Distributed Hydrological Modeling With Physics‐Encoded Deep Learning: A General Framework and Its Application in the Amazon

While deep learning (DL) models exhibit superior simulation accuracy over traditional distributed hydrological models (DHMs), their main limitations lie in opacity and the absence of underlying physical mechanisms. The pursuit of synergies between DL and DHMs is an engaging research domain, yet a definitive roadmap remains elusive. In this study, a novel framework that seamlessly integrates a process‐based hydrological model encoded as a neural network (NN), an additional NN for mapping spatially distributed and physically meaningful parameters from watershed attributes, and NN‐based replacement models representing inadequately understood processes is developed. Multi‐source observations are used as training data, and the framework is fully differentiable, enabling fast parameter tuning by backpropagation. A hybrid DL model of the Amazon Basin (∼6 × 106 km2) was established based on the framework, and HydroPy, a global‐scale DHM, was encoded as its physical backbone. Trained simultaneously with streamflow observations and Gravity Recovery and Climate Experiment satellite data, the hybrid model yielded median Nash‐Sutcliffe efficiencies of 0.83 and 0.77 for dynamic and distributed simulations of streamflow and total water storage, respectively, 41% and 35% higher than those of the original HydroPy model. Replacing the original Penman‒Monteith formulation in HydroPy with a replacement NN produces more plausible potential evapotranspiration (PET) estimates, and unravels the spatial pattern of PET in this giant basin. The NN used for parameterization was interpreted to identify the factors controlling the spatial variability in key parameters. Overall, this study lays out a feasible technical roadmap for distributed hydrological modeling in the big data era.