[Bored chemist]

A quick google search hasn't turned up the infrared absorption coefficient for CO2, so I'm relying on the memory of other people's data. Can you produce a figure? I'd like to review the maths. AFAIK there are only two significant bands in the IR, but I don't have Landolt-Bornstein or whatever standard text you use.   

Here's a copy of the spectrum.
http://www.senseair.com/senseair/gases-applications/carbon-dioxide/
Now, look at it.
Are the sides of the peaks in the spectrum vertical, or do they slope?
If they slope that's enough to show that the transition never actually saturates.

[alancalverd]

Now here's a well-known and widely published set of transmittance spectra for atmospheric gases, including all the pressure broadening and actual parital prsssures - i.e. actual data from the real atmosphere.. The transmittance of CO2 around 4 nm is zero. So adding more won't change anything.

[Bored chemist]

Now here's a well-known and widely published set of transmittance spectra for atmospheric gases, including all the pressure broadening and actual parital prsssures - i.e. actual data from the real atmosphere.. The transmittance of CO2 around 4 nm is zero. So adding more won't change anything.

What has 4nm got to do with anything?

[alancalverd]

Not a lot, admittedly. Try 4 microns* instead! That's the critical wavelength quoted in the paper you cited. Must have had a senior moment.

Also worth noting that at the longer wavelengths the CO₂ band around 12 - 15 microns is also saturated.  Atmospheric behavior in the "thermal IR" region, as everywhere else,  is dominated by the nonsaturated H₂O absorption. Plus of course reflection and a whole lot of far more complicated absorption from liquid and solid H₂O in clouds.

*Note for US readers: 0.00015748 inches.

[Bored chemist]

Not a lot, admittedly. Try 4 microns* instead! That's the critical wavelength quoted in the paper you cited. Must have had a senior moment.

Also worth noting that at the longer wavelengths the CO₂ band around 12 - 15 microns is also saturated.  Atmospheric behavior in the "thermal IR" region, as everywhere else,  is dominated by the nonsaturated H₂O absorption. Plus of course reflection and a whole lot of far more complicated absorption from liquid and solid H₂O in clouds.

*Note for US readers: 0.00015748 inches.

The whole point about the lack of saturation is that absorption isn't at a wavelength, it's over a band of wavelengths.
How wide that band is depends on how hard you look.

[puppypower]

Not a lot, admittedly. Try 4 microns* instead! That's the critical wavelength quoted in the paper you cited. Must have had a senior moment.

Also worth noting that at the longer wavelengths the CO₂ band around 12 - 15 microns is also saturated.  Atmospheric behavior in the "thermal IR" region, as everywhere else,  is dominated by the nonsaturated H₂O absorption. Plus of course reflection and a whole lot of far more complicated absorption from liquid and solid H₂O in clouds.

*Note for US readers: 0.00015748 inches.

The whole point about the lack of saturation is that absorption isn't at a wavelength, it's over a band of wavelengths.
How wide that band is depends on how hard you look.

Another consideration is atmospheric CO2 does not exist in a vacuum, but rather CO2 is reactive with water to form carbonic acid H2CO3. This  has a modified absorption spectrum compared to pure CO2. As the humidity goes up and down the CO2/H2CO3 ratio changes. Below is a graph of CO2 absorption versus CO2 plus H2O.



http://www.astrochem.org/data/CO2H2O/co2fig2.gif


CO2 is roughly a linear molecule that vibrates in a linear fashion, due to the double bonds in O=C=O. When CO2 reacts with H2O, we get H2CO3 where the bond angles around the central carbon are no longer 180 degrees, but closer to 120 degrees. See  below. This alters the vibrational orientation for absorption.



As the concentration of CO2 and water go up, another thing can begin to occur, with is a dimer of carbonic acid, due to hydrogen bonding, as shown below. This further alters bonding vibrations.


At lower CO2 and less water we get more of  pure CO2 absorption spectrum, as the water concentration increases, such as by evaporation due to warming, we get more carbonic acid, and as CO2 plus water increases, we get more of the dimer. The result is the earth can absorb heat by CO2 differently for the deserts and oceans based on the availability of water for carbonic acid. This gets even more complex when you add liquid and solid water from clouds.

[alancalverd]

The whole point about the lack of saturation is that absorption isn't at a wavelength, it's over a band of wavelengths.
How wide that band is depends on how hard you look.

