Articles | Volume 19, issue 18
https://doi.org/10.5194/gmd-19-8801-2026
© 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/gmd-19-8801-2026
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Parameter estimation for land-surface models using Neural Physics
Ruiyue Huang
Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ London, UK
Claire E. Heaney
Department of Earth Science and Engineering, Imperial College London, SW7 2AZ London, UK
Imperial-X, Imperial College London, W12 7SL London, UK
Maarten van Reeuwijk
CORRESPONDING AUTHOR
Department of Civil and Environmental Engineering, Imperial College London, SW7 2AZ London, UK
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Cited articles
Arsenault, K. R., Nearing, G. S., Wang, S., Yatheendradas, S., and Peters-Lidard, C. D.: Parameter Sensitivity of the Noah-MP Land Surface Model with Dynamic Vegetation, J. Hydrometeorol., 19, 815–830, https://doi.org/10.1175/jhm-d-17-0205.1, 2018. a
Bezgin, D. A., Buhendwa, A. B., and Adams, N. A.: JAX-Fluids: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows, Comput. Phys. Commun., 282, 108527, https://doi.org/10.1016/j.cpc.2022.108527, 2023. a
Bradle, B.: A friendly introduction to numerical analysis, Pearson Education, ISBN 8131709426, 2007. a
Brutsaert, W.: Hydrology: An Introduction, Cambridge University Press, ISBN 978-0521824798, 2005. a
Carslaw, H. S. and Jaeger, J. C.: Conduction of Heat in Solids, Oxford University Press, USA, 81 pp., ISBN 0198533039, 1959. a
Cerebras: CS-3 System: Revolutionary AI Infrastructure, https://www.cerebras.ai/system (last access: 3 March 2026), 2026. a
Chaney, N. W., Herman, J. D., Ek, M. B., and Wood, E. F.: Deriving global parameter estimates for the Noah land surface model using FLUXNET and machine learning, J. Geophys. Res-Atmos., 121, 13218–13235, https://doi.org/10.1002/2016JD024821, 2016. a
Chen, B., Heaney, C. E., Gomes, J. L. M. A., Matar, O. K., and Pain, C. C.: Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries, Comput. Method. Appl. M., 426, 116974, https://doi.org/10.1016/j.cma.2024.116974, 2024. a, b
Chen, B., Nadimy, A., Heaney, C. E., Sharifian, M. K., Estrem, L. V., Nicotina, L., Hilberts, A., and Pain, C.: Solving the Discretised Shallow Water Equations Using Neural Networks, Adv. Water Resour., 197, 104903, https://doi.org/10.1016/j.advwatres.2025.104903, 2025. a
Chen, B., Heaney, C. E., and Pain, C. C.: Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics, Comput. Fluids, 308, 106981, https://doi.org/10.1016/j.compfluid.2026.106981, 2026. a, b, c, d
Chow, W. T. L., Volo, T. J., Vivoni, E. R., Jenerette, G. D., and Ruddell, B. L.: Seasonal dynamics of a suburban energy balance in Phoenix, Arizona, Int. J. Climatol., 34, 3863–3880, https://doi.org/10.1002/joc.3947, 2014. a, b, c
Deck, K., Braghiere, R. K., Renchon, A. A., Sloan, J., Bozzola, G., Speer, E., Ben Mackay, J., Reddy, T., Phan, K., Gagné-Landmann, A. L., Li, Y., Yatunin, D., Charbonneau, A., Efrat-Henrici, N., Bach, E., Ma, S., Gentine, P., Frankenberg, C., Bloom, A. A., Wang, Y., Longo, M., and Schneider, T.: ClimaLand: A Land Surface Model Designed to Enable Data-Driven Parameterizations, J. Adv. Model. Earth Sy., 18, e2025MS005118, https://doi.org/10.1029/2025MS005118, 2026. a
Dukes, J. S., Xu, C., Liao, C., Novick, K. A., Phillips, R. P., Beverly, D. P., Fang, Y., Jacobs, E. M., McAdam, S. A. M., Paudel, I., Rimer, I. M., and Robbins, Z. J.: Improving the representation of plant water stress and water use in Earth System Models, New Phytol., 249, 39–55, https://doi.org/10.1111/nph.70687, 2026. a, b
ElGhawi, R., Kraft, B., Reimers, C., Reichstein, M., Körner, M., Gentine, P., and Winkler, A. J.: Hybrid modeling of evapotranspiration: inferring stomatal and aerodynamic resistances using combined physics-based and machine learning, Environ. Res. Lett., 18, 034039, https://doi.org/10.1088/1748-9326/acbbe0, 2023. a
