Development of a Distributed Physics-informed Deep Learning Hydrological Model for Data-scarce Regions

Climate change has exacerbated water stress and water-related disasters, necessitating more precise runoff simulations. However, in the majority of global regions, a deficiency of runoff data constitutes a significant constraint on modeling endeavors. Traditional distributed hydrological models and regionalization approaches have shown suboptimal performance. While current data-driven models trained on large datasets excel in spatial extrapolation, the direct applicability of these models in certain regions with unique hydrological processes may be challenging due to the limited representativeness within the training dataset. Furthermore, transfer learning deep learning models pre-trained on large datasets still necessitate local data for retraining, thereby constraining their applicability. To address these challenges, we present a physics-informed deep learning 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 runoff 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 runoff simulation at both the training station and upstream stations, as well as evapotranspiration spatial patterns. Compared to transfer learning, our model requires less training data, yet achieves higher precision in simulating runoff on spatially hold-out stations and provides more accurate estimates of spatial evapotranspiration. Consequently, this model offers a novel approach to hydrological simulation in data-scarce regions with unique processes.