Articles | Volume 18, issue 23
https://doi.org/10.5194/gmd-18-9257-2025
© 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/gmd-18-9257-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Hybrid Lake Model (HyLake) v1.0: unifying deep learning and physical principles for simulating lake-atmosphere interactions
State Key Laboratory of Earth Surface Processes and Disaster Risk Reduction, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
Guangdong Provincial Observation and Research Station for Coupled Human and Natural Systems in Land-ocean Interaction Zone, Beijing Normal University at Zhuhai, Zhuhai 519087, China
Xiaofan Yang
CORRESPONDING AUTHOR
State Key Laboratory of Earth Surface Processes and Disaster Risk Reduction, Faculty of Geographical Science, Beijing Normal University, Beijing 100875, China
Guangdong Provincial Observation and Research Station for Coupled Human and Natural Systems in Land-ocean Interaction Zone, Beijing Normal University at Zhuhai, Zhuhai 519087, China
Related authors
No articles found.
Shaomin Liu, Ziwei Xu, Tao Che, Xin Li, Tongren Xu, Zhiguo Ren, Yang Zhang, Junlei Tan, Lisheng Song, Ji Zhou, Zhongli Zhu, Xiaofan Yang, Rui Liu, and Yanfei Ma
Earth Syst. Sci. Data, 15, 4959–4981, https://doi.org/10.5194/essd-15-4959-2023, https://doi.org/10.5194/essd-15-4959-2023, 2023
Short summary
Short summary
We present a suite of observational datasets from artificial and natural oases–desert systems that consist of long-term turbulent flux and auxiliary data, including hydrometeorological, vegetation, and soil parameters, from 2012 to 2021. We confirm that the 10-year, long-term dataset presented in this study is of high quality with few missing data, and we believe that the data will support ecological security and sustainable development in oasis–desert areas.
Cited articles
Albergel, C., Dutra, E., Munier, S., Calvet, J.-C., Munoz-Sabater, J., de Rosnay, P., and Balsamo, G.: ERA-5 and ERA-Interim driven ISBA land surface model simulations: which one performs better?, Hydrol. Earth Syst. Sci., 22, 3515–3532, https://doi.org/10.5194/hess-22-3515-2018, 2018.
Almeida, M. C., Shevchuk, Y., Kirillin, G., Soares, P. M. M., Cardoso, R. M., Matos, J. P., Rebelo, R. M., Rodrigues, A. C., and Coelho, P. S.: Modeling reservoir surface temperatures for regional and global climate models: a multi-model study on the inflow and level variation effects, Geosci. Model Dev., 15, 173–197, https://doi.org/10.5194/gmd-15-173-2022, 2022.
Bai, S., Kolter, J. Z., and Koltun, V.: An empirical evaluation of generic convolutional and recurrent networks for sequence modelling, arXiv [preprint], https://doi.org/10.48550/arXiv.1803.01271, 2018.
Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., and Tian, Q.: Accurate medium-range global weather forecasting with 3-D neural networks, Nature, 619, 533–538, https://doi.org/10.1038/s41586-023-06185-3, 2023.
Carpenter, S. R., Stanley, E. H., and Vander Zanden, M. J.: State of the world's freshwater ecosystems: physical, chemical and biological changes, Annu. Rev. Environ. Resour., 36, 75–99, https://doi.org/10.1146/annurev-environ-021810-094524, 2011.
Chakraborty, D., Basagaoglu, H., and Winterle, J.: Interpretable vs. non-interpretable machine-learning models for data-driven hydro-climatological process modelling, Expert Syst. Appl., 170, 114498, https://doi.org/10.1016/j.eswa.2020.114498, 2021.
Chen, L., Zhong, X., Zhang, F., Cheng, Y., Xu, Y., Qi, Y., and Li, H.: FuXi: a cascade machine-learning forecasting system for 15-day global weather forecast, npj Clim. Atmos. Sci., 6, 190, https://doi.org/10.1038/s41612-023-00512-1, 2023.
Culpepper, J., Jakobsson, E., Weyhenmeyer, G. A., Hampton, S. E., Obertegger, U., Shchapov, K., Woolway, R. I., and Sharma, S.: Lake-ice quality in a warming world, Nat. Rev. Earth Environ., 5, 671–685, https://doi.org/10.1038/s43017-024-00590-6, 2024.
