# How much of visible sky is occupied by CO2?

1. Aug 2, 2011

### lancelot

My curiosity has been aroused by climate change debates, but my physics is inadequate. Perhaps I can get some help.

My question is simply: As viewed from the earth surface, what percentage of the area of the visible sky is occupied by CO2 molecules? This could be expressed in simple terms of x% per square metre.

I take as basic data:
Effective height of atmosphere 10,000 m.
CO2 molecules 400 parts per million in volume. (0.04%)
Diameter of Co2 molecule approx 3.23 angstroms.

So consider a shaft of atmosphere, 1 m x 1m x 10 km high.
How many CO2 molecules are in the shaft?
What is their average spacing?
As viewed upwards from the earth surface, what is the effective area of all the CO2 molecules?

The answer is not 0.04% of 1 sq m!

And from this, pro rata, if Co2 molecules were considered as perfectly reflecting mirrors, what proportion of heat radiation emitted from the earth (240 W/sm) would be reflected back?

I dont think the IPCC will be taking this sort of calculation on board, :) but it would be interesting to know.

2. Aug 2, 2011

### xts

You can't think about CO2 molecules as about golf balls, obscuring some part of the sky. It really makes no sense to ask what part of the sky is occupied. You may ask sensibly what percentage of 1000nm infrared is reflected. Or what percentage of X-rays is scattered.
As you go below the wavelength it really loses any sense to consider sizes of interacting particles. You may assume those molecules to be geometrical points, and they still interact.

You may find serious models of warming and CO2 influence on climate on
Nongovernmental International Panel on Climate Change website
http://www.nipccreport.org/

3. Aug 3, 2011

### y33t

Air is composed of different gases but these gases are not bounded to each other at molecular level, they are seperate molecules hanging in the air (assuming static condition for simplicity) and thus permittivity of free air will be in tensor form at small scale. Each molecule has different scattering characteristics thus it seems like a reasonably logical question to me.

On the other hand, CO2 distribution has very dynamic parameters. Since you will never be able to precisely find the value, why not find the total air from ground to last layer of visible sky (can be in volume) and divide it to the known ratio of CO2 in free air. It should give you a rough approximation.

Last edited by a moderator: May 5, 2017
4. Aug 3, 2011

### mikeph

I believe the calculation can be done to yield an answer with meaning if you use absorption cross sections, but then the answer becomes a wavelength-dependant probability function.

Also I don't think any of the light will be reflected. It will be scattered, leading to far more complicated models than I think you are intending to use.

5. Aug 3, 2011

### sophiecentaur

If you know the absorption of a given wavelength of em by a cube of a certain density of Co2 then, by working out the energy of a single Photon and the number of molecules, then you could come up with an 'effective' cross section. But what use would that be - apart from general interest?
The way it's treated at the moment is just as useful. I don't think your alternative view adds anything - so there wouldn't be a need for changing from using an absorption factor with a given density of CO2. In fact, because it would be wavelength dependent, you'd need to do extra calculations to get useful information out.

6. Aug 3, 2011

### schip666!

I had a similar problem a couple years ago... As a simple-minded simplification one could say the the CO2 molecule "coverage" in the sky was .04%. So, even if they acted as perfect reflectors, how could they be responsible for the amount of added surface energy being attributed to them? It's a question I'd never seen being asked, and when asked usually got off on the wrong foot...

After wrangling around the bushes with a bunch of folks who kept accusing me of being a dastardly climate denier, someone finally dropped "mean-free-path" and "Beer's Law" (http://en.wikipedia.org/wiki/Beerâ€“Lambert_law) into the conversation. So I think the answer is that making an assumption of linear coverage, like the .04% simplification, is incorrect. I lost patience with finding the constants and trying to run the Beer's Law numbers, but I feel better about the models now.

In the course of all that previous discussion I also couldn't find any reference to reproductions of Arrhenius's 1896 work defining the CO2 forcing relationship, aside from some refinements to the constant value (c.f. http://en.wikipedia.org/wiki/Radiative_forcing). His original paper uses a very "primitive" -- or brilliant -- measuring methodology and a LOT of post-processing on the data, so I though maybe someone would've repeated the exercise. I was subsequently directed to a couple sources which I immediately forgot...so if anyone has a ref to recent reproductions I'd like to see them.