Articles | Volume 29, issue 23
https://doi.org/10.5194/hess-29-6829-2025
© Author(s) 2025. 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-29-6829-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
01 Dec 2025
Research article |
| 01 Dec 2025
| 01 Dec 2025
Ensembling differentiable process-based and data-driven models with diverse meteorological forcing datasets to advance streamflow simulation
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Yalan Song
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Center for Western Weather and Water Extremes, Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA
Kathryn Lawson
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA, USA
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Cited articles
Aboelyazeed, D., Xu, C., Hoffman, F. M., Liu, J., Jones, A. W., Rackauckas, C., Lawson, K., and Shen, C.: A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations, Biogeosciences, 20, 2671–2692, https://doi.org/10.5194/bg-20-2671-2023, 2023.
Addor, N., Newman, A. J., Mizukami, N., and Clark, M. P.: The CAMELS data set: catchment attributes and meteorology for large-sample studies, Hydrol. Earth Syst. Sci., 21, 5293–5313, https://doi.org/10.5194/hess-21-5293-2017, 2017.
Aghakouchak, A. and Habib, E.: Application of a Conceptual Hydrologic Model in Teaching Hydrologic Processes, International Journal of Engineering Education, 26, 963–973, 2010.
Bandai, T. and Ghezzehei, T. A.: Physics-informed neural networks with monotonicity constraints for Richardson-Richards equation: Estimation of constitutive relationships and soil water flux density from volumetric water content measurements, Water Resources Research, 57, e2020WR027642, https://doi.org/10.1029/2020wr027642, 2021.
Beck, H. E., van Dijk, A. I. J. M., de Roo, A., Dutra, E., Fink, G., Orth, R., and Schellekens, J.: Global evaluation of runoff from 10 state-of-the-art hydrological models, Hydrol. Earth Syst. Sci., 21, 2881–2903, https://doi.org/10.5194/hess-21-2881-2017, 2017.
Beck, H. E., Pan, M., Lin, P., Seibert, J., van Dijk, A. I. J. M., and Wood, E. F.: Global fully distributed parameter regionalization based on observed streamflow from 4,229 headwater catchments, Journal of Geophysical Research: Atmospheres, 125, e2019JD031485, https://doi.org/10.1029/2019JD031485, 2020.
Behnke, R., Vavrus, S., Allstadt, A., Albright, T., Thogmartin, W. E., and Radeloff, V. C.: Evaluation of downscaled, gridded climate data for the conterminous United States, Ecological Applications, 26, 1338–1351, https://doi.org/10.1002/15-1061, 2016.
Bell, V. A. and Moore, R. J.: The sensitivity of catchment runoff models to rainfall data at different spatial scales, Hydrol. Earth Syst. Sci., 4, 653–667, https://doi.org/10.5194/hess-4-653-2000, 2000.
Bellmore, J. R., Duda, J. J., Craig, L. S., Greene, S. L., Torgersen, C. E., Collins, M. J., and Vittum, K.: Status and trends of dam removal research in the United States, Wiley Interdisciplinary Reviews: Water, 4, e1164, https://doi.org/10.1002/wat2.1164, 2017.
Bergström, S.: Development and application of a conceptual runoff model for Scandinavian catchments, PhD Thesis, Swedish Meteorological and Hydrological Institute (SMHI), Norköping, Sweden, urn:nbn:se:smhi:diva-5738, 1976.
Bergström, S.: The HBV model – its structure and applications, SMHI, urn:nbn:se:smhi:diva-2672, 1992.
Bindas, T., Tsai, W.-P., Liu, J., Rahmani, F., Feng, D., Bian, Y., Lawson, K., and Shen, C.: Improving river routing using a differentiable Muskingum-Cunge model and physics-informed machine learning, Water Resources Research, 60, e2023WR035337, https://doi.org/10.1029/2023WR035337, 2024.
Bodnar, C., Bruinsma, W. P., Lucic, A., Stanley, M., Allen, A., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J. A., Dong, H., Gupta, J. K., Thambiratnam, K., Archibald, A. T., Wu, C.-C., Heider, E., Welling, M., Turner, R. E., and Perdikaris, P.: A foundation model for the Earth system, Nature, 641, 1180–1187, https://doi.org/10.1038/s41586-025-09005-y, 2025.
