I tried to write out an explanation of how the heating due to greenhouse gases works, and realized there's a big hole in my understanding. Can someone who understand the detailed physics help or point me to a really clear and thorough explanation?
I omitted the technical details, but it's this: the temperature should be set by: incoming energy flux = epsilon sigma T^4, where epsilon is the emissivity, sigma is the Stefan-Boltzmann constant, and T is the temperature.
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Since anything absorbed by the GHGs has already been absorbed by the Earth, the absorptivity (and thus the emissivity) shouldn't be changed by the GHGs, and so I don't see how T can be changed by the GHGs.
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I should have said earlier in the thread, but the key thing I'm worried about: why is epsilon in the Stefan-Boltzmann relation changed, since net absorptivity apparently isn't? Or is S-B the wrong way to be thinking?
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Update: I believe
@PESimeon has isolated the source of my confusion. A summary (more or less) can be found here:https://twitter.com/michael_nielsen/status/1096990267259809793 …Show this thread -
Thankyou for all the comments and the links. It's very much appreciated, and has clarified matters greatly for me, especially (though certainly not just) in the part of the thread linked in the last tweet.
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You’re above my math pay grade here but you might enjoy a chat with Dr. Dave Robinson, (former professor) and state climatologist of NJ. He’s a super nice guy and has always been open to inquires.
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I think the blackbody equation still works for the whole Earth *including* the atmosphere. But the Earth's atmosphere prevents Earth's *surface* from reaching radiative equilibrium with outer space / the sun.
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This is exactly right, but incoming on the left hand side includes all "bounces." That raises T. (The right hand side is an equilibrium quantity)
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