Articles | Volume 30, issue 17
https://doi.org/10.5194/hess-30-5521-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-30-5521-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
01 Sep 2026
Research article |
| 01 Sep 2026
| 01 Sep 2026
Integrating Physical-Based Xinanjiang Model and Deep Learning for Interpretable Streamflow Simulation: A Multi-Source Data Fusion Approach across Diverse Chinese Basins
Zhaocai Wang
College of Marine Ecology and Environment, Shanghai Ocean University, Shanghai, 201306, P. R. China
Nannan Xu
College of Marine Ecology and Environment, Shanghai Ocean University, Shanghai, 201306, P. R. China
Wei Song
CORRESPONDING AUTHOR
College of Marine Ecology and Environment, Shanghai Ocean University, Shanghai, 201306, P. R. China
Xingxing Zhang
Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing, 100101, P. R. China
Junhao Wu
State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai, 200062, P. R. China
Xi Chen
CORRESPONDING AUTHOR
State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai, 200062, P. R. China
Cited articles
Acuña Espinoza, E., Kratzert, F., Klotz, D., Gauch, M., Álvarez Chaves, M., Loritz, R., and Ehret, U.: Technical note: An approach for handling multiple temporal frequencies with different input dimensions using a single LSTM cell, Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, 2025a.
Acuña Espinoza, E., Loritz, R., Kratzert, F., Klotz, D., Gauch, M., Álvarez Chaves, M., and Ehret, U.: Analyzing the generalization capabilities of a hybrid hydrological model for extrapolation to extreme events, Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, 2025b.
Ahmed, A. A. M., Deo, R. C., Ghahramani, A., Feng, Q., Raj, N., Yin, Z. L., and Yang, L. S.: New double decomposition deep learning methods for river water level forecasting, Sci. Total Environ., 831, 154722, https://doi.org/10.1016/j.scitotenv.2022.154722, 2022.
Alnahit, A. O., Mishra, A. K., and Khan, A. A.: Stream water quality prediction using boosted regression tree and random forest models, Stochastic Environ. Res. Risk Assess., 36, 2661–2680, https://doi.org/10.1007/s00477-021-02152-4, 2022.
Bai, P., Liu, X. M., Liang, K., Liu, X. J., and Liu, C. M.: A comparison of simple and complex versions of the Xinanjiang hydrological model in predicting runoff in ungauged basins, Hydrol. Res., 48, 1282–1295, https://doi.org/10.2166/nh.2016.094, 2017.
Breiman, L.: Random forests, Mach. Learn., 45, 5–32, https://doi.org/10.1023/A:1010933404324, 2001.
Chen, Z. Q., Lin, H., and Shen, G. Y.: TreeLSTM: A spatiotemporal machine learning model for rainfall-runoff estimation, J. Hydrol. Reg. Stud., 48, 101474, https://doi.org/10.1016/j.ejrh.2023.101474, 2023.
Cheng, M., Fang, F., and Pain, C. C.: Long lead-time daily and monthly streamflow forecasting using machine learning methods, J. Hydrol., 590, 125376, https://doi.org/10.1016/j.jhydrol.2020.125376, 2020.
Cho, K. and Kim, Y.: Improving streamflow prediction in the WRF-Hydro model with LSTM networks, J. Hydrol., 605, 127297, https://doi.org/10.1016/j.jhydrol.2021.127297, 2022.
Contreras, P., Orellana-Alvear, J., Muñoz, P., Bendix, J., and Célleri, R.: Influence of Random Forest Hyperparameterization on Short-Term Runoff Forecasting in an Andean Mountain Catchment, Atmosphere, 12, 238, https://doi.org/10.3390/atmos12020238, 2021.
Ding, C., Wang, Z., Tan, Z., and Zhang, X.: Multi-source heterogeneous data-driven interpretable model based on transformer and kolmogorov-arnold networks for streamflow prediction, Expert Syst. Appl., 328, 132862, https://doi.org/10.1016/j.eswa.2026.132862, 2026.
