You ask about a CO2 saturation point for the atmosphere, implying that above a certain value, carbon dioxide would have no further effecton infrared absopption. You received responses that indicated no saturation value exists. But you are trying to get at something important. You have focused on the Earth for CO2 saturation but you may want to add Venus to your model. It has an atmosphere that is 96.5% CO2 more abundant than that of Earth. Its surface pressure is 9.63 mPa, compared to Earth's 101.3 kPa, a ninetyfold higher value. The incredibly high carbon dioxide density at Venus’ surface has attracted greenhouse believers into explaining its high surface temperature, 462-480 oC., using the greenhouse effect. But the massive nature of its atmosphere and its adiabatic behavior are more important in surface temperature production. Venus radiation balance is based on its sulfuric acid cloud, an opaquely thick aerosol that increases its albedo to 65% of solar light and has a temperature at its outer surface of 260 oK, http://www.datasync.com/~rsf1/vel/1918vpt.htm
As with Earth, solar radiation breaks some molecules down. For Earth it is molecular oxygen to atomic oxygen and then ozone. For Venus it is carbon dioxide to carbon monoxide and atomic oxygen. This time the atomic oxygen converts atmospheric sulfur dioxide (150 ppm) to sulfur trioxide that adds water to become sulfuric acid. The effect is to add energy to the layer where chemical change is happening, raising its temperature. In the case of Earth, this makes the top of the stratosphere warmer than its bottom. In the case of Venus, it flattens the rate of fall above the sulfuric acid cloud. The Venus atmosphere above the cloud needs only to reflect 28.5 W/m2 back into the cloud to balance the post-reflection solar radiation input of 230.6 W/m2, a value lower than the 32 W/m2 attributed to CO2 by Kiehl and Trenberth for Earth’s radiation balance http://www.atmo.arizona.edu/students...tionBudget.pdf
. You could see this as a saturation behavior, but I believe that there is a different explanation and will post it on this forum shortly. Please look for it and comment. I have also noted the discussion of the Miskolczi paper by Andre and will try to compare my explanation with his in the future.