Infrared absorption of atmospheric carbon dioxide

Geoff Price made me aware of a paper, by an apparently highly published physicist, that considers the infrared absorption of atmospheric carbon. It concludes that

CO2 is a very weak greenhouse gas and cannot be accepted as the main driver of climate change.

You might suggest that I should just ignore such a clearly nonsensical paper, but it is being promoted on notrickszone (or, as I like to call it, fulloftrickszone) and it’s sometimes useful to try and understand what they’ve done wrong.

Essentially what this paper concludes is that, relative to a baseline CO2 concentration of 400ppm, the change in radiative forcing, \Delta F, if we change the atmospheric CO2 to a new concentration, C_{\rm CO2}, is

\Delta F = 1.881 \ln \left( \dfrac{C_{\rm CO2}}{400} \right),

which is considerably smaller than suggested by other analyses:

\Delta F = 5.35 \ln \left( \dfrac{C_{\rm CO2}}{400} \right).

In others words, this new analysis suggests that doubling atmospheric CO2 should only produce a change in forcing of 1.3 Wm-2, rather than 3.7 Wm-2.

So, what’s wrong with this new analysis? Let me try and explain using the figure on the right, which I produced using MODTRAN. The left-hand panel shows an example of a spectrum that you might measure if you were observing the Earth from space. The right-hand panel is the associated atmospheric temperature profile.

The coloured curves in the left-hand panel are example blackbody spectra at different temperatures. What this shows is that in some wavelength ranges, the spectrum we would observe comes from regions that are quite warm, and in other wavlength ranges, from regions that are quite cool. This is because, in some wavelength bands, the surface can emit directly to space, while in others, its coming from within the atmosphere (in some cases, even from the stratosphere, but I’ll mostly ignore that). Since the temperature drops with altitude (in the troposphere, at least) the emission from within the atmosphere is coming from a region that is colder than the emission coming directly from the surface.

If we then increase atmospheric CO2, while leaving everything else unchanged, that will act to block some of the outgoing flux. What essentially happens is that some of the flux will end up coming from higher in the atmosphere that it did when atmospheric CO2 was lower. Since the temperature drops with altitude (in the troposphere) this means that it will now be coming from regions that are cooler and that, hence, emit less. Therefore, the outgoing flux goes down and the system will have to warm to return to energy balance. As already pointed out, doubling atmospheric CO2 is estimated to reduce the outgoing flux by about 3.7Wm-2.

So, what is wrong with this more recent analysis? I think the answer is on page 5, where it says

we consider an isothermal atmosphere of T = 288 K.

Well, if the atmosphere is isothermal (constant temperature – 288K) then it doesn’t matter where the emission is coming from; it will always look like a 288K blackbody. It could all be coming from the surface, some from the surface and some from within the atmosphere, or all from within the atmosphere; it will make no difference. Similarly, if you change the atmospheric CO2 concentration, then you may change where the emission is coming from, but you won’t change the outgoing spectrum; it will still look like a 288K blackbody.

Therefore, I don’t even really know what the paper has actually calculated, but it almost certainly isn’t what the author thinks it is, and it isn’t a representation of the change in forcing due to a change in atmospheric CO2. Unless I’m missing something, estimating the change in forcing due to a change in atmospheric CO2 requires taking the temperature profile of the atmosphere into account. That this paper did no such thing would seem to immediately mean that what it presents is clearly not representative of the change in forcing due to a change in atmospheric CO2. Essentially, its no great surprise that it gets a result that is inconsistent with other analyses, since it doesn’t even seem to be doing an appropriate calculation.

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40 Responses to Infrared absorption of atmospheric carbon dioxide

  1. I should add that the isothermal assumption in this paper was also pointed out to me by Geoff Price, so I didn’t work this all out by myself. I also think my explanation is probably correct, but happy to be corrected if not.

  2. Dikran Marsupial says:

    I haven’t read the paper yet, but that paragraph on page 5 does seem rather odd:

    The atmosphere exhibits a strong pressure and temperature dependence with the height above sea level, x. … To keep the calculation manageable, we make a number of additional simplifying assumptions. Firstly, we consider an isothermal atmosphere of T = 288 K with an exponential barometric pressure dependence

    [emphasis mine]

    Ekholm in 1901 clearly knew that the decrease in temperature with height is a key component of the mechanism. I hope the paper explores the sensitivity of the results of this assumption at some point?

