From Predictions to Patterns with AI: A Differentiable SPARROW Framework for Improved Water Quality Prediction and Attribution
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Nutrient loss is a major contributor to downstream water quality degradation, including the Gulf hypoxia. Effective nutrient management in upstream watersheds requires models that can identify both the magnitude and spatial distribution of pollutant sources and controlling factors. Traditional modeling efforts often assume spatially homogeneous parameters, which may ignore important regional variability. In this study, we developed an artificial intelligence (AI) framework that integrates SPARROW (SPAtially Referenced Regressions On Watershed attributes) with differentiable parameter learning and deep learning techniques. The differentiable Parameter-Learning SPARROW model (dPL-SPARROW) was used to assess whether key source parameters vary spatially and what landscape features drive this variation. The model was trained to estimate NO23 loads across 104 monitoring sites in the Upper Mississippi River Basin from 2001 to 2020. Compared to the benchmarking SPARROW model, dPL-SPARROW improved accuracy on log-transformed annual loads (kg/year): training MSE decreased from 0.372 to 0.308, and R2 improved from 0.903 to 0.919. The generalization ability was tested using both spatial and temporal five-fold cross-validation. Temporal cross-validation demonstrated consistent performance of dPL-SPARROW (training MSE: 0.312; test MSE: 0.327), outperforming the benchmark (training: 0.371; test: 0.394). Spatial cross-validation also demonstrated strong extrapolation ability and minimal overfitting (training: 0.309; test: 0.372), compared with the benchmark (training: 0.361; test: 0.474). Parameter learning focused on the parameters of three critical nitrogen sources in SPARROW: atmospheric deposition, fertilizer, and manure. Analysis using the explainable AI technique DeepSHAP revealed that spatial variation in these model parameters was most influenced by land use (wetland, forest, cropland) and soil properties (soil erodibility, restrictive layer depth, electrical conductivity). Our results show that dPL-SPARROW not only improves predictive accuracy but also provides interpretable, spatially resolved parameter patterns, enabling more targeted and regionally tailored nutrient management strategies to mitigate nutrient loading and improve downstream water quality.
