Some day ago I came across the following review paper from 1978. Compared to other papers on the subject it appears to be relatively accessible and it contains a lot of references. In particular notice the very first formula describing radiative equilibrium of a "grey" atmosphere. Apparently it originates from a 1958 paper by a guy called Ambartsumyan. That you didn't know, did you?
I am personally convinced that the devil lies somewhere in the equations, and climatologists have indeed made a very good job making these equations as inaccessible as possible, so that virtually nobody can quote them, even less interpret them. But I'll see what information I can extract from it.
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