Thursday, May 25, 2017

CO2 Atmospheric Absorption Is NOT Saturated

It is certainly an evergreen claim by the climate change disbelievings crew that the absorption of CO2 in the atmosphere is saturated.  What does saturated mean to them is a useful question to ask. A useful answer would be that the atmosphere is optically thick at the greenhouse effect relevant frequencies/wavelengths where CO2  absorbs, between about 620 and 840 cm-1.

It would also be useful to describe what is meant by optically thick and optically thin.  To do that we first need to define optical depth.  Optical depth is the fraction of light blocked in passing through a medium.  The transmission is the percentage of light that gets through.  Something is optically thick at a particular wavelength if no light can get through it, It is optically thin if most or all of the light can get through.  If an absorption is not optically thick, it can't be saturated

If the disbelievers are right at current concentrations CO2 is optically thick over the entire region.

We can check on that using Spectral Calc, a program that allows us to calculate the spectrum based on precision and verified measurements.  Let us imagine that the atmosphere is a tube with 400 ppm CO2 at 296K.  How much of the light is absorbed in a 1 m tube

At this point those interested in only the bottom line can skip down to the bottom of the post and pick up the figure the bunnies need for their tweet.


Most of the spectrum is due to transitions from the CO2 ground vibrational level to the first excited vibrational level  The sharp peak in the center is called the Q branch composed of lines that are very close together and corresponds to transitions where the rotation(al quantum number) of the molecule does not change.  The band to the left is the P-branch for transitions where the rotational quantum number decreases by 1.  The band to the right is the R-branch where the rotational quantum number increases by 1.

The two little sharp peaks to the right and left of the main bands are Q-branch transitions between excited vibrational levels.  Even at room temperature a small percentage of the molecules are vibrationally excited by collision.  Of course, they can also lose energy by collisions but there is an equilibrium between excitation and de-excitation by collisions with nitrogen and oxygen molecules (mostly) and a thermally driven equilibrium population in each vibrational level.  If a bunny squints really hard she can see the corresponding P and R-branches. These are called hot bands. Why the excited vibrational levels are split and even what excited levels they connect is complicated.  Google books provides an explanation.

If the distance is increased to 10 meters the lines of the 0-1 band are optically thick but there is still space between them, however, the lines do have wings and the wings overlap so even over a 10 m path, there is a noticeable underlying continuum mostly caused by collisional broadening.  The hot bands on either side of the Q branch are now easy to see.  The Q branch 0-1 band is optically thick
At 100 m or 0.1 km the 0-1 transition is almost optically thick and the 1-2 bands are very clear.  Using the squintosope, Q branches for higher lying hot bands can be seen at the edges
For a 1 km path length, most of the 0-1 transition is optically thick (saturated in the disbelieving sense) but light from the surface would still be seen in the wings, where the hot bands are.  
Finally at 10 km, while the center of the CO2 absorption is optically thick, there are still regions of the spectrum where light from the surface will get through the atmosphere.
Of course, increasing the amount of CO2 in the atmosphere will decrease the transmission in the wings of the bands.  At 560 ppm
and returning to 280 ppm
There are a few things that Eli has not considered in this post but they all would DECREASE the calculated optical thickness. Temperature and pressure decrease with altitude.  This post assumes both are constant. Their effects will be considered in detail in follow on posts,  Simply put the optical depth is directly proportional to density and path length, thus decreasing density with altitude, decreases the average optical depth and increases transmission across the spectrum.  Second at lower temperature there is less population in the excited vibrational levels and the hot bands at the edges of the spectrum are weaker, decreasing the optical depth in the wings, and increasing it in the center 0-1 band.  Since the 0-1 band IS optically thick at very small path lengths anyhow, this increases transmission.  Third, each of the lines is substantially broadened at atmospheric pressure.  A narrower comb of lines is optically thinner.  This would substantially decrease the continuum absorption between the lines.

Bottom line, the 667 cm-1 CO2 vibrational absorption is not optically thick across the entire region of absorption. It is not saturated.


CapitalistImperialistPig said...

Even if CO2 were optically thick, more CO2 in the atmosphere would still tend to increase the surface temperature.

Steve Bloom said...

Useful point, CIP. Perhaps Eli can touch on it.

Shelama said...

I really liked Realclimate's saturated gassy argument at the time, but now I like rabbet better....


barry said...

Arts major here, looking at the light from a great distance...

Was wondering yesterday if differences in wavelength sizes across the EM spectrum are continuous or discrete. IOW, is there a finite, or infinite number of wavelengths between, say 14 and 15um?

And would this matter for the greenhouse effect?

CapitalistImperialistPig said...

