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teal
2014-Apr-22, 04:22 PM
I'm sorry if this wrong section of the forums, i believe it's closest one.

I'm trying to build simple atmospheric model, but i'm kind of stuck at greenhouse effect. I'm looking at this picture http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png and see that CO2 absorption around 15um band is 100%, but i can't figure out how this absorption rate is related to CO2 ppm in atmosphere.

I assume that one molecule of CO2 can't absorb whole Earth's radiation, right? Then it has to be related to CO2 ppm. This my idea might be completely wrong, i'm not a physics student, unfortunately. I would appreciate if you point that out and give me a proper reference to correct theory.

Edit: the following calculations are unscientific and most probably has no relation to any scientific theory.

Atmospheric height is around 10km, CO2 ppm in air is 400. I believe composition of air doesn't change with height, only density changes. If i sum up ppm of 10000 meters of air, then i'll get 4*10^6 ppm of CO2. Then i assume 4*10^6 ppm is roughly 4 cubic meters of CO2 stacked:

+-+
|4| 4th m^3
+-+
|3| 3rd m^3
+-+
|2| 2nd m^3
+-+
|1| 1st m^3
+-+

--- surface ---

Now i can imagine that if this is 4 m^3 of pure CO2, then 1st m^3 will be 100% opaque to 15um radiation band. This also generally means that atmosphere is (over-)saturated with CO2 and greenhouse effect will be significant until CO2 concentration of 100ppm. But if CO2 level would drop below, to 50ppm, then CO2 greenhouse effect will be reduced to roughly 25% (50% of opaque concentration * 0.5 return rate).

To check absorption rate: Earth emits at 255K, and CO2 absorption band is roughly between 15-17um: http://en.wikipedia.org/wiki/File:CO2_H2O_absorption_atmospheric_gases_unique_p attern_energy_wavelengths_of_energy_transparent_to _others.png

I'm using this calculator to figure out what fraction of energy will be absorbed: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html#c1 . 15-17um band of 255K radiation is approximately 9% of the total radiated power. If i put 9% absorption value into one-layer greenhouse model, then i'm getting 257.83K surface temperature, i.e. 2.87K returned to surface, which generally agrees with expected value...

My main concern is that one-layer model assume that half of radiation is returned back to surface, but i think it should be more than that in case of over-saturation. I think this stack of 4m^3 of CO2 might be viewed as 4 layers of CO2 affecting (heating) each other and returned radiation rate must be around 0.6875 (~net return of 3 layers of CO2) instead of 0.5.

Hence i'm still unsure how to calculate greenhouse effect of 50ppm CO2. I would say it should depend on "reflectivity" of the whole CO2 stack, but i don't know where to look to confirm or reject this idea.

Any ideas?

Noclevername
2014-Apr-22, 05:42 PM
The exact details are still being hotly debated. There's all sorts of conflicting information and misinformation; I doubt you could find a single reliable source right now.

Swift
2014-Apr-22, 06:27 PM
The exact details are still being hotly debated. There's all sorts of conflicting information and misinformation; I doubt you could find a single reliable source right now.
I'm surprised to hear that. I didn't think the physics of CO2's contribution to the greenhouse effect was hotly debated. The details of all the impacts on climate, weather, ecosystems, etc., etc, might be, but not the physics of the effect.

Oh, and teal, welcome to CQ. Sorry, I don't know the answer to your question. I think either this section, or Q&A, or Science & Technology would be fine for this thread. You might bet more traffic in Q&A - if you don't get your answer soon, we'll move it.

teal
2014-Apr-22, 07:25 PM
@Noclevername
I've been looking on different sources for quite a while, but unfortunately none of them was linking ppm to absorption in any way.

I think that 1st m^3 should return 0.5 back and propagate 0.5 to 2nd m^3, 2nd m^3 should return 0.25 back to 1st and propagate 0.25 to 3rd m^3. Back to 1st m^3, it should absorb 0.25 returned from 2nd m^3, then emit 0.125 back to surface and 0.125 back to 2nd m^3, and so on..

I really think i'm describing some physics law, but i don't know how it's called and therefore can't complete model. I would appreciate if someone just point me to it, then i can check this model on Venus' atmosphere, i guess.

@Swift Thanks.

Noclevername
2014-Apr-22, 11:48 PM
I'm surprised to hear that. I didn't think the physics of CO2's contribution to the greenhouse effect was hotly debated.

Well, I'm not an expert. I suppose I should have said "as far as I know", as most of my knowledge comes from what is hashed out in the popular media.

