Let's go back to the data.
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Do you have any proof that Motl's formula is wrong?
If I may defer comments on the data, paul's "weather observations," and Motl's formula (who? what?); and hope to stay on the topic of CO2's mechanism of heating, ...for one more round ...let me just say....
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Eggs Ackerly!
That would be fine if you assume that the CO2 holds the heat for more than a few seconds. The atmosphere is most dense near the ground.
Either the CO2 molecule would re-radiate the energy, or it would change its energy level via a collision with another molecule.
contributing to atmospheric heating.
Also, after re-radiating the IR away, it is absorbed by another CO2 quite rapidly, as you mention (and the extinction coeff. also shows).
CO2, on average, is usually "excited" with IR heat. Think of the continual relaxation of CO2 (through re-radiation & collisions), and notice the [whatever] fraction of relaxation that results in those collisions. It is this fraction of energy, the collisions, that determine how much of that absorbed IR gets translated (via those collisions) into heating of the atmosphere.
It is this heating that is proportional to CO2 concentration.Canuck's graph suggests that the collisions are frequent enough that none of the 4.3 or 15 micron wavelengths are able to escape to space;
Exactly, as evidenced by the spectrum showing that very little is escaping into space anymore.
therefore, the area under the curve is the IR that gets absorbed before it is converted to another wavelength.
Exactly; and don't forget that via other collisions and/or the absorption of higher energy wavelengths, CO2 will spontaneously emit the lower energy IR (heat) wavelengths, before then, as you mention, they also eventually get "converted to another [usually longer] wavelength" (if not translated into atmospheric heating, via collisions).
We shouldn't view this as just a snapshot of what happens to one IR quantum; but realize that there is a never-ending, relentlessly ongoing source of these quanta.
It is the net average of all this flux in energy, converting it's wavelength "to what is easiest," that creates the (roughly bell-shaped) blackbody profile that we measure.
Intuitively, if we're shrinking that window through which heat escapes, and retaining that heat here on Earth longer, doesn't it make sense that things would heat up?
I think this is where the "greenhouse analogy" makes the most sense; and not as a proxy for the exact physical mechanism of GHG heating.
How, where, and when Green-House Gas heating affects the climate is open to debate, but I think the physical mechanism of GHG heating is the same regardless of one's worldview or opinion of the "climate change" debate.
Thanks,
