As a newbie on climate science and meteorology I'm trying to understand the almost logarithmic behavior of CO2 concentration on radiation forcing
$$F(c) = A \cdot \ln \frac{c}{c_0}$$
and why there is no "saturation" due to further increasing of CO2 even when the atmosphere is already totally absorbing as a whole.
So far I learned that the air layers which contribute most to outgoing radiation are placed where optical thickness, as measured from TOA, is about 1. Let's say in an undisturbed atmosphere this location is about a height of z=2 (arbitrary units), then a CO2 doubling leads to a shift of this layer to about z=3.
Since this higher layer has usually lower temperature, less energy is irradiated an, therefore, the planet will warm up.
This is described also in some detail in https://escholarship.mcgill.ca/downloads/db78th05j.
On the other hand, other explanations, even mentioned in the cited publication, are based on spectral effects where the wings of the absorption band become more absorbing at higher CO2 concentrations:
Q1: Firstly, I don't understand why this last effect is, because CO2 is quite dilute in atmosphere and this effect cannot be due to pressure broadening. What is the reason for absorbing more CO2 at the wings when concentration rises up?
Q2: secondly, which of the two effects is more relevant to explain the observed log behavior? Are they related in any way or do they just happen to give the same overall result?