Fang, J. and Gentine, P.: Exploring Optimal Complexity for Water Stress Representation in Terrestrial Carbon Models: A Hybrid-Machine Learning Model Approach, J. Adv. Model. Earth Sy., 16, e2024MS004308, https://doi.org/10.1029/2024MS004308, 2024. a, b
Fer, I., Kelly, R., Moorcroft, P. R., Richardson, A. D., Cowdery, E. M., and Dietze, M. C.: Linking big models to big data: efficient ecosystem model calibration through Bayesian model emulation, Biogeosciences, 15, 5801–5830, https://doi.org/10.5194/bg-15-5801-2018, 2018. a
Fletcher, R.: Practical Methods of Optimization, second edn., Wiley & Sons, https://doi.org/10.1002/9781118723203, 1987. a, b
Graphcore: Designed for AI: Intelligence Processing Unit, Graphcore, https://www.graphcore.ai/products/ipu (last access: 3 March 2026), 2026. a
Greenbaum, A.: Iterative Methods for Solving Linear Systems, Society for Industrial and Applied Mathematics, https://doi.org/10.1137/1.9781611970937, 1997. a
Grimmond, C. S. B., Blackett, M., Best, M. J., Barlow, J., Baik, J.-J., Belcher, S. E., Bohnenstengel, S. I., Calmet, I., Chen, F., Dandou, A., Fortuniak, K., Gouvea, M. L., Hamdi, R., Hendry, M., Kawai, T., Kawamoto, Y., Kondo, H., Krayenhoff, E. S., Lee, S.-H., Loridan, T., Martilli, A., Masson, V., Miao, S., Oleson, K., Pigeon, G., Porson, A., Ryu, Y.-H., Salamanca, F., Shashua-Bar, L., Steeneveld, G.-J., Tombrou, M., Voogt, J., Young, D., and Zhang, N.: The International Urban Energy Balance Models Comparison Project: First Results from Phase 1, J. Appl. Meteorol. Clim., 49, 1268–1292, https://doi.org/10.1175/2010JAMC2354.1, 2010. a, b
Grimmond, C. S. B., Blackett, M., Best, M. J., Baik, J.-J., Belcher, S. E., Beringer, J., Bohnenstengel, S. I., Calmet, I., Chen, F., Coutts, A., Dandou, A., Fortuniak, K., Gouvea, M. L., Hamdi, R., Hendry, M., Kanda, M., Kawai, T., Kawamoto, Y., Kondo, H., Krayenhoff, E. S., Lee, S.-H., Loridan, T., Martilli, A., Masson, V., Miao, S., Oleson, K., Ooka, R., Pigeon, G., Porson, A., Ryu, Y.-H., Salamanca, F., Steeneveld, G., Tombrou, M., Voogt, J. A., Young, D. T., and Zhang, N.: Initial results from Phase 2 of the international urban energy balance model comparison, Int. J. Climatol., 31, 244–272, https://doi.org/10.1002/joc.2227, 2011. a, b
Hastings, W. K.: Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika, 57, 97–109, http://www.jstor.org/stable/2334940 (last access: 5 September 2026), 1970. a
Huang, R.: Inverse Modelling of the Surface Energy Balance using Machine Learning Libraries, Master's thesis, Imperial College London, 2024. a
Huang, R.: Solving land surface model using Neural Physics, Zenodo [code], https://doi.org/10.5281/zenodo.19344692, 2026. a
Jiang, P., Kidger, P., Bandai, T., Baldocchi, D., Liu, H., Xiao, Y., Zhang, Q., Wang, C. T., Steefel, C., and Chen, X.: JAX-CanVeg: A Differentiable Land Surface Model, Water Resour. Res., 61, e2024WR038116, https://doi.org/10.1029/2024WR038116, 2025. a
Jones, S., Mercado, L., Bruhn, D., Raoult, N., and Cox, P.: Night-time decline in plant respiration is consistent with substrate depletion, Commun. Earth Environ., 5, 148, https://doi.org/10.1038/s43247-024-01312-y, 2024. a
Kingma, D. P. and Ba, J.: Adam: A Method for Stochastic Optimization, in: 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7–9 May, 2015, Conference Track Proceedings, edited by: Bengio, Y. and LeCun, Y., https://doi.org/10.48550/arXiv.1412.6980, 2015. a
Krayenhoff, E. S. and Voogt, J. A.: A microscale three-dimensional urban energy balance model for studying surface temperatures, Bound.-Lay. Meteorol., 123, 433–461, 2007. a