Doyle, J. M., Hill, R. A., Leibowitz, S. G., and Ebersole, J. L.: Random forest models to estimate bankfull and low flow channel widths and depths across the conterminous United States, J. Am. Water Resour. Assoc., 59, 1099–1114, https://doi.org/10.1111/1752-1688.13116, 2023.
Gao, S., Huang, Y., Zhang, S., Han, J., Wang, G., Zhang, M., and Lin, Q.: Short-term runoff prediction with GRU and LSTM networks without requiring time step optimization during sample generation, J. Hydrol., 589, 125188, https://doi.org/10.1016/j.jhydrol.2020.125188, 2020.
Gebremariam, S. Y., Martin, J. F., DeMarchi, C., Bosch, N. S., Confesor, R., and Ludsin, S. A.: A comprehensive approach to evaluating watershed models for predicting river flow regimes critical to downstream ecosystem services, Environ. Model. Softw., 61, 121–134, https://doi.org/10.1016/j.envsoft.2014.07.004, 2014.
Gil, Y., David, C. H., Demir, I., Essawy, B. T., Fulweiler, R. W., Goodall, J. L., Karlstrom, L., Lee, H., Mills, H. J., Oh, J. H., Pierce, S. A., Pope, A., Tzeng, M. W., Villamizar, S. R., and Yu, X.: Toward the Geoscience Paper of the Future: Best practices for documenting and sharing research from data to software to provenance, Earth Space Sci., 3, 388–415, https://doi.org/10.1002/2015EA000136, 2016.
Gong, J., Yao, C., Li, Z., Chen, Y., Huang, Y., and Tong, B.: Improving the flood forecasting capability of the Xinanjiang model for small- and medium-sized ungauged catchments in South China, Nat. Hazards, 106, 2077–2109, https://doi.org/10.1007/s11069-021-04531-0, 2021.
Granata, F., Zhu, S., and Di Nunno, F.: Advanced streamflow forecasting for Central European Rivers: The Cutting-Edge Kolmogorov-Arnold networks compared to Transformers, J. Hydrol., 645, 132175, https://doi.org/10.1016/j.jhydrol.2024.132175, 2024.
Han, H. and Morrison, R. R.: Improved runoff forecasting performance through error predictions using a deep-learning approach, J. Hydrol., 608, 127653, https://doi.org/10.1016/j.jhydrol.2022.127653, 2022.
Hao, F., Sun, M., Geng, X., Huang, W., and Ouyang, W.: Coupling the Xinanjiang model with geomorphologic instantaneous unit hydrograph for flood forecasting in northeast China, Int. Soil Water Conserv. Res., 3, 66–76, https://doi.org/10.1016/j.iswcr.2015.03.004, 2015.
He, Y., Wang, Z., Cheng, H., and Ding, W.: Multi-scale feature fusion and uncertainty quantification in streamflow prediction: A temporal convolutional network approach with hybrid denoising, Environ. Modell. Softw., 198, 106879, https://doi.org/10.1016/j.envsoft.2026.106879, 2026.
Hosking, J. R. M. and Wallis, J. R.: Regional frequency analysis: an approach based on L-moments, Cambridge University Press, Cambridge, UK, ISBN 9780521430452, 1997.
Hwang, Y., Clark, M. P., and Rajagopalan, B.: Use of daily precipitation uncertainties in streamflow simulation and forecast, Stoch. Env. Res. Risk Assess., 25, 957–972, https://doi.org/10.1007/s00477-011-0460-1, 2011.
Jehanzaib, M., Idrees, M. B., Kim, D., and Kim, T. W.: Comprehensive Evaluation of Machine Learning Techniques for Hydrological Drought Forecasting, J. Irrig. Drain. Eng., 147, 04021022, https://doi.org/10.1061/(ASCE)IR.1943-4774.0001575, 2021.
Jiang, S., Zheng, Y., and Solomatine, D.: Improving AI System Awareness of Geoscience Knowledge: Symbiotic Integration of Physical Approaches and Deep Learning, Geophys. Res. Lett., 47, e2020GL088229, https://doi.org/10.1029/2020GL088229, 2020.
