So we've shown the first reason methane and carbon dioxide are warming gases: because they are among the very few gases in the atmosphere that
have an infrared spectrum.
And we've shown the second: because they stay in the atmosphere a long time, unlike water vapor. In fact the ratio is days to centuries or even millenia.
Now the third is where this gets, to my mind,
interesting. They have to do with the spectra of water vapor, carbon dioxide, and methane, and with the color temperature (more commonly known as blackbody temperature radiation peak) of the Earth. The spectrum of water vapor, as I have already said, is quite broad. However, it is not solid across the entire near infrared. In fact, it has a defect, a gap, a hole, very near the peak of the Earth's radiation at 288K. The relation that determines the peak frequency, or color temperature, of an object is called Planck's Law, because this behavior is of course governed by Planck's Constant, determining the frequency from the adsorbing surface energy, and the photon energy from the frequency. Wien's law is a pretty good approximation of that peak temperature, provided you pick a coefficient that fits the Planck's Law values near the frequency of interest. (The coefficient will be fairly constant for UVb to microwave, for example, but that coefficient is slightly wrong for UVc and soft X-rays, and somewhat more wrong for shortwave radio, and disastrously wrong for, say, AM commercial radio waves. The figures given, however, are more accurate for visible light and infrared than the inputs we'll be using, so that's sufficient.)
Wien's Law approximates Planck's law at visible and infrared frequencies as:
λ
MAX = a/T,
where
λ
MAX is in μm,
T is in K, and
a = 2897 μm·K
So,
λ
MAX = 2897 μm·K/288K
= 2897 μm/288
= 10.06 μm
ETA: And of course, given the graph below (which uses some other average of unknown source, 255K):
λ
MAX = 2897 μm·K/255K
= 2897 μm/255
= 11.36 μm
This is a low temperature, and I include it to show that the variance is not great. The curves of reality vary little from those represented below; this lower bound shows the maximum that variance could be. And in fact this variance would be to my benefit, because it includes more total water blockage, and less CO
2 transmission. /ETA
This is in the long infrared. The significant parts of the spectrum in terms of Earth's heat emission range to about 30% and 600% of this figure; some heat is also emitted above 3μm, and below 60μm, but not much. So we're basically interested in spectral lines between 3μm and 60μm when we talk about global warming.
This diagram shows the situation:
So you can see the 20μm CO
2 line and the water spectrum's climb up to its low energy modes are the most important bands, in terms of total heat blocked or transmitted. Now, do not ignore the lower bands; CO
2 has a 4μm band that's within the region of interest, just where water goes IR transparent below its 6um band and above its 3μm band. So you can see that even with water vapor acting as a warming gas, there simply are IR bands where it is transparent, where CO
2 and methane are not. So water vapor or no water vapor, CO
2 and methane (CH
4) will absorb some heat, and since they're near to the Earth's spectral peak, they have an inordinately large effect.
This, then, is the third reason these gases are important in Earth's climate.
I'll write the fourth reason soon.
ETA: Cool, I found how to do subscripts. We should be able to use proper math symbology here.
We need a directorate of science, and we need it to be voted on only by scientists. You don't get to vote on reality. Get over it. Elected officials that deny the findings of the Science Directorate are subject to immediate impeachment for incompetence.