Zhao et al. (2026) Exploration on Coupling Machine Learning with Hydrological Model to Enhance Runoff Simulation

Identification

• Journal: Water Resources Management
• Year: 2026
• Date: 2026-04-01
• Authors: Yinmao Zhao, Ningpeng Dong, Chao Ma, Hao Wang
• DOI: 10.1007/s11269-026-04624-0

Research Groups

• School of Soil and Water Conservation, Beijing Forestry University, Beijing, China
• China Institute of Water Resources and Hydropower Research, Beijing, China

Short Summary

This study investigates how coupling process-driven hydrological models with varying physical mechanisms with a Long Short-Term Memory (LSTM) model, and introducing a Stacking structure, impacts runoff simulation accuracy and robustness in the Yalong River Basin. It demonstrates that models with stronger physical mechanisms enhance coupling performance, and the Stacking structure significantly improves simulation stability and consistency.

Objective

• To investigate whether hydrological models with stronger physical mechanisms can enhance runoff simulation performance of data-driven models (LSTM) within a unidirectional coupling framework.
• To examine the effect of introducing a Stacking structure on runoff simulation robustness and structural risk reduction.

Study Configuration

• Spatial Scale: Yalong River Basin, a tributary of the Jinsha River in the upper Yangtze River, China. The basin has a drainage area of approximately 1.36 × 10¹¹ square meters. Distributed hydrological models (VIC, CREST) discretized the study area at a resolution of 0.25° × 0.25°, resulting in 250 grid cells. The study area was further divided into three parts (upper, middle, and lower reaches) for LSTM input processing.
• Temporal Scale:
  • Analysis period: 1980–2013 (daily runoff data).
  • Hydrological model calibration period: 1980–1995.
  • Hydrological model validation period: 1996–2013.
  • LSTM training period: 1980–1995.
  • LSTM validation period: 1996–2004.
  • LSTM testing period: 2005–2013.

Methodology and Data

• Models used:
  • Hydrological Models:
    • Variable Infiltration Capacity (VIC) 4.2 (distributed, process-driven, with water balance and snowmelt modules).
    • Coupled Routing and Excess Storage (CREST-snow) (grid-based distributed, with a temperature-index-based snowmelt module).
    • Xinanjiang (lumped, conceptual, with a conceptual snowmelt module developed by the research team).
  • Machine Learning Model: Long Short-Term Memory (LSTM), a specialized recurrent neural network.
  • Ensemble Method: Stacking structure, where outputs from two hydrological models are combined as inputs to the LSTM.
• Data sources:
  • Hydrological Data: Daily runoff from Ertan hydrological station (1980–2013), obtained from the Hydrological Yearbook of the YRB.
  • Meteorological Data: Daily precipitation, maximum temperature, and minimum temperature (1980–2013) from 19 observed stations within the study area, obtained from China Surface Climate Daily Dataset (V3.0) of the China Meteorological Administration.
  • Topographic Data: Digital Elevation Model (DEM), flow direction, flow accumulation, and river network data from USGS HydroSHEDS (0.0833° resolution).
  • Land Cover Data: Vegetation data from the land cover dataset developed by Maryland University.
  • Soil Data: Global 5’ soil texture classification data from the Office of Hydrology of the National Oceanic and Atmospheric Administration (NOAA).
  • Snow Data: Snow Water Equivalent (SWE) estimated from snow depth products (Western China Environmental and Ecological Science Data Center) and snow density calculated from on-site measurements.
  • Evapotranspiration Data: Potential evapotranspiration data from the Famine Early Warning Systems Network Global Data Portal.

Main Results

• Unidirectional coupling schemes significantly improved runoff simulation performance, with Nash–Sutcliffe efficiency coefficient (NSE) and Coefficient of Determination (R²) reaching 0.95 and 0.94, respectively, during the training period, and Root Mean Square Error (RMSE) reduced to approximately 210 cubic meters per second.
• Hydrological models with stronger physical mechanisms (distributed models like VIC and CREST) showed better coupling performance, with their average NSE, R², and Kling Gupta efficiency (KGE) being higher by 0.03, 0.03, and 0.01, respectively, compared to the lumped Xinanjiang model.
• The Stacking framework, while not showing a clear numerical improvement in average RMSE and Percent Bias (Pbias) for Annual Maximum Daily Runoff (AMDR) (1437.74 m³/s and -16.41% respectively) over original models, effectively reduced uncertainty and improved consistency and stability in runoff distribution and temporal variation.
• Flow Duration Curves (FDCs) derived from coupled and Stacking frameworks were generally consistent with observed FDCs, and Pbias across different flow-frequency ranges substantially improved, reducing from a range of -69.19% to 20.39% for original models to -4.28% to 14.78%.
• The Stacking structure led to a consistent optimal marginal distribution function (Generalized extreme value distribution) for both AMDR and Annual Maximum 7-day Total Runoff (AM7TR) across all schemes, indicating reduced structural risk and enhanced stability in extreme runoff simulation.

Contributions

• Systematically evaluated the impact of hydrological models with different levels of physical mechanisms (lumped vs. distributed) on runoff simulation accuracy within a unidirectional coupling framework with machine learning.
• Demonstrated that introducing a Stacking structure significantly enhances the robustness and stability of runoff simulations, particularly in reducing structural uncertainty and stabilizing extreme runoff characteristics.
• Provided evidence that physically richer hydrological model outputs, when used as inputs, facilitate more effective learning by data-driven models in a coupled system.
• Highlighted the importance of effective model utilization and structural integration (e.g., Stacking) as a crucial strategy for improving runoff simulation, beyond focusing solely on individual model improvements.

Funding

• National Natural Science Foundation of China (42401017)
• The Belt and Road Special Foundation of The National Key Laboratory of Water Disaster Prevention (2023490511)

Citation

@article{Zhao2026Exploration,
  author = {Zhao, Yinmao and Dong, Ningpeng and Ma, Chao and Wang, Hao},
  title = {Exploration on Coupling Machine Learning with Hydrological Model to Enhance Runoff Simulation},
  journal = {Water Resources Management},
  year = {2026},
  doi = {10.1007/s11269-026-04624-0},
  url = {https://doi.org/10.1007/s11269-026-04624-0}
}