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The first global warming skeptic

Posted on 9 October 2010 by Riccardo

After the his famous paper in 1896, where Arrhenius did the first calculations of the CO2 greenhouse effect, his theory was dismissed by Angstrom with a simple experiment. He let an infrared beam pass through a tube filled with CO2 and measured the emerging light intensity. Upon reducing CO2 concentration in the tube, only a tiny difference could be found and he concluded that even a small number of CO2 molecules is sufficient to completely absorb the IR beam. The conclusion was that a CO2 increase could not matter. This was the birth of the first skeptic of what was then called "CO2 theory" and of the more recent skeptic argument "the CO2 effect is saturated".

Thirty years later, E. O. Hulburt (Phys. Rev. 38, 1876–1890 (1931)) considered convection in addition to the purely radiative equilibrium assumed by Arrhenius. He found that convective equilibrium holds in the lower part of the troposphere up to about 10 Km, while radiative equilibrium holds above. The important consequence is that the details of the absorption in the lower troposphere do not matter since heat "is spread around and transferred upward by convection". In other words, what governs the energy balance of the earth is the radiative balance in the upper troposphere and CO2 concentration there does matter.

Hulburt was very prudent in his conclusions:

"The agreement is no doubt better than is warranted by the accuracy of the data on which the calculations are based. Apparently the uncertainties and omissions have conspired to counteract each other to some extent."

Nevertheless, his work is definitely a milestone in the understanding of our atmosphere.

Hulburt's work should have put the controversy on the CO2 theory to an end, since "objections which have been raised against it by some physicists are not valid". Unfortunately, this paper passed almost unnoticed, I guess because meteorologists and geologists do not read Physical Review so often.

At the time of Hulburt the CO2 absorption coefficient was not known very accurately and even less its line shape, forcing Hulburt to use a "box-like" shape. We may now build a simple model with a more realistic line shape and show that we get an increased absorption with increasing CO2 concentration in any case.

Consider the CO2 absorption band around 15 μm (about 650 cm-1), it is strong enough to not let any light go through after a few tens of meters at surface temperature and pressure. Did this energy disappear forever? Surely not, radiatively or convectively this energy "is spread around and transferred upward". But on the way up this light will encounter fewer and fewer CO2 molecules. There will be a point where the light can escape to the outer space. The intensity of the emerging light will be appropriate to the temperature of this "last" layer.

We can crudely model this behavior using the Planck law and a gaussian-shaped absorption coefficient. We consider just two layers, the surface and the "last" layer, and the emissivity of this outer layer is modulated between 0 and 1 according to the absorption coefficient α. The result is shown in the figure below.

In the calculations, I focused on absorption near the wavenumber of 650 cm-1 and tuned the optical depth to reach saturation. The two dashed lines correspond to the Planck law for T=300 K and T=220 K. The red curve is the calculated emission; it follows the 300 K curve but deviates from it near the absorption band. This bite taken out of the 300 K curve represents the energy prevented fron reaching outer space, i.e. the greenhouse effect.

This graph can be qualitatively compared with real measurements (from G.W. Petty 2006) to be sure we're not too far off.

We can now look at what happens when we increase α. Following Angstrom (and many others in his times) the energy absorbed should not change. On the contrary, if we recall that the absorption coefficient is gaussian we would expect an increase in the energy retained by our layer along the wings. The effect is shown in the figure below.

We can see that although the absorption dip cannot fall below the 220 K curve, it becomes wider and the absorbed energy increases accordingly. This is as far as we can get with this simple model. Needless to say that there's much more than what can be done with the very crude model presented here. We know, for example, that the line shape of the absorption coefficient changes with both pressure and temperature due to what are called pressure and Doppler broadening. In the upper layers of the atmosphere the band initially gets narrower and then splits into several narrow bands (the roto-vibrational spectrum) leaving more room for the increase in CO2 concentration being more effective. We also know that there are weaker absorption peaks other than the stronger one quoted above which are not saturated.

Gilbert Plass in 1956 used these words:

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.

There's one more subtle effect related to increased absorption. Upon increasing CO2 concentration, the layer at which the absorption coefficient at each wavelength is low enough to let the IR light escape will be found higher in the atmosphere. The emitting layer will then have a lower temperature, at least until the tropopause is reached, and hence a lower emitting power.

Clearly there's a world behind the absorption of IR light by CO2 in the atmosphere which I omitted. The physics behind it is now solid thanks to the decades of work of many different scientists, and despite the first highly respected skeptic ever who put the CO2 theory on hold for half a century. But you know, this is how science works.

