Yang et al. (2026) A hybrid deep learning-Muskingum framework for enhanced runoff prediction: Model coupling and hydrological process integration

Identification

• Journal: Journal of Hydrology Regional Studies
• Year: 2026
• Date: 2026-01-06
• Authors: Dongxu Yang, Baowei Yan, Donglin Gu, Jianbo Chang, Shixiong Du
• DOI: 10.1016/j.ejrh.2025.103077

Research Groups

• School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, China
• Hubei Key Laboratory of Digital River Basin Science and Technology, Huazhong University of Science and Technology, Wuhan, China
• Sichuan Water Development Investigation, Design & Research Co.,Ltd., Shunshen Road, Chengdu, China

Short Summary

This study proposes a hybrid deep learning-Muskingum framework with differentiable programming and Bayesian Optimization to enhance reservoir inflow forecasting accuracy and physical consistency. The optimal four-segment hybrid model achieved a Nash–Sutcliffe efficiency (NSE) of 0.94 during the test period, outperforming pure data-driven and one-way coupled models.

Objective

• To enhance the accuracy and physical consistency of reservoir inflow forecasting by proposing a hybrid modeling framework that couples an enhanced Muskingum model with a bidirectional long short-term memory (BiLSTM) network, integrating physical processes and optimizing parameters jointly.

Study Configuration

• Spatial Scale: An approximately 260 km uncontrolled segment of the Hanjiang River's mainstem between the Ankang Reservoir and the Danjiangkou Reservoir, China, encompassing a controlled drainage area of roughly 42,000 km².
• Temporal Scale: Daily inflow and outflow records from 2013 to 2023 (10 years), with data partitioned into training (2013.06–2019.06), validation (2019.07–2021.06), and testing (2021.07–2023.06) subsets.

Methodology and Data

• Models used:
  • Enhanced Muskingum model (restructured via differentiable programming)
  • Bidirectional Long Short-Term Memory (BiLSTM) network
  • Bayesian Optimization (BO) for joint parameter and hyperparameter calibration
• Data sources:
  • Flow data: Hydrological Bureau, Changjiang Water Resources Commission (daily inflow/outflow for Ankang, Huanglongtan, Danjiangkou reservoirs).
  • Precipitation data: Multi-Source Weighted-Ensemble Precipitation Version 2 (MSWEP-V2) dataset (Princeton University).
  • Evaporation data: Global Land Evaporation Amsterdam Model (GLEAM) dataset (University of Amsterdam).

Main Results

• The proposed hybrid framework, particularly with a four-segment configuration, significantly improved runoff prediction accuracy.
• The optimal four-segment hybrid model achieved a Nash–Sutcliffe efficiency (NSE) of 0.94, a Kling–Gupta efficiency (KGE) of 0.95, and a Root Mean Square Error (RMSE) of 598 m³/s during the test period.
• This represents a 4.4 % improvement in NSE over both the pure BiLSTM model and the one-way coupled model, and a 20.7 % reduction in RMSE compared to the pure machine learning model.
• Model performance initially improved with finer segmentation, peaking at four segments, then declined due to likely over-parameterization with five segments.
• Sensitivity analysis showed that the number of hidden units (NumUnits) in the neural network was the most influential parameter (ST for NSE = 0.889, ST for KGE = 0.920), followed by the Muskingum weighting factor (x1), while the storage coefficient (K1) had a relatively lower impact.

Contributions

• Integration of a differentiable Muskingum layer with a BiLSTM network, forming a coupled model that combines physical interpretability with adaptive deep learning capabilities for enhanced prediction accuracy.
• Application of Bayesian Optimization for joint calibration of segmented Muskingum parameters and neural network hyperparameters, addressing calibration challenges and improving model robustness.
• Implementation of river segmentation with tailored Muskingum parameters for each sub-reach, enabling a more accurate representation of spatial variability in hydraulic behavior and runoff propagation in cascade reservoir systems.

Funding

• The National Natural Science Foundation of Hubei Province (2024AFB646).

Citation

@article{Yang2026hybrid,
  author = {Yang, Dongxu and Yan, Baowei and Gu, Donglin and Chang, Jianbo and Du, Shixiong},
  title = {A hybrid deep learning-Muskingum framework for enhanced runoff prediction: Model coupling and hydrological process integration},
  journal = {Journal of Hydrology Regional Studies},
  year = {2026},
  doi = {10.1016/j.ejrh.2025.103077},
  url = {https://doi.org/10.1016/j.ejrh.2025.103077}
}