Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics by Gerhard Gerlich and Ralf D. Tscheuschner, arXiv:0707.1161v1 [physics.ao-ph]. [PDF]

I don’t actually recommend reading this. But one gem that they propose is that there isn’t a thing called an average temperature. Of course there is. When attempting to derive such a temperature, Gerlich and Tscheuschner arrive at a value of 87.6 C. This is clearly wrong. If the Earth were that warm, humans wouldn’t exist. They then “explain” how climatologists get their value to explain the greenhouse effect as follows:

This fictitious [greenhouse] effect is based on the assumption that one should have an average effective temperature of -18 [degrees] C. One will get this if one weights the solar constant with a factor of 0.7 and inserts a quarter of the solar constant into the “radiative balance” equation. The factor of a quarter is introduced by “distributing” the incoming solar radiation seeing a cross section σ

_{Earth}over the global surface ΩEarth.

[Added August 7, 2007: This post has been linked from a comment in a Scienceblogs.com post. For those who don’t believe in the greenhouse effect, please explain how the average temperature on the moon is lower, in spite of the fact that it has a lower albedo.]

Actually, the value of -18 C falls right out of the equations, not the other way around. Assume that the sun radiates at a certain temperature such that it can reasonably be modeled by the blackbody curve for some effective temperature. This shouldn’t be that hard to do, even Gerlich and Tscheuschner do so in their paper. By the time this radiation reaches the Earth, it’s intensity has decreased according to the ^{1}/_{R2} law. Again, this is exactly what Gerlich and Tscheuschner do. At the Earth, this value is roughly constant – 1367 ^{W}/_{m2}. Gerlich and Tscheuschner do not use this number, they keep their equation in terms of the temperature of the sun, radius of the sun, and distance from the Earth to the sun. It doesn’t matter, the finals answers will end up the same.

Therefore, the total energy absorbed by the Earth is related to its albedo and its radius.

E_{A} = (1-A)S_{0}πR^{2}

The term 1-A is the percentage of incoming solar radiation absorbed by the Earth; the albedo (A) is the percentage reflected. S_{0} is the solar constant. And πR^{2} is the cross-sectional area of the Earth that absorbs radiation. The dark side of the Earth cannot absorb radiation from the sun.

The total energy emitted by the Earth is related to its temperature and its radius.

E_{E} = σT^{4}4πR^{2}

Because the Earth emits radiation from its entire surface and not just the side facing the sun, the surface area of the Earth is used (4πR^{2}) is used instead of the cross-sectional area. The σT^{4} term is the blackbody emission for an object at a given temperature.

Setting the two equations equal – assuming the energy absorbed equals the energy emitted – and simplifying, we see that

(1-A)S_{0} = 4σT^{4}

So, for a given A and S_{0}, we can find the effective temperature. In the case of the Earth, the albedo (A) is about 0.3, so 1-A is 0.7, which magically explains where that factor comes from that Gerlich and Tscheuschner couldn’t explain. The factor of 4 is just a consequence of the fact that the Earth can only absorb radiation on the side facing the sun, but emits in all directions. When the values are plugged in, we (and Gerlich and Tscheuschner) get a value of -18 C.

So, Gerlich and Tscheuschner couldn’t figure out where the magical values of 0.7 and 0.25 [1/4] came from, but they are just misleading their readers. They [should] know how to compute an effective temperature. And they [should] know that such a value exists, and is physically meaningful.