Couture, R. M., de Wit, H. A., Tominaga, K., Kiuru, P., and Markelov, I.: Oxygen dynamics in a boreal lake respond to long-term changes in climate, ice phenology and DOC inputs, J. Geophys. Res.-Biogeosci., 120, 2441–2456, https://doi.org/10.1002/2015JG003065, 2015.
De la Fuente, L. A., Ehsani, M. R., Gupta, H. V., and Condon, L. E.: Toward interpretable LSTM-based modeling of hydrological systems, Hydrol. Earth Syst. Sci., 28, 945–971, https://doi.org/10.5194/hess-28-945-2024, 2024.
Erkkilä, K.-M., Ojala, A., Bastviken, D., Biermann, T., Heiskanen, J. J., Lindroth, A., Peltola, O., Rantakari, M., Vesala, T., and Mammarella, I.: Methane and carbon dioxide fluxes over a lake: comparison between eddy covariance, floating chambers and boundary layer method, Biogeosciences, 15, 429–445, https://doi.org/10.5194/bg-15-429-2018, 2018.
Exley, G., Page, T., Thackeray, S. J., Folkard, A. M., Couture, R. M., Hernandez, R. R., Cagle, A. E., Salk, K. R., Clous, L., Whittaker, P., Chipps, M., and Armstrong, A.: Floating solar panels on reservoirs impact phytoplankton populations: a modelling experiment, J. Environ. Manage., 324, 116410, https://doi.org/10.1016/j.jenvman.2022.116410, 2022.
Feng, D. P., Liu, J. T., Lawson, K., and Shen, C. P.: Differentiable, learnable, regionalized process-based models with multiphysical outputs can approach state-of-the-art hydrologic-prediction accuracy, Water Resour. Res., 58, e2022WR032404, https://doi.org/10.1029/2022WR032404, 2022.
Ferianc, M., Que, Z., Fan, H., Luk, W., and Rodrigues, M.: Optimizing Bayesian recurrent neural networks on an FPGA-based accelerator, in: 2021 International Conference on Field-Programmable Technology (ICFPT), IEEE, December, 1–10, https://doi.org/10.1109/ICFPT52863.2021.9609847, 2021.
Gawlikowski, J., Tassi, C. R. N., Ali, M., Lee, J., Humt, M., Feng, J., Kruspe, A., Triebel, R., Jung, P., Roscher, R., Shahzad, M., Yang, W., Bamler, R., and Zhu, X. X.: A survey of uncertainty in deep neural networks, Artif. Intell. Rev., 56, 1513–1589, https://doi.org/10.1007/s10462-023-10562-9, 2023.
Gers, F. A., Schmidhuber, J., and Cummins, F.: Learning to forget: continual prediction with LSTM, Neural Comput., 12, 2451–2471, https://doi.org/10.1162/089976600300015015, 2000.
Golub, M., Thiery, W., Marcé, R., Pierson, D., Vanderkelen, I., Mercado-Bettin, D., Woolway, R. I., Grant, L., Jennings, E., Kraemer, B. M., Schewe, J., Zhao, F., Frieler, K., Mengel, M., Bogomolov, V. Y., Bouffard, D., Côté, M., Couture, R.-M., Debolskiy, A. V., Droppers, B., Gal, G., Guo, M., Janssen, A. B. G., Kirillin, G., Ladwig, R., Magee, M., Moore, T., Perroud, M., Piccolroaz, S., Raaman Vinnaa, L., Schmid, M., Shatwell, T., Stepanenko, V. M., Tan, Z., Woodward, B., Yao, H., Adrian, R., Allan, M., Anneville, O., Arvola, L., Atkins, K., Boegman, L., Carey, C., Christianson, K., de Eyto, E., DeGasperi, C., Grechushnikova, M., Hejzlar, J., Joehnk, K., Jones, I. D., Laas, A., Mackay, E. B., Mammarella, I., Markensten, H., McBride, C., Özkundakci, D., Potes, M., Rinke, K., Robertson, D., Rusak, J. A., Salgado, R., van der Linden, L., Verburg, P., Wain, D., Ward, N. K., Wollrab, S., and Zdorovennova, G.: A framework for ensemble modelling of climate change impacts on lakes worldwide: the ISIMIP Lake Sector, Geosci. Model Dev., 15, 4597–4623, https://doi.org/10.5194/gmd-15-4597-2022, 2022.
Gu, H., Jin, J., Wu, Y., Ek, M. B., and Subin, Z. M.: Calibration and validation of lake surface temperature simulations with the coupled WRF-lake model, Clim. Change, 129, 471–483, https://doi.org/10.1007/s10584-013-0978-y, 2015.