Brunner, M. I., Slater, L., Tallaksen, L. M., and Clark, M.: Challenges in modeling and predicting floods and droughts: A review, WIREs Water, 8, e1520, https://doi.org/10.1002/wat2.1520, 2021.
Clark, M. P., Slater, A. G., Rupp, D. E., Woods, R. A., Vrugt, J. A., Gupta, H. V., Wagener, T., and Hay, L. E.: Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models, Water Resources Research, 44, https://doi.org/10/chvc6k, 2008.
Clark, M. P., Nijssen, B., Lundquist, J. D., Kavetski, D., Rupp, D. E., Woods, R. A., Freer, J. E., Gutmann, E. D., Wood, A. W., Brekke, L. D., Arnold, J. R., Gochis, D. J., and Rasmussen, R. M.: A unified approach for process-based hydrologic modeling: 1. Modeling concept, Water Resources Research, 51, 2498–2514, https://doi.org/10/f7db99, 2015.
Clark, M. P., Wilby, R. L., Gutmann, E. D., Vano, J. A., Gangopadhyay, S., Wood, A. W., Fowler, H. J., Prudhomme, C., Arnold, J. R., and Brekke, L. D.: Characterizing uncertainty of the hydrologic impacts of climate change, Curr. Clim. Change Rep., 2, 55–64, https://doi.org/10.1007/s40641-016-0034-x, 2016.
Dion, P., Martel, J.-L., and Arsenault, R.: Hydrological ensemble forecasting using a multi-model framework, Journal of Hydrology, 600, 126537, https://doi.org/10.1016/j.jhydrol.2021.126537, 2021.
Feng, D., Fang, K., and Shen, C.: Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales, Water Resources Research, 56, e2019WR026793, https://doi.org/10.1029/2019WR026793, 2020.
Feng, D., Lawson, K., and Shen, C.: Mitigating prediction error of deep learning streamflow models in large data-sparse regions with ensemble modeling and soft data, Geophysical Research Letters, 48, e2021GL092999, https://doi.org/10.1029/2021GL092999, 2021.
Feng, D., Liu, J., Lawson, K., and Shen, C.: Differentiable, learnable, regionalized process-based models with multiphysical outputs can approach state-of-the-art hydrologic prediction accuracy, Water Resources Research, 58, e2022WR032404, https://doi.org/10.1029/2022WR032404, 2022.
Feng, D., Shen, C., Liu, J., Lawson, K., and Beck, H.: differentiable parameter learning (dPL) + HBV hydrologic model, Zenodo [code, data set], https://doi.org/10.5281/zenodo.7943626, 2023a.
Feng, D., Beck, H., Lawson, K., and Shen, C.: The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment, Hydrol. Earth Syst. Sci., 27, 2357–2373, https://doi.org/10.5194/hess-27-2357-2023, 2023b.
Frame, J. M., Kratzert, F., Klotz, D., Gauch, M., Shalev, G., Gilon, O., Qualls, L. M., Gupta, H. V., and Nearing, G. S.: Deep learning rainfall–runoff predictions of extreme events, Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, 2022.
Hanazaki, R., Yamazaki, D., and Yoshimura, K.: Development of a reservoir flood control scheme for global flood models, JAMES, 14, e2021MS002944, https://doi.org/10.1029/2021MS002944, 2022.
Hargreaves, G. H.: Defining and using reference evapotranspiration, Journal of Irrigation and Drainage Engineering, 120, 1132–1139, https://doi.org/10.1061/(ASCE)0733-9437(1994)120:6(1132), 1994.
He, Y., Chen, M., Wen, Y., Duan, Q., Yue, S., Zhang, J., Li, W., Sun, R., Zhang, Z., Tao, R., Tang, W., and Lü, G.: An open online simulation strategy for hydrological ensemble forecasting, Environmental Modelling & Software, 174, 105975, https://doi.org/10.1016/j.envsoft.2024.105975, 2024.
Heidari, H., Arabi, M., Warziniack, T., and Kao, S.-C.: Assessing shifts in regional hydroclimatic conditions of U.S. river basins in response to climate change over the 21st century, Earth's Future, 8, e2020EF001657, https://doi.org/10.1029/2020EF001657, 2020.
