Semi-Distributed Hydrological Modeling Based on Deep Learning at Scale

In recent years, deep learning models have gained traction in hydrology, particularly in streamflow modeling, which is a prerequisite for accurate riverine flood forecasts. However, current state-of-the-art streamflow models are generally lumped setups that ingest meteorological information only as spatial averages over the upstream area. Unfortunately, this withholds information that is relevant to precisely predict floods: for example, rainfall far upstream will take much longer to arrive at the outlet than rainfall further downstream.

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 (e.g., Kratzert et al., 2021), lag behind the performance of lumped models (e.g., Kirschstein et al., 2021), or cannot generalize to unseen river networks (e.g., Vischer et al., 2025).

With the learnings and experience from operating lumped LSTM models at a global scale (Nearing et al., 2024), we revisit semi-distributed modeling with deep learning, however, at a much larger scale than previous efforts. While the core idea remains the same—i.e., processing time series with Long Short-Term Memory networks (LSTMs) and performing routing through Graph Neural Networks—many details have changed since 2021.

In this submission, we therefore 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 strong performance especially for large, ungauged rivers. Finally, we highlight how this modeling approach is a step towards a broader multi-output system that provides more information than just streamflow.

 

References:

• Kirschstein, Nikolas, et al. "The Merit of River Network Topology for Neural Flood Forecasting." Forty-first International Conference on Machine Learning. 2024.
• Kratzert, Frederik, et al. "Large-scale river network modeling using graph neural networks." EGU General Assembly Conference Abstracts. 2021.
• Nearing, Grey, et al. "Global prediction of extreme floods in ungauged watersheds." Nature 627.8004 (2024): 559-563.
• Vischer, Marc Aurel, et al. "Spatially Resolved Rainfall Streamflow Modeling in Central Europe." EGUsphere 2025 (2025): 1-26.