Distributed Hydrological Modeling in the Feature Space

Accurate forecasting of river discharge and floods is very challenging. River dynamics are affected by storage, meteorological forcing, and flow propagation at different spatial and temporal scales. Forecasting thus requires a framework that considers the upstream-to-downstream flow through river networks across grid cells and catchments. This modeling is known in hydrology as distributed modeling and routing. Existing deep learning approaches either ignore this topology, operate on lumped catchments, or route predicted physical quantities through a separate graph or physical routing model. We instead introduce feature-space routing: a topology-aware state-space operator embedded directly in the forecasting dynamics. At every forecast step, the operator gathers latent states from upstream grid cells and causally updates the downstream state according to the known river network. This preserves the physical connectivity of the river system while allowing the propagated state itself to be learned end-to-end and allows the model to predict river discharge considering both local dynamics and neighboring upstream contributions. To address uncertainty and provide probabilistic forecasts, we minimize the fair continuous ranked probability score (fCRPS) as a training objective. Our experiments on the European Flood Awareness System (EFAS) and observational data for river discharge forecasting demonstrate that encoding the physical structure of river networks explicitly in the feature space substantially improves the forecasting skill, particularly in an ungauged setting. This enabled us to achieve state-of-the-art results on both reanalysis and observational data and to be able to forecast maps of river discharge at $1$ arcminute and $6$-hourly resolution up to $10$ days lead time.