Atmospheric absorbance of CO2 and impact of increaseing concentration

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Summary
If the transmittance of IR to space is already zero in CO2 bands, how can adding more CO2 change anything?
This is a serious question, and it is not meant as an attempt to "debunk" greenhouse warming of the earth.

Wikipedia has the below image, which shows the atmospheric transmittance as a function of wavelength. Notice the red vertical line through one of the CO2 absorption bands. We see that the light emitted in that band is nearly totally absorbed by the CO2 in the atmosphere, i.e., the transmittance is near zero in that band (and the same for the thinner band at shorter wavelength). Now the question arises: how could adding more CO2 make it so that even more light is absorbed in that band, when all the IR emitted in that band is already absorbed by CO2?

My understanding is that the AGW hypothesis is that IR emitted from the ground is absorbed by CO2 in the atmosphere and this prevents it from getting to space and thereby cooling the earth. If this is so, then isn't the atmosphere already at a point where it cannot absorb more (than 100%) of the light in that band?

Thank you!




Absorption_bands.png
 
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Thank you, Bandersnatch. That does help me understand what is going on.

I follow him in the "Advanced" tab until this point:

"We can now look at what happens when we increase α [the absorption constant]."

He displays a graph that shows the impact of "Increasing α." This shows the range of wavelengths absorbed gets extended with increased α. What he doesn't say is why α would increase in the first place. Does he mean the absorption would increase on the edges of the absorption band (where saturation has not been reached) because of increasing concentrations of CO2? If that is correct, then can I summarize as below?

Though there are some places on the emitted spectrum where the absorption is saturated (in the center of the absorption bands), increasing CO2 concentration increases absorption in those frequencies (on the edges of the absorption bands) which are not currently saturated.

Is that an accurate summary? If so, then two interesting questions arise.

1. How much would the edges contribute to overall absorption (percent-wise), even if they became saturated?
2. What level of CO2 would saturate all the bands?


Thanks again. I think I may be getting a clearer picture of what the skeptic is saying, and why it is not quite right.
 
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Raymond T. Pierrehumbert in Infrared radiation and planetary temperature (2011):

The path to the present understanding of the effect of carbon dioxide on climate was not without its missteps. Notably, in 1900 Knut Ångström (son of Anders Ångström, whose name graces a unit of length widely used among spectroscopists) argued in opposition to his fellow Swedish scientist Svante Arrhenius that increasing CO2 could not affect Earth’s climate. Ångström claimed that IR absorption by CO2 was saturated in the sense that, for those wavelengths CO2 could absorb at all, the CO2 already present in Earth’s atmosphere was absorbing essentially all of the IR. With regard to Earth like atmospheres, Ångström was doubly wrong. First, modern spectroscopy shows that CO2 is nowhere near being saturated. Ångström’s laboratory experiments were simply too inaccurate to show the additional absorption in the wings of the 667-cm−1 CO2 feature that follows upon increasing CO2. But even if CO2 were saturated in Ångström’s sense —as indeed it is on Venus— his argument would nonetheless be fallacious. The Venusian atmosphere as a whole may be saturated with regard to IR absorption, but the radiation only escapes from the thin upper portions of the atmosphere that are not saturated. Hot as Venus is, it would become still hotter if one added CO2 to its atmosphere. A related saturation fallacy, also popularized by Ångström, is that CO2 could have no influence on radiation balance because water vapor already absorbs all the IR that CO2 would absorb. Earth’s very moist, near-surface tropical atmosphere is nearly saturated in that sense, but the flaw in Ångström’s argument is that radiation in the portion of the spectrum affected by CO2 escapes to space from the cold, dry upper portions of the atmosphere, not from the warm, moist lower portions. Also, as displayed in the inset to figure 2, the individual water-vapor and CO2 spectral lines interleave but do not totally overlap. That structure limits the competition between CO2 and water vapor.

Gilbert N. Plass in Carbon Dioxide and the Climate (1956):

The carbon dioxide theory was first proposed in 1861 by Tyndall. The first extensive calculations were necessarily done by very approximate methods. There are thousands of spectral lines due to carbon dioxide which are responsible for the absorption and each of these lines occurs in a complicated pattern with variations in intensity and the width of the spectral lines. Further the pattern is not even the same at all heights in the atmosphere, since the width and intensity of the spectral lines varies with the temperature and pressure. Only recently has a reasonably accurate solution to the problem of the influence of carbon dioxide on surface temperature been possible, because of accurate infrared measurements, theoretical developments, and the availability of a high-speed electronic computer.