Jiang, X. L., Zhang, L. P., Liang, Z. M., Fu, X. L., Wang, J., Xu, J. X., Zhang, Y. C., and Zhong, Q.: Study of early flood warning based on postprocessed predicted precipitation and Xinanjiang model, Weather Clim. Extremes, 42, 100611, https://doi.org/10.1016/j.wace.2023.100611, 2023.
Kang, N., Wang, Z., Zhang, A., and Chen, H.: Improving the prediction of streamflow in large watersheds based on seasonal trend decomposition and vectorized deep learning models, Ecol. Inform., 90, 103291, https://doi.org/10.1016/j.ecoinf.2025.103291, 2025.
Katipoğlu, O. M. and Sarıgöl, M.: Improving the accuracy of rainfall-runoff relationship estimation using signal processing techniques, bio-inspired swarm intelligence and artificial intelligence algorithms, Earth Sci. Inform., 16, 3125–3141, https://doi.org/10.1007/s12145-023-01081-w, 2023.
Kim, T., Yang, T., Gao, S., Zhang, L., Ding, Z., Wen, X., Gourley, J. J., and Hong, Y.: Can artificial intelligence and data-driven machine learning models match or even replace process-driven hydrologic models for streamflow simulation?: A case study of four watersheds with different hydro-climatic regions across the CONUS, J. Hydrol., 598, 126423, https://doi.org/10.1016/j.jhydrol.2021.126423, 2021.
Kratzert, F., Klotz, D., Hochreiter, S., and Nearing, G. S.: A note on leveraging synergy in multiple meteorological data sets with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 25, 2685–2703, https://doi.org/10.5194/hess-25-2685-2021, 2021.
Kratzert, F., Gauch, M., Klotz, D., and Nearing, G.: HESS Opinions: Never train a Long Short-Term Memory (LSTM) network on a single basin, Hydrol. Earth Syst. Sci., 28, 4187–4201, https://doi.org/10.5194/hess-28-4187-2024, 2024.
Kurian, C., Sudheer, K., Vema, V., and Sahoo, D.: Effective flood forecasting at higher lead times through hybrid modelling framework, J. Hydrol., 587, 124945, https://doi.org/10.1016/j.jhydrol.2020.124945, 2020.
Lei, X., Cheng, L., Ye, L., Zhang, L., Kim, J., Qin, S., and Liu, P.: Integration of the generalized complementary relationship into a lumped hydrological model for improving water balance partitioning: A case study with the Xinanjiang model, J. Hydrol., 621, 129569, https://doi.org/10.1016/j.jhydrol.2023.129569, 2023.
Leonarduzzi, E., Maxwell, R., and Mirus, B.: Numerical Analysis of the Effect of Subgrid Variability in a Physically Based Hydrological Model on Runoff, Soil Moisture, and Slope Stability, Water Resour. Res., 57, e2020WR027326, https://doi.org/10.1029/2020WR027326, 2021.
Li, P., Song, Y., Pan, M., Lawson, K., and Shen, C.: Ensembling differentiable process-based and data-driven models with diverse meteorological forcing datasets to advance streamflow simulation, Hydrol. Earth Syst. Sci., 29, 6829–6861, https://doi.org/10.5194/hess-29-6829-2025, 2025.
Lin, K., Sheng, S., Zhou, Y., Liu, F., Li, Z., Chen, H., Xu, C., Chen, J., and Guo, S.: The exploration of a Temporal Convolutional Network combined with Encoder-Decoder framework for runoff forecasting, Hydrol. Res., 51, 1136–1149, https://doi.org/10.2166/nh.2020.100, 2020.
Liu, S., Qin, H., Liu, G., Xu, Y., Zhu, X., and Qi, X.: Runoff Forecasting of Machine Learning Model Based on Selective Ensemble, Water Resour. Manage., 37, 4459–4473, https://doi.org/10.1007/s11269-023-03566-1, 2023.
