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?

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?