Hochreiter, S. and Schmidhuber, J.: Long Short-Term Memory, Neural Computation, 9, 1735–1780, https://doi.org/10.1162/neco.1997.9.8.1735, 1997.
Ji, H., Song, Y., Bindas, T., Shen, C., Yang, Y., Pan, M., Liu, J., Rahmani, F., Abbas, A., Beck, H., Lawson, K., and Wada, Y.: Distinct hydrologic response patterns and trends worldwide revealed by physics-embedded learning, Nat. Commun., 16, 9169, https://doi.org/10.1038/s41467-025-64367-1, 2025.
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.
Kling, H., Fuchs, M., and Paulin, M.: Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios, Journal of Hydrology, 424–425, 264–277, https://doi.org/10.1016/j.jhydrol.2012.01.011, 2012.
Kraft, B., Jung, M., Körner, M., Koirala, S., and Reichstein, M.: Towards hybrid modeling of the global hydrological cycle, Hydrol. Earth Syst. Sci., 26, 1579–1614, https://doi.org/10.5194/hess-26-1579-2022, 2022.
Kratzert, F., Klotz, D., Brenner, C., Schulz, K., and Herrnegger, M.: Rainfall-Runoff modelling using Long-Short-Term-Memory (LSTM) networks, Hydrology and Earth System Sciences, 22, 6005–6022, https://doi.org/10.17605/OSF.IO/QV5JZ, 2018.
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., and Nearing, G. S.: Toward improved predictions in ungauged basins: Exploiting the power of machine learning, Water Resources Research, 55, 11344–11354, https://doi.org/10/gg4ck8, 2019.
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., Nearing, G., and Klotz, D.: NeuralHydrology – A Python library for Deep Learning research in hydrology, Zenodo [data set], https://doi.org/10.5281/zenodo.6326394, 2022.
Leube, P. C., de Barros, F. P. J., Nowak, W., and Rajagopal, R.: Towards optimal allocation of computer resources: Trade-offs between uncertainty quantification, discretization and model reduction, Environmental Modelling & Software, 50, 97–107, https://doi.org/10.1016/j.envsoft.2013.08.008, 2013.
Li, P., Zha, Y., Shi, L., Tso, C. H. M., Zhang, Y., and Zeng, W.: Comparison of the use of a physical-based model with data assimilation and machine learning methods for simulating soil water dynamics, Journal of Hydrology, 584, 124692, https://doi.org/10.1016/j.jhydrol.2020.124692, 2020a.
Li, P., Zha, Y., Tso, C. H. M., Shi, L., Yu, D., Zhang, Y., and Zeng, W.: Data assimilation of uncalibrated soil moisture measurements from frequency-domain reflectometry, Geoderma, 374, 114432, https://doi.org/10.1016/j.geoderma.2020.114432, 2020b.
Li, P., Zha, Y., Shi, L., and Zhong, H.: Identification of the terrestrial water storage change features in the North China Plain via independent component analysis, Journal of Hydrology: Regional Studies, 38, 100955, https://doi.org/10.1016/j.ejrh.2021.100955, 2021.
Li, P., Zha, Y., Shi, L., and Zhong, H.: Assessing the Global Relationships Between Teleconnection Factors and Terrestrial Water Storage Components, Water Resources Management, 36, 119–133, https://doi.org/10.1007/s11269-021-03015-x, 2022.
Li, P., Zha, Y., Zuo, B., and Zhang, Y.: A family of soil water retention models based on sigmoid functions, Water Resources Research, 59, e2022WR033160, https://doi.org/10.1029/2022WR033160, 2023a.
Li, P., Zha, Y., and Tso, C.-H. M.: Reconstructing GRACE-derived terrestrial water storage anomalies with in-situ groundwater level measurements and meteorological forcing data, Journal of Hydrology: Regional Studies, 50, 101528, https://doi.org/10.1016/j.ejrh.2023.101528, 2023b.
Li, P., Zha, Y., Zhang, Y., Michael Tso, C.-H., Attinger, S., Samaniego, L., and Peng, J.: Deep learning integrating scale conversion and pedo-transfer function to avoid potential errors in cross-scale transfer, Water Resources Research, 60, e2023WR035543, https://doi.org/10.1029/2023WR035543, 2024.
