Mixing or confusing physical concepts can be devastating. In previous posts we have seen examples of such confusion which appear to be almost semantical. In my view, many misunderstandings could be avoided if
1. The distinctions between dynamic/absolute temperature, kinetic temeparture and empirical temperature were made clear.
2. It was made clear whether the incoming sunlight should be treated as a heat flow or as an energy source.
Moreover, there seems to be a mixing of physical models. On one occasion (radiation) the atmospheric layers are treated as black-bodies, on another occasion (convective overturning, adiabat etc.) they are suddenly transformed into an almost ideal gas. If you follow the links you will discover that their thermodynamic properties, like pressure and heat capacity, differ in a qualitative way.
However, is there any other way forward? In the end we must have a model that takes into account both radiation and kinetic energy of air molecules. Could such a model be that of a "boson gas"? The idea would be to treat all thermal excitations in the atmosphere, including photons, phonons, molecular momentum and so on as one kind of particle: boson. What would it be like?
Since the number of bosons is not limited we would have to treat it as a grand canonical ensemble. As a matter of fact, papers have been written on this subject: