1179: Machine learning-based parametrisations and analysis for the ICON model (ICON-ML)

Principal investigator: Veronika Eyring

DLR, Institut für Physik der Atmosphäre (Community project)

Project abstract

Report 7/2021 to 6/2022
Report 7/2022 to 6/2023
Report 7/2023 to 6/2024
Report 7/2024 to 6/2025
Report 7/2025 to 6/2026

Publications

• DOI: 10.1038/s41598-025-29155-3, A. Grundner et al., Reduced cloud cover errors in a hybrid AI-climate model through equation discovery and automatic tuning, Scientific Reports 15.43836 (2025).
• DOI: 10.1088/3049-4753/ae4981, Pastori et al., Quantum neural networks for cloud cover parameterizations in climate models, Machine Learning: Earth, 1, 2 (2025)
• DOI: 10.1029/2024JH000501, Hafner et al., Interpretable Machine Learning-Based Radiation Emulation for ICON, JGR: Machine Learning and computation, 2, e2024JH000501 (2025)
• DOI: 10.22541/essoar.176676912.24375190/v1, Klamt et al., A Machine Learning-based Planetary Boundary Layer Height Scheme for ICON-A Learned from Vertically Highly Resolved Simulations, ESS Open Archive (2025)
• DOI: 10.48550/arXiv.2510.08107, Heuer et al., Beyond the Training Data: Confidence-Guided Mixing of Parameterizations in a Hybrid AI-Climate Model, arXiv (2025)
• DOI: 10.1017/eds.2025.10016, Sarauer et al., A physics-informed machine learning parameterization for cloud microphysics in ICON, Environmental Data Science, 4, e40 (2025)
• DOI: 10.48550/arXiv.2510.05963, Hafner et al., Representing Subgrid-Scale Cloud Effects in a Radiation Parameterization using Machine Learning: MLe-radiation v1.0, arXiv (2025)
• DOI: 10.5194/gmd-2024-236, Schlund, M., et al., Advanced climate model evaluation with ESMValTool v2.11.0 using parallel, out-of-core, and distributed computing. Submitted to GMD
• DOI: 10.22541/essoar.173169996.65100750/v1, Hafner, K, Iglesias-Suarez F., ​Shamekh S., Gentine P., Giorgetta M. A., Pincus R., Eyring V., Interpretable Machine Learning-based Radiation Emulation for ICON​, submitted to JGR-MLC 10/2024, ESSOpenArchive preprint
• DOI: 10.1029/2024MS004272, Behrens, G., Beucler, T., Iglesias-Suarez, F., Yu, S., Gentine, P., Schwabe, M. and Eyring, V. (2025). Simulating atmospheric processes in Earth system models and quantifying uncertainties with deep learning multi-member and stochastic parameterizations. Journal of Advances in Modeling Earth Systems, 17, e2024MS004272
• DOI: 10.1029/2023MS003763, @article{https://doi.org/10.1029/2023MS003763, author = {Grundner, Arthur and Beucler, Tom and Gentine, Pierre and Eyring, Veronika}, title = {Data-Driven Equation Discovery of a Cloud Cover Parameterization}, journal = {Journal of Advances in Modeling Earth Systems}, volume = {16}, number = {3}, pages = {e2023MS003763}, keywords = {symbolic regression, cloud fraction, cloud cover, parameterization, Pareto frontier}, doi = {https://doi.org/10.1029/2023MS003763}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2023MS003763}, eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS003763}, note = {e2023MS003763 2023MS003763}, abstract = {Abstract A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks (NNs) can achieve state-of-the-art performance within their training distribution, they can make unreliable predictions outside of it. Additionally, they often require post-hoc tools for interpretation. To avoid these limitations, we combine symbolic regression, sequential feature selection, and physical constraints in a hierarchical modeling framework. This framework allows us to discover new equations diagnosing cloud cover from coarse-grained variables of global storm-resolving model simulations. These analytical equations are interpretable by construction and easily transferable to other grids or climate models. Our best equation balances performance and