  3. thanks for the quick eval. My guess is we will all see this CO2 is a weak greenhouse gas meme go from zero to 60 in nothing flat. I appreciate your analysis and presentation every time I stop in. This is as good as it gets in a physics and climate science blog.

  4. I hope the paper explores the sensitivity of the results of this assumption at some point?

    It tries to, but it argues that there assumption of an isothermal atmosphere produces an upper limit:

    We emphasize that our simplifying assumptions are by no means trying to minimize the absorption potential of CO2. To the contrary, they lead to overestimating the limiting values. The assumption of a constant temperature and black body radiation definitely violates reality and even the principles of thermodynamics. But this is not of great importance, because we are only interested in an upper limit.

    I think what the author is calculating is how much energy is absorbed in the atmosphere (and how much it changes as you change atmospheric CO2), rather than trying to determine how changing atmospheric CO2 will change the outgoing flux.

  5. Bob Loblaw says:

    Going back to Manabe and Wetherald (1967), where they do a 1-D radiative-convective model, they show the results for pure radiative equilibrium in the atmosphere, and add the convective adjustment. With convection (i.e., another means of vertical energy transport), tropospheric lapse rates are much smaller than pure radiative equilibrium. The “greenhouse effect” is considerably smaller in the atmosphere with convection.

    Assuming an isothermal atmosphere is akin to saying that some other factor (convection, perhaps?) is so strong that energy is instantly transferred vertically along a zero temperature gradient. It is therefore no surprise that changing the radiative properties has little effect in this scenario.

    It reminds me of the joke abut the economist that lost his can opener and can’t open his can of beans. He solves the problem by assuming that he has a can opener.

  6. Martin Vermeer says:

    I’m not sure the isothermal assumption is the big villain here, at least not on its own. The author appears to compute the amount of IR energy from the ground absorbed by this atmosphere, and the change therein for a doubling. But I don’t think that is what is commonly understood as forcing! E.g., the amount of IR emitted to space, which is substantial, also changes (which is indeed largely due to the real atmosphere being not even close to isothermal!). I don’t find anywhere in the paper that he has thought of this.

    I seem to remember Arrhenius had, in his model calculations, a similarly primitive neglect of atmospheric vertical structure. But it gave him a too big sensitivity, by a similar factor. Perhaps that is what happens when you get it sort-of right, but not quite right…

  7. Martin,

    The author appears to compute the amount of IR energy from the ground absorbed by this atmosphere, and the change therein for a doubling. But I don’t think that is what is commonly understood as forcing! E.g., the amount of IR emitted to space, which is substantial, also changes (which is indeed largely due to the real atmosphere being not even close to isothermal!). I don’t find anywhere in the paper that he has thought of this.

    Yes, but isn’t this the same point? What he’s computing is not a change in forcing, but the amount absorbed in the atmosphere (or absorbed by the ground). As I understand it, by assuming an isothermal atmosphere, the amount emitted into space will be the same for any atmospheric CO2 concentration, so I don’t think that he can compute a change in forcing (unless there is some clever way of doing it that I haven’t understood).

    I seem to remember Arrhenius had, in his model calculations, a similarly primitive neglect of atmospheric vertical structure. But it gave him a too big sensitivity, by a similar factor.

    I thought that Arrhenius did a proper radiative transfer calculating that also produced a temperature gradient. The problem (IIRC) is that he didn’t (couldn’t at that time, maybe) consider convection, so he got a steeper temperature gradient (by about a factor of 2) than he would have got if he had included convection.

  8. Bob Loblaw says:

    Martin’s point about absorption vs. emission ties with ATTP’s point (in the original post) about how the atmosphere adjusts so that it can emit more radiation. In an isothermal atmosphere with infinite convection, you can instantly get the energy to where it needs to be emitted regardless of where it is absorbed.

