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Old 23rd June 2010, 10:32 AM   #38
Ziggurat
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Originally Posted by lomiller View Post
As I said weve seen this all before. Atmospheric height is not a constant, its a function of surface temperature and lapse rate.. The equation you cite is perfectly acceptable to us in that context. You cannot use the way you are attempting and try to pick a fixed atmospheric height and us lapse rate to derive surface temperature.
I'm not picking a fixed atmospheric height. Rather, you are assuming that the surface temperature is the only relevant boundary condition. And it isn't. The convective zone where the adiabatic lapse rate dominates does not extend to the edge of space. Where the adiabatic lapse regions meets the upper atmosphere, the temperatures AND the pressures must be equal. This region will end when the atmosphere gets thick enough, and its temperature will be determined largely by radiative balance between the sun and space. That sets our pressure and temperature for the top of the adiabatic lapse region.

If you try to fix a set surface temperature and use the adiabatic lapse rate, you can calculate an altitude where it will match our upper atmosphere, and it will indeed vary depending on the surface temperature you picked. But since the pressure will also need to match, doing this also constrains the amount of gas that the atmosphere has. But of course, that's wrong: temperature can vary quite a bit, but atmospheric content is essentially a conserved quantity, at least over the time scales needed to reach thermal equilibrium. Pick the wrong surface temperature, and you'll have the wrong amount of gas. Going the other direction, starting from the upper atmosphere at a fixed temperature and pressure, we can use the adiabatic lapse rate PLUS the total atmospheric content to calculate an altitude, which will give us a final surface temperature. And more atmosphere means more altitude, and higher surface temperature. That's a simplification, of course, but it's a far more accurate simplification than what you suggest.

But it's more than a little ironic that you basically ignored radiative transfer in the upper atmosphere in order to defend your understanding of the green house effect.
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