Friday, October 7, 2011

Poisson! Poisson!

The Poisson equation can be simplified to calculate the potential temperature of a parcel of air at an altitude(pressure) and temperature(K) should it drop to the surface of the earth and sea level. Using the neat stuff from the Kimoto equation, modified be me :)

The effective temperature of the atmosphere due to greenhouse and solar absorption is equal to the sum of the total energy absorbed by the atmosphere, 195Wm-2. The surface fluxes, reguire correction for the 0.825 emissivity of the atmosphere, 24+79+51=154, the total combined surface flux absorbed per the NASA data, with 65 solar absorbed, 10 by the clouds at low altitude and 55 absorbed by the upper atmosphere.

For the surface, 154/.825=187Wm-2 plus 10 absorb by clouds plus approximatey 50% of the upper atmosphere absorbtion, 27.5, felt in the lower atmosphere yielding 187+10+27.5=224Wm-2, the equivalent greenhouse effect. The effective temperature of the greenhouse effect is 250.7K at 3800 meters, based on the dry adiabative lapse rate. Per the Poisson ralationship, a parcel of air at 250 and ~600mb(equivalent to 4Km) is equal to 289.3K. Considering the approximation of 4Km instead of 3.8Km, that is pretty close. Kinda neat :)

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