Kuppel, S., Peylin, P., Maignan, F., Chevallier, F., Kiely, G., Montagnani, L., and Cescatti, A.: Model–data fusion across ecosystems: from multisite optimizations to global simulations, Geosci. Model Dev., 7, 2581–2597, https://doi.org/10.5194/gmd-7-2581-2014, 2014. a
Laloui, L. and Rotta Loria, A. F.: Chapter 3 – Heat and mass transfers in the context of energy geostructures, in: Analysis and Design of Energy Geostructures, edited by: Laloui, L. and Rotta Loria, A. F., Academic Press, pp. 69–135, https://doi.org/10.1016/B978-0-12-816223-1.00003-5, 2020. a
Lee, D.-I. and Lee, S.-H.: The Microscale Urban Surface Energy (MUSE) Model for Real Urban Application, Atmosphere, 11, https://doi.org/10.3390/atmos11121347, 2020. a
Li, Y., Heaney, C. E., Chen, B., Wilkinson, P. B. , Kuras, O., Herwanger, J. V., and Pain, C. C.: A differentiable framework for 3D anisotropic ERT inversion using Neural Physics and Latent Diffusion, submitted, 2026. a
Lipson, M., Grimmond, S., Best, M., Chow, W., Christen, A., Chrysoulakis, N., Coutts, A., Crawford, B., Earl, S., Evans, J., Fortuniak, K., Heusinkveld, B. G., Hong, J.-W., Hong, J., Järvi, L., Jo, S., Kim, Y.-H., Kotthaus, S., Lee, K., Masson, V., McFadden, J. P., Michels, O., Pawlak, W., Roth, M., Sugawara, H., Tapper, N., Velasco, E., and Ward, H. C.: Data for “Harmonized gap-filled dataset from 20 urban flux tower sites” for the Urban-PLUMBER project, Zenodo [data set], https://doi.org/10.5281/zenodo.7104984, 2022a. a, b
Lipson, M., Grimmond, S., Best, M., Chow, W. T. L., Christen, A., Chrysoulakis, N., Coutts, A., Crawford, B., Earl, S., Evans, J., Fortuniak, K., Heusinkveld, B. G., Hong, J.-W., Hong, J., Järvi, L., Jo, S., Kim, Y.-H., Kotthaus, S., Lee, K., Masson, V., McFadden, J. P., Michels, O., Pawlak, W., Roth, M., Sugawara, H., Tapper, N., Velasco, E., and Ward, H. C.: Harmonized gap-filled datasets from 20 urban flux tower sites, Earth Syst. Sci. Data, 14, 5157–5178, https://doi.org/10.5194/essd-14-5157-2022, 2022b. a, b, c
Lipson, M. J., Hart, M. A., and Thatcher, M.: Efficiently modelling urban heat storage: an interface conduction scheme in an urban land surface model (aTEB v2.0), Geosci. Model Dev., 10, 991–1007, https://doi.org/10.5194/gmd-10-991-2017, 2017. a, b
Lipson, M. J., Grimmond, S., Best, M., Abramowitz, G., Coutts, A., Tapper, N., Baik, J.-J., Beyers, M., Blunn, L., Boussetta, S., Bou-Zeid, E., De Kauwe, M. G., de Munck, C., Demuzere, M., Fatichi, S., Fortuniak, K., Han, B.-S., Hendry, M. A., Kikegawa, Y., Kondo, H., Lee, D.-I., Lee, S.-H., Lemonsu, A., Machado, T., Manoli, G., Martilli, A., Masson, V., McNorton, J., Meili, N., Meyer, D., Nice, K. A., Oleson, K. W., Park, S.-B., Roth, M., Schoetter, R., Simón-Moral, A., Steeneveld, G.-J., Sun, T., Takane, Y., Thatcher, M., Tsiringakis, A., Varentsov, M., Wang, C., Wang, Z.-H., and Pitman, A. J.: Evaluation of 30 urban land surface models in the Urban-PLUMBER project: Phase 1 results, Q. J. Roy. Meteorol. Soc., 150, 126–169, https://doi.org/10.1002/qj.4589, 2024. a, b, c, d, e, f
Massoud, E. C., Xu, C., Fisher, R. A., Knox, R. G., Walker, A. P., Serbin, S. P., Christoffersen, B. O., Holm, J. A., Kueppers, L. M., Ricciuto, D. M., Wei, L., Johnson, D. J., Chambers, J. Q., Koven, C. D., McDowell, N. G., and Vrugt, J. A.: Identification of key parameters controlling demographically structured vegetation dynamics in a land surface model: CLM4.5(FATES), Geosci. Model Dev., 12, 4133–4164, https://doi.org/10.5194/gmd-12-4133-2019, 2019. a
Nocedal, J. and Wright, S. J.: Numerical Optimization, 2nd edn., Springer, https://doi.org/10.1007/978-0-387-40065-5, 2006. a, b
Norouzi, S., Moldrup, P., Moseley, B., Robinson, D., Or, D., Hohenbrink, T. L., Minasny, B., Sadeghi, M., Arthur, E., Tuller, M., Greve, M. H., and de Jonge, L. W.: A differentiable hybrid modeling approach for learning soil water retention mechanisms from partial knowledge and data, J. Hydrol., 668, 135008, https://doi.org/10.1016/j.jhydrol.2026.135008, 2026. a
