Physics-Guided Deep Learning for Rainfall-Runoff Modeling: Integrating Physical Constraints and Data-Driven Approaches

This study addresses the limitations of traditional deep learning models in hydrological forecasting, which often lack physical interpretability and struggle with extreme events. We propose a hybrid framework that combines data-driven deep learning with physical constraints to enhance model accuracy and robustness. Traditional deep learning models (e.g., LSTM) have shown promise in rainfall-runoff prediction but are criticized for their "black-box" nature and poor performance under extreme conditions, while physical-based models, though interpretable, are computationally expensive and rely on detailed parameterization. To bridge this gap, we integrate physical constraints (e.g., water balance, monotonicity) into LSTM networks through three key approaches: extreme event constraints that add penalties for violating physical laws, monotonicity constraints ensuring runoff increases with rainfall intensity via ReLU-based loss functions, and hard constraints projecting outputs to strictly adhere to hydrological laws. Applied to 2683 basins globally, our physics-guided LSTM (PHY-LSTM) improved the Nash-Sutcliffe Efficiency (NSE) by 0.10 and reduced the Root Mean Square Error (RMSE) by 15% compared to standard LSTM, with a 20% enhancement in flood peak prediction using synthetic extreme samples. Additionally, we identified time-varying parameters across climate zones, revealing trends in water storage capacity (1.7mm/decade in wet regions, -0.6mm/decade in arid regions). This framework bridges data-driven efficiency and physical interpretability, enabling reliable predictions under extreme conditions and providing insights into hydrological processes, validated globally and applicable to water resource management and climate change impact assessments.