Guo, M. Y., Zhuang, Q. L., Yao, H. X., Golub, M., Leung, L. R., Pierson, D., and Tan, Z. L.: Validation and sensitivity analysis of a 1-D lake model across global lakes, J. Geophys. Res.-Atmos., 126, e2020JD033417, https://doi.org/10.1029/2020JD033417, 2021.
Halevy, A., Norvig, P., and Pereira, F.: The unreasonable effectiveness of data, IEEE Intell. Syst., 24, 8–12, https://doi.org/10.1109/MIS.2009.36, 2009.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Adrian, S., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., Chiara, G. D., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P. Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.: The ERA-5 global reanalysis, Q. J. R. Meteorol. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020.
Hestness, J., Narang, S., Ardalani, N., Diamos, G., Jun, H., Kianinejad, H., Patwary, M. M. A., Yang, Y., and Zhou, Y.: Deep-learning scaling is predictable, empirically, arXiv [preprint], https://doi.org/10.48550/arXiv.1712.00409, 2017.
He, Y.: Code and datasets of paper “Hybrid Lake Model (HyLake) v1.0: unifying deep learning and physical principles for simulating lake-atmosphere interactions”, Zenodo [code and data set], https://doi.org/10.5281/zenodo.15289113, 2025.
He, Y. and Yang, X.: A physics-informed deep learning framework for estimating thermal stratification in a large deep reservoir, Water Resour. Res., 61, e2025WR040592, https://doi.org/10.1029/2025WR040592, 2025.
Hipsey, M. R., Bruce, L. C., Boon, C., Busch, B., Carey, C. C., Hamilton, D. P., Hanson, P. C., Read, J. S., de Sousa, E., Weber, M., and Winslow, L. A.: A General Lake Model (GLM 3.0) for linking with high-frequency sensor data from the Global Lake Ecological Observatory Network (GLEON), Geosci. Model Dev., 12, 473–523, https://doi.org/10.5194/gmd-12-473-2019, 2019.
Hochreiter, S.: Long short-term memory, Neural Comput., 9, 1735–1780, https://doi.org/10.1162/neco.1997.9.8.1735, 1997.
Holmberg, M., Futter, M. N., Kotamäki, N., Fronzek, S., Forsius, M., Kiuru, P., Pirttioja, N., Rasmus, K., Starr, M., and Vuorenmaa, J.: Effects of changing climate on the hydrology of a boreal catchment and lake DOC – probabilistic assessment of a dynamic-model chain, Boreal Environ. Res., 19, 66–82, 2014.
Hostetler, S. W., Bates, G. T., and Giorgi, F.: Interactive coupling of a lake-thermal model with a regional climate model, J. Geophys. Res.-Atmos., 98, 5045–5057, https://doi.org/10.1029/92JD02843, 1993.
Huang, L., Wang, X., Sang, Y., Tang, S., Jin, L., Yang, H., Ottlé, C., Bernus, A., Wang, S., Wang, C., and Zhang, Y.: Optimising lake-surface-water-temperature simulations over large lakes in China with FLake model, Earth Space Sci., 8, e2021EA001737, https://doi.org/10.1029/2021EA001737, 2021.
Jiao, Y., Yang, C., He, W., Liu, W. X., and Xu, F. L.: The spatial distribution of phosphorus and their correlations in surface sediments and pore water in Lake Chaohu, China, Environ. Sci. Pollut. Res., 25, 25906–25915, https://doi.org/10.1007/s11356-018-2606-x, 2018.
Kar, S., McKenna, J. R., Sunkara, V., Coniglione, R., Stanic, S., and Bernard, L.: XWaveNet: enabling uncertainty quantification in short-term ocean wave height forecasts and extreme event prediction, Appl. Ocean Res., 148, 103994, https://doi.org/10.1016/j.apor.2024.103994, 2024.
Kayastha, M. B., Huang, C. F., Wang, J. L., Pringle, W. J., Chakraborty, T. C., Yang, Z., Hetland, R. D., Qian, Y., and Xue, P.: Insights on simulating summer warming of the Great Lakes: understanding the behaviour of a newly developed coupled lake-atmosphere modelling system, J. Adv. Model. Earth Syst., 15, e2023MS003620, https://doi.org/10.1029/2023MS003620, 2023.
