Advancing Multi-step Streamflow Forecasting with an Embedding Multi-Layer Perceptron

Reliable multi-step streamflow prediction is essential for effective water resources management. In recent years, deep learning (DL) approaches have been increasingly adopted for streamflow forecasting as alternatives to process-based hydrological models. These approaches have partially reduced the reliance on high-quality and comprehensive hydrological observations required for robust parameterization of the process-based models. Nonetheless, the predictive performance of DL-based hydrological models often deteriorates as the forecast horizon extends, posing critical challenges to their reliability and practical applicability. Moreover, due to the scarcity of storage-related observations, most existing DL-based hydrological models are primarily driven by flux variables (e.g., precipitation and streamflow), while watershed memory effects related to storage regulation remain largely underrepresented. To address these limitations, this study proposes a multi-step streamflow forecasting model that incorporates a proxy representation of watershed memory through a DL approach, namely the Embedding Multi-Layer Perceptron (E-MLP). The proposed model was developed using only precipitation and streamflow time-series, without relying on explicit storage-related variables. Two widely used DL models, i.e., Long Short-Term Memory (LSTM) and Multi-Layer Perceptron (MLP) models, were employed as benchmark approaches. Each model was evaluated in a flood-prone watershed, the Upper Wapsipinicon River watershed near Anamosa gauging station (USGS-05421740) in Iowa, United States. Comparative analyses across the three models demonstrated that incorporating a proxy representation of watershed memory yielded more stable predictive skill at longer forecast horizons, effectively mitigating performance degradation with increasing lead time. These findings highlight the critical role of watershed memory in DL-based streamflow forecasting and point to a viable pathway toward more robust multi-step forecasting frameworks.

Acknowledgements

This work was supported by the Creative-Pioneering Researchers Program through Seoul National University and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2025-00523350). Additional support was provided by the National Institute of International Education of Korea (NIIED-230724-0041) and the China Scholarship Council (CSC No. 202208230007).