I should start by saying that this post was partly motivated by an intersting comment from Pekke Pirila on another thread. Also, Eli already has a post that mostly cover this, so this is more from completeness, than anything else.
In a number of my recent posts, I’ve been referring to an effective emission height in the atmosphere that is set by the greenhouse gas concentration. Given that the tropospheric temperature gradient (lapse rate) is largely set by convection, if you know the temperature at some height in the atmosphere, then one can work back down the lapse to the surface in order to determine the surface warming due to greenhouse effect. I haven’t, however, really defined this effective emission height. In equilibrium, the Earth radiates as much energy back into space per unit time as it receives from the Sun. If you determine the average amount of energy radiated per square metre per second (about 240 Wm-2) you can use the Stefan-Boltzmann law (F = σT4) to determine the temperature a blackbody would need to have so as to radiate this amount of energy per square metre per second. For the Earth (with an albedo of 0.3) it is about 255 K. The effective emission height is the height in the atmosphere at which the temperature matches this temperature. In the Earth’s atmosphere it is at about 5km.
In reality, however, the actual emission is much more complicated. To illustrate this, I’ve used the MODTRAN radiation transfer code. If you use the 1976 U.S.Standard Atmosphere, set the CO2 concentration to 400 ppm, and lookdown from 70km, you get the following.
The left-hand panel is the spectrum, and the right-panel is the temperature profile. The outgoing flux is 258.58 Wm-2 which, if you use the Stefan-Boltzmann law, corresponds to a blackbody temperature of 259.9K. Looking at the temperature profile, this would correspond to an effective emission height of between 4 and 5km. However, the spectrum itself is clearly not a 259.9K blackbody spectrum. For wavelengths beyond 17 microns, the emission is coming from temperatures between 260K and 240K (so heights around 5km in the troposphere). Between about 13 and 17 microns, the emission’s coming from a region with temperatures close to 220K – so, near the troposphere/stratosphere boundary. Between 7 and 13 microns, the emission is coming from a region with temperatures in excess of 280K which, in this example, is actually the surface. So, there isn’t a single emission region, but the emission is still equivalent to a blackbody with a temperature of 259.9K.
Now, if you change the CO2 concentration from 400ppm to 800ppm, the outgoing flux drops to 255.75 Wm-2, equivalent to a blackbody with a temperature of 259.1 K. If the system was in equilibrium at a CO2 concentration of 400ppm, it would now be emitting less energy per square metre per second than it receives. To retain equilibrium, it must warm. Again using MODTRAN, this requires increasing the surface temperature by 0.9K (here I’m considering only the influence of changing CO2 concentrations, and am not considering feedbacks). Since the temperature gradient in the troposphere is – to a large extent – set by convection, this means that if the surface warms by 0.9K, the temperature at all altitudes in the troposphere must increase by 0.9K (in this example I’ve, again, ignored water vapour feedback). Hence, once the system returns to equilibrium, the effective temperature will again be 259.9K, but this will now be at a higher altitude than when the CO2 concentration was 400ppm. Therefore, a significant fraction of the outgoing emission will come from higher in the atmosphere when the CO2 concentration is 800ppm, than when it is 400ppm.
So, I hope that’s reasonable clear and basically correct. It’s clear that there isn’t a single emission height in the atmosphere, but it is clear that one can define such a height, and it’s clear that increasing the greenhouse gas concentration increases the temperature at all altitudes in the troposphere and increases the height at which a significant fraction of the emission is coming from. That both illustrates the greenhouse effect and the consequences of increasing greenhouse gas concentrations. As usual corrections or comments welcome.