Combining Data assimilation and long short-term memory (LSTM) surrogate models for streamflow forecasting in Denmark

Streamflow forecasting is critical in facilitating informed decision-making and mitigating the socio-economic and environmental impacts of extreme events. While physically based hydrological models are commonly employed to extrapolate hydrological variables in space and time, their forecasting accuracy is often limited by uncertainties stemming from inputs, model structure, and parameterization.
Data-driven algorithms, based on machine learning (ML) techniques have shown promise in enhancing prediction reliability compared to physically based hydrological models. ML methods excel at extracting meaningful features and capturing complex relationships from high-dimensional data, offering an alternative to inefficient physical models. However, ML-based models contain uncertainties due to dimensionality constraints, noisy and low-quality inputs, and the forecasting precision decreases as the forecasting horizon extends beyond the training period. Data assimilation (DA) , which incorporates observations into prediction models, is a suitable approach to address this issue. The combination of ML model and DA for streamflow forecasting is still relatively novel.
Thus, this study aims to integrate DA and ML techniques for streamflow forecasting at a national scale. We first trained and tested a physics-aware long short-term memory (LSTM) model using historical data, including precipitation, temperature, potential evapotranspiration (ET), as well as discharge, soil moisture, actual ET and phreatic depth simulated by the Danish National Water Resources Model (DK-model). The trained LSTM model served as a surrogate model of the DK-model, enabling the provision of predicted discharge efficiently. The trained LSTM model shows better performance compared with DK-model in the test basins and lower computational costs. Subsequently, Ensemble Kalman Filter (EnKF) was employed to assimilate observations into the surrogate model, facilitating forecasting with a higher lead time.