complexity, achieving a performance comparable to that of NNs (R2 = 0.94) while remaining simple (with only 11 trainable parameters). It reproduces cloud cover distributions more accurately than the Xu-Randall scheme across all cloud regimes (Hellinger distances < 0.09), and matches NNs in condensate-rich regimes. When applied and fine-tuned to the ERA5 reanalysis, the equation exhibits superior transferability to new data compared to all other optimal cloud cover schemes. Our findings demonstrate the effectiveness of symbolic regression in discovering interpretable, physically-consistent, and nonlinear equations to parameterize cloud cover.}, year = {2024} }
• DOI: ​https://doi.org/10.1029/2024MS004398, Heuer, H., Schwabe, M., Gentine, P., Giorgetta, M. A., Eyring, V. (2024), Interpretable multiscale Machine-Learning-based Parameterizations of Convection for ICON, Journal of Advances in Modeling Earth Systems
• DOI: 10.1029/2023JD039202, @article{Iglesias-Suarez2024, author = {Iglesias-Suarez, Fernando and Gentine, Pierre and Solino-Fernandez, Breixo and Beucler, Tom and Pritchard, Michael and Runge, Jakob and Eyring, Veronika}, title = {Causally-Informed Deep Learning to Improve Climate Models and Projections}, journal = {Journal of Geophysical Research: Atmospheres}, volume = {129}, number = {4}, pages = {e2023JD039202}, keywords = {climate modeling, causal discovery, deep learning, subgrid parameterization, convection}, doi = {10.1029/2023JD039202}, year = {2024} }
• DOI: 10.5194/egusphere-2024-2508, Bonnet, P., Pastori, L., Schwabe, M., Giorgetta, M. A., Iglesias-Suarez, F., and Eyring, V. (2024): Tuning a Climate Model with Machine-learning based Emulators and History Matching, EGUsphere [preprint]
• DOI: 10.48550/arXiv.2311.03251, @misc{heuer2024interpretable, title={Interpretable multiscale Machine Learning-Based Parameterizations of Convection for ICON}, author={Helge Heuer and Mierk Schwabe and Pierre Gentine and Marco A. Giorgetta and Veronika Eyring}, year={2024}, eprint={2311.03251}, archivePrefix={arXiv}, primaryClass={physics.ao-ph} }
• DOI: 10.1029/2023MS003763, @article{https://doi.org/10.1029/2023MS003763, author = {Grundner, Arthur and Beucler, Tom and Gentine, Pierre and Eyring, Veronika}, title = {Data-Driven Equation Discovery of a Cloud Cover Parameterization}, journal = {Journal of Advances in Modeling Earth Systems}, volume = {16}, number = {3}, pages = {e2023MS003763}, keywords = {symbolic regression, cloud fraction, cloud cover, parameterization, Pareto frontier}, doi = {https://doi.org/10.1029/2023MS003763}, url = {https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2023MS003763}, eprint = {https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS003763}, note = {e2023MS003763 2023MS003763}, abstract = {Abstract A promising method for improving the representation of clouds in climate models, and hence climate projections, is to develop machine learning-based parameterizations using output from global storm-resolving models. While neural networks (NNs) can achieve state-of-the-art performance within their training distribution, they can make unreliable predictions outside of it. Additionally, they often require post-hoc tools for interpretation. To avoid these limitations, we combine symbolic regression, sequential feature selection, and physical constraints in a hierarchical modeling framework. This framework allows us to discover new equations diagnosing cloud cover from coarse-grained variables of global storm-resolving model simulations. These analytical equations are interpretable by construction and easily transferable to other grids or climate models. Our best equation balances performance and complexity, achieving a performance comparable to that of NNs (R2 = 0.94) while remaining simple (with only 11 trainable parameters). It reproduces cloud cover distributions more accurately than the Xu-Randall scheme across all cloud regimes (Hellinger distances < 0.09), and matches NNs in condensate-rich regimes. When applied and fine-tuned to the ERA5 reanalysis, the equation exhibits superior transferability to new data compared to all other optimal cloud cover schemes. Our findings demonstrate the effectiveness of symbolic regression in discovering interpretable, physically-consistent, and nonlinear equations to parameterize cloud cover.}, year = {2024} }