Kiuru, P., Ojala, A., Mammarella, I., Heiskanen, J., Erkkilä, K.-M., Miettinen, H., Vesala, T., and Huttula, T.: Applicability and consequences of the integration of alternative models for CO2 transfer velocity into a process-based lake model, Biogeosciences, 16, 3297–3317, https://doi.org/10.5194/bg-16-3297-2019, 2019.
Klotz, D., Kratzert, F., Gauch, M., Keefe Sampson, A., Brandstetter, J., Klambauer, G., Hochreiter, S., and Nearing, G.: Uncertainty estimation with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, 2022.
Korbmacher, R. and Tordeux, A.: Review of pedestrian-trajectory-prediction methods: comparing deep-learning and knowledge-based approaches, IEEE Trans. Intell. Transp. Syst., 23, 24126–24144, https://doi.org/10.1109/TITS.2022.3205676, 2022.
Koya, S. R. and Roy, T.: Temporal-fusion transformers for stream-flow prediction: value of combining attention with recurrence, J. Hydrol., 637, 131301, https://doi.org/10.1016/j.jhydrol.2024.131301, 2024.
Kratzert, F., Klotz, D., Brenner, C., Schulz, K., and Herrnegger, M.: Rainfall–runoff modelling using Long Short-Term Memory (LSTM) networks, Hydrol. Earth Syst. Sci., 22, 6005–6022, https://doi.org/10.5194/hess-22-6005-2018, 2018.
Kurz, S., De Gersem, H., Galetzka, A., Klaedtke, A., Liebsch, M., Loukrezis, D., Russenschuck, S., and Schmidt, M.: Hybrid modelling: towards the next level of scientific computing in engineering, J. Math. Ind., 12, 8, https://doi.org/10.1186/s13362-022-00123-0, 2022.
Ladwig, R., Daw, A., Albright, E. A., Buelo, C., Karpatne, A., Meyer, M. F., Neog, A., Hanson, P. C., and Dugan, H. A..: Modular compositional learning improves 1-D hydrodynamic lake-model performance by merging process-based modelling with deep learning, J. Adv. Model. Earth Syst., 16, e2023MS003953, https://doi.org/10.1029/2023MS003953, 2024.
Lee, X.: Handbook of Micrometeorology: A Guide for Surface-Flux Measurement and Analysis, Kluwer Acad., Dordrecht, https://doi.org/10.1007/1-4020-2265-4, 2004.
Li, D., Marshall, L., Liang, Z., Sharma, A., and Zhou, Y.: Bayesian LSTM with stochastic variational inference for estimating model uncertainty in process-based hydrological models, Water Resour. Res., 57, e2021WR029772, https://doi.org/10.1029/2021WR029772, 2021a.
Li, L., Sullivan, P. L., Benettin, P., Cirpka, O. A., Bishop, K., Brantley, S. L., Knapp, J. L. A., van Meerveld, I., Rinaldo, A., Seibert, J., Wen, H., and Kirchner, J. W.: Toward catchment hydro-biogeochemical theories, WIREs Water, 8, e1495, https://doi.org/10.1002/wat2.1495, 2021b.
Liu, J., Bian, Y., Lawson, K., and Shen, C.: Probing the limit of hydrologic predictability with the transformer network, J. Hydrol., 637, 131389, https://doi.org/10.1016/j.jhydrol.2024.131389, 2024a.
Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J., Soljačić, M., Hou, T. Y., and Tegmark, M.: KAN: Kolmogorov–Arnold networks, arXiv [preprint], https://doi.org/10.48550/arXiv.2404.19756, 2024b.
Long, M., Cao, Y., Wang, J., and Jordan, M.: Learning transferable features with deep adaptation networks, in: 2015 International conference on machine learning, PMLR, June, 97–105 pp., 2015.
Lu, D., Liu, S., and Ricciuto, D.: An efficient bayesian method for advancing the application of deep learning in earth science, in: Proceedings of the 2019 International Conference on Data Mining Workshops (ICDMW), IEEE, November, 270–278, https://doi.org/10.1109/ICDMW.2019.00048, 2019.
Markelov, I., Couture, R. M., Fischer, R., Haande, S., and Van Cappellen, P.: Coupling water-column and sediment biogeochemical dynamics: modelling internal phosphorus loading, climate-change responses and mitigation measures in Lake Vansjø, Norway, J. Geophys. Res.-Biogeosci., 124, 3847–3866, https://doi.org/10.1029/2019JG005254, 2019.
