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The temperature of the earth at the ground is not the same as the temperature of the upper atmosphere, where the IR has its last chance to radiate from Earth. Analogy: your clothes radiate at a lower temperature than your skin. Your clothes make the air above your skin warmer.
Good point. So you're saying the temp of the Earth+atmosphere system is determined by the Stefan-Boltzmann relation, but the Earth may be quite a bit warmer.
In more detail, the temperature of the Earth+atmosphere system isn't changed by GHGs (since the absorptivity and thus emissivity isn't changed, and ignoring the role of water vapour in setting emissivity). But the ground temperature may well be.
That sounds pretty plausible to me. I'll want to think on it. It may help explain something else I've been confused about, which is that I've read that the altitude of GHGs in the atmosphere matters.
Just linking to your other tweet, to collect everything before Twitter's multithreading makes a mess:https://twitter.com/PESimeon/status/1096989969225154560 …
Summing up further: do a Stefan-Boltzmann calculation with the combined Earth+atmosphere system. This _isn't_ changed by the GHGs. But then you can construct some simple model of atmospheric heating based on GHG absoption which lets you infer the ground temperature.
And I totally buy that that will be determined by the concentration of GHGs, probably in quite an interesting way, possibly dependent quite a bit on the variation of density with altitude (not just overall concentration).
Thanks again @PESimeon - I'll want to work through the details, but it seems very likely you've pointed out the source of my confusion.
There is no single temperature for the system. Maybe you could say the effective temperature for radiation purposes is the temperature of the outermost optically thick surface at the relevant wavelengths, which would be the cold temp of the upper atmosphere. Ground is warmer.
Perhaps I am thinking of this too much as individual systems, but doesn't SB primarily apply to thermal based EM radiation. And the whole issue with GHG is that their absorption spectrum is slightly elevated compared to a standard gas. So you can't extrapolate SB in this case?
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