• DOI: 10.1029/2023JD039202, @article{Iglesias-Suarez2024, author = {Iglesias-Suarez, Fernando and Gentine, Pierre and Solino-Fernandez, Breixo and Beucler, Tom and Pritchard, Michael and Runge, Jakob and Eyring, Veronika}, title = {Causally-Informed Deep Learning to Improve Climate Models and Projections}, journal = {Journal of Geophysical Research: Atmospheres}, volume = {129}, number = {4}, pages = {e2023JD039202}, keywords = {climate modeling, causal discovery, deep learning, subgrid parameterization, convection}, doi = {10.1029/2023JD039202}, year = {2024} }
• @article{sarauer2024microphysics, title={Physics-informed Machine Learning-Based Cloud Microphysics Parameterization for Earth System Models}, author={Sarauer, E. and Schwabe, M. and Lauer, A. and Stier, P. and Weiss, P. and Eyring, V.}, journal={Accepted to ICLR}, year={2024} }
• DOI: 10.5194/essd-2023-424, @Article{Kaps23_CCClim_paper, AUTHOR = {Kaps, A. and Lauer, A. and Kazeroni, R. and Stengel, M. and Eyring, V.}, TITLE = {Characterizing clouds with the CCClim dataset, a machine learning cloud class climatology}, JOURNAL = {Earth System Science Data Discussions}, VOLUME = {2023}, YEAR = {2023}, PAGES = {1--26}, DOI = {10.5194/essd-2023-424}, }
• DOI: 10.5194/gmd-16-315-2023, Schlund, Manuel, Birgit Hassler, Axel Lauer, Bouwe Andela, Patrick Joeckel, Saskia Loosveldt Tomas, Rémi Kazeroni et al. "Evaluation of Native Earth System Model Output with ESMValTool." In AGU Fall Meeting Abstracts, vol. 2022, pp. GC42L-0856. 2022. https://doi.org/10.5194/gmd-16-315-2023
• DOI: 10.1029/2022ms003130, Behrens, G., Beucler, T., Gentine, P., Iglesias-Suarez, F., Pritchard, M., & Eyring, V. (2022). Non-linear dimensionality reduction with a variational encoder decoder to understand convective processes in climate models. Journal of Advances in Modeling Earth Systems, 14, e2022MS003130. https://doi.org/10.1029/2022MS003130
• DOI: 10.1029/2021ms002959, Grundner, A., Beucler, T., Gentine, P., Iglesias-Suarez, F., Giorgetta, M. A., & Eyring, V. (2022). Deep learning based cloud cover parameterization for ICON. Journal of Advances in Modeling Earth Systems, 14, e2021MS002959. https://doi.org/10.1029/2021MS002959
• DOI: 10.1109/TGRS.2023.3237008, A. Kaps, A. Lauer, G. Camps-Valls, P. Gentine, L. Gómez-Chova and V. Eyring, "Machine-Learned Cloud Classes From Satellite Data for Process-Oriented Climate Model Evaluation," in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-15, 2023, Art no. 4100515, doi: 10.1109/TGRS.2023.3237008.
• Kaps, A., Lauer, A., Camps-Valls, G., Gentine, P., Gómez-Chova, L., Eyring, V., "Machine-learned cloud classes from satellite data for process-oriented climate model evaluation", IEEE Trans. Geosci. Rem. Sens., to be uploaded on arXiv e-prints, 2022
• DOI: 10.48550/arXiv.2112.11317, Grundner, A., Beucler, T., Iglesias-Suarez, F., Gentine, P., Giorgetta, M. A., and Eyring, V., “Deep Learning Based Cloud Cover Parameterization for ICON”, arXiv e-prints, 2021
• DOI: 10.48550/arXiv.2204.08708, Behrens, G., Beucler, T., Gentine, P., Iglesias-Suarez, F., Pritchard, M., and Eyring, V., “Non-Linear Dimensionality Reduction with a Variational Autoencoder Decoder to Understand Convective Processes in Climate Models”, arXiv e-prints, 2022