Reduced cloud cover errors in a hybrid AI-climate model through equation discovery and automatic tuning

Hybrid Earth system models (ESMs) that combine physical laws with machine learning (ML) demonstrate great potential to reduce uncertainties in climate projections, particularly for subgrid processes like clouds. However, widespread adoption faces critical challenges: deep learning "black boxes" often lack interpretability and physical consistency, and coupling them with standard ESMs remains difficult due to stability issues and the need for complex re-calibration. 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, into the ICON atmospheric climate model. We refer to this hybrid configuration, which retains the interpretability and efficiency of the traditional model, as ICON-A-MLe. Second, we address the coupling and tuning bottleneck by introducing an automated, gradient-free calibration procedure based on the Nelder-Mead algorithm. This method efficiently calibrates ICON-A-MLe without requiring differentiable physical components, making it easily extendable to other ESMs. Our results show that the tuned ICON-A-MLe substantially reduces long-standing biases. Specifically, it reduces cloud cover errors over the Southern Ocean by 75% and in subtropical stratocumulus regions by 44%. These improvements also lead to a better top-of-atmosphere radiative budget. Crucially, the model demonstrates strong generalization capabilities: it remains robust and physically consistent under significantly warmer climate scenarios. These results demonstrate that interpretable machine-learned parameterizations, paired with practical tuning, can efficiently and transparently strengthen ESM fidelity.