Then, since I originally said "around 4 microns",  by all means look at all the infrared bands of  CO₂ absorption. They are all saturated in the atmosphere except for the 10.6 micron laser band. The 4 or 12 micron figure refers to the band center frequency. Pressure broadening has merged the fine spectrum into a fairly continuous band, but doubling the CO₂ content of the atmosphere won't  have much effect as the  broadening is mostly due to interactions with oxygen, nitrogen, argon and of course water, whose pressure won't be much affected by adding 400 ppm of anything else.

[Tim the Plumber]

Just for those of us who are not really able to follow this, can you explain in Watts per square meter what the difference in energy balance the differencies you are talking about would cause.
Thanks.

[Bored chemist]

The whole point about the lack of saturation is that absorption isn't at a wavelength, it's over a band of wavelengths.
How wide that band is depends on how hard you look.

Then, since I originally said "around 4 microns",  by all means look at all the infrared bands of  CO₂ absorption. They are all saturated in the atmosphere except for the 10.6 micron laser band. The 4 or 12 micron figure refers to the band center frequency. Pressure broadening has merged the fine spectrum into a fairly continuous band, but doubling the CO₂ content of the atmosphere won't  have much effect as the  broadening is mostly due to interactions with oxygen, nitrogen, argon and of course water, whose pressure won't be much affected by adding 400 ppm of anything else.

By all means read my earlier point.
"Now, look at it.
Are the sides of the peaks in the spectrum vertical, or do they slope?
If they slope that's enough to show that the transition never actually saturates."
And, of course, there are the weaker transitions as well as things like hydrated CO2.

[alancalverd]

Compared with the water spectrum, the CO₂ spectrum edges are indeed vertical.  Any further broadening can only come from significantly increased pressure or temperature.

Anyway. as you are a spectroscopist, you can easily do the experiment. Isolate a metre or so of dry air, measure the transmittance in the CO2 spectrum, and add another 400 ppm of CO2. Now extrapolate to 5000 m or whatever you consider to be the effective thickness of the atmosphere, and see what happens.

[Bored chemist]

Compared with the water spectrum, the CO₂ spectrum edges are indeed vertical. 

Compared to vertical; they aren't.
So, the absorption will still increase with concentration.
Obviously, it's not linear (It never is), but it's still an increasing function.
More CO2 means more absorption of IR.
Are you trying to claim otherwise?
Because, if you are not, then the saturation isn't just not true, it's not relevant.

[alancalverd]

It is true that I = I₀e^-mx never quite reaches zero, but I am appealing to your scientific ability to predict by a simple experiment what will happen if the CO₂ concentration of the atmosphere doubles. I don't have the necessary equipment to hand, but my estimate is "negligible".

What I find surprising about the CO₂ debate is that nobody seems to have published the experimental result, which would be a lot easier to obtain than a model prediction, and a lot more credible since all the models to date seem to have been wrong or dependent on suspiciously "adjusted" data.

[Bored chemist]

"It is true that I = I0e-mx "
The point I keep trying to make is that it doesn't apply.
That expression only works for monochromatic radiation

"What I find surprising about the CO2 debate is that nobody seems to have published the experimental result"
What experiment have you in mind?

[alancalverd]

Wrong. The extinction equation is true for all photons for which we can measure m, and this includes integrating  over a finite spectral width since we never encounter true monochromaticity.

"The experiment" is the one I described: measure m for a sample of ambient air over the IR spectrum, then double the concentration of carbon dioxide and measure it again. Now extrapolate your result to 50 km path length. My original suggestion of using dry air was misleading.

[puppypower]

Compared with the water spectrum, the CO₂ spectrum edges are indeed vertical. 

Compared to vertical; they aren't.
So, the absorption will still increase with concentration.
Obviously, it's not linear (It never is), but it's still an increasing function.
More CO2 means more absorption of IR.
Are you trying to claim otherwise?
Because, if you are not, then the saturation isn't just not true, it's not relevant.

There is a saturation point, where all the energy levels of the CO2, become filled, such that any new energy added, will release other energy. The CO2 cannot just keep absorbing. The analogy is like a sponge can continue to absorb water, until it becomes saturated. At the saturation point, each new drop of water added, will result in an old drop leaking out.