  9. Magma says:

    A few predictable points:

    1. Franz-Karl Reinhart’s field was optoelectronics.
    2. He’s been emeritus since 1999.
    3. His unpublished, unreviewed paper is padded with gibberish and filler from the first sentence on.
    4. He neglects any previous work on radiative transfer in grey or more realistic absorbing/emitting media (a field that was maturing when he was a young physicist), instead choosing to derive his own from basic principles.
    5. To call the only figure in his manuscript a ‘cartoon’ would be an insult to figures desperately scribbled by undergraduate students in the final minutes of exams.
    6. With 99% of the mass of the atmosphere (and almost all of its H2O) occurring below an altitude of 30 km, a 1D (or plane-parallel) approximation is more than sufficient to deal with radiative heat transfer for the case of the Earth’s 6370 km radius. Raymond Pierrehumbert considered this so obvious that he dispensed with it in a couple of sentences in his Principles of Planetary Climate textbook for advanced undergraduate or early graduate students.

    No doubt Reinhart’s arguments could be carefully deconstructed and every error identified and listed. But would that be a good use of anyone’s weekend?

  10. Magma,
    Actually, I tried to email him today, but the email bounced. Pretty sure I hadn’t typed it incorrectly, so it may even be that his institutional email is no longer even active (even though he is still listed on their website).

  11. Magma says:

    Something occurred to me after I wrote my last comment: leaving aside contrarian scientists like Curry, Spencer, Lindzen, etc., I can’t recall a single one of the various engineers and physicists and oil/resource geologists I’ve seen and heard denying AGW over the years ever mentioning reading _any_ textbook on climate, introductory or advanced, even the draft versions that can easily be found for free. Yet some of them have written tens of thousands of words over more than a decade on this topic. [The same would apply even more so to some of the regular contributors Watts Up With That and similar sites.]

    Considering how few of them are actually paid disinformers, what an enormous, damaging waste of time and misguided effort this has amounted to.

  12. Considering how few of them are actually paid disinformers, what an enormous, damaging waste of time and misguided effort this has amounted to.

    It’s one reason why it’s hard to believe that there is a great deal of money in climate denial (apart from within formal think tanks). People seem to be more than willing to promote it for free.

  13. Eli Rabett says:

    Was this actually published or is it an early Halloween joke along the line of the spherical elephant?

  14. I’m not sure. I’ve seen it described as peer-reviewed, but I don’t know if that means actually reviewed by experts in the field, or looked at by Matt Ridley.

  15. Eli Rabett says:

    Think you have the right of it. Bcs the ghgs in the atmosphere emit to space at lower temperature than the surface the surface has to warm to make up the difference if energy balance is to be maintained.

  16. Jon Kirwan says:

    I haven’t spent enough time reading all you’ve referenced and I may be talking at cross-purposes as a result, but all this reminds me of my first excursion into reading papers on CO2 as a greenhouse gas. I chose to start out with Rasool & Schneider’s 1971 paper, “Atmospheric Carbon Dioxide and Aerosols: Effects of Large Increases on Global Climate.” The paper writes, “On the short time scale, if CO2, is augmented by another 10 percent in the next 30 years, the increase in the global temperature may be as small as 0.1°K.” They applied a very simple 1D model and focused on the central band (which is indeed “black” already) and failed to take into account the grayer sidebands and the changing effective radiation altitude. There actually were a number of problems with the paper, as pointed out almost immediately through letters from other scientists — as well as a couple of fatal flaws that Rasool & Schneider themselves found and reported quite soon after. (Their paper is still significant, not for its CO2 conclusions, but for the fact that it brought aerosols into serious discussion.)

    Overly narrow and simplistic views are most worthless. One must be comprehensive in view.

    It sounds to me as though Reinhart is just at the very early stages of a very simplistic and yet perhaps necessary beginning to his own understanding. That’s no reflection on the understanding of others. Just his own. I suppose I can’t entirely fault such neophyte mistakes, since we all have to start somewhere, and very good scientists (eg., Rasool & Schneider) also have made mistakes in their views (for hopefully short times, soon improved.)

    But this is almost 50 years later and Reinhart has access to a great deal more today and has far less excuses for failing to read and learn from them.

  17. Nick Stokes says:

    The isothermal assumption is right up there in the abstract
    “The earth is considered as a homogeneous spherical black body emitter with a temperature of 288 K. An idealized atmosphere, the CO2 content of which is the only infrared absorber, surrounds the emitter.”
    I think it is part of the problem. But the main one is, I think, that he does not consider re-emission.

