BTW, the temperature increase is not linear, but logarithmic: see http://motls.blogspot.com/2006/05/climate-sensitivity-and-editorial.html: You should realize that the carbon dioxide only absorbs the infrared radiation at certain frequencies, and it can only absorb the maximum of 100% of the radiation at these frequencies. By this comment, I want to point out that the "forcing" - the expected additive shift of the terrestrial equilibrium temperature - is not a linear function of the carbon dioxide concentration. Instead, the additional greenhouse effect becomes increasingly unimportant as the concentration increases: the expected temperature increase is something like
* 1.5 ( 1 - exp[-(concentration-280)/200 ppm] ) Celsius
Your link neglects to consider pressure broadening (CO2 in the lower atmosphere has a significant linewidth; as you go up in elevation, it narrows). So while the extinction at the top of each rovibrational line may be close to saturated, that on the flanks will continue to increase with concentration. An absorbtion line with finite linewidth will never give rise to an equation of the form you show, because there will always be regions in the flanks of the lines whose absorbtion continues to increase with concentration.