Li, P., Song, Y., Pan, M., Lawson, K., and Shen, C.: Streamflow Simulation Data from Differentiable HBV and LSTM Models Using CAMELS Datasets, Zenodo [data set], https://doi.org/10.5281/zenodo.16895228, 2025.
Lin, Y., Wang, D., Zhu, J., Sun, W., Shen, C., and Shangguan, W.: Development of objective function-based ensemble model for streamflow forecasts, Journal of Hydrology, 632, 130861, https://doi.org/10.1016/j.jhydrol.2024.130861, 2024.
Lins, H. F. and Slack, J. R.: Streamflow trends in the United States, Geophysical Research Letters, 26, 227–230, https://doi.org/10/d5zbbd, 1999.
Liu, J., Rahmani, F., Lawson, K., and Shen, C.: A multiscale deep learning model for soil moisture integrating satellite and in situ data, Geophysical Research Letters, 49, e2021GL096847, https://doi.org/10.1029/2021GL096847, 2022.
Liu, J., Bian, Y., Lawson, K., and Shen, C.: Probing the limit of hydrologic predictability with the Transformer network, Journal of Hydrology, 637, 131389, https://doi.org/10.1016/j.jhydrol.2024.131389, 2024.
Mai, J., Craig, J. R., Tolson, B. A., and Arsenault, R.: The sensitivity of simulated streamflow to individual hydrologic processes across North America, Nat. Commun., 13, 455, https://doi.org/10.1038/s41467-022-28010-7, 2022.
Maurer, E. P., Wood, A. W., Adam, J. C., Lettenmaier, D. P., and Nijssen, B.: A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States, Journal of Climate, 15, 3237–3251, https://doi.org/10.1175/1520-0442(2002)015<3237:ALTHBD>2.0.CO;2, 2002.
Moges, E., Demissie, Y., and Li, H.-Y.: Hierarchical mixture of experts and diagnostic modeling approach to reduce hydrologic model structural uncertainty, Water Resources Research, 52, 2551–2570, https://doi.org/10.1002/2015WR018266, 2016.
Nai, C., Liu, X., Tang, Q., Liu, L., Sun, S., and Gaffney, P. P. J.: A novel strategy for automatic selection of cross-basin data to improve local machine learning-based runoff models, Water Resources Research, 60, e2023WR035051, https://doi.org/10.1029/2023WR035051, 2024.
Narkhede, M. V., Bartakke, P. P., and Sutaone, M. S.: A review on weight initialization strategies for neural networks, Artificial Intelligence Review, 55, 291–322, https://doi.org/10.1007/s10462-021-10033-z, 2022.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I – A discussion of principles, Journal of Hydrology, 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
Nearing, G., Cohen, D., Dube, V., Gauch, M., Gilon, O., Harrigan, S., Hassidim, A., Klotz, D., Kratzert, F., Metzger, A., Nevo, S., Pappenberger, F., Prudhomme, C., Shalev, G., Shenzis, S., Tekalign, T. Y., Weitzner, D., and Matias, Y.: Global prediction of extreme floods in ungauged watersheds, Nature, 627, 559–563, https://doi.org/10.1038/s41586-024-07145-1, 2024.
Newman, A. J., Mizukami, N., Clark, M. P., Wood, A. W., Nijssen, B., Nearing, G., Newman, A. J., Mizukami, N., Clark, M. P., Wood, A. W., Nijssen, B., and Nearing, G.: Benchmarking of a Physically Based Hydrologic Model, Journal of Hydrometeorology, 18, 2215–2225, https://doi.org/10/gbwr9s, 2017.
Newman, A. J., Clark, M. P., Longman, R. J., and Giambelluca, T. W.: Methodological intercomparisons of station-based gridded meteorological products: Utility, limitations, and paths forward, Journal of Hydrometeorology, 20, 531–547, https://doi.org/10.1175/JHM-D-18-0114.1, 2019.
Newman, A. J., Sampson, K., Clark, M., Bock, A., Viger, R., Blodgett, D., Addor, N. and Mizukami, M.: CAMELS: Catchment Attributes and MEteorology for Large-sample Studies (1.2), Zenodo [data set], https://doi.org/10.5065/D6MW2F4D, 2022.
