Why would an atmosphere without greenhouse gasses be colder than with them?

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Graeme M said:
What I am struggling with is the suggestion that without GHGs, the atmosphere will be at equilibrium at -18C.
Without the GHGs, radiation would pass both ways through the atmosphere with relatively little interaction (absorption or radiation and both are equal, for basic reasons and the thermal mass of that atmosphere would be also very small). So the atmosphere would have very little effect on the surface temperature; it would be like a large piece of rock at 1AU.
 
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I wonder if part of the lack of clarity is from the difference between ground heat radiating upwards and the re-radiation in all directions of the portion GHG's absorb out of that. Ground is heated largely by sunlight in parts of the spectrum that are not absorbed by GHG's (unimpeded) but radiates back largely in IR that is absorbed and impeded. - absorbed from one direction but the re-radiation is in all directions, effectively half what is absorbed radiates back down and only half radiates upwards. (Not precisely half - going sideways can reach space but has to travel through more atmosphere and more GHG molecules, yet depth of atmosphere is actually quite thin compared to the diameter of the planet so this is not a big effect).

Some of that upward radiating half gets absorbed again, half of that re-radiates back down. The IR component is relatively small, but the consequences accumulate.

This aspect is not the whole story; what happens higher in the atmosphere where re-radiation upwards meets less GHG molecules and the 'IR fog' clears and IR can reach and be lost to space plays a critical role. As GHG concentrations rise the altitude where the IR fog clears rises. Not only a bit deeper but the temperatures at higher altitude are lower and that slows the re-radiation rate; more of the energy is retained.

Hope this helps.
 
Thank you everyone for your comments. I hadn't realised this would be such a tricky question, but perhaps the problem is I am asking about an entirely unphysical situation. I will leave it there, though happy to respond to any more comments.
 
Graeme M said:
I hadn't realised this would be such a tricky question
Oh yes!! Very tricky, once you look deeper.