It is certainly an evergreen claim by the climate change disbelievings crew that the absorption of CO2 in the atmosphere is saturated. What does saturated mean to them is a useful question to ask. A useful answer would be that the atmosphere is optically thick at the greenhouse effect relevant frequencies/wavelengths where CO2 absorbs, between about 620 and 840 cm-1.
It would also be useful to describe what is meant by optically thick and optically thin. To do that we first need to define optical depth. Optical depth is the fraction of light blocked in passing through a medium. The transmission is the percentage of light that gets through. Something is optically thick at a particular wavelength if no light can get through it, It is optically thin if most or all of the light can get through. If an absorption is not optically thick, it can't be saturated
If the disbelievers are right at current concentrations CO2 is optically thick over the entire region.
We can check on that using Spectral Calc, a program that allows us to calculate the spectrum based on precision and verified measurements. Let us imagine that the atmosphere is a tube with 400 ppm CO2 at 296K. How much of the light is absorbed in a 1 m tube
At this point those interested in only the bottom line can skip down to the bottom of the post and pick up the figure the bunnies need for their tweet.
ORIENTATION
Most of the spectrum is due to transitions from the CO2 ground vibrational level to the first excited vibrational level The sharp peak in the center is called the Q branch composed of lines that are very close together and corresponds to transitions where the rotation(al quantum number) of the molecule does not change. The band to the left is the P-branch for transitions where the rotational quantum number decreases by 1. The band to the right is the R-branch where the rotational quantum number increases by 1.
The two little sharp peaks to the right and left of the main bands are Q-branch transitions between excited vibrational levels. Even at room temperature a small percentage of the molecules are vibrationally excited by collision. Of course, they can also lose energy by collisions but there is an equilibrium between excitation and de-excitation by collisions with nitrogen and oxygen molecules (mostly) and a thermally driven equilibrium population in each vibrational level. If a bunny squints really hard she can see the corresponding P and R-branches. These are called hot bands. Why the excited vibrational levels are split and even what excited levels they connect is complicated.
Google books provides an explanation.
If the distance is increased to 10 meters the lines of the 0-1 band are optically thick but there is still space between them, however, the lines do have wings and the wings overlap so even over a 10 m path, there is a noticeable underlying continuum mostly caused by collisional broadening. The hot bands on either side of the Q branch are now easy to see. The Q branch 0-1 band is optically thick
At 100 m or 0.1 km the 0-1 transition is almost optically thick and the 1-2 bands are very clear. Using the squintosope, Q branches for higher lying hot bands can be seen at the edges
For a 1 km path length, most of the 0-1 transition is optically thick (saturated in the disbelieving sense) but light from the surface would still be seen in the wings, where the hot bands are.
BOTTOM LINE
Finally at 10 km, while the center of the CO2 absorption is optically thick, there are still regions of the spectrum where light from the surface will get through the atmosphere.
Of course, increasing the amount of CO2 in the atmosphere will decrease the transmission in the wings of the bands. At 560 ppm
and returning to 280 ppm
There are a few things that Eli has not considered in this post but they all would DECREASE the calculated optical thickness. Temperature and pressure decrease with altitude. This post assumes both are constant. Their effects will be considered in detail in follow on posts, Simply put the optical depth is directly proportional to density and path length, thus decreasing density with altitude, decreases the average optical depth and increases transmission across the spectrum. Second at lower temperature there is less population in the excited vibrational levels and the hot bands at the edges of the spectrum are weaker, decreasing the optical depth in the wings, and increasing it in the center 0-1 band. Since the 0-1 band IS optically thick at very small path lengths anyhow, this increases transmission. Third, each of the lines is substantially broadened at atmospheric pressure. A narrower comb of lines is optically thinner. This would substantially decrease the continuum absorption between the lines.
Bottom line, the 667 cm-1 CO2 vibrational absorption is not optically thick across the entire region of absorption. It is not saturated.