2014-Apr-23, 01:11 AM
Well for the actual effect, there's always this paper:

On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground
Svante Arrhenius, April 1896:

http://rsclive3.rsc.org/images/Arrhenius1896_tcm18-173546.pdf

Squink
2014-Apr-23, 03:50 PM
I'm trying to build simple atmospheric model, but i'm kind of stuck at greenhouse effect. I'm looking at this picture http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png and see that CO2 absorption around 15um band is 100%, but i can't figure out how this absorption rate is related to CO2 ppm in atmosphere.I like this graph better (http://www.google.com/imgres?imgurl=http%3A%2F%2Fwww.worldclimatereport. com%2Farchive%2Fprevious_issues%2Fvol4%2Fv4n19%2Ff igures%2Fp7.gif&imgrefurl=http%3A%2F%2Fwww.worldclimatereport.com% 2Farchive%2Fprevious_issues%2Fvol4%2Fv4n19%2Fcutti ng.htm&h=194&w=480&tbnid=2t4PxHP6PcyaLM%3A&zoom=1&docid=2ywfQgfgTZ-PEM&ei=d91XU-n6A6auyAHu0oGoAw&tbm=isch&client=firefox-a&ved=0CBYQMygOMA44ZA&iact=rc&uact=3&dur=659&page=6&start=110&ndsp=21&biw=1217&bih=672), for explaining part of the difficulty you're having. Here's a more detailed spectra of CO2 absorption (http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Type=IR-SPEC&Index=1).

It's easy to see that the atmosphere will be opaque at those particular wavelengths, however, it's not just the 15.0 uM line that counts towards total heat absorption. The peaks have width, shoulders, and it's the integral including those that determines total heat retained. Likely if you got atmosperic CO2 up to 10,000 megabars, the breadth of those absorption lines would prove sufficient to 100% block everything from far UV to microwave.

Ari Jokimaki
2014-Apr-23, 04:06 PM
While I'm not exactly sure what kind of information you are looking for, but one place you might want to check is HITRAN:

http://www.cfa.harvard.edu/hitran/

And no, there's no hot debate around this issue, just some succesful propaganda from climate change deniers in popular media.

teal
2014-Apr-24, 01:11 PM
Thank you for the useful links. I can hardly understand some parts of them, but i will research them for my better understanding of this problem.

@Squink

Likely if you got atmosperic CO2 up to 10,000 megabars, the breadth of those absorption lines would prove sufficient to 100% block everything from far UV to microwave.

I also suspect this. I can imagine this situation, but exact relation of ppm/density to absorption is not quite clear to me. Meanwhile i've made another greenhouse model which seems to exhibit relatively realistic behavior.

The following description is unscientific and uneducated, you shouldn't do that.

Optical depth concept is appealing to me because it links amount of matter in the path of radiation to absorption properties. This particular equation: Tg^4 = (1+tau)*Teff^4 describes relation of surface temperature (Tg) to effective temperature (Teff) and optical depth of athmosphere (tau).

Unfortunately, it's not that easy to calculate tau from ground up. But i've made the following observation: with effective temperature of the Earth being 255K, tau need to be 0.05 to produce 288K surface temperature. Then, knowing Earth's atmosphere mass (5.1*10^18) and CO2 in it (0.04%), i've derived the following relation: 0.04 CO2 in atmosphere of mass 5.1*10^18 produce tau of 0.05.

Then i've tried to project this relation to the other planets. Mars has 0.005 mass of Earth's atmosphere, CO2 concentration is 0.9632 -> tau of 0.004822. This shows that even if Mars has higher concentration of CO2, it's greenhouse effect is much weaker (as expected). Venus has 94.1 mass of Earth atmosphere, CO2 concentration is 0.965 -> tau of 90.33.

I assume that water vapor follow the same rule, so i've got numbers for it also. Sum of produced numbers give me the following surface temperature:

Earth: 288K - or 291K for 800ppm of CO2
Mars: 210.5K - that is, greenhouse effect is almost negligible
Venus: 611K

To compare this numbers, i've used NASA planetary facts: http://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html

Earth is a reference point of all calculations, so 288K is natural to comply with NASA value. Mars also fits NASA value. Temperature of Venus is mostly incorrect, it should be 737K according to NASA. However, i've used Venus effective temperature of 184K to get 611K at surface, this corresponds to albedo of 0.9 (by NASA), but if change albedo to 0.78, effective temperature raises to 222K and surface temperature will be 738K.

Generally i believe this is not a bad approximation of greenhouse effect, but my approach is unscientific, unfortunately, thus this question is still open for me.