Fully differentiable, fully distributed Rainfall-Runoff Modeling

Abstract. Traditional hydrological modeling simulates rainfall-runoff dynamics using process-based models (PBMs), which are grounded in physical laws and therefore highly interpretable. Due to environmental systems being highly complex, though, sub-processes are sometimes hard or even impossible to identify and quantify. Alternatively, data-driven approaches, like deep neural networks (DNNs), can automatically discover relationships within the data, which often leads to superior performance. Due to DNNs' complexity, however, these relationships are hard to investigate and often fail to respect physical laws. Differentiable modeling calls for knowledge discovery by combining both approaches to benefit from their respective advantages. In this work, we present DRRAiNN (Distributed Rainfall-Runoff ArtIficial Neural Network), a targeted neural network architecture that successfully estimates river discharge based on meteorological forcings and elevation in the Neckar river basin, relying on daily water discharge measurements from only 17 stations. We evaluate our model against the European Flood Awareness System (EFAS) reanalysis on the Neckar river catchment in Southwest Germany, where some instances of our model outperform EFAS at lead times of over 100 days. Our model architecture is physically inspired, fully differentiable, and fully distributed. This combination enables the use of efficient source allocation algorithms, which help us identify the water sources responsible for the water discharge dynamics at specific gauging stations. In the future, this approach could be utilized to, e.g., infer erosion sites from turbidity data when integrated with an appropriate erosion model.