Coupling process-based and deep learning models for interpretable prediction of urban stormwater quality

Numerical simulation of urban stormwater processes is essential for effective non-point source (NPS) pollutant load estimation and adaptive management of receiving waters. However, coupling hydrological dynamics with water quality responses involves intricate nonlinear interactions, making the balance between model accuracy and computational efficiency a major challenge. Here, we develop a physics-augmented deep learning framework coupling the process-based Storm Water Management Model (SWMM) with the data-driven Long Short-Term Memory (LSTM) networks. The framework was optimized and validated using high-frequency monitoring data from a spectrum of rainfall events in a representative urban catchment in southern China. Compared with the standalone SWMM and LSTM, the hybrid model achieved the best performance to predict the rainfall-driven runoff and NPS pollution responses. The results revealed that the coupling of the physical-process embedded in SWMM into LSTM with high time-resolution was significant to predict the nonlinear correlation and dynamics between the hydrological and water-quality variables, and accurately characterize the short time-scale first-flush typically with majority of pollution load. Coupling-interface ablation experiments and SHapley Additive exPlanations algorithm were applied to assess multi-factor contributions to the prediction, and key attribution patterns and dominant pollution regions were determined. The proposed framework showed good transferability and potential to technically support the targeted control of urban NPS pollution and smart water management.