@Barry - Light can be any wavelength, but as the spiky looking absorption spectra Eli exhibited show, in accordance with quantum mechanics, molecules absorb at discrete wavelengths, although there are effects that tend to broaden those discrete wavelengths (mainly pressure and molecular motion). Solids and liquids pack molecules closely enough together that their emission spectra are essentially continuous.

Brandon R. Gates said...

Right. So the argument is that since the wings are already allowing some transmission at 400 ppm, until some very high concentration is reached, it is the wings which dominate how much LW makes it through our 10 km iso-everything tube of simulated atmosphere. Bunnies (and at least one pig) will still be curious about what would happen past the point the entire band were saturated in the zero-transmission sense, but onebunny will be content to fiddle with MODTRAN and review some maths in preparation for the next installment of the series.

CapitalistImperialistPig said...

@BRG - Stars are extremely saturated absorbers at all the relevant wavelengths - the mean free path of a photon in the Sun is less than 1 cm. And the center is 15,000,000 K hotter than the surface. More opacity between surface and last radiating surface means more temperature difference.

Brandon R. Gates said...


Understood, and this is actually my more "traditional" understanding of how radiative "greenhouses" work vis a vis Beer-Lambert law and partial back-radiation from reemission -- a process which I understand to never "saturate". Venus being another canonical example, yes?

I believe the point Eli is driving at is that on Earth at present, most of the action is in the wings where transmission is still well greater than 0%.


You left out the absorbtion bands for the ubiquitous Sky Dragon wings, a spectrum now in its second volume:

TransparencyCNP said...

I was once shown a rectangular prism about 1x3 cm containing a translucent liquid. It appeared pinkish when viewed the long way but blueish the short way (or vice-versa, I don't remember). The explanation was the phenomenon discussed here.

Is this a common demo (and what is it called)?

Nick Stokes said...

It seems to me that the sidebands are more important than their proportion of the spectrum would indicate. Although at 667cm-1 the atmosphere is opaque, it's important that heat is still radiated at such frequencies, at about 225 K. That heat has to get to TOA somehow, and radiatively, it can't be transported at atmospheric window frequencies. AW heat gets there easily, but won't stop to be re-radiated at 667. It is only in the sidebands that there is a long enough mean free path to carry heat flux, but enough absorption to supply the heat that is radiated at the much wider range of frequencies that have low OD.


WUWT has revealed the Fatal Flaw in this so-called 'spectroscopy' flim -flam:

It's cosmic rays all the way downthe availability cascade:

Jonathan Gilligan said...

If the main CO2 bands were not saturated, temperature would follow a power law relationship to CO2 concentration. The fact that temperature has a logarithmic relationship to CO2 concentration is the primary reason for saying that the absorption is saturated. David Archer explains this very clearly in his textbook, "Global Warming: Understanding the Forecast."

I also like the approach that John Houghton takes in "Complete Briefing" and that F.W. Taylor also takes in "Elementary Climate Physics" of relating surface temperature to lapse rate and skin height in a gray atmosphere, which uses the relationship between CO2 concentration and skin height to show that rising CO2 concentrations lead to warming, even if the atmosphere were completely opaque to longwave emissions from the surface.

EliRabett said...

Nick, stay tuned:)

Transparency, Eli suspects that the answer to your question is the same as to why the sky is blue during the day and pink at sunset (again ;). You can try this yourself

UplayOnline said...

I really liked Realclimate's saturated gassy argument at the time, but now I like rabbet better....



Peter CARSON (aka pjcarson2015) said...

You state CO2 is unsaturated. I agree. In fact, it is completely UNsaturated.
All Earth’s IR at that wavelength has already been absorbed at very low altitudes by CO2 (Chapter 1). Adding more CO2 cannot absorb any more IR.

Anyway, this is irrelevant.
Despite AGW implicit supposition that only some atmospheric molecules - the IR gases - can absorb heat. ALL molecules absorb heat one way or another (Chapter 1B) closely in proportion to their concentration, and so, CO2’s contribution, IR or otherwise, is negligible due to its tiny concentration.

[AGW’s is an implicit supposition because it would be absurd if stated explicitly. It would mean that samples of non-IR gases could not change their temperature!]

The Chapters are my website, Planet Earth Climate Topics (

TransparencyCNP said...

EliRabett : It was clear, not murky. The explanation given was that there was a strong but narrow adsorption band in one colour and a weak but wide band in the other, so the latter predominated over the longer distance. Is that plausible?

Alastair said...


It is obvious that absorption of terrestrial radiation is not saturated if only because there is an IR window, but don't you agree that the band from 600 to 750 rcm (reciprocal centimeters)where the transmission is zero, is saturated?

lifeisthermal said...

So, spectrums showing the quantum properties of atmospheric molecules as they get heated by earth, show us what?

