Reduced Cloud Cover Errors in a Hybrid AI-Climate Model Through Equation Discovery And Automatic Tuning

TL;DR

This work incorporates a physically consistent cloud cover parameterization—derived from storm-resolving simulations via symbolic regression, preserving interpretability while enhancing accuracy—into the ICON global atmospheric model and applies the gradient-free Nelder–Mead optimizer to automatically recalibrate the hybrid model.

Abstract

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical consistency, and smooth integration into ESMs. Here, a two-step method is presented to improve a climate model with data-driven parameterizations. First, we incorporate a physically consistent cloud cover parameterization -- derived from storm-resolving simulations via symbolic regression, preserving interpretability while enhancing accuracy -- into the ICON global atmospheric model. Second, we apply the gradient-free Nelder-Mead optimizer to automatically recalibrate the hybrid model against Earth observations, tuning in nested stages (2-, 7-, 30- and 365-day runs) to ensure stability and tractability. The tuned hybrid model substantially reduces long-standing biases in cloud cover -- particularly over the Southern Ocean (by 75%) and subtropical stratocumulus regions (by 44%) -- and remains robust under +4K surface warming. These results demonstrate that interpretable machine-learned parameterizations, paired with practical tuning, can efficiently and transparently strengthen ESM fidelity.

Figures (16)

• Figure 1: The automatic tuning pipeline of ICON-A-MLe, i.e., the ICON atmospheric climate model including our data-driven cloud cover equation (equation (\ref{['data_driven_eq']})). The only manual step involves selecting the climate metrics to be optimized, such as globally averaged cloud cover, and determining which tunable parameters should be adjusted. Reasonable target ranges for these metrics are derived from observational and reanalysis data. The core of the tuning pipeline consists of the Nelder-Mead algorithm iteratively searching for a setting of the tunable parameters that enables ICON-A-MLe simulations to optimize all specified metrics. The length of these simulations and the strictness of evaluating the metrics increases with the number of iterations. The underlying strategy leverages the fact that some climate metrics exhibit rapid responses to parameter changes, allowing for efficient feedback and early adjustments. Finally a historical AMIP simulation is benchmarked to Earth observations with the ESMValTool
• Figure 2: A qualitative evaluation of 20-year ICON-A-MLe simulations using parameter settings extracted at three different stages of the tuning pipeline. The panels display radiative measures computed at the top of the atmosphere, illustrating the model's progression through the tuning process. Circular arrows denote intermediate tuning steps involving week- and month-long ICON-A-MLe simulations. Observational references are derived from MERRA2 gelaro2017modern, CERES loeb2018clouds, and ISCCP zhang2023global. The solid gray lines represent historical CMIP6 model simulations eyring2016overview, providing a benchmark for comparison
• Figure 3: Biases in three key climate metrics, temporally averaged over 20-year simulations (1979–1999), for our automatically tuned (at.) ICON-A-MLe (first row) and ICON-A models (second row), and a manually tuned (mt.) ICON-A reference (third row). Root-mean-square errors (RMSEs) are computed after remapping the data onto a horizontal grid with nearly identical grid cell sizes. While the ICON-A panels utilize the full range of each colorbar (otherwise indicated by black vertical lines in the colorbars), the values from the ICON-A-MLe model are confined to the green rectangles. To enhance the robustness of our observational reference (OBS), we take an average across multiple observational cloud cover datasets (CLARA-AVHRR CLARA_AVHRR, ESA CCI stengel2017cloud, MODIS platnick2003modis, PATMOS heidinger2014pathfinder), as well as two reanalysis products (MERRA2 gelaro2017modern, ERA5 hersbach2020era5). For radiative metrics, we use ESA CCI stengel2017cloud (1982–1999) and ISCCP zhang2023global (1984–1999), as these observations are among the most reliable spanning the majority of the simulated 1979–1999 period. The plots in the panels were created by visualizing the output from ESMValTool (v2.12.0, https://www.esmvaltool.org/) using the Psyplot software (v1.5.1, https://psyplot.github.io/) psyplot for final customization
• Figure 4: Evaluation of ICON-A-MLe* and ICON-A* 20-year simulations as in Fig. \ref{['fig:iconml_eval']}
• Figure 5: Vertical profiles of the contributions from each term ($I_1$, $I_2$, $I_3$) of the data-driven cloud cover equation (\ref{['data_driven_eq']}) to the total cloud fraction on each height level. Values are annual means from an $\text{ICON-A-MLe}$ simulation (1979–1980), spatially averaged globally, as well as over two distinct regions. The 'Stratocumulus' regions combine the west coasts of Chile/Peru, Namibia/Angola, California, Morocco, and Australia