A Deep State Space Model for Rainfall-Runoff Simulations

Yihan Wang

doi:10.1029/2025WR039888

A Deep State Space Model for Rainfall-Runoff Simulations

2025-12-06

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DOI：10.1029/2025WR039888

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The classical way of studying the rainfall-runoff processes in the water cycle relies on conceptual or physically-based hydrologic models. Deep learning (DL) has recently emerged as an alternative and blossomed in the hydrology community for rainfall-runoff simulations. However, the decades-old Long Short-Term Memory (LSTM) network remains the benchmark for this task, outperforming newer architectures like Transformers. In this work, we propose a State Space Model (SSM), specifically the Frequency Tuned Diagonal State Space Sequence (S4D-FT) model, for rainfall-runoff simulations. The proposed S4D-FT is benchmarked against the established LSTM and a physically-based Sacramento Soil Moisture Accounting model under in-sample and out-of-sample simulation setups across 531 watersheds in the contiguous United States (CONUS). Results show that S4D-FT is able to outperform the LSTM model across diverse regions under both simulation setups, especially for regions that feature snowmelt-driven or intermittent flow regimes. In contrast, S4D-FT tends to underperform in flashier, high-magnitude flow regimes, likely due to its global state-space convolution computation that emphasizes slow, storage-driven dynamics, which makes it less effective at picking up short bursts and noisy spikes in the data. In summary, our pioneering introduction of the S4D-FT for rainfall-runoff simulations challenges the dominance of LSTM in the hydrology community and expands the arsenal of DL tools available for hydrological modeling.

Keywords:

deep learning

hydrologic model

rainfall-runoff simulation

watershed modeling

state space model

artificial intelligence

A Deep State Space Model for Rainfall-Runoff Simulations

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