Dear Judge Alsup: The Spectroscopic basis

In a suit brought by cities in California against Exxon, Judge Alsup has asked of the parties a set of questions which some parties on the INTERNET are busy crowd sourcing the answers to.  Now Eli has never been one to avoid a pile on, so the Bunny thought he might essay an answer to two of the questions

2.  What is the molecular difference by which CO₂ absorbs infrared radiation but oxygen and nitrogen do not? 

3.  What is the mechanism by which infrared radiation trapped by CO₂ in the atmosphere is turned into heat and finds its way back to sea level?

Let Rabett Run start with question 2. Many of the answers start and end with what was learned in Modern Physics or Physical Chemistry.  Real Climate has settled on

Greenhouse gases are those that are able to absorb and emit radiation in the infrared, but this is highly dependent on the gases molecular structure. Diatomic molecules (like N2 or O2) have stretching modes (with the distance between the two molecules expanding and contracting), but these require a lot of energy (so they absorb only at higher energies. Vibrational modes in molecules with three or more atoms (H2O, CO2, O3, N2O, CH4, CFCs, HFCs…) include bending motions that are easier to excite and so will absorb and emit lower energy photons which coincide with the infrared radiation that the Earth emits. Thus it is these molecules that intercept the radiation that the Earth emits, delaying its escape to space.

This is approximately true, but not quite the whole story and much can be learned by going a bit deeper.  It is not that N2 or O2 cannot absorb or emit IR, but their absorption and emission is many orders of magnitude weaker than H2O, CO2 and other greenhouse gases found in the atmosphere.   How many orders of magnitude?  Well about ten.

A good place to start is the HITRAN data base maintained by the Harvard Smithsonian Center for Astrophysics.  HITRAN stands for High Resolution Transmission.  The database, just like the JANAF tables, is a fruit of the cold war started when the US Air Force was interested in learning more about the propagation of light in the atmosphere for such things as aiming missiles and such.  It is essentially a list of lines in the transmission spectra of various molecules under different conditions of  temperature, and pressure.  Using the database one can generate spectra of self-same molecules which are eerily accurate.  GATS among others provides a front end to calculate spectra using HITRAN, so let us start to explore.

The first question is does N2 or O2 absorb IR light. We know the vibrational frequency of these molecules, so we can look at what the database tells us how much light nitrogen would absorb in the atmosphere at a pressure of 1 mbar (1000th of atmospheric pressure. Be patient the reason for this choice will become clear in a few minutes), a temperature of 296 K and a path length of 1000 km.  Yes Eli knows that such a gas cell is not currently available, but with HITRAN we can accurately model this.

The alternating intensities of the lines are due to the symmetry of the nitrogen molecule but that is another story with which we need not concern ourselves at this time.  We can do the same for O2 

Turns out that the triplets seen in this spectrum are the source of the signal that the Microwave Sounding Units that measure tropospheric temperatures monitor.

But now we can do the same for CO2

The difference in path length for absorbing about the same amount of light by CO2 is 0.1 cm, or, if you wish 10^-6 km.  So the difference in the absorption would be a factor of 10^-9.  

But you say, the mixing ratio of CO2 in the atmosphere is 410 parts per million or 0.00041, and the concentration of N2 is 0.70 thus the number  of N2 molecules per CO2 molecule is just 1.75 x 10⁴ while the N2 absorption is 10^-9th of the CO2 absorption.  Put that together and the amount of IR absorbed by N2 is roughly 0.00002 of that absorbed by CO2.

Ms. Rabett is calling, so let Eli provide a bit of a teaser for Part II.  Here is the absorption of 400 ppm CO2 at atmospheric pressure across a 3 m cell.