Note: I cannot conclude without acknowledging the fundamental role of Spencer Weart "The Discovery of Global Warming" from which I borrowed (and learned) a lot. His book and the supporting website are a treasure cove for anyone interested in how our current knowledge has been built step by step over time.

This post is the Advanced version (written by Riccardo) of the skeptic argument "CO2 effect is saturated".

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Comments

Comments 1 to 26:

  1. Well done. The basic mechanism was never better explained in a sentence than by Tyndall, who said CO2 acts like a dam that raises the water level behind it. At whatever level the radiation escapes into space--pretty high up, it turns out, for the affected infrared--the temperature has to rise until the energy can escape. (By the way, that's Planck, not Plank).
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  2. Where are the figures of "real measurements" from?
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  3. Thanks, Riccardo, terrific job.

    Seconding and extending your thoughts on Spencer Weart's book, if people would read Weart before commencing to argue against facts as opposed to discussing actual open issues, the general quality of discussion on this matter would be much better.
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  4. The more complex the model, the more important the empirical data. Fortunately there have been very detailed studies of IR transmission in the atmosphere. Many from before AGW was popular. Here is the measured transmittance of the IR band. This is freely distributed to people that use IR transmission in their work.

    It uses wavelength instead of wavenumber, so you will need to compare to the top axis of Riccardo's post.

    The picture is large and I can't do it justice here. This has been in use since the 1970's when CO2 was about 330 ppm. It has not changed since then.

    Always test the theory against the data. The amount of widening is limited, but visible. The amount of IR energy available for CO2 absorption after 1km in the horizontal direction is approaching zero W/m2.

    John Kehr

    The Inconvenient Skeptic
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  5. So John, still using that highly misleading graphic on your website. Fixing that soon?

    As to this argument, perhaps time to at the reference to Harries 2001 for a proper test of theory against data.
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  6. Dr. Weart
    thanks a lot. I like the dam analogy too, it gives the right impression of something that can not be stopped forever. Sooner or later it will come out one way or another and in the meanwhile it produces an effect.

    Kooiti Masuda,
    you're right, I did not quote the source. It is from G.W. Petty 2006, Sundog Publishing, Madison, Wisconsin. In the sample pages online you will find more.

    Doug,
    hundreds of researchers did a terrific job, we're just trying to keep up. But apparently we're culturally lagging some 60 years; or is it just cultural internal variability? :)

    The Inconvenient Skeptic
    the horizontal direction is irrelevant/misleading. Look upward and think about how the absorption coefficient changes with altitude (Plass 1956) and how heat is redistributed (Hulburt 1931).
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  7. @ The Inconvenient Skeptic, if one points a pyrgeometers at the sky on a clear night what are we measuring?
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  8. Riccardo,

    You are correct that there is some variation and additional absorption in the vertical direction, but the difference is not significant. CO2 does have some additional absorption in the vertical.


    Brightness temperature (referenced by scaddenp) is interesting, but it is not a measure of energy or transmission, it is only a measure of perceived temperature. Brightness temperature can change without a change in the energy absorption.

    Also, using the data is not misleading when it is a direct plot of the data. A 200-year moving average would include recent data, but in the average 100 years ago. Adding 9 year averaged instrument would make no difference. I can show that on another forum if you wish.
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  9. The Inconvenient Skeptic
    I'm glad you accept that increased CO2 concentration does increase the energy absorbed. This was the very point I was making in the post, one thing that some people do not agree with.
    If it is significant or not is a completely different question. It's widely accepted, even in some skeptic quarters, that it amounts to about 3.7 W/m2 for doubling CO2 concentration. Compared to, say, thermal emission from the earth surface (see e.g. Trenberth 2009) it's a tiny fraction, not even 1%. Are we allowed to say it's insignificant just because it's "just" 1%? No for sure, it depends on how sensistive is the system under study. You can find more on this here.
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  10. Remember that a 1% increase in mean global temperature would be just under 3 C*, which is about half the difference between an ice age and today.

    So a 1% change could still be very important to us!

    (ofc, you need positive feedback to get the 1% reaction, but articles on here go through that pretty well too)


    *global temperature averages to something like 293 K iirc, so 10% more is 2.93 K = just under 3 C
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  11. (Excuse me for re-using something I have written elsewhere recently.)

    Even if absorption is saturated, it does not mean that the greenhouse effect is saturated.

