High climatological cloud cover limits its response to aerosols in ICON-HAM

Abstract. Marine low-level clouds substantially cool the climate and are sensitive to aerosols. Observations suggest strong cooling from cloud fraction (CF) adjustments, yet global climate models (GCMs) may underestimate this process. We apply explainable machine-learning with SHapley Additive exPlanations (SHAP) to the ICOsahedral Nonhydrostatic atmosphere model coupled with the Hamburg Aerosol Module (ICON-HAM) to quantify CF sensitivity to cloud droplet number concentration (N_d). We analyze six experiments combining two cloud cover parameterizations, an RH-only scheme (CC–RH) and a cloud-water-dependent scheme (CC–RH–LWC), with three prescribed lower bounds for N_d (N_d,min = 10, 40, 100 cm^-3). The lnN_d–CF relationships in ICON–HAM are more nonlinear than in satellite observations and exhibit saturation. We quantify sensitivities using piecewise linear regression (PLR) separating low- and high-N_d regimes. Sensitivities are stronger in the low-N_d regime, while inter-scheme and inter-N_d,min differences are negligible at high N_d. Unexpectedly, CC-RH-LWC shows weaker sensitivity than CC-RH at high N_d,min, despite explicit CF–cloud water coupling. We attribute this to a "headroom effect'': higher N_d,min suppresses autoconversion and enhances liquid water path in both schemes, but CC-RH-LWC converts this into higher mean CF, limiting headroom for aerosol-induced CF increases. These findings are robust across three PLR breakpoint strategies. Our results demonstrate that GCM CF responses are state-dependent and strongly influenced by model configuration choices, which can pre-saturate cloud cover responses and mask true CF adjustment magnitudes. We suggest that model–observation comparisons should account for baseline mean CF to avoid misinterpretation.