A distributed hybrid physics–AI framework for learning corrections of internal hydrological fluxes and enhancing high-resolution regionalized flood modeling

Abstract. To advance the discovery of scale-relevant hydrological laws while better exploiting massive multisource data, merging artificial intelligence with process-based modeling has emerged as a compelling approach, as demonstrated in recent lumped hydrological modeling studies. This research proposes a general spatially distributed hybrid modeling framework that seamlessly combines differentiable process-based models with neural networks. Specifically, we focus on hybridizing the hydrological module – built atop a differentiable kinematic wave routing over a flow direction grid – using a process-parameterization network that refines internal water fluxes, with all conceptual parameters estimated by a regionalization network trained simultaneously. We evaluate flood modeling performance and analyze the interpretability of learned conceptual parameters and corrections of internal fluxes using two high-resolution datasets (dx=1 km and dt=1 h). The first dataset involves 235 catchments in France, used for local calibration–validation and model structure comparisons between the classical Génie Rural (GR)-like model and the hybrid approach. The second dataset presents a challenging multi-catchment modeling setup in flash-flood-prone areas to demonstrate the framework's regionalization learning capabilities. The results show that the hybrid models achieve superior accuracy and robustness compared to classical approaches in both spatial and temporal validation. Analysis of the spatially distributed parameters and internal fluxes reveals the hybrid models' nuanced behavior, their adaptability to diverse hydrological responses, and their potential to uncover physical processes.