Using Physics-Encoded GeoAI to Improve the Physical Realism of Deep Learning′s Rainfall-Runoff Responses under Climate Change

• A physics-encoded deep learning (DL) rainfall-runoff model ( d NN ) is developed. • d NN has interpretable model structure and advanced simulations than pure DL. • d NN improves the physical realism of pure DL′s runoff responses under warming. • Apart from predicting runoff, d NN exhibits strong process inference capability. Recent research has shown that deep learning (DL) faces physical realism challenges in predicting runoff responses under climate change, mainly due to DL’s data dependence and lack of process understanding. In this study, a physics-encoded neural network model ( d NN ) was developed to adress this. d NN enables a fully process-based way to training and prediction by encoding process-based modeling knowledge into the DL architecture, including the water balance principle and causal linkages of catchment hydrological processes. To examine whether d NN can produce reliable runoff responses under warming scenarios, we first conducted regional training for d NN on daily runoff in 29 catchment in California. Two process-based models, EXP-HYDRO and HBV, were then developed as benchmarks. Both d NN and a pure data-driven LSTM were forced under warming scenarios, and the monthly hydrographs and total runoff ratios metrics were evaluated relative to the benchmarks. The results demonstrated: (1) For monthly hydrographs, d NN exhibited advantages in capturing cold-season runoff increase and warm-season recession than LSTM, effectively predicting the changes and trends in monthly runoff under warming scenarios; (2) For total runoff ratios, d NN predicted fewer catchments with increased runoff, indicating it can better maintain the total water budget under warming scenarios; (3) Through the synergy with physics, d NN was able to reasonably infer unobserved snowpack dynamics under warming scenarios. These results highlight the credibility and necessity of considering physics for DL in predicting runoff responses under climate change. Overall, this study provides a promising solution for considering physics in DL to further improve the process understanding in changing environments.