Development of a Distributed Physics‐Informed Deep Learning Hydrological Model for Data‐Scarce Regions

Abstract Climate change has exacerbated water stress and water‐related disasters, necessitating more precise streamflow simulations. However, in the majority of global regions, a deficiency of streamflow data constitutes a significant constraint on modeling endeavors. Traditional distributed hydrological models and regionalization approaches have shown suboptimal performance. While current deep learning (DL)‐related models trained on large data sets excel in spatial generalization, the direct applicability of these models in certain regions with unique hydrological processes can be challenging due to the limited representativeness within the training data set. Furthermore, transfer learning DL models pre‐trained on large data sets still necessitate local data for retraining, thereby constraining their applicability. To address these challenges, we present a physics‐informed DL model based on a distributed framework. It involves spatial discretization and the establishment of differentiable hydrological models for discrete sub‐basins, coupled with a differentiable Muskingum method for channel routing. By introducing upstream‐downstream relationships, model errors in sub‐basins propagate through the river network to the watershed outlet, enabling the optimization using limited downstream streamflow data, thereby achieving spatial simulation of ungauged internal sub‐basins. The model, when trained solely on the downstream‐most station, outperforms the distributed hydrological model in streamflow simulation at both the training station and upstream held‐out stations. Additionally, in comparison to transfer learning models, our model requires fewer gauge stations for training, but achieves higher precision in simulating streamflow on spatially held‐out stations, indicating better spatial generalization ability. Consequently, this model offers a novel approach to hydrological simulation in data‐scarce regions, especially those with poor hydrological representativeness.