Application research of physically constrained AI hydrological models in typical watersheds of high-altitude cold regions

High-altitude cold regions are a critical component of the global hydrological ecosystem. The Tongtian River Basin, as a typical example, is characterized by complex topography, vertically differentiated hydrometeorological and vegetation conditions, and the impacts of global climate change. Consequently, hydrological processes exhibit high uncertainty, and the scarcity of monitoring stations and inconsistent data quality in the basin make hydrological research particularly challenging. To evaluate the benefits of incorporating physical constraints into AI-based hydrological models for alpine regions, this study utilized meteorological and hydrological data from the basin spanning 1971–2024 to construct and compare the runoff simulation performance of a purely data-driven deep learning model (LSTM) with a deep learning model incorporating physical constraints (PHY-LSTM). The results indicate that the model incorporating physical constraints significantly outperforms the purely data-driven model in simulation performance, with the Nash-Sutcliffe Efficiency Coefficient (NSE) during the validation period increasing to 0.82, the Kring-Gupta Efficiency Coefficient (KGE) rising to 0.83, and the Peak Time Difference (PTD) decreasing to 4.61. Particularly during extreme hydrological events, the physical constraints effectively corrected simulation errors in flood peaks and prevented the occurrence of unreasonable negative flow values during the dry season. Although the PHY-LSTM performed slightly worse than the LSTM on validation-period metrics, this indicates that the physical constraints mitigated overfitting to the training samples to some extent and improved generalization capabilities on independent samples. This study demonstrates that integrating physical mechanisms into deep learning models can significantly improve model accuracy, physical consistency, and interpretability, thereby providing scientific support for water resources management and disaster prevention and control in high-altitude cold regions.