    There is a mode of transmission at wavelengths of optical depth >3 which is called Rosseland transport. In this range, the radiative transfer equations become approximately diffusive, with the diffusivity inversely proportional to absorbance. For in-between OD, it’s still useful conceptual model. It’s a significant mode of transport, and depends entirely on a temperature gradient. Part of the GHE is that inverse dependence; more CO2 raises absorbance and lowers transport.

    The effect (somewhat related) that people normally think of is the raising of the effective emmission level to a colder region, inhibiting outflux. Reinhart’s model, if it included emission, would undoubtedly fall down here. High GHGs at 288K would emit far more than is available. But it is the change as the emission level cools that is a big part of the GHE. Isothermal rubs that bit out.

    On peer review, no, it isn’t, in the regular way. He lists four people that he says have “critically read” it. That doesn’t mean they approved.

  18. angech says:

    Only trivial but…
    The earth does not act as a homogeneous black body emitter of T = 288 K as seen from space.
    It is only the surface temp.
    The irradiance is known.
    The temperature it heats up to [less that due to its albedo] is known.
    Seen from space the Earth radiates from its TOA at 254-255 K.
    It cannot radiate out more energy than it absorbs [except for the little it makes].
    The albedo reflection component is not part of a black body radiation

    Moon Fact Sheet NASA
    moon earth ratio
    Geometric albedo 0.12 0.434 0.28-
    Solar irradiance (W/m2) 1361.0 1361.0 1.000
    Black-body temperature (K) 270.4 254.0 1.065

    Wiki
    “As a result, the Earth’s actual average surface temperature is about 288 K (15 °C), which is higher than the 255 K effective temperature, and even higher than the 279 K temperature that a black body would have.”

  19. angech says:

    The issue is what degree of warming does the 400 ppm of CO2 add to the surface temperature.
    Most of the rise from 255 to 288 C [ 33 C] is as a result of water vapor as the predominant GHG.
    CO2 is an integral and vital sub component.
    At a guess if it contributed 10% that would make a 3.3 C contribution to the total temperature which is not insignificant for 400 ppm.
    Hopefully others can provide the true contribution figure.
    Recognized science says a doubling from 280 ppm to 560 would give a 1.8 C rise with no feedbacks, perhaps up to 3.4 C with feedbacks [ECS].
    It is an interesting exercise to deny these effects and say they are up to 10 times smaller.
    It shows if you make a lot of assumptions you can move a long way from accepted reality.

  20. Marco says:

    What came to my mind is
    “Assume a spherical cow…”

  21. Ian Roberts says:

    Potholer 54 has a short video on this. Always worth a look.

  22. Ian,
    Thanks, I hadn’t seen that. I think it’s this one

  23. Nick,
    Thanks, this is a nice way of putting it.

    High GHGs at 288K would emit far more than is available. But it is the change as the emission level cools that is a big part of the GHE. Isothermal rubs that bit out.

  24. angech,

    Most of the rise from 255 to 288 C [ 33 C] is as a result of water vapor as the predominant GHG.
    CO2 is an integral and vital sub component.

    There is a paper about the Attribution of the present-day total greenhouse effect. Quite how you quantify it depends on whether you consider the addition of a single species when there is no GHE, or the removal of a single species when there is already a GHE. Since some of the absorption bands of the different species overlap, these are not quite the same. For single species removal, long-lived GHGs are about 20% and water vapour and clouds are just below 70%. (single species addition is more like 30% and 80% respectively).

  25. You link directly to the PDF. It is also possible to go via their blog: either in Kraut+Frog http://www.entrelemanetjura.ch/BLOG_WP_351/kohlendioxid-und-erderwarmung/ or Frog http://www.entrelemanetjura.ch/BLOG_WP_351/co2-une-chimere-climatique/.

    The Frog one says it was published in 2014 but ignored, which was the fate it deserved :-).

    The K+F one says “Si le Pr. Franz-Karl Reinhart, spécialiste de physique quantique, ancien Professeur de physique à l’Ecole polytechnique fédérale de Lausanne (EPFL), démontre que le CO2 est une source très secondaire du réchauffement climatique, le doute n’est plus permis” but doesn’t explain why, if argument from authority is the test of validity as it supposes, Reinhart is supposed to be the Uber-Authority in this area. Perhaps he’s just the bloke they know in their village cafe? It seems to be a local blog.

  26. angech, there is a good article at realclimate.org on that issue (I think it is intended as an more approachable introduction to the paper?)

