# Global warming and planetary thermodynamics

To a first approximation, the earth currently radiates out as low frequency thermal radiation the same amount of energy as it absorbs as high frequency solar radiation. (This ignores energy generated within the earth, which is also radiated away. But that amount is constant and is not relevant to my question. It also ignores energy stored or burned as fossil fuels.)

Let's assume that global warming will not change the amount of energy received from the sun and absorbed by the earth. (I realize that's not true. Global warming melts the ice caps, which reflect solar radiation. With the ice caps melted, the earth absorbs more of the solar radiation it receives.) But if we ignore the melting of the ice caps, the earth must receive and radiate away a fixed amount of solar radiation, which is independent of its temperature.

I would have thought that a warmer earth would radiate more thermal radiation than a cooler earth. But the argument above says that's not the case. How is this explained?

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It looks to me that you are mixing up the thermal radiation itself with the reflection, these are different terms in the budget. – Bernhard Jan 24 '12 at 7:36
There are a lot of details that could be discussed, but the basic point is that "global warming" means that the atmosphere becomes a better insulator, which raises the the surface temperature at which outgoing radiation balances incoming radiation. – Colin K Jan 24 '12 at 8:13
The troposphere is heated by the greenhouse effect whereas at the same time the stratosphere is cooled (it is not called "greenhouse effect in the stratosphere ...). Indepentent of how the absorbed solare radiaton is processed due to radiative transfer by absorption, scattering, emission, etc, the global annual mean of the absorbed solar ratiation must still be equal to the global annual mean of the outgoing long-wave ratiation at the top of the atmosphere in climatological equilibrium. – Dilaton Jan 24 '12 at 11:58
A change of the amount of LW absorbers in the atmosphere can be regarded as an "external prturbation" of the current steady state which leads to a (vertical in a simple model) redistribution of temperature corresponding to the new steady state of the system. – Dilaton Jan 24 '12 at 12:06

Colin's comment is spot on, but to expand a bit on the "lots of details" he mentioned, heat radiated from the Earth's surface is partially absorbed by greenhouse gases in the troposphere, and because the troposphere is turbulent this heat gets redistributed throughout the troposphere instead of escaping into space.

If you e.g. double the CO$_2$ content of the troposphere it will intercept and redistribute more of the heat radiated from the Earth, so the Earth will overall radiate less heat into space. Because the Earth is now radiating less heat than it receives, it gets hotter. But as it gets hotter more heat is radiated from the surface and more escapes into space. Eventually the temperature rises until the heat radiated once again matches the heat received, and the temperature stabilises.

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