DROP: A scalable deep learning approach for runoff simulation and river routing

In this study, we propose a deep runoff prediction and propagation model (DROP), a framework designed for spatially explicit discharge prediction along the river network with computational efficiency and physical interpretability. DROP consists of three modules: a long short-term memory (LSTM) network that predicts local runoff at the hydrological drainage unit (DU) scale, a conceptual water surface evaporation module, and an explicit routing module that propagates water along the river network, operating on predefined DU connectivity. Both local runoff generating and the routing processes can be modulated by arbitrary features, such as soil properties, topography, or water management infrastructure.   Applied on more than 22000 DUs and calibrated on 273 gauging stations across hydrological Switzerland, the model achieved strong spatial generalization and reproduced realistic runoff and routing dynamics across diverse climatic and physiographic regions. Compared to the lumped baseline, DROP achieved markedly improved overall performance—rising from 24 to 62 % in Kling–Gupta efficiency (KGE) across different evaluation setups—and better captured extreme events, discharge variability, and temporal dynamics. The framework is computationally lightweight and provides interpretable, spatially resolved diagnostics, such as source contribution maps, supporting hydrological process understanding and operational applications. DROP bridges the gap between data-driven and spatially explicit modeling, offering a scalable, transparent, and physically informed approach for large-scale hydrological monitoring, forecasting, and flood risk assessment.