Luo, Y., Zhou, Y., Xu, H., Chen, H., Chang, F.-J., and Xu, C.-Y.: Enhancing physically-based flood forecasts through fusion of long short-term memory neural network with unscented Kalman filter, J. Hydrol., 641, 131819, https://doi.org/10.1016/j.jhydrol.2024.131819, 2024.
Ng, K., Huang, Y., Koo, C., Chong, K., El-Shafie, A., and Ahmed, A.: A review of hybrid deep learning applications for streamflow forecasting, J. Hydrol., 625, 130141, https://doi.org/10.1016/j.jhydrol.2023.130141, 2023.
Ni, L., Wang, W., Wang, D., Singh, V. P., Yin, X., Kang, X., Tao, Y., and Gu, Z.: Improving Monthly Streamflow Prediction by Deep Learning Model With Physics-Based Rules, Hydrol. Process., 39, e70123, https://doi.org/10.1002/hyp.70123, 2025.
Oruc, H., Celen, M., Gulgen, F., Oncel, M., Vural, S., and Kilic, B.: Evaluating the effects of soil data quality on the SWAT runoff prediction Performance; A case study of Saz-Cayirova catchment, Turkey, Urban Water J., 20, 1592–1607, https://doi.org/10.1080/1573062X.2022.2056060, 2023.
Özgen-Xian, I., Kesserwani, G., Caviedes-Voullième, D., Molins, S., Xu, Z., Dwivedi, D., Moulton, J., and Steefel, C.: Wavelet-based local mesh refinement for rainfall-runoff simulations, J. Hydroinform., 22, 1059–1077, https://doi.org/10.2166/hydro.2020.198, 2020.
Parisouj, P., Mokari, E., Mohebzadeh, H., Goharnejad, H., Jun, C., Oh, J., and Bateni, S.: Physics-Informed Data-Driven Model for Predicting Streamflow: A Case Study of the Voshmgir Basin, Iran, Appl. Sci., 12, 7464, https://doi.org/10.3390/app12157464, 2022.
Qiao, X., Peng, T., Sun, N., Zhang, C., Liu, Q., Zhang, Y., Wang, Y., and Nazir, M.: Metaheuristic evolutionary deep learning model based on temporal convolutional network, improved aquila optimizer and random forest for rainfall-runoff simulation and multi runoff, Expert Syst. Appl., 229, 120616, https://doi.org/10.1016/j.eswa.2023.120616, 2023.
Samantaray, S., Das, S., Sahoo, A., and Satapathy, D.: Monthly runoff prediction at Baitarani river basin by support vector machine based on Salp swarm algorithm, Ain Shams Eng. J., 13, 101732, https://doi.org/10.1016/j.asej.2022.101732, 2022.
Shao, P., Feng, J., Lu, J., Zhang, P., and Zou, C.: Data-driven and knowledge-guided denoising diffusion model for flood forecasting, Expert Syst. Appl., 244, 122908, https://doi.org/10.1016/j.eswa.2023.122908, 2024.
Solanki, H., Vegad, U., Kushwaha, A., and Mishra, V.: Improving Streamflow Prediction Using Multiple Hydrological Models and Machine Learning Methods, Water Resour. Res., 61, e2024WR038192, https://doi.org/10.1029/2024WR038192, 2025.
Song, J., Meng, H., Kang, Y., Zhu, M., Zhu, Y., and Zhang, J.: A method for predicting water quality of river basin based on OVMD-GAT-GRU, Stoch. Environ. Res. Risk Assess., 38, 339–356, https://doi.org/10.1007/s00477-023-02584-0, 2024.
Song, Y., Qin, S., Qu, J., and Liu, F.: The forecasting research of early warning systems for atmospheric pollutants: A case in Yangtze River Delta region, Atmos. Environ., 118, 58–69, https://doi.org/10.1016/j.atmosenv.2015.06.032, 2015.
Sun, P., Wang, J., and Yan, Z.: Ultra-short-term wind speed prediction based on TCN-MCM-EKF, Energy Rep., 11, 2127–2140, https://doi.org/10.1016/j.egyr.2024.01.058, 2024.
