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

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.