Mironov, D., Heise, E., Kourzeneva, E., Ritter, B., Schneider, N., and Terzhevik, A.: Implementation of the lake-parameterization scheme FLake into the numerical-weather-prediction model COSMO, Boreal Environ. Res., 15, 218–230, 2010.
Monin, A. S. and Obukhov, A. M.: Basic laws of turbulent mixing in the surface layer of the atmosphere, Tr. Akad. Nauk SSSR Geophiz. Inst., 24, 163–187, 1954.
Monteiro, M. J., Couto, F. T., Bernardino, M., Cardoso, R. M., Carvalho, D., Martins, J. P. A., Santos, J. A., Argain, J. L., and Salgado, R.: A review on the current status of numerical-weather prediction in Portugal 2021: surface–atmosphere interactions, Atmosphere, 13, 1356, https://doi.org/10.3390/atmos13091356, 2022.
Mooij, W. M., Trolle, D., Jeppesen, E., Arhonditsis, G., Belolipetsky, P. V., Chitamwebwa, D. B. R., Degermendzhy, A. G., DeAngelis, D. L., De Senerpont Domis, L. N., Downing, A. S., Elliott, J. A., Fragoso Jr., C. R., Gaedke, U., Genova, S. N., Gulati, R. D., Håkanson, L., Hamilton, D. P., Hipsey, M. R., 't Hoen, J., Hülsmann, S., Los, F. H., Makler-Pick, V., Petzoldt, T., Prokopkin, I. G., Rinke, K., Schep, S. A., Tominaga, K., Van Dam, A. A., Van Nes, E. H., Wells, S. A., and Janse, J. H.: Challenges and opportunities for integrating lake-ecosystem-modelling approaches, Aquat. Ecol., 44, 633–667, https://doi.org/10.1007/s10452-010-9339-3, 2010.
Nordbo, A., Launiainen, S., Mammarella, I., Leppäranta, M., Huotari, J., Ojala, A., and Vesala, T.: Long-term energy-flux measurements and energy balance over a small boreal lake using eddy-covariance technique, J. Geophys. Res.-Atmos., 116, D02119, https://doi.org/10.1029/2010JD014542, 2011.
Notaro, M., Jorns, J., and Briley, L.: Representation of lake–atmosphere interactions and lake-effect snowfall in the Laurentian Great Lakes Basin among HighResMIP global-climate models, J. Atmos. Sci., 79, 1325–1347, https://doi.org/10.1175/JAS-D-21-0249.1, 2022.
O'Reilly, C. M., Sharma, S., Gray, D. K., Hampton, S. E., Read, J. S., Rowley, R. J., Schneider, P., Lenters, J. D., McIntyre, P. B., Kraemer, B. M., Weyhenmeyer, G. A., Straile, D., Dong, B., Adrian, R., Allan, M. G., Anneville, O., Arvola, L., Austin, J., Bailey, J. L., Baron, J. S., Brookes, J. D., de Eyto, E., Dokulil, M. T., Hamilton, D. P., Havens, K., Hetherington, A. L., Higgins, S. N., Hook, S., Izmest'eva, L. R., Joehnk, K. D., Kangur, K., Kasprzak, P., Kumagai, M., Kuusisto, E., Leshkevich, G., Livingstone, D. M., MacIntyre, S., May, L., Melack, J. M., Mueller-Navarra, D. C., Naumenko, M., Nõges, P., Nõges, T., North, R. P., Plisnier, P.-D., Rigosi, A., Rimmer, A., Rogora, M., Rudstam, L. G., Rusak, J. A., Salmaso, N., Samal, N. R., Schindler, D. E., Schladow, S. G., Schmid, M., Schmidt, S. R., Silow, E., Soylu, M. E., Teubner, K., Verburg, P., Voutilainen, A., Watkinson, A., Williamson, C. E., and Zhang, G.: Rapid and highly variable warming of lake-surface waters around the globe, Geophys. Res. Lett., 42, 10773–10781, https://doi.org/10.1002/2015GL066235, 2015.
Peng, Z., Mo, S., Sun, A. Y., Wu, J., Zeng, X., Lu, M., and Shi, X.: An explainable Bayesian TimesNet for probabilistic groundwater level prediction, Water Resour. Res., 61, e2025WR040191, https://doi.org/10.1029/2025WR040191, 2025.
Piccolroaz, S., Woolway, R. I., and Merchant, C. J.: Global reconstruction of twentieth-century lake-surface-water temperature reveals different warming trends depending on the climatic zone, Clim. Change, 160, 427–442, https://doi.org/10.1007/s10584-020-02663-z, 2020.