Ouyang, W., Lawson, K., Feng, D., Ye, L., Zhang, C., and Shen, C.: Continental-scale streamflow modeling of basins with reservoirs: Towards a coherent deep-learning-based strategy, Journal of Hydrology, 599, 126455, https://doi.org/10.1016/j.jhydrol.2021.126455, 2021.
Paul, P. K., Zhang, Y., Ma, N., Mishra, A., Panigrahy, N., and Singh, R.: Selecting hydrological models for developing countries: Perspective of global, continental, and country scale models over catchment scale models, Journal of Hydrology, 600, 126561, https://doi.org/10.1016/j.jhydrol.2021.126561, 2021.
Rahmani, F., Appling, A., Feng, D., Lawson, K., and Shen, C.: Identifying structural priors in a hybrid differentiable model for stream water temperature modeling, Water Resources Research, 59, e2023WR034420, https://doi.org/10.1029/2023WR034420, 2023.
Reichle, R. H. and Koster, R. D.: Assessing the impact of horizontal error correlations in background fields on soil moisture estimation, Journal of Hydrometeorology, 4, 1229–1242, https://doi.org/10.1175/1525-7541(2003)004<1229:ATIOHE>2.0.CO;2, 2003.
Sawadekar, K., Song, Y., Pan, M., Beck, H., McCrary, R., Ullrich, P., Lawson, K., and Shen, C.: Improving differentiable hydrologic modeling with interpretable forcing fusion, J. Hydrol., 659, 133320, https://doi.org/10.1016/j.jhydrol.2025.133320, 2025.
Shen, C., Appling, A. P., Gentine, P., Bandai, T., Gupta, H., Tartakovsky, A., Baity-Jesi, M., Fenicia, F., Kifer, D., Li, L., Liu, X., Ren, W., Zheng, Y., Harman, C. J., Clark, M., Farthing, M., Feng, D., Kumar, P., Aboelyazeed, D., Rahmani, F., Song, Y., Beck, H. E., Bindas, T., Dwivedi, D., Fang, K., Höge, M., Rackauckas, C., Mohanty, B., Roy, T., Xu, C., and Lawson, K.: Differentiable modelling to unify machine learning and physical models for geosciences, Nat. Rev. Earth Environ., 4, 552–567, https://doi.org/10.1038/s43017-023-00450-9, 2023.
Solanki, H., Vegad, U., Kushwaha, A., and Mishra, V.: Improving streamflow prediction using multiple hydrological models and machine learning methods, Water Resources Research, 61, e2024WR038192, https://doi.org/10.1029/2024WR038192, 2025.
Song, Y., Knoben, W. J. M., Clark, M. P., Feng, D., Lawson, K., Sawadekar, K., and Shen, C.: When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling, Hydrol. Earth Syst. Sci., 28, 3051–3077, https://doi.org/10.5194/hess-28-3051-2024, 2024.
Song, Y., Bindas, T., Shen, C., Ji, H., Knoben, W. J. M., Lonzarich, L., Clark, M. P., Liu, J., van Werkhoven, K., Lamont, S., Denno, M., Pan, M., Yang, Y., Rapp, J., Kumar, M., Rahmani, F., Thébault, C., Adkins, R., Halgren, J., Patel, T., Patel, A., Sawadekar, K. A., and Lawson, K.: High-resolution national-scale water modeling is enhanced by multiscale differentiable physics-informed machine learning, Water Resour. Res., 61, e2024WR038928, https://doi.org/10.1029/2024WR038928, 2025a.
Song, Y., Sawadekar, K., Frame, J. M., Pan, M., Clark, M., Knoben, W. J. M., Wood, A. W., Lawson, K. E., Patel, T., and Shen, C.: Physics-informed, differentiable hydrologic models for capturing unseen extreme events, ESS Open Archive, https://doi.org/10.22541/essoar.172304428.82707157/v2, 2025b.
Thornton, P. E., Running, S. W., and White, M. A.: Generating surfaces of daily meteorological variables over large regions of complex terrain, Journal of Hydrology, 190, 214–251, https://doi.org/10.1016/S0022-1694(96)03128-9, 1997.