All we need to do is multiply the heat capacity of CO2 times the total mass of CO2 in the atmosphere, to determine the saturation point where all energy levels are filled. Once you know that, we can calculate what percent this energy represents, compared to the total solar input flux.  I would guess this is a very small percent. This would suggest that the sun saturates the CO2 during the day, where the sun is shining. At night, the solar factor becomes zero, with the CO2 losing energy, but never all the way to zero,  due to the earth's surface energy flux going into space. The next day, it saturates again.

The water in the atmosphere is doing the same thing, with the impact of the water, much more complicated. Water will exist as three phases, solid, liquid and gas, with water having a high heat capacity. The concentration of water, is less uniform across the globe; rain forest to deserts to oceans. The water can also discharge local saturation potential in various ways, such as via rain and lightning.  The heat of the oceans, are a huge energy sink which radiates to the CO2 at night.
 

[alancalverd]

Wrong concept of saturation, I'm afraid. CO₂ has very few, and very narrow,  IR absorption bands anyway, but what matters here is "extinction length".

The equation I = I₀e^-cx means that the intensity of light at any given wavelength, passing through a length x of an absorber, decreases exponentially with a coefficient c which is characteristic of the absorber at that wavelength. Where we know the total incident intensity across all wavelengths and the relative strengths of the absorption bands, we can assign an integrated value m instead of the individual band characteristics c, and this is the case for solar irradiation through the atmosphere.

Now whilst e^-mx, and hence I, never quite reaches zero, it is obvious that doubling the concentration of CO₂ from 10 to 20 ppm will have a much greater effect than doubling it from 300 to 600 ppm. Think about adding layers of blankets to a bed  (the same equation applies). The first blanket makes a huge difference to your heat loss, but the difference between 20 and 21 blankets is negligible.

There are essentially two ways of establishing the greenhouse effect of CO₂. You can measure the IR absorption of a given length of ambient air, then double the CO₂ concentration, which will give you a measure of the "relative " effect, or you can say that the present concentration is equivalent  to a path of about 2m through pure CO₂ at atmospheric pressure, so you can measure the transmission of 2 and 4 m of pure CO₂ to estimate the "absolute" effect.

For reasons that I cannot fathom, I have seen no experimental results of either test.     

[Bored chemist]

"CO2 has very few, and very narrow,  IR absorption bands anyway."
you can calculate how many bands it has very easily from the structure.
It has 3 atoms in a line. so it has 4 fundamental vibrational modes, and some of those might be degenerate.
(rocket science is somewhere else at the moment)
However all of those are spread by rotational bands and those in turn are spread by Doppler, pressure, and other sorts of broadening.
So the idea that they are very narrow just isn't true.
What's more difficult is to take account of the weaker absorptions- the ones you don't see in a short path length because they get lost in the noise, but which become important when you have a path length of miles.
That's why your proposed experiment is a bit pointless. You change the nature of the transitions.

Imagine, however, that you did it- what would you expect to learn?

[alancalverd]

http://www.randombio.com/co2.html gives a very cogent and readable account of CO₂ "saturation" and some credible spectra (they are pretty much the same as everyone else's published spectra).

[Bored chemist]

http://www.randombio.com/co2.html gives a very cogent and readable account of CO₂ "saturation" and some credible spectra (they are pretty much the same as everyone else's published spectra).

And...?
They simply point out that the absorption vs concn curve is not linear.

Nobody said it was.

However, what they don't say is that there's some concentration, above which adding more CO2 doesn't matter.
In particular, they don't claim that happens at, say 300 ppm.

So, "Saturation" is  a bit meaningless since it never really happens. There's never a concentration at which the absorption is "saturated" and no further increase in absorption will take place if you raise the concentration.

Nobody ever said it's linear.
Nobody is saying that it's not monotonically increasing.


Incidentally, as I asked, what would you do with the data from the experiment you proposed?

[alancalverd]

What I would do with the data is: publish a credible estimate of the effect of CO2 variation on mean atmospheric temperature based on a priori calculation, not a posteriori modelling. Then wait and see what happens.

If my prediction turns out to be correct, we have a rational basis for reducing CO2 emissions, or ignoring them, depending on the magnitude and sign of the predicted effect.

If my prediction turns out to be incorrect, then we have a rational basis for doing something positive about mitigating the effects of climate change rather than worrying about a non-cause.