A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models

Runoff forecasting is essential for flood control, disaster mitigation, and sustainable water resources management. However, runoff processes are highly nonlinear and uncertain due to multiple interacting meteorological and underlying surface factors. Current models can be divided into process-driven and data-driven types. The former offers clear physical interpretability but involves complex calibration and simplifications, while the latter captures nonlinear relationships effectively but lacks physical consistency. To integrate their strengths, this study constructs process-based models and data-driven models, and proposes two hybrid strategies: (1) incorporating intermediate variables from physical models, such as soil moisture and runoff yield, as additional features for data-driven models, and (2) embedding physics-based constraints and synthetic data into loss functions. Using the Songxi River Basin as a case study, results show that both hybrid strategies significantly outperform standalone models. SHapley Additive exPlanations (SHAP)-based interpretability analysis further reveals the contribution mechanisms of key physical variables. This study demonstrates that coupling physical processes with data-driven learning effectively enhances runoff forecasting accuracy and offers a promising paradigm to support sustainable watershed management, climate-resilient water regulation, and flood risk reduction.