Abstract Deep Learning (DL) approaches have shown high accuracy in rainfall runoff modeling. Currently, however, large‐scale DL hydrological simulations at national and global scales still rely on external routing schemes to propagate runoff outputs through river networks, preventing them from leveraging the benefits of end‐to‐end learning of hydrological processes from observations. One main reason is the lack of differentiable routing operator to natively integrate into DL pipelines. To address this limitation, we propose a unified formulation of linear time‐invariant (LTI) routing schemes as block‐sparse convolutions. This formulation allows for efficient GPU acceleration and automatic differentiation, enabling end‐to‐end gradient‐based learning of both runoff and routing model components. The proposed model is general, scalable, and fast: on a single GPU, we reproduce the Group on Earth Observations Global Water Sustainability (GEOGloWS) simulation with high accuracy (median daily Nash–Sutcliffe efficiency of 0.9994), routing daily runoff at hourly resolution over 85 years globally, in less than 2 min. We demonstrate the ability of the proposed model to learn physically meaningful dynamics at diverse scales by (a) inferring routing parameters at global climatic scales and (b) jointly learning runoff generation and river routing parameters at hourly and catchment scales.
Hascoet et al. (Sat,) studied this question.