Piccolroaz, S., Zhu, S., Ladwig, R., Carrea, L., Oliver, S., Piotrowski, A. P., Ptak, M., Shinohara, R., Sojka, M., Woolway, R. I., and Zhu, D. Z.: Lake-water-temperature modelling in an era of climate change: data sources, models and future prospects, Rev. Geophys., 62, e2023RG000816, https://doi.org/10.1029/2023RG000816, 2024.
Pilla, R. M. and Couture, R. M.: Attenuation of photosynthetically active radiation and ultraviolet radiation in response to changing dissolved-organic carbon in browning lakes: modelling and parametrisation, Limnol. Oceanogr., 66, 2278–2289, https://doi.org/10.1002/lno.11753, 2021.
Raissi, M., Perdikaris, P., and Karniadakis, G. E.: Physics-informed neural networks: a deep-learning framework for solving forward and inverse problems involving nonlinear partial-differential equations, J. Comput. Phys., 378, 686–707, https://doi.org/10.1016/j.jcp.2018.10.045, 2019.
Read, J. S., Jia, X. W., Willard, J. D., Appling, A. P., Zwart, J. A., Oliver, S. K., Karpatne, A., Hansen, G. J. A., Hanson, P. C., Watkins, W., Steinbach, M., and Kumar, V.: Process-guided deep-learning predictions of lake-water temperature, Water Resour. Res., 55, 9173–9190, https://doi.org/10.1029/2019WR024922, 2019.
Salk, K. R., Venkiteswaran, J. J., Couture, R. M., Higgins, S. N., Paterson, M. J., and Schiff, S. L.: Warming combined with experimental eutrophication intensifies lake-phytoplankton blooms, Limnol. Oceanogr., 67, 147–158, https://doi.org/10.1002/lno.11982, 2022.
Saloranta, T. M. and Andersen, T.: MyLake – a multi-year lake-simulation-model code suitable for uncertainty- and sensitivity-analysis simulations, Ecol. Model., 207, 45–60, https://doi.org/10.1016/j.ecolmodel.2007.03.018, 2007.
Šarović, K., Burić, M., and Klaić, Z. B.: SIMO v1.0: simplified model of the vertical temperature profile in a small, warm, monomictic lake, Geosci. Model Dev., 15, 8349–8375, https://doi.org/10.5194/gmd-15-8349-2022, 2022.
Shahriari, B., Swersky, K., Wang, Z. Y., Adams, R. P., and de Freitas, N.: Taking the human out of the loop: a review of Bayesian optimisation, Proc. IEEE, 104, 148–175, https://doi.org/10.1109/JPROC.2015.2494218, 2016.
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.
Sherstinsky, A.: Fundamentals of recurrent-neural-network and long-short-term-memory network, Physica D, 404, 132306, https://doi.org/10.1016/j.physd.2019.132306, 2020.
Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., and Vesala, T.: LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes, Geosci. Model Dev., 9, 1977–2006, https://doi.org/10.5194/gmd-9-1977-2016, 2016.
Subin, Z. M., Riley, W. J., and Mironov, D.: An improved lake model for climate simulations: model structure, evaluation and sensitivity analyses in CESM1, J. Adv. Model. Earth Syst., 4, M02001, https://doi.org/10.1029/2011MS000072, 2012.
Sun, A. Y., Jiang, P. S., Mudunuru, M. K., and Chen, X. Y.: Explore spatio-temporal learning of large-sample hydrology using graph-neural networks, Water Resour. Res., 57, e2021WR030394, https://doi.org/10.1029/2021WR030394, 2021.
Tong, Y., Feng, L., Wang, X., Pi, X., Xu, W., and Woolway, R. I.: Global lakes are warming slower than surface-air temperature due to accelerated evaporation, Nat. Water, 1, 929–940, https://doi.org/10.1038/s44221-023-00148-8, 2023.
Verburg, P. and Antenucci, J. P.: Persistent unstable atmospheric boundary layer enhances sensible- and latent-heat loss in a tropical great lake: Lake Tanganyika, J. Geophys. Res.-Atmos., 115, D11109, https://doi.org/10.1029/2009JD012839, 2010.
Wang, B. B., Ma, Y. M., Wang, Y., Su, Z. B., and Ma, W. Q.: Significant differences exist in lake–atmosphere interactions and evaporation rates of high-elevation small and large lakes, J. Hydrol., 573, 220–234, https://doi.org/10.1016/j.jhydrol.2019.03.066, 2019a.