Oke, T. R.: Boundary layer climates, Routledge, ISBN 0-203-40721-0, 2002. a
Oke, T. R.: Urban climates, Cambridge University Press, https://doi.org/10.1017/9781139016476, 2017. a, b, c
Ouyang, W., Ye, L., Chai, Y., Ma, H., Chu, J., Peng, Y., and Zhang, C.: A differentiable, physics-based hydrological model and its evaluation for data-limited basins, J. Hydrol., 649, 132471, https://doi.org/10.1016/j.jhydrol.2024.132471, 2025. a
Phillips, T. R. F., Heaney, C. E., Chen, B., Buchan, A. G., and Pain, C. C.: Solving the Discretised Neutron Diffusion Equations Using Neural Networks, Int. J. Numer. Meth. Eng., 124, 4659–4686, https://doi.org/10.1002/nme.7321, 2023. a, b, c, d
Phillips, T. R. F., Heaney, C. E., Chen, B., Buchan, A. G., and Pain, C. C.: Solving the Discretised Boltzmann Transport Equations Using Neural Networks: Applications in Neutron Transport, arXiv [preprint], https://doi.org/10.48550/arXiv.2301.09991, 2024. a
Raoult, N., Douglas, N., MacBean, N., Kolassa, J., Quaife, T., Roberts, A., Rosie, F., Fer, I., Bacour, C., Dagon, K., Hawkins, L., Carvalhais, N., Cooper, E., Dietze, M., Gentine, P., Kaminski, T., Kennedy, D., Liddy, H., Moore, D., and Zobitz, J.: Parameter Estimation in Land Surface Models: Challenges and Opportunities with Data Assimilation and Machine Learning, ESS Open Archive, 2024, https://doi.org/10.22541/essoar.172838640.01153603/v1, 2024. a, b
Raoult, N. M., Jupp, T. E., Cox, P. M., and Luke, C. M.: Land-surface parameter optimisation using data assimilation techniques: the adJULES system V1.0, Geosci. Model Dev., 9, 2833–2852, https://doi.org/10.5194/gmd-9-2833-2016, 2016. a
Ren, Y., Gou, L., Xiao, M., Liu, Z. L., and Shen, C.: DMFS: differentiable modeling for frozen soil thermodynamic characteristics, Can. Geotech. J., 63, 1–19, https://doi.org/10.1139/cgj-2025-0364, 2026. a
Schmid, H., Cleugh, H., Grimmond, S., and Oke, T.: Spatial variability of energy fluxes in suburban terrain, Bound.-Lay. Meteorol., 54, 249–276, https://doi.org/10.1007/BF00183956, 1991. a
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., C., X., 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. a
Tian, W., Yu, H., Zhao, S., Cao, Y., Yi, W., Xu, J., and Nan, Z.: NoahPy: a differentiable Noah land surface model for simulating permafrost thermo-hydrology, Geosci. Model Dev., 19, 57–72, https://doi.org/10.5194/gmd-19-57-2026, 2026. a
Xue, T., Jiao, Y., Ba, T., Wang, J., Yang, J., See, S., Chen, B., Heaney, C. E., Pain, C. C., Kang, C. W., Mohamed, M. A. B., and Li, H.: NeuralFVM: Neural-physics-based Finite Volume Method for Turbulent Flows Using the k-ω Model, arXiv [preprint], 2603.21869, https://doi.org/10.48550/arXiv.2603.21869, 2026. a
Zhou, A., Hawkins, L., and Gentine, P.: Proof-of-concept: Using ChatGPT to Translate and Modernize an Earth System Model from Fortran to Python/JAX, arXiv [preprint], 2405.00018, https://doi.org/10.48550/arXiv.2405.00018, 2024. a
Zhu, W., Xu, K., Darve, E., and Beroza, G. C.: A general approach to seismic inversion with automatic differentiation, Comput. Geosci., 151, 104751, https://doi.org/10.1016/j.cageo.2021.104751, 2021. a
Short summary
This paper uses the Neural Physics approach to determine parameters of a simple land-surface model. We show that we can only obtain a reliable parameter estimation using soil temperature measurements at more than one depth, and that latent and sensible heat fluxes cannot be differentiated. We then apply the inverse model to real urban flux tower data and show that parameters, as well as various heat fluxes, can be reliably estimated using an observed value for the effective surface albedo.
This paper uses the Neural Physics approach to determine parameters of a simple land-surface...