Semi-Distributed Deep Learning Models at Global Scale

Hydrological modeling has reached a point where deep learning models, especially those based on the LSTM architecture, are being used operationally by national agencies, the private sector, as well as across thousands of academic publications. However, by far the most common strategy is to use these models in a lumped setup, no matter the scale of the application. For example, Nearing et al. (2024) apply LSTM based models in a lumped setup at a global scale. Unfortunately, this withholds information that is relevant to precisely predict floods, such as the location of a precipitation event relative to the prediction point. Similarly, the spatial averaging over the entire upstream area dampens the precipitation signal that is provided to the model.

Classical hydrologic models use distributed or semi-distributed setups to solve this problem: they divide the basin into pixels or subpolygons and route streamflow along the river graph. There are first attempts to translate this semi-distributed modeling paradigm to end-to-end deep learning models, but so far they are typically trained only on individual river networks or select geographical regions (e.g., Kratzert et al., 2021, Kraft et al., 2025), lag behind the performance of lumped models (e.g., Kirschstein et al., 2021), cannot generalize to unseen river networks (e.g., Vischer et al., 2025), or are global and applicable ungauged basins but not trained end-to-end (e.g., Yang et al., 2025).

With the learnings and experience from operating lumped LSTM models at a global scale for multiple years, we revisit semi-distributed modeling with deep learning at a global scale with a focus on end-to-end training. In this submission, we present our version of a global end-to-end semi-distributed hydrologic model. We detail the model setup, its training procedure, and compare this model to the lumped setup. Our evaluation shows that the semi-distributed model has superior performance compared to the lumped model, especially for large, ungauged rivers. Finally, we highlight how this modeling approach is a step towards a broader multi-output, multi-modal system that propagates more information than just streamflow or physical quantities in general.

References:

• Kirschstein, N., et al. "The Merit of River Network Topology for Neural Flood Forecasting." Forty-first International Conference on Machine Learning. 2024.
• Kraft, B., et al. DROP: A scalable deep learning approach for runoff simulation and river routing. Authorea. November 25, 2025.
• Kratzert, F., et al. "Large-scale river network modeling using graph neural networks." EGU General Assembly Conference Abstracts. 2021.
• Nearing, G., et al. "Global prediction of extreme floods in ungauged watersheds." Nature 627.8004 (2024): 559-563.
• Vischer, M., et al. "Spatially Resolved Rainfall Streamflow Modeling in Central Europe." EGUsphere 2025 (2025): 1-26.
• Yang, Y., et al. (2025). Global daily discharge estimation based on grid long short-term memory (LSTM) model and river routing. Water Resources Research, 61.