TOA is around -80C?
I'm not sure what your point is.
Emission height is a function of density. More molecules of a particular type raises the emission height. Higher is cooler, until you get into the stratosphere.
An exception often illustrates the rule, as is the case for CO2.
CO2 has a high affinity for 15 micron photons, it latches on to them easily. 14.5 and 15.5 microns can also be absorbed but the CO2 molecule must present in a specific orientation, therefore the emmisivity is lower. As the amount of CO2 increases, the likelihood of specific orientations goes up and the wings around 15 microns gets wider.
What is the apparent exception? At exactly 15 microns the emission height appears to be warmer than the wings. Ordinarily this would mean emission from a lower level. But not in this case. The affinity for 15.00 micron radiation is so strong that it does not escape until well into the stratosphere. At that height in the stratosphere, the lapse rate has reversed and temperature is actually increasing with height. There are two answers to the problem, and the counter intuative one higher up is actually the right one.
![spect.lw.jpg](/proxy.php?image=http%3A%2F%2Fatoc.colorado.edu%2F%7Efasullo%2Fpjw_class%2Fimages%2Fspect.lw.jpg&hash=b3804285284cbf4914a4713cd04d1d0b)
![g9wjN.jpg](https://i.stack.imgur.com/g9wjN.jpg)
The bottom of the CO2 notch is about -60C. 15 micron radiation appears to come from a -50C height, either 9km in the troposphere or 25km in the stratosphere.