Abstract Global storm resolving models (GSRMs) represent the next generation of global climate models. One of them is a 5‐km Icosahedral Nonhydrostatic Weather and Climate Model (ICON). Its high resolution means that parameterizations of convection and clouds, including subgrid‐scale clouds, are omitted, relying on explicit simulation but necessarily utilizing microphysics and turbulence parameterizations. Standard‐resolution (10–100 km) models, which use convection and cloud parameterizations, have substantial cloud biases over the Southern Ocean (SO), adversely affecting radiation and sea surface temperature. The SO is dominated by low clouds, which cannot be observed accurately from space due to overlapping clouds, attenuation, and ground clutter. We evaluated SO clouds in ICON and the ERA5 and MERRA‐2 reanalyzes using approximately 2400 days of lidar observations and 2300 radiosonde profiles from 31 voyages and a Macquarie Island station during 2010–2021, compared to the model and reanalyzes using a ground‐based lidar simulator. We found that ICON and the reanalyzes underestimate the total cloud fraction by about 10% and 20%, respectively. ICON and ERA5 overestimate the cloud occurrence peak at about 500 m, associated with underestimated lower tropospheric stability and overestimated lifting condensation level. The reanalyzes strongly underestimate fog and very low‐level clouds, and MERRA‐2 underestimates cloud occurrence at almost all heights. Outgoing shortwave radiation is overestimated in MERRA‐2, implying a “too few, too bright” cloud problem. SO cloud and fog biases are a substantial issue in the analyzed model and reanalyzes and result in shortwave and longwave radiation biases.