Tan, Z., Li, H., Song, Q., Wang, Z., and Cao, Y.: Synergistic optimization and interaction evaluation of water-energy-food-ecology nexus under uncertainty from the perspective of urban agglomeration, Sustain. Cities Soc., 124, 106291, https://doi.org/10.1016/j.scs.2025.106291, 2025.
Thébault, C., Perrin, C., Andréassian, V., Thirel, G., Legrand, S., and Delaigue, O.: Multi-model approach in a variable spatial framework for streamflow simulation, Hydrol. Earth Syst. Sci., 28, 1539–1566, https://doi.org/10.5194/hess-28-1539-2024, 2024.
Vilaseca, F., Castro, A., Chreties, C., and Gorgoglione, A.: Assessing influential rainfall-runoff variables to simulate daily streamflow using random forest, Hydrol. Sci. J., 68, 1738–1753, https://doi.org/10.1080/02626667.2023.2232356, 2023.
Wang, H., Qin, H., Liu, G., Liu, S., Qu, Y., Wang, K., and Zhou, J.: A novel feature attention mechanism for improving the accuracy and robustness of runoff forecasting, J. Hydrol., 618, 129200, https://doi.org/10.1016/j.jhydrol.2023.129200, 2023.
Wang, J. and Dong, Y.: An interpretable deep learning multi-dimensional integration framework for exchange rate forecasting based on deep and shallow feature selection and snapshot ensemble technology, Eng. Appl. Artif. Intell., 133, 108282, https://doi.org/10.1016/j.engappai.2024.108282, 2024.
Wang, Z., Xu, N., Bao, X., Wu, J., and Cui, X.: Spatio-temporal deep learning model for accurate streamflow prediction with multi-source data fusion, Environ. Model. Softw., 178, 106091, https://doi.org/10.1016/j.envsoft.2024.106091, 2024.
Wang, Z., Ma, C., Tan, Z., and Wu, T.: Low-carbon development pathways for the water-energy-food-carbon nexus in the Yangtze river economic Belt: Insights from coupling coordination and obstacle degree analysis, J. Clean. Prod., 523, 146399, https://doi.org/10.1016/j.jclepro.2025.146399, 2025a.
Wang, Z., Zhu, Z., Luan, H., and Wu, T.: Multi-objective optimal scheduling of cascade reservoirs in complex basin systems: Case study of the Jinsha River-Yalong River confluence basin in China, J. Hydrol. Reg. Stud., 58, 102240, https://doi.org/10.1016/j.ejrh.2025.102240, 2025b.
Wei, X., Wang, G., Schmalz, B., Hagan, D., and Duan, Z.: Evaluation of Transformer model and Self-Attention mechanism in the Yangtze River basin runoff prediction, J. Hydrol. Reg. Stud., 47, 101438, https://doi.org/10.1016/j.ejrh.2023.101438, 2023.
Willard, J., Jia, X., Xu, S., Steinbach, M., and Kumar, V.: Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems, ACM Comput. Surv., 55, 66, https://doi.org/10.1145/3514228, 2023.
Wu, J., Wang, Z., Dong, J., Cui, X., Tao, S., and Chen, X.: Robust Runoff Prediction With Explainable Artificial Intelligence and Meteorological Variables From Deep Learning Ensemble Model, Water Resour. Res., 59, e2023WR035676, https://doi.org/10.1029/2023WR035676, 2023.
Xu, N.: Code and Data for XAJ-TCN-GRU, Zenodo [data set], https://doi.org/10.5281/zenodo.22159416, 2026.
Xu, C., Chen, Y., Wang, D., Zhao, Y., Hou, Y., Zhu, Y., and Shen, Q.: Uncertainty and driving factor analysis of streamflow forecasting for closed-basin and interval-basin: Based on a probabilistic and interpretable deep learning model, J. Hydrol. Reg. Stud., 60, 102483, https://doi.org/10.1016/j.ejrh.2025.102483, 2025.
