Note that during the very first convective cycle, whilst KE (equivalent to 33K) is being converted to PE and no PE is yet being returned to the near surface, the surface is losing energy by radiation to space AND to the first convective cycle via conduction.so the surface temperature will drop below 255K for a while.
When the first convective cycle completes and adiabatically warmed air is being returned to the surface at the same rate as surface warmth is being taken up adiabatically then the surface temperature rises to 288K because:
i) Incoming solar energy continues to arrive at a rate commensurate with a surface temperature of 255K AND
ii) Descending adiabatically warmed air is returning to the surface at a rate commensurate with surface warming of 33K AND
iii) The next convective cycle is simultaneously removing KE from the surface at a rate commensurate with surface warming of 33K thereby locking it away in PE which is not heat and does not radiate.
The net outcome is that the surface temperature of 288K is provided by 255K from the sun plus 33K from descending air but the surface cannot use that 33K for radiation to space because it is recycled into further convective uplift. Nevertheless the surface temperature will still be enhanced by 33K because the energy required by the ongoing convective cycle is still held at the surface.
The result is a surface temperature of 288K, 255K escaping via radiation to space and 33K continuing to support the weight of the atmosphere.
Some AGW proponents say that adiabatically descending air that has been warmed cannot heat the surface.
It doesn’t have to warm the surface directly. All it has to do is provide a less steep lapse rate which inhibits convection so that the surface warms from solar irradiation more than it otherwise would have done.
We see that all the time within atmospheric high pressure cells containing descending air and often they create an inversion which blocks convection altogether.
The irony is that reducing or blocking convection is what the glass in greenhouses does.
That descending adiabatically warmed air acts just like the glass on a greenhouse roof by reducing convection so it is mass acting via the adiabatic convective overturning cycle that is and always was the true greenhouse effect.
The term ‘Greenhouse Effect’ must have been originally coined by a meteorologist maybe 100 years or more ago who realised that adiabatically warmed air by virtue of being transparent and inhibiting convection would act exactly like a greenhouse roof.
The radiative chaps never learned that so they often say that the term is misleading.
The term might be misleading in terms of their attempt to use it in connection with their imagined radiative only scenario but it is spot on in terms of long established meteorology.
The thing is that meteorology was a very arcane subject in the 20th century and earlier.
Hardly anyone knew anything about it and a lot of the ways the laws of physics play out within an actual atmosphere are counterintuitive and hard to envisage such as the thorny concept of adiabatic processes.Everyone I discuss it with is oblivious to its true nature.
In the 1980s or thereabouts a bunch of astrophysicists thought they could take over climate science with no knowledge of basic meteorolgy and they have spread nothing but confusion in their wake.
Made them rich and famous though.
The Greenhouse Effect is perfectly described as a process that occurs as a result of a transparent layer of warm air that inhibits convection so as to allow the sun to warm the surface to above the S-B figure of 255K.
On average for the Earth as a whole the surface temperature enhancement for the mass induced ghreenhouse effect is 33K leaving no room for any contribution from radiative gases.
Believe it or not. Your choice :)