A couple of days ago Eli posted two MODTRAN calculations showing what would be seen at 70 km with CO2 for 375 ppm and 37500 ppm CO2 (Eli is a lazy bunny, he just added two zeros to 375)
and asked for an explanation of the donut hole when the CO2 mixing ratio is real high. The answer turns out to be both simple and a key to understanding the greenhouse effect. The clue was that temperature in this simulation decreased from 300 K at the surface to ~190 K at the 18 km tropopause and then increased again in the stratosphere up to where the ozone concentration was highest at ~30 km.
The answer is that at any frequency you are looking at emission from molecules (or aerosols) that are at the level where the emission can reach the detector without being absorbed again. If there is no absorption at a particular frequency you are looking at emission from the surface.
If the concentration is very high, this level moves up for any absorption band. If it moves up higher than the tropopause the temperature at which the CO2 emission that reaches you was emitted will be warmer than for lower CO2 concentrations. Take a look at the emission seen at 70 km if the concentration was 3.75 ppm
km (Eli is a lazy bunny. . . )
In this case the strong Q-branch (the sharp part pointing downwards in the middle of the CO2 bending absorption, reaches down to about the 220 K Planck function, indicating that the emission at that wavelength is so strongly absorbed, that one has to get to about 12 km where the temperature is ~220K before the emission would reach a detector at 70 km altitude. Other parts of the band absorb more weakly, and thus the emission that reaches the detector comes from lower down in the atmosphere.
If the CO2 mixing ratio is 37500 ppm then the absorption is so strong that to reach our detector at 70km, it has to be emitted from relatively high in the stratosphere, between 25 and 30 km where the temperature is above 240 K. In the wings of the band, where the absorption is weaker, the emitting level sits below or at the tropopause. Thus the donut hole. Even in the 375 ppm spectra, the Q branch emission comes from above the tropopause as can be seen by the sharp line pointing upwards at the position of the Q branch.
Another way of looking at this is to look at the emission seen at 10 km/375 ppm where the temperature is ~240 K. As can be seen to the left, the center of the line extends down to ~240 K.
There are a bunch of caveats here, the most important of which is that the MODTRAN temperature profile is not adjusted to take feedbacks into account. As raypierre says, if we really stepped the CO2 up to 37500 ppm, all hell would break loose and the temperature profile would in the stratosphere would cool "hiding the blip", a good trick. Bunnies should also note that the CO2 band widens as the concentration increases. This accounts for a great deal of the greenhouse effect.
The idea is very useful for understanding the greenhouse effect.