This subject is described on the Real Climate web site the usual reference for alarmistssort of the way I describe it on the page titled Disputed Area, except with some real absurdities here. Their conclusion is explained with this image:
(Image at Real Climate)
This thing is nothing but engine noise. It has no resemblance to absorption spectra. It's a sine wave. Absorption spectra are never sine waves, but noise always is. The repeated patterns are engine cycles.
Their explanation is a total fraud, because it says the bandwidth widens with increased CO2 in the atmosphere. It does not. Only energy state of the molecules determines bandwidth, and it does not change with more being added to the atmosphere.
Heinz Hug measured absorption with doubling of CO2 and showed that the bandwidth does not increase.
Notice that the slope of the absorption spectrum used by alarmists is about 45 degrees of angle. This leaves a lot of space for change. But the actual absorption spectrum for CO2 is nothing resembling this. The edges are sharp. The actual absorption spectrum for CO2 is bounded by the wavelengths 14 to 16 microns. In the above image, the relevant band is shown as 13 to 17.5 microns. CO2 cannot absorb at such wavelengths. The wavelength of absorption is determined by the energy state of the molecules, while increasing the amount of CO2 does not change the energy state.
So where do these 45 degree angles come from? This graph is based upon measurements high in the atmosphere by the Air Force during WW-II. The atmosphere doesn't represent anything close to an absorption spectrum for a single gas such as CO2. After radiation goes through several kilometers of atmosphere it is influence by a large number of unknown factors including scattering and absorption by any number of unknown substances. This means that the angled slopes on the curve are not caused by CO2 but other things. So the entire rationale for absorption on the edges of the absorption spectrum is not valid.
This graph is not a properly scaled representation of anything. It's designed to catch the eye of the unwary, much like the fake hockey stick graph. Oddly, they multiplied the CO2 level by a factor of four, where the usual question is what happens upon doubling of CO2. Then the lines across the graph for 1X and 4X have no meaning. They don't intersect with anything relevant on the graph.
The 1X line is arbitrarily placed at one absorption unit, and the 4X line is placed at the 0.5 absorption units, while the peak is at 10,000 absorption units. So how do they know that the increase will widen the effective absorption by almost one micron of wavelength? There is nothing on the graph or anywhere in science which will tell them that.
As the CO2 concentration increases, the slopes on the absorption curves absorb more infrared. This would be irrelevant at ground level, but it supposedly prevents more radiation from going into space at the top of the troposphere. But is the amount a lot of very little? I explain why it is very little, while alarmists say it is a lot. Is there a science to resolve this dispute? None what-so-ever. In fact, the only resolution of this whole subject is to measure the claimed temperature increase of the past and assume something similar will happen in the future. (See above)
I give explanations and logic for a miniscule effect (see Crunching the Numbers), while alarmists do not explain why the heat would be significant. But regardless of the numbers, there is no explanation of how the supposed temperature increase at the top of the troposphere, which is very cold, can produce heat at ground level.
The primary effect of increasing CO2 in the atmosphere is to shorten the distance by which it does exactly the same thing it was doing. Shortening the distance is not increasing the temperature.
Over long distances, reducing the distance to one half might seem like a lot, but a few watts of heat spread over a few kilometers of height is an irrelevant temperature increaselike 16 millionths of a degree centigrade if allowed to accumulate for ten seconds, but will equilibrate with heat leaving on an instantaneous basis. And this is supposed to create 3°C temperature increase at the surface upon doubling of CO2 in the atmosphere.