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?
 A: 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.
A: The greenhouse effect has nothing to do with the insulating effect of the atmosphere, as claimed in some of the comments already posted. Nor does the CO2 absorb significantly more solar energy than ordinary air. It is the frequency selectivity that causes the greenhouse effect. 
The CO2 is transparent to solar energy, at least the visible component: we can see through it. It is opaqe to thermal energy. The same amount of solar energy is absorbed at the Earth's surface with or without CO2, and the same amount is radiated back outwards by the earth's surface. The problem is that the re-radiated energy is now in the infrared range, so some of it is absorbed by the CO2 and re-radiated back to the surface. This inhibits the effective emissivity of the planet, so the surface has to get warmer in order to acheive thermal balance with the incoming radiation from the sun. 
