Fully differentiable, fully distributed rainfall-runoff modeling

Abstract. Traditional hydrological modeling simulates rainfall-runoff process dynamics using process-based models (PBMs). PBMs are grounded in physical laws and therefore highly interpretable. As environmental systems are highly complex, though, subprocesses are sometimes hard or even impossible to identify and quantify. Data-driven approaches, like artificial neural networks (ANNs), offer an alternative. Such approaches can automatically discover hidden relationships within the data. As a result, superior model performance may be achieved. However, the uncovered relationships are hard to analyze within black-box ANNs and often fail to respect physical laws. Differentiable modeling calls for knowledge discovery by combining both approaches, benefiting from their respective advantages. In this work, we present a physically inspired, fully differentiable, and fully distributed model, which we term DRRAiNN (Distributed Rainfall-Runoff ArtIficial Neural Network). DRRAiNN is a neural network model that estimates river discharge at gauging stations based on meteorological forcings and elevation. Focusing on the Neckar river catchment in Southwest Germany, DRRAiNN is trained to predict daily water discharge measurements using data from 17 stations and from ten meteorological years only. DRRAiNN's performance is compared to the performance of the European Flood Awareness System (EFAS) reanalysis. Some instances of our model outperform EFAS at lead times of over 50 d in terms of the applied metrics for model performance. As DRRAiNN is fully differentiable and fully distributed, efficient source allocation algorithms can be used to identify the precipitation sources responsible for the water discharge dynamics at specific gauging stations. Besides DRRAiNN's potential to forecast upcoming water discharge dynamics, its full differentiability could be utilized to infer erosion sites from turbidity data, particularly when integrated with an appropriate erosion model.