  27. Harry Twinotter says:

    Strange paper. I recall Youtuber Potholer54 saying be suspicious of a study that includes a political point:

    “Therefore, demands for sequestering CO2 are unjustified and trading of CO2 certificates is an economic absurdity”

  28. Eli Rabett says:

    On the wordsmithing front Icarus 62 had a useful way of putting it

  29. jacksmith4tx says:

    I got this book last week and I was impressed with the depth and breadth of his narrative.
    Author Peter Brannen – The Ends of the World: Supervolcanoes, Lethal Oceans, and the Search for Past Apocalypses
    “It’s pretty clear that times of high carbon dioxide—and especially times when carbon dioxide levels rapidly rose—coincided with the mass extinctions,” writes University of Washington paleontologist and End-Permian mass extinction expert Peter Ward. “Here is the driver of extinction.”
    https://www.goodreads.com/book/show/32075449-the-ends-of-the-world

    My thoughts…
    If we manage to survive the beyond the next 100 years it will be because we used genetic engineering to modify not only homo-sapiens but also hundreds of other species to adapt to the changes we are making to the chemistry of the environment.

  30. jz3 says:

    FYI, Kenneth Richards is the pseudonym of an Illinois man and children’s entertainer named Rick Cina. Man got his start spamming livescience 24/7 and apparently writes full time for fulllftricks now.

  31. jz3,
    Thanks, I did wonder who Kenneth Richards was.

  32. jz3 says:

    He is also quite paranoid. Him and his wife are supposedly foster parents for many children, so I wouldn’t be surprised if he was getting some sort of kickback for the amount of bullchit he produces. All of his credentials are fake if it wasn’t obvious.

  33. eadler2 says:

    Reinhart has specialized in writing papers optical properties of semiconductors . It is pretty clear that he has no idea how the atmospheric greenhouse effect works. It seems that he has not done the basic thing that any scientist thinking of publishing something his field of specialization should do – understand the basic work already done in the new field. He can easily find the right way of looking at this on the internet: ACS.org/content/acs/en/climatescience/atmosphericwarming.html

  34. Jeffrey Weiss says:

    This episode highlights the importance of the fact that the troposphere cools with height. But this is never included in explanations of the greenhouse effect for the general public, or even at the undergraduate level. Why do we leave this out? I can’t say I’ve ever emphasized this myself.

    A nice simple example of the greenhouse effect is Eli’s green plate effect. https://rabett.blogspot.com/2017/10/an-evergreen-of-denial-is-that-colder.html This thought experiment only has radiative fluxes, no convection. Not to pick on Eli, but like most (all) simple explanations of the greenhouse effect, he doesn’t mention that the green plate (representing the atmosphere) is cooler than the blue plate (representing the surface), although he shows the equation that says it must be.

    It turns out this is also a nice model for looking at the role of non-radiative fluxes. If you add non-radiative energy fluxes between the two plates you get different greenhouse warmings. If you add a flux that keeps the two plates at the same temperature, modeling an isothermal atmosphere, then the greenhouse effect goes away completely. If you add a flux modeling radiative-convective equilibrium, you get another magnitude for the greenhouse warming.

    [Mod: I’ve edited the time on this comment so that it appears in the right order.]

  35. Eli Rabett says:

    Jeffrey, indeed there are some things to be cleaned up, but it has been a splendid adventure watching heads explode.

  36. Jeffrey,

    This episode highlights the importance of the fact that the troposphere cools with height. But this is never included in explanations of the greenhouse effect for the general public, or even at the undergraduate level. Why do we leave this out? I can’t say I’ve ever emphasized this myself.

    It often is ignored, but I have tried to explain it this way before myself, and there is this nice Realclimate post with a nice animation.

    For some reason your comment appeared after Eli’s, even though his is a response to yours (time zones?). [Okay, even mine ended up appearing before Jeffrey’s, so I’ve edited the time on Jeffrey’s comment so that these comments appears in the correct order.]

  37. eadler2 says:

    I did some looking on the internet to figure out who FK Reinhart is. He is a professor emeritus at the Polytechnic Institute in Lausanne, born in 1933. His specialties were optical properties of semiconductors. Clearly he was overconfident about his ability in a field that he had no background in.

