Vischer et al. (2025) Spatially resolved rainfall streamflow modeling in central Europe

Identification

• Journal: Hydrology and earth system sciences
• Year: 2025
• Date: 2025-10-16
• Authors: Marc Aurel Vischer, Noelia Otero, Jackie Ma
• DOI: 10.5194/hess-29-5233-2025

Research Groups

Fraunhofer Heinrich-Hertz Institute, Applied Machine Learning Group

Short Summary

This study develops an end-to-end, spatially resolved neural network pipeline for rainfall-streamflow modeling in central Europe, addressing the limitations of previous aggregated approaches in large and human-impacted catchments. The pipeline demonstrates improved accuracy, data efficiency, and interpretability, particularly for larger river basins.

Objective

• To develop and evaluate a spatially resolved, end-to-end neural network pipeline for rainfall-streamflow modeling that can accurately predict streamflow in large catchments, including those characterized by human activity, by processing inputs on a regular grid rather than aggregating them per catchment.

Study Configuration

• Spatial Scale: Five major river basins in central Europe (Elbe, Oder, Weser, Rhine, and the upstream Danube River up to Bratislava), covering a contiguous area of 570 581 square kilometers. Input data are on a regular grid with a spatial resolution of 0.1° × 0.1° (approximately 9 km × 9 km). The study includes 239 river gauging stations.
• Temporal Scale: Water years 1981–2011 (October 1 to September 30 annually) at a daily temporal resolution.

Methodology and Data

• Models used:
  • A two-stage neural network pipeline trained end-to-end:
    • Local Stage: An LSTM-based network (250 units) processes meteorological and static inputs in parallel for each grid cell, predicting local runoff. It includes a fully connected embedding layer for static inputs.
    • Routing Stage: Consists of two linear layers (a fully connected layer and a 1D-convolution layer with a 9-day kernel) without nonlinearity, mapping local runoff to streamflow along the river network. River network connectivity is incorporated as an inductive bias.
  • Baselines: An aggregated LSTM model (similar to Kratzert et al., 2019b) and a "naive routing" model (spatially resolved local stage but unconstrained routing stage).
• Data sources:
  • Dynamic input data: Daily minimum, average, and maximum temperature; daily sum and standard deviation of precipitation; and average potential evaporation from ERA5-Land (0.1° × 0.1° resolution). Also, sine-cosine embeddings of the day of the week and day of the year.
  • Static input data: 46 feature dimensions including hydrogeological properties, soil class, land cover, and orographic features derived from a digital elevation map.
  • Target streamflow time series: Daily streamflow records from the Global Runoff Data Center (GRDC) data portal.

Main Results

• The spatially resolved pipeline with structured routing achieved a median Nash–Sutcliffe Efficiency (NSE) of 0.773 on the test dataset, outperforming the aggregated baseline (median NSE 0.691) and naive routing (median NSE 0.719).
• Spatially resolved processing demonstrated a positive correlation between performance and catchment size, showing particular benefits for larger catchments where it outperformed aggregated processing.
• The spatially resolved model exhibited greater robustness against overfitting, with a more graceful performance deterioration from training (median NSE 0.90) to test (median NSE 0.77) compared to the aggregated baseline (0.86 to 0.69).
• The approach showed increased data efficiency, yielding stronger performance gains over aggregated processing when training data were limited (e.g., 6 years of data).
• The internal states of the model's local stage were found to be hydrologically interpretable, reflecting plausible runoff generation patterns (e.g., snowmelt in spring, precipitation-driven runoff in summer).
• Human influence, particularly from large-scale brown coal mining operations, was identified as a significant challenge, leading to negative NSE values for specific affected stations.

Contributions

• Presentation of a novel end-to-end neural network pipeline for spatially resolved rainfall-streamflow modeling that integrates local runoff generation on a regular grid with routing along river networks.
• Introduction of a simple, linear routing module that enhances interpretability and offers potential for simulating human water management activities (e.g., extraction/injection).
• Development and public release of a new, spatially resolved dataset for five central European river basins, suitable for distributed hydrological modeling and representative of areas with significant human impact.
• Demonstration that this spatially resolved approach improves prediction accuracy, especially for large and heterogeneous catchments, enhances data efficiency, and reduces overfitting compared to traditional aggregated neural network models.
• Revelation of hydrologically interpretable internal model states, an emergent property that facilitates scientific discovery and potential for internal model control.

Funding

• Federal Ministry for Economic Affairs and Climate Action (BMWK) under grant DAKI-FWS (01MK21009A).
• European Union’s Horizon Europe research and innovation program (EU Horizon Europe) project MedEWSa under grant agreement no. 101121192.

Citation

@article{Vischer2025Spatially,
  author = {Vischer, Marc Aurel and Otero, Noelia and Ma, Jackie},
  title = {Spatially resolved rainfall streamflow modeling in central Europe},
  journal = {Hydrology and earth system sciences},
  year = {2025},
  doi = {10.5194/hess-29-5233-2025},
  url = {https://doi.org/10.5194/hess-29-5233-2025}
}