Upon further reading of Pierrehumbert's "Principles of Planetary Climate" I found the following passage explaining the cooling of the stratosphere:
Note especially that he writes
"Moreover, as the optical thickness of the atmosphere is increased, the stratosphere actually
becomes colder than even the semigrey skin temperature; this contrasts with the grey case, where
the temperature of the uppermost part of the atmosphere always approaches the skin temperature, regardless of how optically thick the rest of the atmosphere is."
The boldfaced statement seems to be what I concluded myself in the previous post "A discrete model atmosphere", thus it is not news to Pierrehumbert. However, there are a lot of questions urging for an answer now. For example:
1. In my very first post "What is the greenhouse effect" I calculated the temperature profile using the formulas provided by Goody and Yung where the stratospheric cooling fell out quite simply apparently without any assumption about a "grey" or "non-grey" atmosphere. Hence, are these formulas valid at all? Are there several greenhouse effects, in that case, which is the IPCC one?
2. If there is no cooling of the stratosphere for a "grey" atmosphere, then why is it generally portayed as a triviality, taking as an example Spencers "blanket analogy". (Maybe we have to assume a non-grey blanket?)
3. Where is the observational evidence for all these claims? As far as I can see, the stratospheric temperature of most planets can be calculated from the incident solar energy without any special consideration of the spectral properties of the constituent gases.