A differentiable modeling approach to systematically integrating deep learning and physical models for large-scale hydrologic prediction and knowledge discovery

Although deep learning (DL) models have shown extraordinary performance in hydrologic modeling, they are still hard to interpret and not able to predict untrained hydrologic variables due to lacking physical meanings and constraints. This study established hybrid differentiable models (namely the delta models) with regionalized parameterization and learnable structures based on a DL-based differentiable parameter learning (dPL) framework. The simulation experiments on both US and global basins demonstrate that the delta models can approach the performance of the state-of-the-art long short-term memory (LSTM) network on discharge prediction. Different from the pure data-driven LSTM model, the delta models can output a full set of hydrologic variables not used as training targets. The evaluation with independent data sources showed that the delta models, only trained on discharge observations, can also give decent predictions for ET and baseflow. The spatial extrapolation experiments showed that the delta models can surpass the performance of the LSTM model for predictions in large ungauged regions in terms of the daily hydrographic metrics and multi-year trend prediction. The spatial patterns of the parameters learned by the delta models remain remarkably stable from the in-sample to spatial out-of-sample predictions, which explains the robustness of the delta models for spatial extrapolation. More importantly, the proposed modeling framework enables directly learning new relations between intermediate variables from large observations. This study shows that the model performance and physical meanings can be balanced with the differentiable modeling approach which is promising to large-scale hydrologic prediction and knowledge discovery.