A Deep State Space Model for Rainfall‐Runoff Simulations

Journal Article · Mon Dec 01 00:00:00 EST 2025 · Water Resources Research

DOI:https://doi.org/10.1029/2025wr039888· OSTI ID:3012842

Wang, Yihan; Zhang, Lujun; Yu, Annan; Erichson, N Benjamin; Yang, Tiantian

Abstract 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. Plain Language Summary Traditionally, scientists study how rainfall becomes runoff in the water cycle using models based on physical principles. Recently, Artificial Intelligence (AI) and Deep Learning (DL) have emerged as alternative approaches, receiving increased attention in hydrology for simulating rainfall‐runoff with notable success. Despite advancements in AI/DL, the Long Short‐Term Memory (LSTM) network, a decades‐old technique, remains the standard, outperforming newer approaches like Transformers and gradually becoming a go‐to DL model for rainfall‐runoff simulations. In this study, we introduce the Frequency Tuned Diagonal State Space Sequence (S4D‐FT) model, a novel DL architecture distinct from both Transformers and LSTMs, for rainfall‐runoff simulations. We tested S4D‐FT against the well‐established LSTM and a physically‐based hydrologic model called the Sacramento Soil Moisture Accounting (Sac‐SMA) model across 531 watersheds in the United States. The results show that S4D‐FT outperforms LSTM in various regions. Our work introduces the S4D‐FT as a new tool for rainfall‐runoff simulations, challenging the dominance of LSTM and expanding DL options for hydrological modeling. Key Points A novel Deep Learning model termed the Frequency Tuned Diagonal State Space Sequence (S4D‐FT) is introduced for rainfall‐runoff simulations S4D‐FT generally outperforms the decades‐old LSTM at 531 watersheds in CONUS, providing a new DL benchmark for rainfall‐runoff simulations S4D‐FT prevails in watersheds with frequent, prolonged high‐ and low‐flow events of smaller runoffs with snowmelt and intermittent regimes

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23), Climate and Environmental Sciences Division (SC-23.1 )
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 3012842
• Journal Information: Water Resources Research, Journal Name: Water Resources Research Journal Issue: 12 Vol. 61
• Country of Publication: United States
• Language: English