    It is because molecules absorbing radiation are also molecules emitting radiation. As the concentration of absorber molecules increases, shorter geometrical depth of air becomes enough to attain "effectively full" absorption. Then, if we envisage the atmosphere consisting of "fully absorptive layers", the number of such layers increases. So the number of occurrence of absorption and re-emission increases in the pathway from the ground to the top of the atmosphere. The process results in larger difference of temperature between the surface and the height from where the upward emission escapes to outer space, i.e. greater greenhouse effect.

    Note that "re-emission" here does not mean that excited absorber molecules simply de-excite. Instead, the energy of absorbed radiation is transferred from absorber molecules to surrounding molecules (not usually absorbers), in other words, increases internal energy of air, or raising air temperature there. Then, part of internal energy is transferred to absorber molecules again, and then these molecules emit radiation according to the local temperature and emissivity of air (which is dependent on concentration of absorber molecules etc.). Thus, air cools by emission of radiation.

    Because internal energy is involved, greenhouse effect cannot be closed within a limited wavelength range. Radiative processes of all wavelength range (and also convective processes when relevant) must be taken into account together. (Therefore, the "fully absorptive layers" approximation is not useful for quantitative evaluation, regrettably.)
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  12. I'm curious about one thing (evidence of my ignorance, no doubt). While energy is transmitted to the earth in a range of wavelengths, are we right to assume that the same energy retains the same wavelengths once in the troposphere? Presumably some UV energy may convert to IR energy and some visible light to UV. Does anyone have any idea of the extent radiation retains its wavelengths and how much if any impact this has on radiative transfer?

    For example, visible light becomes co-opted by photosynthesis into glucose which in turn powers the creation of complex carbohydrates, formation of proteins, etc, becoming dissipated through the biosphere.

    However, much of this would be potential energy which is presumably now in forms which would not affect our radiative budget greatly (or does it?).

    So what happens with visible light, UV light and other wavelengths?
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  13. chriscanaris,
    the conversion of UV or visible photons to IR is mediated by absorption and heating of something, earth surface or molecules in the atmosphere. You cannot have (to first order) the "upward" conversion, like from visible to UV or IR to visible.
    The light from the sun contains UV and visible frequencies; the former is absorbed in the stratosphere by ozone, the latter reaches the ground. Both results in warming where they're absorbed. (On passing, Hulburt 1931 pointed out the essential role of ozone in determining the structure of our atmosphere).
    In a few words, frequencies that are not absorbed retain their characteristics; if they are absorbed, they produce warming and then increase the IR emission.
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  14. I like Kooiti Masudas description but have some questions:

    If you had pure CO2, would photons be emitted and absorbed between the CO2 molecules until a path out of the gas was found?

    Or is the photon frequency degraded when emitted, to a point where it is no longer the correct frequency to be absorbed by another CO2 molecule?
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  15. Thanks Riccardo - so absorption is the key variable. Clearly then, in burning fossil fuel or biomass, we release IR energy which has been 'absorbed' via photosynthesis (some also sequestered via conversion to fossil fuel) but much more importantly release CO2 which increases absorption of further incoming IR which in remaining IR will cause increased temperature.

    Interesting looking at Hulbert to see how 'old' the science is.

    I guess for many folk it's all Climate 101 but it's helpful to get one's mind around the concepts. What's even more interesting is how little of this was in public consciousness back in the seventies (which was when I had my last formal exposure to physics).
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  16. Riccardo,
    Interesting article. Although it's hard to understand why Arrhenius himself did not take charge of experimentation and run these tests for himself.
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  17. I'm not sure you would call it IR energy chris. The plant would retain some of the energy from a visible light photon and re-emit at a less energetic frequency, retaining some of the energy for the processes that it requires to produce glucose etc.
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  18. The Ville @14 asks about emission.

    A CO2 molecule could "relax" from its excited state emitting a photon of IR, which would obviously be the correct frequency to be absorbed by another molecule: In more technical language: The rules that allow transitions between states in the molecule (known as "selection rules") apply to both absorption and emission.

    The molecule can also loose energy by collision with other molecules loosing its vibrational(IR) energy by dissipating it into smaller rotational and translational energy. As Riccardo states above, upward conversion of photons is unusual, so this pathway will not lead to photons that can be reabsorbed by CO2 vibrations.
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  19. Thanks Phil, that clarifies that issue for me.
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  20. chriscanaris,
    thank you for noticing the age of the paper quoted in my post. I could have found more recent and accurate papers, but I wanted to show that the basic physics is quite old and solid.
    In the seventies the post WWII huge increase in CO2 emissions had just started and the understanding of the impacts on climate was in its infancy. Honestly, it was too early to call for a radical change in the way we use energy and resources in general. Now we have no excuses.

