I am trying to back-calculate the greenhouse effect on planetary equilibrium temperature for Earth (in the hope I can then attempt applying it to other calculations.)(adsbygoogle = window.adsbygoogle || []).push({});

I know that the actual equilibrium temperature of Earth is 287.89K, +33K above the calculated equilibrium temperature:

T_{eq }= (Q x (1- albedo)/ 4 x Stefan-Boltzmann constant)^{0.25}

When Q = 1400 W/m^{2}, (1 - albedo) = 0.7.

From here, if I am understanding it aright, the greenhouse effect is (in a simplified form enough for my purposes) basically a multiplier of Q, respresenting the amount of energy reflected back off the atmosphere to the planet.

I put the T_{eq}as a spread sheet calculation, with an additional factor (let's call it Z) which multiplies Q that I coud alter manually; experimentally it looks like for Earth it's Z is about 1.6ish.

T_{eq }= (Q x Z x (1- albedo)/ 4 x Stefan-Boltzmann constant)^{0.25}

T_{eq}= 254.89K for Earth

What I would like to do is see if I can work back, using the known values from Earth, and see if I can determine Z, which would at least give me something more to work with. (At the moment, my estimations for greenhouse effects are "add about 33ºK")

I tried rearranging the formula

287.89K = 33K + 254.89K = (Q × Z × (1- albedo)/ 4 × 5.67 × 10^{-8})0.25

287.89^{4}= Q × Z × (1- albedo)/ 4 × 5.67 × 10^{-8}

287.89^{4}× 4 × 5.67 × 10^{-8}= Q × Z × (1- albedo)

287.89^{4}× 4 × 5.67 × 10^{-8}/ Q × (1- albedo) = Z

However, this came out as 3.97, which is clearly wrong. I've obviosuy messed up somewhere, but for the life of me I'm not sure where.

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# Greenhouse effect on planetary equilibrium temperature help

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