Integration of physics-informed deep learning with a distributed hydrological model (PIDL-DHM): A hybrid model for runoff simulation

Abstract. Climate change and vegetation restoration have altered hydrological processes, but quantifying vegetation-runoff interactions remains challenging due to complex feedback and data scarcity. We developed a physics-informed deep learning hybrid model that couples process-based hydrology with deep learning to improve runoff prediction in vegetation-altered basins. The model explicitly represents transpiration, interception, snow dynamics, dual runoff generation, water-balance constraints, and distributed spatial heterogeneity. Evaluations in three Chinese basins spanning hydroclimatic and vegetation gradients show that the hybrid models outperform pure deep learning, with the strongest improvements in semi-arid and vegetation-transition basins. Correlation coefficients exceeded 0.8 at monthly/annual scales and 0.75 at daily scales in the most responsive basins. Compared with GR4J, the added complexity is most beneficial in heterogeneous semi-arid and ungauged sub-basins. These results demonstrate that physical constraints improve extrapolation reliability and support hybrid models for sustainable basin management under climate change.