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The effect of clouds on climate remains the largest uncertainty in climate change predictions, due to the inability of global climate models (GCMs) to resolve essential small-scale cloud and convection processes. We compare preindustrial and quadrupled CO2 simulations between a conventional GCM in which convection is parameterized and a "superparameterized" model in which convection is explicitly simulated with a cloud-permitting model in each grid cell. We find that the global responses of the two models to increased CO2 are broadly similar: both simulate ice-free Arctic summers, wintertime Arctic convection, and enhanced Madden-Julian oscillation (MJO) activity. Superparameterization produces significant differences at both CO2 levels, including greater Arctic cloud cover, further reduced sea ice area at high CO2, and a stronger increase with CO2 of the MJO.