Tsai, W.-P., Feng, D., Pan, M., Beck, H., Lawson, K., Yang, Y., Liu, J., and Shen, C.: From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling, Nat. Commun., 12, 5988, https://doi.org/10.1038/s41467-021-26107-z, 2021.
Wada, Y., de Graaf, I. E. M., and van Beek, L. P. H.: High-resolution modeling of human and climate impacts on global water resources, Journal of Advances in Modeling Earth Systems, 8, 735–763, https://doi.org/10/f8wgpv, 2016.
Wang, N., Zhang, D., Chang, H., and Li, H.: Deep learning of subsurface flow via theory-guided neural network, Journal of Hydrology, 584, 124700, https://doi.org/10.1016/j.jhydrol.2020.124700, 2020.
West, B. D., Maxwell, R. M., and Condon, L. E.: A scalable and modular reservoir implementation for large-scale integrated hydrologic simulations, Hydrol. Earth Syst. Sci., 29, 245–259, https://doi.org/10.5194/hess-29-245-2025, 2025.
Wilbrand, K., Taormina, R., ten Veldhuis, M.-C., Visser, M., Hrachowitz, M., Nuttall, J., and Dahm, R.: Predicting streamflow with LSTM networks using global datasets, Front. Water, 5, https://doi.org/10.3389/frwa.2023.1166124, 2023.
Xia, Y., Mitchell, K., Ek, M., Sheffield, J., Cosgrove, B., Wood, E., Luo, L., Alonge, C., Wei, H., Meng, J., Livneh, B., Lettenmaier, D., Koren, V., Duan, Q., Mo, K., Fan, Y., and Mocko, D.: Continental-scale water and energy flux analysis and validation for the North American Land Data Assimilation System project phase 2 (NLDAS-2): 1. Intercomparison and application of model products, Journal of Geophysical Research: Atmospheres, 117, https://doi.org/10.1029/2011JD016048, 2012.
Xie, K., Liu, P., Zhang, J., Han, D., Wang, G., and Shen, C.: Physics-guided deep learning for rainfall-runoff modeling by considering extreme events and monotonic relationships, Journal of Hydrology, 603, 127043, https://doi.org/10.1016/j.jhydrol.2021.127043, 2021.
Yao, L., Libera, D. A., Kheimi, M., Sankarasubramanian, A., and Wang, D.: The roles of climate forcing and its variability on streamflow at daily, monthly, annual, and long-term scales, Water Resources Research, 56, e2020WR027111, https://doi.org/10.1029/2020WR027111, 2020.
Yilmaz, K. K., Gupta, H. V., and Wagener, T.: A process-based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model, Water Resources Research, 44, https://doi.org/10/fpvsgb, 2008.
Yu, D., Yang, J., Shi, L., Zhang, Q., Huang, K., Fang, Y., and Zha, Y.: On the uncertainty of initial condition and initialization approaches in variably saturated flow modeling, Hydrol. Earth Syst. Sci., 23, 2897–2914, https://doi.org/10.5194/hess-23-2897-2019, 2019.
Yu, M., Huang, Q., and Li, Z.: Deep learning for spatiotemporal forecasting in Earth system science: a review, International Journal of Digital Earth, 17, 2391952, https://doi.org/10.1080/17538947.2024.2391952, 2024.
Zhang, Q., Shi, L., Holzman, M., Ye, M., Wang, Y., Carmona, F., and Zha, Y.: A dynamic data-driven method for dealing with model structural error in soil moisture data assimilation, Advances in Water Resources, 132, 103407, https://doi.org/10.1016/j.advwatres.2019.103407, 2019.
Zounemat-Kermani, M., Batelaan, O., Fadaee, M., and Hinkelmann, R.: Ensemble machine learning paradigms in hydrology: A review, Journal of Hydrology, 598, 126266, https://doi.org/10.1016/j.jhydrol.2021.126266, 2021.
Short summary
This study explores how combining different model types improves streamflow predictions, especially in data-sparse scenarios. By integrating two highly accurate models with distinct mechanisms and leveraging multiple meteorological datasets, we highlight their unique strengths and set new accuracy benchmarks across spatiotemporal conditions. Our findings enhance the understanding of how diverse models and multi-source data can be effectively used to improve hydrological predictions.
This study explores how combining different model types improves streamflow predictions,...
