Eli has been a happy hare with the new chewy carrot colored Spectral Calculator toy the mice left in the burrow. He is digging out the effects of increasing CO2 concentrations on the greenhouse effect from the spectroscopic point of view. Recent posts on Real Climate by Spencer Weart and Ray Pierrehumbert touched this off, and, of course Motl's folly aggravated the lab bunnies beyond the breaking point. Yesterday Eli looked at the effect of temperature on the CO2 bending mode absorption spectrum. Today we are under pressure. If you don't know much about pressure, you could do a very lot worse than looking at our mob blogging friend Tamino's Introduction to the Gas Laws and his post on Pressure and Height, how pressure varies with altitude.
where z is the altitude, g the
We will use the Spectral Calculator to look at this. First, let us look at the 300 K CO2 absorption spectrum (mice wanting to play along should fire up Spectral Calculator and follow the instruction in the preceding post on Temperature
We want to select a couple of lines from this, so after setting all the parameters as before (CO2 gas, the O(16)C(12)O(16) isotopomer, 10 cm cell length, 296K, 100 mbar total pressure, 0.000380 volume mixing ratio CO2) go to the observer page and set the upper and lower wavelength ranges as 680 and 684 cm-1. You will then see this spectrumIf we now increase the total pressure to 1000 mbar (~one atm), keeping the mixing ratio constant the result isand looking carefully (you might have to click on each graph to bring up full screen images) we see that the transmission at each of the peaks in both spectra is ~93% (7% of the incident light is absorbed).
Wait a minute. The volume mixing ratio in both spectra is 380 ppm. The total pressure in the first case was 100 mbar. The total pressure in the second case was 1000 mbar, ten times greater. That means that the amount of CO2 is ten times greater. We can, of course, keep the amount of CO2 constant by decreasing the mixing ratio in the second case to 38 ppm.Transmission at the line centers is not 99.3%!. If we carefully integrated under each peak in this spectrum and the one taken at 100 mbar the integrated amount of absorbed light would be the same, just that the peaks are wider and shorter at 1000 mbar. Total absorption does not increase due to pressure broadening (within limits, see below), but it is spread to a wider range of frequencies /wavelengths.
Finally a bit of ear waving about the origin of the pressure broadening. An isolated molecule's energy levels are shifted slightly when another atom or molecule nears and their electric fields interact. This changes the wavelengths at which molecules can absorb or emit. At low pressures only a relatively few molecules will collide at any instant, and pressure broadening occurs in the so called binary collision limit.
One can order the strength of electric interactions as ion > dipole > neutral. As a general rule, broadening by an ion is much longer range and stronger than broadening by a neutral. Broadening by a molecule with a permanent dipole moment stronger than broadening by one without. O2, because it has a magnetic moment in the ground state (two unpaired electrons) will be more effective as a broadener than nitrogen.
Having simplified all this, Eli will now point to the brier patch where there are lots and lots of nettles to sting you. First, as the molecules pass near to each other, the interaction will mix nearby quantum states. Transitions can borrow strength from each other and the absorption coefficients in each line can change. Second, collisions are of finite duration and range, which has the effect of decreasing intensity in the wings and increasing that at line center. Third, if absorption is observed for a relatively long path length (km) and for a molecule with a relatively high mixing ratio (CO2, H2O) absorption due to broadening can be significant 30 cm-1 or more away from the line center.
Now THAT would be a post.
UPDATE: If you want to learn about temperature effects see here and for more on pressure broadening see here and finally here