The above charts are thanks to the Forecast at University of Chicago website and its MODTRAN program. This time we are looking at the mid latitudes with the first chart at 100ppm, it also shows the basic stuff, particularly the 4km looking up. The second chart is the same but with 400PPM CO2 and the third is with 800PPM. I selected 4 kilometers as an estimated average radiant layer and will assume the tropopause can provide a sink temperature of -89C. The initial surface temperature is zero C, so the atmospheric R-value would be 89 degrees/250.4Wm-2=0.355 and the emissivity of the tropopause would be 0.207 unitless.
For the 400PPM chart, Iout is 168.5 versus the initial 160.1 at 100PPM. That implies an 8.4Wm-2 increase at the radiant layer so a double or 16.8Wm-2 impact at the surface. That should increase the surface temperature by 3.6 degrees and change the R-value to 0.0.333 and the emissivity to 0.1961and for the final 800PPM, Iout increase to 172.95Wm-2 of an increase of 12.85 from 100PPM producing 25.7Wm-2 increase at the surface, for a T of 5.4C, R-value of 0.322 and E-value of 0.191 still unitless.
The initial R-value was 0.355@ 250.4Wm-2. When the temperature increases by 5.4C the R-value would flux to increase by 5.4/0.355=15.2 instead of the 25.7 indicated by the radiant change. That would result in a surface temperature increase of 2.18C instead of 5.4C or 40% of the estimate based solely on radiant forcing.
That happens to agree rather well with the observed change, but does not mean that is the solution of the CO2 forcing issue. Every variable in a dynamic system has a maximum impact that is not sustainable. This only indicates a range of relative radiant and conductive combined impact, from 2.18C to 5.4C for a double doubling. The approximate glacial would be the first doubling (190 is almost 200), we are now at the second doubling (390 is almost 400) and the 800PPM would be the next doubling.
I will attempt to fine tune this a little, but global impact is not all that meaningful, regional should be more informative.
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