The fact that water vapor absorbs to some extent in the same spectral interval as carbon dioxide is the basis for the usual objection to the carbon dioxide theory. According to this argument the water vapor absorption is so large that there would be virtually no change in the outgoing radiation if the carbon dioxide concentration should change. However, this conclusion was based on early, very approximate treatments of the very complex problem of the calculation of the infrared flux in the atmosphere. Recent and more accurate calculations that take into account the detailed structure of the spectra of these two gases show that they are relatively independent of one another in their influence on the infrared absorption. There are two main reasons for this result: (1) there is no correlation between the frequencies of the spectral lines for carbon dioxide and water vapor and so the lines do not often overlap because of nearly coincident positions for the spectral lines; (2) the fractional concentration of water vapor falls off very rapidly with height whereas carbon dioxide is nearly uniformly distributed. Because of this last fact, even if the water vapor absorption were larger than that of carbon dioxide in a certain spectral interval at the surface of the Earth, at only a short distance above the ground the carbon dioxide absorption would be considerably larger than that of the water vapor. Careful estimates show that the temperature changes given above for carbon dioxide would not be reduced by more than 20 per cent because of water vapor absorption.

One further objection has been raised to the carbon dioxide theory: the atmosphere is completely opaque at the center of the carbon dioxide band and therefore there is no change in the absorption as the carbon dioxide amount varies. This is entirely true for a spectral interval about one micron wide on either side of the center of the carbon dioxide band. However, the argument neglects the hundreds of spectral lines from carbon dioxide that are outside this interval of complete absorption. The change in absorption for a given variation in carbon dioxide amount is greatest for a spectral interval that is only partially opaque; the temperature variation at the surface of the Earth is determined by the change in absorption of such intervals.
For estimation from calculations and lab measurements:
- The greenhouse effect and carbon dioxide https://rmets.onlinelibrary.wiley.com/doi/pdf/10.1002/wea.2072
- The spectroscopic foundation of radiative forcing of climate by carbon dioxide https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2016GL068837

For evidence from observation :
- Increases in greenhouse forcing inferred from the outgoing longwave radiation spectra of the Earth in 1970 and 1997 https://www.nature.com/articles/35066553
- Observational determination of surface radiative forcing by CO2 from 2000 to 2010 https://www.nature.com/articles/nature14240
 

Bandersnatch

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Though there are some places on the emitted spectrum where the absorption is saturated (in the center of the absorption bands), increasing CO2 concentration increases absorption in those frequencies (on the edges of the absorption bands) which are not currently saturated.

Is that an accurate summary? If so, then two interesting questions arise.

1. How much would the edges contribute to overall absorption (percent-wise), even if they became saturated?
2. What level of CO2 would saturate all the bands?
I don't fully understand the physics of how the bands widen with concentration, but from what I read this is overall a minor effect. I've found this graph on some sites discussing CO2 saturation:
1572022927525.png

(although I can't identify the primary source, might be database-generated; to be found e.g. here:
http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii)
which suggests that while there is no theoretical cut-off that would fully saturate all bands, the additional energy stopped is relatively minor even as the CO2 concentration increases manyfold.

The main effect seems to be the one discussed earlier on the site, i.e. the layered nature of the atmosphere.
 

haruspex

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the physics of how the bands widen with concentration
That it is a band at all, rather than very precise spikes, is down to the Doppler effect. A molecule that happens to be moving towards the source sees the frequency as higher, so can absorb a photon that would otherwise have too great a wavelength. Conversely for a molecule moving away from the source.
The more molecules of the gas there are, the more will have extreme speeds and the wider the absorption band.
I believe this is why the increased absorption is taken to be approximately logarithmic (over some range), but I do not know the algebraic details.
 
45
5
Summary: If the transmittance of IR to space is already zero in CO2 bands, how can adding more CO2 change anything?

This is a serious question, and it is not meant as an attempt to "debunk" greenhouse warming of the earth.

Wikipedia has the below image, which shows the atmospheric transmittance as a function of wavelength. Notice the red vertical line through one of the CO2 absorption bands. We see that the light emitted in that band is nearly totally absorbed by the CO2 in the atmosphere, i.e., the transmittance is near zero in that band (and the same for the thinner band at shorter wavelength). Now the question arises: how could adding more CO2 make it so that even more light is absorbed in that band, when all the IR emitted in that band is already absorbed by CO2?

My understanding is that the AGW hypothesis is that IR emitted from the ground is absorbed by CO2 in the atmosphere and this prevents it from getting to space and thereby cooling the earth. If this is so, then isn't the atmosphere already at a point where it cannot absorb more (than 100%) of the light in that band?

Thank you!




View attachment 251718
This diagram describes what happens to the radiation that leaves from the Earths surface.
But you have to remember that the CO2 in the atmosphere radiates too.
From space the radiation in this band all the way from the ground is not detectable;
what is detectable comes from CO2 high in the atmosphere.

To balance out the Sun's input at Earth's orbit (and taking into account albedo),
the effective blackbody radiation surface has to be approximately -18C
which is what satellites measuring Earth's temperature using infrared see.
Water vapor drowns out the CO2 until you reach a height where the temp is around 0C.
The more CO2/H2O you have the higher this effective surface will be.
The lapse rate then determines the temperature at the ground.
 

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