML algorithms (support vector machine, artificial neural network, random forest, and random forest for spatial data) against two non-ML algorithms (ordinary least squares regression and spatial filtering regression). None of the ML algorithms produced residuals that had lower mean values or were less autocorrelated over space compared with the non-ML approaches. We recommend the use of random forest when a soil variable of interest is weakly autocorrelated (Moran\u27s I \u3c 0.1) and spatial filtering regression when it is relatively strongly autocorrelated (Moran\u27s I \u3e 0.4). Overall, this work opens the door to a more consistent selection of model algorithms through the establishment of threshold criteria for spatial autocorrelation of input variables