Wang, J., Fu, Z., Qiao, H., and Liu, F.: Assessment of eutrophication and water quality in the estuarine area of Lake Wuli, Lake Taihu, China, Sci. Total Environ., 650, 1392–1402, https://doi.org/10.1016/j.scitotenv.2018.09.137, 2019b.
Wang, J. L., Xue, P. F., Pringle, W., Yang, Z., and Qian, Y.: Impacts of lake-surface temperature on the summer climate over the Great-Lakes region, J. Geophys. Res.-Atmos., 127, e2021JD036231, https://doi.org/10.1029/2021JD036231, 2022.
Wang, S., Yu, L., Gao, C., Zheng, C., Liu, S., Lu, R., Dang K., Chen, X., Yang, J., Zhang, Z., Liu, Y., Yang, A., Zhao, A., Yue, Y., Song, S., Yu, B., Huang, G., and Lin, J.: Beyond the 80/20 rule: High-entropy minority tokens drive effective reinforcement learning for LLM reasoning, arXiv [preprint], arXiv:2506.01939, 2025.
Wang, W. J., Shi, K., Wang, X. W., Zhang, Y. L., Qin, B. Q., Zhang, Y. B., and Woolway, R. I.: The impact of extreme heat on lake warming in China, Nat. Commun., 15, 70, https://doi.org/10.1038/s41467-023-44404-7, 2024a.
Wang, X. W., Shi, K., Qin, B. Q., Zhang, Y. B., and Woolway, R. I.: Disproportionate impact of atmospheric-heat events on lake-surface-water-temperature increases, Nat. Clim. Change, 14, 1172–1177, https://doi.org/10.1038/s41558-024-02122-y, 2024b.
Wang, X. W., Woolway, R. I., Shi, K., Qin, B. Q., and Zhang, Y. L.: Lake cold spells are declining worldwide, Geophys. Res. Lett., 51, e2024GL111300, https://doi.org/10.1029/2024GL111300, 2024c.
Wang, Z. C., Xu, N. N., Bao, X. G., Wu, J. H., and Cui, X. F.: Spatio-temporal deep-learning model for accurate stream-flow prediction with multi-source data fusion, Environ. Model. Softw., 178, 106091, https://doi.org/10.1016/j.envsoft.2024.106091, 2024d.
Wen, Q., Zhou, T., Zhang, C., Chen, W., Ma, Z., Yan, J., and Sun, L.: Transformers in time series: a survey, arXiv [preprint], https://doi.org/10.48550/arXiv.2202.07125, 2022.
Wikle, C. K. and Zammit-Mangion, A.: Statistical deep learning for spatial and spatiotemporal data, Annu. Rev. Stat. Appl., 10, 247–270, https://doi.org/10.1146/annurev-statistics-033021-112628, 2023.
Willard, J. D., Read, J. S., Appling, A. P., Oliver, S. K., Jia, X. W., and Kumar, V.: Predicting water-temperature dynamics of unmonitored lakes with meta-transfer learning, Water Resour. Res., 57, e2021WR029579, https://doi.org/10.1029/2021WR029579, 2021.
Willard, J. D., Read, J. S., Topp, S., Hansen, G. J. A., and Kumar, V.: Daily surface temperatures for 185 549 lakes in the conterminous United States estimated using deep learning (1980–2020), Limnol. Oceanogr. Lett., 7, 287–301, https://doi.org/10.1002/lol2.10249, 2022.
Willard, J. D., Jia, X. W., Xu, S. M., Steinbach, M., and Kumar, V.: Integrating scientific knowledge with machine learning for engineering and environmental systems, ACM Comput. Surv., 55, 1–37, https://doi.org/10.1145/3514228, 2023.
Woolway, R. I., Jones, I. D., Hamilton, D. P., Maberly, S. C., Muraoka, K., Read, J. S., Smyth, R. L., and Winslow, L. A.: Automated calculation of surface-energy fluxes with high-frequency lake-buoy data, Environ. Model. Softw., 70, 191–198, https://doi.org/10.1016/j.envsoft.2015.04.013, 2015.
Woolway, R. I., Kraemer, B. M., Lenters, J. D., Merchant, C. J., O'Reilly, C. M., and Sharma, S.: Global lake responses to climate change, Nat. Rev. Earth Environ., 1, 388–403, https://doi.org/10.1038/s43017-020-0067-5, 2020.