  38. Smansion says:

    For this case the “RRTM Earth’s Energy Budget” model might be even more helpful:

    http://climatemodels.uchicago.edu/rrtm/

    –> reference case: Double the CO2 concentration: +4.2 Wm-2 energy input into the system (let everything else fixed)

    –> set lapse rate to 0K/km (isotherm atmosphere): Again a CO2 doubling experiment and you’ll see that CO2 has basically no effect anymore.

  39. Smansion’s point of view is very relevant and appears to me to result in a straightforward refutation of the result by F.K. Reinhart.

    For this case the “RRTM Earth’s Energy Budget” model might be even more helpful:

    http://climatemodels.uchicago.edu/rrtm/

    –> reference case: Double the CO2 concentration: +4.2 Wm-2 energy input into the system (let everything else fixed)

    I have made some elaborations on this using the “RRTM Earth’s Energy Budget” model. Note at first that in the reference case with CO2 at 400 ppm the Earth’s energy budget is balanced and that the surface temperature equals 284.42 K. When CO2 is doubled to 800 ppm with all other conditions constant, that is the surface temperature remaining at 284.42 K, the forcing is obtained as +4.2 Wm-2. The Earth is now gaining more heat than it is losing and will be heated with a positive forcing until the surface temperature has increased to the value where the energy budget is again balanced.

    By changing the surface temperature keeping CO2 at 800 ppm we find that the Earth is gaining as much energy as it is losing with a surface temperature of 286.9 K. Thus, the increase in temperature for doubling CO2 from 400 ppm to 800 ppm is 2.5 K according to this calculation.

    Now change the lapse rate from 6 K/km to 0 K/km with CO2 at 400 ppm. At this new conditions, the Earth will lose much more energy than it gains. There is a theoretical explanation for this that when the temperature of the atmosphere is at a constant value equal to the surface temperature of the planet there is no greenhouse effect. In such a case the temperature of the planet surface at a balanced energy budget will become the same as if there were no atmosphere at all.

    Thus, we find by changing the surface temperature in the RRTM program in this case that the Earth is gaining as much energy as it is losing when the surface temperature equals 256.06 K. This agrees with the well-known average surface temperature of the Earth without an atmosphere calculated in all fundamental books on atmospheric physics.

    Now double CO2 to 800 ppm. The result is that the Earth is gaining 0.1 Wm-2, that is practically zero forcing considering numerical uncertainties. Because there is no greenhouse effect with the assumed temperature conditions of zero lapse rate, that is a constant temperature of the atmosphere, and of equal atmospheric and planet surface temperature, the doubling of CO2 has no effect.

    If F.K. Reinhart would have made his calculations correctly he would have found the same result. He assumed that the atmosphere has a constant temperature of 288 K equal to the surface temperature of the planet. From fundamental atmospheric physics, it follows that there should be no greenhouse effect at such conditions giving that the forcing obtained by doubling the CO2 concentration must be zero, what is also demonstrated by our calculations. Thus, our results show straightforwardly that the paper by F.K. Reinhart is fundamentally flawed.

  40. Here is some more information with pictures on the calculations with the “RRTM Earth’s Energy Budget” model in my previous comment. Link to the model: http://climatemodels.uchicago.edu/rrtm/

    This is the base case with 400 ppm CO2 and a lapse rate of 6 K/km:

    The Earth is in energy balance, that is it loses as much energy as it gains at a surface temperature of 284.42 K.

    After doubling to 800 ppm CO2, keeping all other conditions constant, the Earth will gain 4.2 W m-2, that is the radiative forcing in this case:

    This is the base case with 400 ppm CO2 and zero lapse rate. The surface temperature of the Earth in energy balance is 256.05 K:

    After doubling to 800 ppm CO2, keeping all other conditions constant, the Earth will gain 0.1 W m-2, that is practically zero radiative forcing:

    Note from the pictures that the Earth in the two base cases at the top of the atmosphere receives as much energy from the Sun as it gives to the space in the form of reflected sunlight and infrared radiation. On the other hand, the planet surface receives more radiative energy from the atmosphere than it emits to the atmosphere.

    However, the planet surface is in fact also in energy balance. The difference between absorbed and emitted radiation is in the form of convective transfer of latent and sensible heat that is not seen in those pictures. This is because the two base cases are examples of so-called radiative-convective thermal equilibrium.

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