Daily runoff prediction based on lightweight Mamba with partial normalization

ABSTRACT Runoff prediction serves as the cornerstone for the effective management, allocation, and utilization of water resources, playing a key role in hydrological research. This study employs a newly reported deep learning model, Mamba, to forecast river daily runoff and compared the proposed model with various benchmark methods, including statistical models, machine learning methods, recurrent neural networks, and attention-based models. Application of these models is implemented on three hydrological stations situated along the middle and lower reaches of the Mississippi River. Daily runoff from 1983 to 2023 were used to build the model for 7-day prediction. Findings demonstrate the superiority of the Mamba model over its counterparts, showcasing its potential as a backbone model. In response to the necessity for a more lightweight approach, a refined variant of the Mamba model is proposed, called LightMamba. LightMamba incorporates partial normalization and MPM (Multi-Path-Mamba) to enhance its efficacy in discerning nonlinear trends and capturing long-term dependencies within the streamflow data. Notably, LightMamba achieves commendable performance with an average NSE of 0.904, 0.907, and 0.900 on the three stations. This study introduces an innovative backbone model for time series forecasting, which offers a novel approach to hybrid modeling for future daily runoff prediction.