Good. So you admit that the process is controlled entirely by radiative transfer to space. Well, that's a start.
Really? That's all you've got? UV interaction with the oceans has nothing to do with it? Long wave IR's inability to penetrate the skin of the water sails right over your tiny little head?
LOL So, if IR cannot penetrate the skin of water it cannot warm it? LOL So that rock that you just burned your hand on in July in the desert must have been heated by magic. LOL Because the IR did not penetrate the skin of the rock.
What a dolt. Visible and UV light warmed the rock.
IR returning from the atmosphere does not directly warm anything, it has no capacity to do work. On the other hand it does change surface conditions so that solar insolation, which is capable of doing work, can warm the surface faster and to a higher degree.
Surface temperature is dependent on both energy input and energy output. Higher atmospheric temperature means lower surface loss, a la the S-B equation.