Dr. Houghton has a Question

John Houghton, in his book Global Warming : The Complete Briefing, has an exercise:
“It is sometimes argued that the greenhouse effect of carbon dioxide is negligible because its absorption band in the infrared is so close to saturation that there is very little additional absorption of radiation emitted from the surface. What are the fallacies in this argument?”

Indeed it has been so argued, by Harvard Physics Prof Lubos Motl quite recently. This post is in answer Houghton’s question.

As I remarked in a previous post, the energy balance of absorbed radiation and emitted radiation has to be in nearly exact balance. The amount absorbed implies that the Earth has a mean radiating temperature of -18 C, which is to say it emits as much radiation as a black body at -18 C. I need to start with a few more relevant and probably familiar facts:

a)The atmosphere gets colder as you get higher, until you reach the stratosphere.

b)The surface emits a more or less continuous spectrum centered in the infrared, but the atmospheric gases emit and absorb only in discrete bands. See for example this link provided by Lumo.

c)Much of the Earth's emitted radiation is in the so-called window region between 8 and 14 micrometers where surface emission is highest and the atmosphere is relatively transparent, but another large fraction is emitted in the absorbing regions above 14 micrometers. The distribution can be seen in figure 2.4 (page 19) of Houghton's book, which can be accessed here (do a search on 19 or 2.4).

Because absorption is nearly saturated in much of the absorbing region, radiation emitted in such a region is likely to be absorbed before it exits the atmosphere. Such absorbed radiation will be re-emitted, again in an absorption band (because molecules emit in the same bands as they absorb). It will be re-emitted with an intensity characteristic of the temperature of the atmosphere where it is emitted, and cooler temperatures imply less emission - all this is shown in figure 2.4.

Thus, the absorbing regions of the spectrum exhibit an intensity characteristic of a cooler temperature than the surface. The greater the CO2 concentration in the atmosphere, the higher the level at which photons need to be emitted in order to be likely to escape. Consequently, increasing the CO2 decreases the emission from the absorbing portions of the spectrum, a decrease which needs to be balanced in order to maintain thermal equilibrium. That balance can only come from increasing the emission from the window region, which in turn implies increase in the surface temperature.

There is a second, probably less important, factor at work as well. The CO2 bands don't have sharp cut-offs, but gradually decreasing shoulders. Increasing the CO2 increases the "width" of those shoulders, narrowing the radiation passband between 8 and 14. Once again, an increase in surface temperature is required to balance the decrease in radiation from the partially blocked region.

Which is to say Lumo, about that 1-exp factor - nope, not really!

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