Why does the radiative forcing from strongly-absorbing gases depend logarithmically on concentration?

It is universally accepted that the radiative forcing due to changes in atmospheric concentrations of strong LW (longwave: terrestrial thermal radiation) absorbers such as CO₂ varies logarithmically with concentration.

However, there seems to be no explanation in the peer-reviewed atmospheric-science literature. It seems everyone thinks they know, or at least someone knows so they could find out, but in fact contradictory physical explanations are in circulation.

We shall present the result of calculations to test these explanations, and show why it makes sense to conclude that there is in fact no general physical explanation