CO2 and Infrared Radiation

[Sciencerocks]

So the following question came up the other day, that I was trying to do some research to solve, but I couldn't find the answer. It was: "How long does the average infrared photon take to exit the atmosphere." Of course, this depends on the density of green house gasses in the atmosphere, so I am most interested in how long it would take with pre industrial greenhouse gas levels and present day levels. I also understand that when a photon strikes a molecule and causes it to vibrate, the photon ceases to exist, and a new photon is eventually re-emmitted. However, to make this more simple, let's pretend that the photon a molecule absorbes is the same one it emmits. I need to know the probablility that a photon will encounter a green house molecule based on the ratio of that greenouse gas to other gases, (ppm), and how long a carbon dioxide molecule will vibrate when struck by 15micrometer wavelength IR radiation, and 4.3 micrometer wavelength IR radiation. Thanks!

[Mr Skeptic]

Well, I think that what matters more, is how much IR actually makes it through the atmosphere, rather than being absorbed and re-emitted back to earth. They are re-emitted in random directions.

[louis wu]

Sciencerocks

 

Your question is actually an interesting one.

 

Firstly an average photon will be one not at a wavelength suitable for absorption by CO₂ or H₂O.

If you take the edge of the atmosphere to be the top of the mesosphere, then that is 85Km high.

As the speed of light is reduced only very slightly by passage through air I calculate the passage to take ~0.00028 sec.

 

Now photons that are at the correct wavelengths for absorption by CO₂ have a very different fate.

Effectively all these photons have been redirected to the ground or transferred as heat energy to surrounding molecules within the lowest 10 metres of atmosphere. In pre-industrial times I guess it would take ~13.5 metres of atmosphere for the same effect.

 

The fact that photons susceptible to capture by CO₂ would all be absorbed in the first few metres of atmosphere was used to discredit Arrhenius' theory of atmospheric warming from back in the 1890's. It was argued that as CO₂ blocked all photons in its absorption bands so effectively, addition of extra CO₂ into the atmosphere could make little difference.

This line of argument seems fine as long as you consider the atmosphere as a static single slab. When the atmosphere is viewed as a dynamic system with many different layers it is seen that extra CO₂ can indeed trap more energy within the system.

The exact amount of extra energy trapped per ppm of CO₂ is still vigorously debated.

So the answer is that photons in CO₂'s absorption bands do not get out of the atmosphere at all.

 

Decay times for vibrational excitement are usually ~ 10s of pico seconds. As CO₂ is a linear molecule with fewer vibrational modes I would expect its decay to be relatively fast.