Optically thick, or saturated, that would be useful if I had eyes with IR-receptors. But why would I need quantum theory to determine temperature or to investigate possible changes in temperature? Are there any other examples where quantum physics are used to determine bulk properties of mass like temperature? Isn´t that one of the things we can´t do with physics describing relations on the microscopic scale of photons, atoms and molecules?

The relevant action of atmospheric gases for temperature is determined by thermal physics, why the talk about quantum interactions of molecules? It´s not like quantum physics can change how thermodynamics work on bulk scale.

lifeisthermal said...

Blogger CapitalistImperialistPig said...
"Even if CO2 were optically thick, more CO2 in the atmosphere would still tend to increase the surface temperature."

Interesting. How much dry ice can we put in the atmosphere before it starts behaving like we are used to? It usually cools things effectively, how come it warms things when diluted to small fractions. How many other substances have the opposite effect on heat when diluted to small fractions?

Another question: since the flow of heat is limited to what the surface emits, how can temperature increase by distributing the heat over more heat absorbing molecules? There is no added heat. Less heat per molecule is the result, without doubt. So, where is the extra energy created?

Peter CARSON (aka pjcarson2015) said...

To lifeisthermal
Heat is released from Earth’s interior by (observed) increased seismic activity.
[See Chapter 2 of my site,]

Edgar53 said...

To my opinion, we should repect common sense (i.e. sense of proportionality) when assessing the causes of the (obvious) climate change. There are two infrared-absorbing gases in the earth atmosphere, noteworthy water vapor (H2O), present at locally variable concentrations ranging from 0.1% (arctic climates) up to 5% (tropic climates after rain), and CO2, present actually at a concentration of 0.040% and about homogeneously distributed in the atmosphere. In a moderate climate atmosphere, there are about 1'000 to 2'000 molécules of water, and 40 molécules of CO2 in 100'000 molécules of air. The remaining infrared-absorbing constituents of the atmosphere, such as methane, etc., are present at less than 1 molecule out of 1'000'000.

Comparing the %-quantitative infrared spectral absorptions profiles of CO2 and H2O through the thickness of the earth atmosphere, it becomes obvious that the infrared absorption increase of CO2 due to the raising of the atmospheric CO2 concentration from the pre-industrial level of 0.028% to the actual level of 0.040% is barely noticeable, because most of the spectral absorption band is already saturated, whereas the infrared spectral absorption profile of water vapor strongly varies with varying air humidity. Water vapor (H2O) defines the "atmospheric infrared window" between 8 and 15 micrometer wavelength, and at low air humidity, this window is widely open, whereas at high air humidity, it is narrowly closed.

Summing up: the atmospheric infrared absorption increase due to the rising CO2 concentration (from 0.028% to 0.040%) is far too small to have a noticeable effect on the earth's radiation balance, compared to the effect of varying the air humidity. The actual climate change correlates not only with the rising CO2-concentration, but also with an increase of humidity in the interior of the continents (e.g. it is now raining in the American mid-west and in Sibiria). The conclusion is that not the CO2, but the water (H2O) must be blamed for the climate change!

Edgar53 said...

A further comment to the vibration-rotation spectra presented is that the "spectrally thin" condition for rotation spectra is only present at pressures below about 250 mbar. At ambient pressure, all rotation bands are further split and broadened by the molecular interactions (random collisions) which happen at frequencies comparable with the rotation frequency. Hence, a rotation Spectrum at ambient pressure is generally totally opaque.

Edgar53 said...

Further to this we must consider that an experimental determination of the optical density of the CO2 infrared absorption spectrum at the pre-industrial concentration of 280ppm and at the atual concentration of 400ppm the is easily made:
The earth atmosphere has a reduced optical path of 10km at 1 atm pressure (this follows from the definition of the atm which is 1 kg/cm2. 1 m3 of air weighs also about 1kg. Piling it up on 1cm2 yields a heigth of 10km)
280ppm CO2 at 1 atm correspond thus to an optical path of 2.8m.
400ppm CO2 at 1 atm correspond then to an optical path of 4.0m.
Hence, take a tube of 2.8m length, fill it with CO2 at 1 atm, then measure its infrared absorption Spectrum on a 0 to 100% scale.
Then take a tube of 4.0m length, fill it with CO2 at 1 atm, then measure its infrared absorption Spectrum on a 0 to 100% scale.
Now compare both spectra and convince yourself that there is only a tiny absorption increase; far too few to explain the climate change, because the slightest variation of air humidity has a far stronger effect on the atmospheric infrared absorption.
As water vapor and CO2 are the only atmospheric components which show significant infrared absorption, the climate change must be caused by the water vapor, i.e. by a significant redistribution of water into the interior of the continents!