According to the authors, "In the most of models, the longwave radiation [from greenhouse gases]... exert a warming effect, and the shortwave radiation [from the Sun] exerts a cooling effect." However, it appears the models have the basic physics backwards, because longwave radiation from greenhouse gases cannot penetrate the sea surface and thus only causes evaporative cooling of the ocean 'skin' surface, whereas shortwave radiation from the Sun can penetrate to depths of up to 100 meters to cause bulk ocean warming.
Theoretical and Applied Climatology October 2013, Volume 114, Issue 1-2, pp 9-19
Various ocean reanalysis data reveal that the subarctic Atlantic sea surface temperature (SST) has been cooling during the twentieth century. A similar cooling pattern is found in the doubling CO2 experiment obtained from the CMIP3 (coupled model intercomparison project third phase) compared to the pre-industrial experiment. Here, in order to investigate the main driver of this cooling, we perform the heat budget analysis on the subarctic Atlantic upper ocean temperature. The net surface heat flux associated with the increased concentration of greenhouse gases heats the subarctic ocean surface. In the most of models, the longwave radiation [from greenhouse gases], latent heat flux, and sensible heat flux exert a warming effect, and the shortwave radiation exerts a cooling effect. On the other hand, the thermal advection by the meridional current reduces the subarctic upper ocean temperature in all models. This cold advection is attributed to the weakening of the meridional overturning circulation, which is related to the reduction in the ocean surface density. In particular, greater warming of the surface air than of the sea surface results in the reduction of surface evaporation and thereby enhanced freshening of the ocean surface water, while precipitation change was smaller than evaporation change. The thermal advections by both the wind-driven Ekman current and the density-driven geostrophic current contribute to cooling in most of the models, where the heat transport by the geostrophic current tends to be larger than that by the Ekman current.
Related: There is also a negative feedback phenomenon on CO2 levels discussed in a paper published in Nature which shows that the evaporative cooling of the ocean 'skin' from increased downwelling longwave radiation allows increased uptake of CO2 due to increased solubility of CO2 at lower temperatures.