Neural Rainfall-Runoff Modeling

Abstract

Hydrological modeling traditionally relies on mechanistic models that, while physically interpretable, struggle to capture the nonlinear dynamics of environmental systems. Data-driven approaches such as Artificial Neural Networks (ANNs) can automatically discover patterns in observational data, often achieving superior performance, but typically operate as black boxes that may not adhere to established physical constraints. This dissertation introduces DRRAiNN (Distributed Rainfall-Runoff ArtIficial Neural Network), a fully differentiable and fully distributed ANN architecture for rainfall-runoff modeling. DRRAiNN consists of two components: a spatially distributed rainfall-runoff model operating on a regular grid, and a graph-based river discharge model that captures flow dynamics along the river network. The rainfall-runoff component uses specialized convolutional recurrent networks with physics-informed inductive biases to model lateral water propagation and evapotranspiration processes. The discharge component employs a graph neural network that respects the connectivity of gauging stations. This modular architecture enables end-to-end optimization using sparse discharge measurements while maintaining physical plausibility through architectural constraints. The model is evaluated on the Neckar river catchment in Southwest Germany using data from 17 gauging stations. DRRAiNN demonstrates improved performance compared to the European Flood Awareness System across multiple metrics. The fully differentiable architecture enables interpretability analysis through gradient-based attribution methods. These techniques demonstrate the ability to reconstruct physically meaningful catchment boundaries that exhibit reasonable correspondence with topographically derived watersheds, which shows that the model learns interpretable spatial patterns. Leave-one-out cross-validation experiments evaluate the model's ability to generalize to ungauged basins, which is a critical requirement for practical hydrological applications. Analysis reveals important insights about ANN behavior in environmental modeling. The model achieves strong performance partly by using elevation data as positional encoding rather than explicit flow routing, which explains both its effectiveness within the training domain and its spatial generalization challenges. A notable trade-off emerges between predictive accuracy and physical plausibility, with the most physically realistic model instances not corresponding to those with optimal forecast performance. Key limitations include dependency on accurate precipitation forecasts, evaluation restricted to a single river network, and resolution constraints. The daily data resolution limits the model's ability to capture rapid hydrological responses, while the 4km x 4km grid may inadequately represent fine-scale processes. Future work should focus on multi-catchment training, higher temporal resolution data, and satellite-based approaches for ungauged regions. Overall, this work advances the field of hydrological modeling by demonstrating that carefully designed ANN architectures can achieve both high predictive accuracy and physical interpretability, opening new possibilities for knowledge discovery in hydrology while highlighting the importance of balancing performance optimization with physical realism.