Woolway, R. I., Tong, Y., Feng, L., Zhao, G., Dinh, D. A., Shi, H. R., Zhang, Y. L., and Shi, K.: Multivariate extremes in lakes, Nat. Commun., 15, 4559, https://doi.org/10.1038/s41467-024-49012-7, 2024.
Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M.: TimesNet: temporal 2-D-variation modelling for general time-series analysis, arXiv [preprint], https://doi.org/10.48550/arXiv.2210.02186, 2022.
Xu, L. J., Liu, H. Z., Du, Q., and Wang, L.: Evaluation of the WRF-lake model over a highland freshwater lake in southwest China, J. Geophys. Res.-Atmos., 121, 13989–14005, https://doi.org/10.1002/2016JD025396, 2016.
Xu, T. F. and Liang, F.: Machine learning for hydrologic sciences: an introductory overview, WIREs Water, 8, e1533, https://doi.org/10.1002/wat2.1533, 2021.
Yan, X., Xia, Y. Q., Ti, C. P., Shan, J., Wu, Y. H., and Yan, X. Y.: Thirty years of experience in water-pollution control in Taihu Lake: a review, Sci. Total Environ., 914, 169821, https://doi.org/10.1016/j.scitotenv.2023.169821, 2024.
Yang, C., Yang, P., Geng, J., Yin, H., and Chen, K.: Sediment internal nutrient loading in the most polluted area of a shallow eutrophic lake (Lake Chaohu, China) and its contribution to lake eutrophication, Environ. Pollut., 262, 114292, https://doi.org/10.1016/j.envpol.2020.114292, 2020.
Zhang, Y. L., Qin, B. Q., Zhu, G. W., Shi, K., and Zhou, Y. Q.: Profound changes in the physical environment of Lake Taihu from 25 years of long-term observations: implications for algal-bloom outbreaks and aquatic-macrophyte loss, Water Resour. Res., 54, 4319–4331, https://doi.org/10.1029/2017WR022401, 2018.
Zhang, Z., Zhang, M., Cao, C., Wang, W., Xiao, W., Xie, C., Chu, H., Wang, J., Zhao, J., Jia, L., Liu, Q., Huang, W., Zhang, W., Lu, Y., Xie, Y., Wang, Y., Pu, Y., Hu, Y., Chen, Z., Qin, Z., and Lee, X.: A dataset of microclimate and radiation and energy fluxes from the Lake Taihu eddy flux network, Earth Syst. Sci. Data, 12, 2635–2645, https://doi.org/10.5194/essd-12-2635-2020, 2020b.
Zhang, Z., Zhang, M., Cao, C., Wang, W., Xiao, W., Xie, C., Chu, H., Wang, J., Zhao, J., Jia, L., Liu, Q., Huang, W., Zhang, W., Lu, Y., Xie, Y., Wang, Y., Pu, Y., Hu, Y., Chen, Z., Qin, Z., and Lee, X.: A dataset of microclimate and radiation and energy fluxes from the Lake Taihu Eddy Flux Network, V2, Harvard Dataverse [data set], https://doi.org/10.7910/DVN/HEWCWM, 2020c.
Zhang, C., Bengio, S., Hardt, M., Recht, B., and Vinyals, O.: Understanding deep learning (still) requires rethinking generalization. Commun. ACM, 64, 107–115, https://doi.org/10.1145/3446776, 2021.
Zhong, L. J., Lei, H. M., and Yang, J. J.: Development of a distributed physics-informed deep-learning hydrological model for data-scarce regions, Water Resour. Res., 60, e2023WR036333, https://doi.org/10.1029/2023WR036333, 2024.
Zhong, W., Yu, N., and Ai, C. Y.: Applying big-data-based deep-learning system to intrusion detection, Big Data Min. Anal., 3, 181–195, https://doi.org/10.26599/BDMA.2020.9020003, 2020.
Short summary
This study introduces HyLake, a hybrid lake model that embeds a deep-learning surrogate for the water temperature module within a process-based backbone. HyLake simulates lake surface temperature and the latent and sensible heat fluxes in Lake Taihu more accurately than traditional process-based models and other hybrid experiments across different forcing datasets. The proposed coupling strategy provides a reliable tool for quantifying the impacts of climate change on aquatic ecosystems.
This study introduces HyLake, a hybrid lake model that embeds a deep-learning surrogate for the...