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Sustainability
Volume 17
Issue 24
10.3390/su172411120
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models

by
Muzi Zhang
1,2,
Tailun Yao
3,
Hongbin Gu
1,2,
Weiwei Wang
1,2,
Linying Pan
4,
Huanghe Gu
4,
Ying Pei
4 and
Baohong Lu
4,*
1
China Renewable Energy Engineering Institute, Beijing 100120, China
2
Ecosystem Study Commission for International Rivers, Beijing 100120, China
3
Qiantang River Basin Center of Zhejiang Province, Hangzhou 310016, China
4
College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China
*
Author to whom correspondence should be addressed.
Sustainability 2025, 17(24), 11120; https://doi.org/10.3390/su172411120
Submission received: 3 November 2025 / Revised: 3 December 2025 / Accepted: 9 December 2025 / Published: 11 December 2025
Versions Notes

Abstract

Runoff forecasting is essential for flood control, disaster mitigation, and sustainable water resources management. However, runoff processes are highly nonlinear and uncertain due to multiple interacting meteorological and underlying surface factors. Current models can be divided into process-driven and data-driven types. The former offers clear physical interpretability but involves complex calibration and simplifications, while the latter captures nonlinear relationships effectively but lacks physical consistency. To integrate their strengths, this study constructs process-based models and data-driven models, and proposes two hybrid strategies: (1) incorporating intermediate variables from physical models, such as soil moisture and runoff yield, as additional features for data-driven models, and (2) embedding physics-based constraints and synthetic data into loss functions. Using the Songxi River Basin as a case study, results show that both hybrid strategies significantly outperform standalone models. SHapley Additive exPlanations (SHAP)-based interpretability analysis further reveals the contribution mechanisms of key physical variables. This study demonstrates that coupling physical processes with data-driven learning effectively enhances runoff forecasting accuracy and offers a promising paradigm to support sustainable watershed management, climate-resilient water regulation, and flood risk reduction.
Keywords: runoff forecasting; hydrological modeling; machine learning; process–data fusion; explainable AI; sustainable watershed management runoff forecasting; hydrological modeling; machine learning; process–data fusion; explainable AI; sustainable watershed management

Share and Cite

MDPI and ACS Style

Zhang, M.; Yao, T.; Gu, H.; Wang, W.; Pan, L.; Gu, H.; Pei, Y.; Lu, B. A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models. Sustainability 2025, 17, 11120. https://doi.org/10.3390/su172411120

AMA Style

Zhang M, Yao T, Gu H, Wang W, Pan L, Gu H, Pei Y, Lu B. A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models. Sustainability. 2025; 17(24):11120. https://doi.org/10.3390/su172411120

Chicago/Turabian Style

Zhang, Muzi, Tailun Yao, Hongbin Gu, Weiwei Wang, Linying Pan, Huanghe Gu, Ying Pei, and Baohong Lu. 2025. "A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models" Sustainability 17, no. 24: 11120. https://doi.org/10.3390/su172411120

APA Style

Zhang, M., Yao, T., Gu, H., Wang, W., Pan, L., Gu, H., Pei, Y., & Lu, B. (2025). A Hybrid Runoff Forecasting Framework Integrating Hydrological Physics and Data-Driven Models. Sustainability, 17(24), 11120. https://doi.org/10.3390/su172411120

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