One of the “climate zombies” that get’s trotted out from time to time and at places on the Internet is the argument of Knut Ångström, trying to rebut the calculations of Svante Arrhenius regarding the impact a doubling of carbon dioxide concentration would have in atmosphere. You can find one of these zombies here.
The saturation argument basically says that carbon dioxide is an excellent absorber of thermal radiation in some infrared bands, so much so that it blocks this radiation altogether. This blockage is so complete, so says the argument, that adding additional CO2 doesn’t increase the absorption. Ergo, CO2 is absorbing as much thermal radiation as it can, and, so, adding more isn’t going to increase absorption.
This is wrong because while the center of such bands may block all of the radiation, the bands are not at all infinitesimally thin lines. The less absorbing “tails” of the lines where thermal radiation is not all blocked do increase in effectiveness of blocking as concentration of CO2 increases. Moreover, the absorption spectrum of CO2, like that of most atmospheric species, consists of a very large assortment of single lines, some more effective than others. A few dominate. But if the concentration increases, then the less effective ones become better blockers of thermal emissions, and, so, produce radiative forcing.
These points are also made at the following sites, more completely than I did here: