Grundner et al. (2025) Reduced cloud cover errors in a hybrid AI-climate model through equation discovery and automatic tuning

Identification

• Journal: Scientific Reports
• Year: 2025
• Date: 2025-12-13
• Authors: Arthur Grundner, Tom Beucler, Julien Savre, Axel Lauer, Manuel Schlund, Veronika Eyring
• DOI: 10.1038/s41598-025-29155-3

Research Groups

• Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany
• Faculty of Geosciences and Environment, University of Lausanne, Lausanne, Switzerland
• Expertise Center for Climate Extremes, University of Lausanne, Lausanne, Switzerland
• University of Bremen, Institute of Environmental Physics (IUP), Bremen, Germany

Short Summary

This study presents a two-step method combining symbolic regression for an interpretable cloud cover parameterization and an automatic tuning pipeline to improve a hybrid AI-climate model. The approach significantly reduces cloud cover biases in the ICON global atmospheric model, particularly over the Southern Ocean and subtropical stratocumulus regions, while maintaining physical consistency and robustness under warming scenarios.

Objective

• To develop and demonstrate a two-step method—incorporating a physically consistent, interpretable cloud cover parameterization derived from symbolic regression into a global climate model and automatically tuning the hybrid model against Earth observations—to reduce cloud cover errors and enhance the fidelity and robustness of Earth System Models.

Study Configuration

• Spatial Scale: Global atmospheric model (ICON 2.6.4) with a horizontal resolution of 80 km and a vertical grid of 47 levels extending up to 83 km.
• Temporal Scale: Automatic tuning performed in nested stages (2-day, 7-day, 30-day, and 365-day simulations). Model evaluation conducted over 20-year historical AMIP simulations (1979–1999) and a 20-year +4 K surface warming scenario (last 10 years evaluated). Model time step of 10 minutes, radiation time step of 2 hours.

Methodology and Data

• Models used:
  • ICON 2.6.4 (ICOsahedral Non-hydrostatic) global atmospheric model (ICON-A).
  • Data-driven cloud cover parameterization (equation (3) from Grundner et al., 2024), derived via symbolic regression.
  • Nelder–Mead optimization algorithm for automatic tuning.
  • Earth System Model Evaluation Tool (ESMValTool v2.12.0) for evaluation.
  • Psyplot software (v1.5.1) for visualization.
• Data sources:
  • Observational/Reanalysis for tuning and evaluation: MERRA2, CERES, ISCCP, CLARA-AVHRR, ESA CCI, MODIS, PATMOS, ERA5, GPCP-SG.
  • Training data for symbolic regression: Coarse-grained data from storm-resolving DYAMOND simulations.
  • Benchmark comparison: Historical CMIP6 model simulations.

Main Results

• The tuned hybrid model (ICON-A-MLe) substantially reduces long-standing biases in total cloud cover, achieving a global Root Mean Square Error (RMSE) reduction of 15.4% compared to the manually tuned ICON-A.
• Specific regional improvements in total cloud cover RMSE include a 75.8% reduction over the Southern Ocean and reductions ranging from 24.1% to 54.2% over subtropical stratocumulus regions (e.g., west coasts of Chile/Peru, Namibia/Angola, California, Morocco, Australia).
• These cloud cover improvements lead to consistently lower RMSE values for outgoing longwave (LW) and reflected shortwave (SW) radiation compared to both automatically and manually tuned ICON-A models.
• A "scheme-swap" experiment quantifies the direct contribution of the data-driven cloud scheme to error reduction, showing average RMSE reductions of 1.84% for total cloud cover, 0.21 W/m² for LW radiation, and 1.27 W/m² for SW radiation.
• The physical interpretability of the data-driven equation reveals that the I1 term improves Southern Ocean cloudiness (temperature dependence), while the I2 term enhances subtropical stratocumulus decks (vertical gradient of relative humidity).
• Under a +4 K surface warming scenario, ICON-A-MLe exhibits physically plausible changes in cloud top heights (rise), low-level cloud cover (decrease at low-mid latitudes, increase in Arctic), radiative effects, and precipitation, with a global total cloud cover decrease of 1.65%.
• The automatic tuning process for ICON-A-MLe required approximately 400 node-hours, demonstrating computational efficiency compared to the 600 node-hours for tuning the ICON-A baseline.

Contributions

• Presents the first application of a machine-learning based parameterization, derived via symbolic regression, that significantly reduces persistent cloud cover biases in a global climate simulation.
• Introduces a novel, simple, fast, and extensible automatic tuning pipeline for hybrid AI-climate models, utilizing the Nelder–Mead algorithm with nested simulation durations to optimize computational resources.
• Demonstrates the strong online skill of an offline-trained, data-driven, physically constrained, and interpretable cloud cover parameterization, which introduces no additional computational burden.
• Provides a quantitative assessment of the direct contribution of the new cloud scheme to error reduction through a "scheme-swap" experiment.
• Leverages the interpretability of the symbolic regression-derived equation to identify and validate the physical drivers behind improved cloud representation in specific climate regimes.
• Confirms the robustness and physical plausibility of the hybrid model's response to a +4 K warming scenario, a crucial step for reliable climate projections.
• Establishes a practical, computationally efficient, and interpretable framework for improving climate models using data-driven methods.

Funding

• European Research Council (ERC) Synergy Grant “Understanding and modeling the Earth System with Machine Learning (USMILE)” (Horizon 2020 research and innovation programme, Grant agreement No. 855187).
• Horizon Europe project “Artificial Intelligence for enhanced representation of processes and extremes in Earth System Models (AI4PEX)” (Grant agreement ID: 101137682).
• AIPEX, funded by the Swiss State Secretariat for Education, Research and Innovation (SERI, Grant No. 23.00546).
• Deutsche Forschungsgemeinschaft (DFG) through the Gottfried Wilhelm Leibniz Prize awarded to V.E. (reference no. EY 22/2-1).

Citation

@article{Grundner2025Reduced,
  author = {Grundner, Arthur and Beucler, Tom and Savre, Julien and Lauer, Axel and Schlund, Manuel and Eyring, Veronika},
  title = {Reduced cloud cover errors in a hybrid AI-climate model through equation discovery and automatic tuning},
  journal = {Scientific Reports},
  year = {2025},
  doi = {10.1038/s41598-025-29155-3},
  url = {https://doi.org/10.1038/s41598-025-29155-3}
}