wirebender
Senior Member
Real physics, real math. Something Bent doesn't understand.
Physics of the Greenhouse Effect Pt 1 | Climate Change
Just to get a bit of this out of the way, the effective temperature of the Earth with radius r is:
πr2(1 – a)S= 4πr2σT4, or
Teff = [S(1 -a)/4σ]1/4 = 255 K
We can then write an equation for the energy balance of the atmosphere, as
Iup,atmosphere + Idown, atmosphere = Iup, ground
= 2ɛTatmosphere4 = ɛTground4 (also accounting for emissivity), or
Tground = fourthroot (2Tatmosphere)
This temperature is below freezing, and so this shows that if the Earth’s temperature were purely based on the amount of solar radiation it receives, it would be far from habitable. The gap between our present day comfort, and an iceball planet is due to the fact that some of the outgoing infrared radiation is not immediately sent right back to space, but is absorbed by the atmosphere, where some is radiated downward to the surface. This is due to the fact that we have greenhouse gases, which are transparent to incoming solar radiation, but absorb outgoing infrared radiation strongly. The mean surface temperature difference is,
Δ T ≡ Ts – Teff = 33 K
The mean temperature of the Earth’s surface is actually 288 K, which says that the greenhouse gases are responsible for a 33 K enhancement. No longer freezing, but rather comfortable and unique to the solar system.
So what is going with this greenhouse??
The following image shows a spectra at the top of the atmosphere which shows the absorption of photons by CO2, water vapor, ozone, etc.
Rocks, if your equation is built upon the radius of the earth, why does it present incoming radiation as if it were hitting a flat body with no curvature. Your equation divides incoming radiation by 4 making the surface of the earth a flat surface being irradiated by incoming radiation that is 1/4 the strength of the actual incoming radiation rather than by 2 making it a sphere that is being irradiated across 180 degrees of its surface and dark across 180 degrees of its surface.
Also, is that a derivation of Stefan-Boltzman? If so, which derivation, by whom, based on what, and where is it supported in the physics literature?
How do you expect a formula that doesn't represent the earth as it is to predict temperature with any degree of accuracy? Also, if you apply that formula to any other body in our solar system, the result doesn't even come close to the known reality. It is an ad hoc formula put together to reach a pre determined quantity.
Don't worry rocks, I don't expect you to actually answer my question as we both know that you don't have the slightest understanding of what you posted. If you did, you wouldn't have posted it in the first place.
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