    RSVP
    thank you. As for your question, had you read the paper you would have found the answer (pag. 239): "But such experiment have not been made as yet, and, as they would require very expensive apparatus beyond that at my disposal, I have not been in a position to execute them".
    Never think that scientists are not aware of the problems and limitations of their work.
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  21. chriscanaris @15.

    You have the jist, but as The Ville suggests, some of the detail is a little awry.

    Firstly the Sun emits little or no IR radiation; photosynthesis absorbs a lot of visible light (not green, obviously!). Subsequent processes such as respiration convert that energy to vibrational (IR) radiation which the atmosphere can absorb. It is this asymmetry between incoming (visible) and outgoing(IR) radiation that allows the greenhouse effect to function.

    Burning fuel does not, of course, result exclusively in IR radiation; you may have noticed that gas burners produce blue visible light, log fires yellow and embers red as well as heat.
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  22. Phil at 22:23 PM says

    "Firstly the Sun emits little or no IR radiation; photosynthesis absorbs a lot of visible light (not green, obviously!). Subsequent processes such as respiration convert that energy to vibrational (IR) radiation which the atmosphere can absorb."

    Taken in the context it was written that makes sense... but it does also come across as a little misleading, as in it implies that IR is the result of biological process's. I know thats not what youre meaning. Radiation is a product of the temperature of its source. Shortwave from the sun is coming from 5800k, red light is the longest visible wave length to our eyes(think red hot iron etc) , infra red is longer than red light, and thus has come from a source cooler than this, a longer wave length than is visible to our eyes. But its a product of the temperature of the source material(emissivity pending) , on earth, the absorption of shortwave, by materials opaque to its wavelength... earth/ water/ rock etc.

    I know you were talking specifically about biological endothermic/exothermic process's... but i can see that being misinterpreted.
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  23. Riccardo

    I have read a similar description over at RealClimate and the general point being made seems to be that a major part of the increased absorption involves CO2 (and I presume other GH gases in their behaviour) absorbing at some central wavelengths first and this absorption then 'spreading' to adjacent absorption lines at higher concentration. You describe it as following a gaussian distribution.

    The point that isn't clear is why, if CO2 has a range of absorption frequencies, the central lines would absorb preferentially and thus saturate first. Why don't we see equal degrees of absorption across all the absorption lines. All the descriptions I have read to date make good sense apart from the explaining the causal mechanism of WHY that gaussian spread occurs. Is this theoretically derived, observational, what? This seems the only missing piece in the puzzle as far as an explanation of this goes.
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  24. Glenn Tamblyn
    the gaussian shape was used just to show the behaviour in the wings of the absorption. It's not really a gaussian but a convolution of different broadening mechanisms.

    The line width of an isolated molecule would be very small. It would be given by the so called natural width, which is a manifestation of the uncertainty principle applied to time and energy. If the molucule is not isolated, the two most important broadening mechanisms are Doppler and pressure broadening.
    The former is the well known Doppler effect applied to the emission of electromagnetic waves by moving molecules. The speed of the molecules depends on temperature, so the effect will be larger at higher temperatures.
    The latter is due to the influence exerted by nearby molecules on the emitting molecule. Usually collisions dominate, but there could also be an electrostatic contribution. It depends on pressure (through the number of molecules) and on temperature (through their speed). It depends also on the gas composition, i.e. the species that collide or otherwise interact with the emitting molecule.
    The broadening effects have been first noted exeperimentally, the theory followed to explain the mechanisms.

    The reason why different absorption lines have different strength is quantum-mechanical in nature and involves the probability of transition between quantum states. In classical physics terms, we may immagine the strength of the line as dependent on the change in the dipole moment during the vibrations. On passing, this is the reason why O2 and N2 in the atmosphere do not interact with IR waves, no change in dipole moment during the vibration.

    Absorption strength and line broadening are two really complicated issues; a proper treatment is way beyond the reach of a blog post. I apologize for being so generic.
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  25. I assume it can be allowed that as the absorption spectrum broadens, so in turn does the emmision spectrum. Angstrom may have been the first, but definitely not the last skeptic.
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  26. RSVP
    yes, the emission spectrum will be broader too, and that's why it will more easily go through regions with narrower absorption.
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