That doesn't debunk anything I said. I never implied the 2x M&M theory. In fact, I always said it is not a linear function. Why does the IPCC treat is as a linear function, along with other climatologists that are in line with you?
Notice how little more of the band a four-fold increase by that link gives. My contention is that CO2 has the ability to trap about 16% of the radiated heat at current levels. Your link suggests a four-fold increase changes transmission from about 66.2% to about 59.8%. I can live with that, although I know of some finer nuances that will reduce the change. For the sake of argument, I will accept those numbers.
OK, 33.8% absorption and the maximum argued amount of 26% that CO2 contributes to the greenhouse effect. The greenhouse effect is estimated to be 32 C. That equates to 8.32 C warming by CO2. A fourfold increase and we now have 40.2% absorption. That is 19% more absorption and now the CO2 effect on temperature is 9.9 C. So it takes a fourfold increase in CO2 to increase the global temperature by 1.58 degrees C!
Now remember, I'm allowing for worse case numbers which I don't agree with. That 26% only applies at a humidity of ZERO! H2O is already trapping half the spectra, so the effect this can cause is about half, or only 0.8 C for a four-fold. If we linearize that small segment, then that amounts to 0.088 Celsius for every 100 ppm worse case.
The truth of the outer range of the absorption spectra is that it is not smooth. It is averaged on most any graph you see. When you look at the data in 0.1 micro-meter resolutions, it peaks and goes to 100% transmission for hundreds of micrometers. Those outer areas cannot peak at 0 transmission, only about 50% because of that nuance.
If I were to accept that data, I will say that when you consider the common spectra absorption with H2O, out industrialized CO2 can only account for 0.06 C increase in temperature.