A Knowledge-guided LSTM reservoir outflow model and its application to streamflow simulation in reservoir-regulated basins

Accurate reservoir outflow simulation is crucial for modeling streamflow in reservoir-regulated basins. In this study, we introduce a knowledge-guided Long Short-Term Memory model (KG-LSTM) to simulate the outflow of reservoirs-Fengshuba, Xinfengjiang, and Baipenzhu in the Dongjiang River Basin, China. KG-LSTM is built on the standard hyperparameters-optimized-LSTM and the loss function considering reservoir operation knowledge, while traditional reservoir model level pool scheme (LPS) is used as a benchmark model. Model uncertainty is analyzed using the bootstrap method. We then propose a hybrid approach that combines KG-LSTM with the Three-parameter monthly hydrological Model based on the Proportionality Hypothesis (KG-LSTM-TMPH) for streamflow simulation. The propagation of inflow errors to outflow simulations is studied across the three reservoirs. Results indicate that LSTM-based models greatly outperform LPS in all three reservoirs, with KG-LSTM demonstrating superior capability in capture reservoir outflow dynamics compared to the standard LSTM model. In the multi-year regulated Xinfengjiang Reservoir, KG-LSTM improves Nash-Sutcliffe efficiency (NSE) from 0.59 to 0.64, and reduces root mean squared error (RMSE) from 55.59 m³/s to 54.84 m³/s during the testing period. KG-LSTM shows reduced model uncertainty, decreasing the relative width (RW) from 0.55 to 0.51 in the Xinfengjiang Reservoir and from 0.48 to 0.44 in the Baipenzhu Reservoir, while demonstrating limited change in the Fengshuba Reservoir. For streamflow simulation, KG-LSTM-TMPH performs best across all four stations, achieving NSE values of approximately 0.87, 0.88, 0.91, and 0.92 at Longchuan, Heyuan, Lingxia, and Boluo stations, respectively. In the dry season, KG-LSTM-TMPH demonstrates substantial improvement over LSTM-TMPH, increasing R² by +0.11 and reducing RMSE by -4.22 m³/s at Heyuan station. Inflow errors impact outflow most significantly for the Xinfengjiang Reservoir in April and May, for the Fengshuba Reservoir throughout the year (particularly in April, May, July, and August), and for the Baipenzhu Reservoir primarily in July and August. This study enhances reservoir outflow modeling by integrating reservoir operation knowledge with deep learning. The hybrid KG-LSTM-TMPH approach shows practical potential for streamflow simulation in reservoir-regulated basins, offering valuable applications for water resource management.