Developing a Physics-Informed Deep Learning Model to Simulate Runoff Response to Climate Change in Alpine Catchments

Climate change has rapidly degraded the cryosphere in alpine headwaters, altering the runoff regime of alpine watersheds and threatening water security worldwide. To precisely simulate runoff response to climate change in alpine catchments, we took the source region of the Yellow River as a case to develop a physics-informed deep learning (DL) model that tightly hybridizes DL with the physics of dominant hydrological processes, including the neural network-based coupling of soil freeze-thaw physics inspired by the Stefan equation. A physics-informed DL model without soil freeze-thaw representation was also established as a benchmark. Results demonstrated the former model's superiority in capturing streamflow's inter-annual dynamics and reproducing baseflow recession properties caused by soil freeze-thaw when average temperature rises by 1?. This emphasizes the importance of the physics of dominant hydrological processes for DL to make credible runoff projections under rapid climate change. Furthermore, we comprehensively compared the physics-informed DL model with a lumped model, physically-based distributed model, and standard DL model, showing that the physics-informed DL model performs best in simulating streamflow at multi-timescales and the impacts of soil freeze-thaw on runoff, and is more capable of simulating runoff relative change and trend in response to climate change. In summary, our findings demonstrate physics-informed DL's credibility in runoff projections under drastic climate change when infused with the physics of dominant hydrological processes, and illustrate its superior ability to learn complex hydrological processes, providing a new approach for runoff simulation in permafrost-affected alpine catchments under climate change.