Xu, Y., Lin, K., Hu, C., Wang, S., Wu, Q., Zhang, L., and Ran, G.: Deep transfer learning based on transformer for flood forecasting in data-sparse basins, J. Hydrol., 625, 129956, https://doi.org/10.1016/j.jhydrol.2023.129956, 2023.
Xu, Y., Liu, T., Fang, Q., Du, P., and Wang, J.: Crude oil price forecasting with multivariate selection, machine learning, and a nonlinear combination strategy, Eng. Appl. Artif. Intell., 139, 109510, https://doi.org/10.1016/j.engappai.2024.109510, 2025.
Yao, Z., Wang, Z., Wang, D., Wu, J., and Chen, L.: An ensemble CNN-LSTM and GRU adaptive weighting model based improved sparrow search algorithm for predicting runoff using historical meteorological and runoff data as input, J. Hydrol., 625, 129977, https://doi.org/10.1016/j.jhydrol.2023.129977, 2023.
Zhang, Y., Ye, A., Analui, B., Nguyen, P., Sorooshian, S., Hsu, K., and Wang, Y.: Comparing quantile regression forest and mixture density long short-term memory models for probabilistic post-processing of satellite precipitation-driven streamflow simulations, Hydrol. Earth Syst. Sci., 27, 4529–4550, https://doi.org/10.5194/hess-27-4529-2023, 2023.
Zhao, R. J.: The Xinanjiang model applied in China, J. Hydrol., 135, 371–381, https://doi.org/10.1016/0022-1694(92)90096-E, 1992.
Zhao, Y., Huang, Y., Wang, Z., and Liu, X.: Carbon futures price forecasting based on feature selection, Eng. Appl. Artif. Intell., 135, 108646, https://doi.org/10.1016/j.engappai.2024.108646, 2024.
Zheng, Z., Ali, M., Jamei, M., Xiang, Y., Karbasi, M., Yaseen, Z., and Farooque, A.: Design data decomposition-based reference evapotranspiration forecasting model: A soft feature filter based deep learning driven approach, Eng. Appl. Artif. Intell., 121, 105984, https://doi.org/10.1016/j.engappai.2023.105984, 2023.
Zhu, S., Wei, J., Zhang, H., Xu, Y., and Qin, H.: Spatiotemporal deep learning rainfall-runoff forecasting combined with remote sensing precipitation products in large scale basins, J. Hydrol., 616, 128727, https://doi.org/10.1016/j.jhydrol.2022.128727, 2023.
Zhu, Z., Li, H., Wang, Z., Zhang, X., and Tan, Z.: Integration of deep learning and improved multi-objective algorithm to optimize cascade reservoirs operation with consideration of ecological dissolved oxygen needs, J. Hydrol., 667, 134899, https://doi.org/10.1016/j.jhydrol.2025.134899, 2026a.
Zhu, Z., Wu, H., Wang, Z., Zhang, X., Kong, J., Liu, C., Tan, Z., and Liu, Q.: Physics-AI Synergized Optimization-Learning-Simulation Framework for Robust Cascade Reservoir Scheduling Under Future Hydrological Uncertainty, Water Resour. Res., 62, e2025WR042149, https://doi.org/10.1029/2025WR042149, 2026b.
Zuo, G., Luo, J., Wang, N., Lian, Y., and He, X.: Decomposition ensemble model based on variational mode decomposition and long short-term memory for streamflow forecasting, J. Hydrol., 585, 124776, https://doi.org/10.1016/j.jhydrol.2020.124776, 2020.
Short summary
This study integrates Xinanjiang (XAJ) and Temporal Convolutional Network - Gated Recurrent Unit (TCN-GRU) via Random Forest (RF) for streamflow simulation. It combines XAJ’s physical modeling with TCN-GRU’s temporal analysis. Validated in four hydrologically diverse basins, the model achieves Nash-Sutcliffe Efficiency (NSE) 0.971–0.991, outperforming traditional models. Robust in flood/interval simulations, analysis identifies dew point temperature and evaporation as key factors through three interpretable methods.
This study integrates Xinanjiang (XAJ) and Temporal Convolutional Network - Gated Recurrent Unit...
