A national-scale hybrid model for enhanced streamflow estimation – consolidating a physically based hydrological model with long short-term memory (LSTM) networks

Abstract. Accurate streamflow estimation is essential for effective water resource management and adapting to extreme events in the face of changing climate conditions. Hydrological models have been the conventional approach for streamflow interpolation and extrapolation in time and space for the past few decades. However, their large-scale applications have encountered challenges, including issues related to efficiency, complex parameterization, and constrained performance. Deep learning methods, such as long short-term memory (LSTM) networks, have emerged as a promising and efficient approach for large-scale streamflow estimation. In this study, we have conducted a series of experiments to identify optimal hybrid modeling schemes to consolidate physically based models with LSTM aimed at enhancing streamflow estimation in Denmark. The results show that the hybrid modeling schemes outperformed the Danish National Water Resources Model (DKM) in both gauged and ungauged basins. While the standalone LSTM rainfall–runoff model outperformed DKM in many basins, it faced challenges when predicting the streamflow in groundwater-dependent catchments. A serial hybrid modeling scheme (LSTM-q), which used DKM outputs and climate forcings as dynamic inputs for LSTM training, demonstrated higher performance. LSTM-q improved the mean Nash–Sutcliffe efficiency (NSE) by 0.22 in gauged basins and 0.12 in ungauged basins compared to DKM. Similar accuracy improvements were achieved with alternative hybrid schemes, i.e., by predicting the residuals between DKM-simulated streamflow and observations using LSTM. Moreover, the developed hybrid models enhanced the accuracy of extreme events, which encourages the integration of hybrid models within an operational forecasting framework. This study highlights the advantages of synergizing existing physically based hydrological models (PBMs) with LSTM models, and the proposed hybrid schemes hold the potential to achieve high-quality large-scale streamflow estimations.