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Doubling the concentration, doubles the value of it's term for the total energy absorption.

Actually doubling the concentration increments absorption of CO2 by a fixed increment due to the fact that CO2 spectal lines are saturated (i.e. not enough IR at the right wavelengths to go around for the density of CO2 molecules in the atmosphere).

The only additional absorption that can occur by increasing CO2 concentration is in those areas of the spectrum at the tails of strong line responses and in the weak spectral lines of CO2 thus the absorption of IR is logarithmic as opposed to linear increasing at something less than 5.35*ln(C/Co) w/m², how much less depending on amount of water vapor in the atmosphere overlapping CO2 spectral lines reducing the amount of IR available to CO2.

" Actually doubling the concentration increments absorption of CO2 by a fixed increment due to the fact that CO2 spectal lines are saturated (i.e. not enough IR at the right wavelengths to go around for the density of CO2 molecules in the atmosphere). The only additional absorption that can occur by increasing CO2 concentration is in those areas of the spectrum at the tails of strong line responses and in the weak spectral lines of CO2 thus the absorption of IR is logarithmic as opposed to linear increasing at something less than 5.35*ln(C/Co) w/m2, how much less depending on amount of water vapor in the atmosphere overlapping CO2 spectral lines reducing the amount of IR available to CO2."

The CO₂ is contained in a bulk of other gasses. It transfers kinetic energy to those other gases, so that equation doesn't apply. The equation you posted is a version of Beer's law. That equation only applies if there is no other interactions. In this case there is. So, CO₂ is not near saturation and has considerable absorbing power. It absorbs about 6.5 W/M² and doubling the concentration, ~doubles the energy absorbed, because it transfers the energy to the atmosphere. edsheppa wrote out the idea in #103. The transfer is probably not complete though, because there's an equilibrium established here. The effective "C_o and the "5.xx", change with C, so it's pointless to use Beer's law. Here's a plot that shows the Earth's black body profile from space, showing the CO₂ is still strongly absobing.