A hybrid deep learning-Muskingum framework for enhanced runoff prediction: Model coupling and hydrological process integration

The upper reaches of the Hanjiang River, China To enhance the accuracy and physical consistency of reservoir inflow forecasting, this study proposes a hybrid modeling framework that couples an enhanced Muskingum model with a bidirectional long short-term memory (BiLSTM) network. The Muskingum model was restructured via differentiable programming to allow dynamic calibration of physical parameters across river sub-reaches. This physics-based layer was embedded within the BiLSTM network to learn the relationship between meteorological forcing inputs and runoff dynamics. Bayesian Optimization (BO) was adopted to co-optimize the Muskingum parameters and neural network hyperparameters, mitigating error propagation and thus enhancing predictive robustness. The proposed framework was evaluated on a reach of the upper Hanjiang River between Ankang and Danjiangkou Reservoirs. Results showed that model performance initially improved with finer segmentation, peaking with a four-segment configuration, after which performance declined—likely due to over-parameterization. The optimal four-segment hybrid model achieved a Nash–Sutcliffe efficiency (NSE) of 0.94 during the test period, representing a 4.4 % improvement over both the pure BiLSTM model and the one-way coupled model. In addition, it achieved a Kling–Gupta efficiency (KGE) of 0.95 and a Root Mean Square Error (RMSE) of 598 m³ /s, exhibiting more stable predictive behavior. This further demonstrates the framework’s capability for accurate runoff characterization and high-precision inflow forecasting in complex reservoir systems. • Differentiable BO-Muskingum–BiLSTM framework unifies physical routing and learning. • Bayesian optimization co-calibrates routing parameters and BiLSTM settings. • Four-segment hybrid model improves NSE, RMSE, and KGE in the upper Hanjiang Basin.