A large, long-standing, and pervasive climate model bias is excessive absorbed shortwave radiation (ASR) over the mid-latitude oceans, especially the Southern Ocean. We investigate both the underlying mechanisms for and climate impacts of this bias within a single climate model (CESM-CAM5). Excessive Southern Ocean ASR in CESM-CAM5 results in part because low-level clouds contain insufficient amounts of supercooled liquid. In a present-day atmosphere-only run, an observationally motivated modification to the shallow convection detrainment increases supercooled cloud liquid, brightens low-level clouds, and substantially reduces the Southern Ocean ASR bias. Tuning to maintain global energy balance enables reduction of a compensating tropical ASR bias. In the resulting pre-industrial fully coupled run with a brighter Southern Ocean and dimmer Tropics, the Southern Ocean cools and the Tropics warm. As a result of the enhanced meridional temperature gradient, poleward heat transport increases in both hemispheres (especially the Southern Hemisphere) and the Southern Hemisphere atmospheric jet strengthens. Cross-equatorial heat transport increases in the ocean, but not in the atmosphere. As a result, a proposed atmospheric teleconnection that links Southern Ocean ASR bias reduction and cooling with northward shifts in the Intertropical Convergence Zone is not found. Our work illustrates the power of using observationally constrained climate models to understand the impact of clouds on the large scale atmosphere and ocean circulation.