A differentiability-based processes and parameters learning hydrologic model for advancing runoff prediction and process understanding

Differentiable parameterized learning (dPL) represents a cutting-edge advancement in synergizing process-based models (PBMs) and machine learning to improve both the model prediction and interpretability. However, dPL mainly focuses on refining parameters within a predefined process-based structure, which limits its performance and process understanding to the constraints of existing PBM frameworks. To address this limitation, we propose an extended framework: Differentiable Process and Parameter Learnings (dP2Ls). dP2Ls incorporate regionalized neural networks (NNs) to simultaneously improve both the modeling of process variables and parameter learnings. Within dP2Ls, the EXP-HYDRO model serves as a differentiable physical backbone, where the potential evapotranspiration (PET) process is modeled using a regionalized long short-term memory (LSTM), while the dPL strategy is independently applied to learning hydrological parameters. Experiments with runoff prediction in ungauged catchments across the contiguous United States revealed that: (1) The median Nash-Sutcliffe efficiency (NSE) of regionalized dP2Ls in ungauged catchments surpassed that of all models using NNs for either process learning or parameter learning and approached the LSTM model (the median NSE differs by only 0.021); (2) Regionalized dP2Ls enhanced the interpretability of some intermediate variables by jointly learning the process variables and parameters, resulting in the correlation coefficients of snowpack and ET fitting the estimation products increased by 0.022 and 0.026, respectively; (3) The embedded regionalized LSTM outputs more interpretable PET than EXP-HYDRO, demonstrating the capability of NNs to improve traditional process understanding. In summary, this study demonstrates the advantages of dP2Ls in regionalized modeling, overcoming the limitations of traditional process-based structures through flexible NN configurations, and providing a reliable pathway for the future in-depth diagnosis and transformation of existing hydrological knowledge using NNs.