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Plass and the Surface Budget Fallacy

Filed under: — raypierre @ 13 January 2010

RealClimate is run by a rather loosely organized volunteer consortium of people with day jobs that in and of themselves can be quite consuming of attention. And so it came to pass that the first I learned about Gavin’s interest in the work of Plass was — by reading RealClimate! In fact, David Archer and I have a book due to appear this year from Wiley/Blackwell (The Warming Papers), which is a collection of historic papers on global warming, together with interpretive essays by David and myself. Needless to say, we pay a lot of attention to the seminal work by Plass in this book. His 1956 QJRMS technical paper on radiative transfer, which is largely the basis of his more popular writings on global warming, was one of the papers we chose to reprint in our collection. In reading historic papers, it is easy to fall into the trap of assuming that investigators of the past are working on the basis of the same underlying set of assumptions in common use today. Through a very close reading of the paper, David and I noticed something about the way Plass estimated surface temperature increase, that Gavin and all previous commentators on Plass — including Kaplan himself — seem to have overlooked.

These days, it is fairly common knowledge that determination of surface temperature change requires simultaneous satisfaction of the top-of-atmosphere energy budget and surface energy budget, and that in most circumstances it is the top-of-atmosphere budget that plays by far the leading role. This is one of the many things that Arrhenius got spot-on right in his conceptual framework for computing surface temperature. His computation explicitly takes both balance requirements into account, though substantial inaccuracies were introduced because the onerous computations involved in solving the model pretty much restricted him to a one-layer representation of the atmosphere. Later workers improved on Arrhenius by introducing multiple layers and more accurate spectroscopy, but did not always note the importance of satisfying the top-of-atmosphere balance. I think it seems natural to most people to assume that if one is interested in surface temperature, the surface budget must be the most important thing to look at. Plass, for all his brilliance in computing the radiative effects of CO2, was one of the ones who was led astray by this fallacy.

Since discussions of radiative forcing today are almost invariably based on top-of-atmosphere budgets (or at least top-of- troposphere budgets, which are almost the same thing), it is natural for the modern reader to assume that when a paper quotes a radiative forcing, it must be a top-of-atmosphere forcing. This is what Gavin assumed, but a close reading of the 1956 QJRMS paper shows that this is not, in fact, what Plass was talking about. In that paper, Plass does not get around to turning his voluminous radiative calculations into a surface temperature change until nearly the last page of the paper, and when he does, he spends barely a page explaining the reasoning.

The radiative forcing Plass quotes is actually the increase in downward infrared radiation to the surface, which you get if you double CO2 while holding the atmospheric temperature fixed . This back-radiation increases because increasing the concentration of a greenhouse gas makes the atmosphere a more efficient emitter of infrared radiation, at least up to the point where the lowest bits of the atmosphere emit so well that they essentially have become a blackbody, whereafter the emission to the ground can no longer increase unless the air temperature changes. For Earthlike conditions, the emission from CO2 is nowhere near saturated in this sense (see this post ) , so Plass was entirely correct in inferring an increase in the back-radiation, at least for a relatively dry atmosphere. Adding CO2 to the atmosphere is a bit like turning up the dial on a heat lamp you are lying underneath.

It is in the final stages of the calculation that Plass went wrong. He assumed that the surface would get rid of the extra infrared radiation it was receiving by heating up until it was able to radiate away the excess. This reasoning ignores the fact that radiation is not the only means of exchanging heat between the atmosphere and the surface. There are also turbulent exchanges, including evaporation, and these would tend to limit the surface warming to values far less than the values Plass estimated. Further, when the lower atmosphere is warm and moist, such as in the tropics, the great infrared opacity of the large quantity of water vapor tends to limit the direct effect of CO2 on back-radiation into the surface, which further limits the surface warming if the air temperature is held fixed as Plass did. To be fair, Plass does include a sentence implying that he was concerned about the portion of the retained flux that exited through the top of the atmosphere, but even if one gives the most generous interpretation to what might have been meant by this statement, there is no way to make a consistent calculation out of it, given the use of the surface back-radiation as radiative forcing.

The way the greenhouse effect really works is that adding CO2 reduces the infrared out the top of the atmosphere, which means the planet receives more solar energy than it is getting rid of as infrared out the top. The only way to bring the system back into balance is for the whole troposphere to warm up. It is the corresponding warming of the low level air that drags the surface temperature along with it — an effect left entirely out of Plass’ calculation.

A more quantitative discussion of the way all this works can be found in The Warming Papers, and a yet more advanced discussion of such things can be found in Chapter 6 of my book Principles of Planetary Climate (which at long last has been shipped off to Cambridge University press, animula vagula blandula)

In point of fact, Plass did compute the top-of-atmosphere radiative forcing due to doubling or halving the concentration of CO2. The result is plainly shown in the rightmost graph of his Figure 7, where he shows the vertical profile of upward and downward flux for three different CO2 concentrations. Reading the values from the top of the graph, I get that Plass computes a 3.2 Watt per square meter reduction in the outgoing radiation for a doubling of CO2. This is really quite close to the modern value. Plass does not mention this number, or its importance, anywhere in the text, however. Still, it would be fair to give Plass the credit for the first calculation of top-of-atmosphere radiative forcing using correct modern radiative physics. Though he did not make good use of the calculation himself, the methods he introduced are largely the same as those used by Manabe and Wetherald in 1967, who were the first to put together correct spectroscopy with a correct framework for computing surface temperature, adding in accurate water vapor spectroscopy and the effects of convection along the way.

Thus, while Plass made seminal contributions to radiative transfer, his actual estimate of surface temperature increase cannot be regarded as an improvement over Arrhenius. Plass had better spectroscopy than Arrhenius, but a framework that would not give the right answer no matter how good the radiative transfer was. The point of all this historical deconstruction is not to poke fun at Plass or detract from his contributions. Theories do not spring from scientists full-formed like Athena from the head of Zeuss. Science often proceeds through a series of errors and corrections, and those who move the ball forward are in the thick of this process even if they have made some mistakes. The point is that our current understanding of global warming rests on the shoulders of some of the greatest giants of physics of the past century or more, and myriad lesser but still substantial intellects as well.

So, when push comes to shove, was Plass a Hedgehog or a Fox? The answer is: a bit of both. With regard to computing the radiative fluxes due to CO2, Plass was a true hedgehog — he knew that one thing really, really well, and that had a lasting impact on our science. But in his Tellus article, he also showed himself to be quite a fox, in that by knowing (and explaining) many independent lines of thinking, he helped to revive attention to the wide-ranging importance of CO2 in climate. You could say he was not enough of a fox to have also absorbed the lesson of the importance of top-of-atmosphere balance, known already to Arrhenius. But also, you could say that if you’re going to be a hedgehog and pick one thing to be the central organizing principle of your world view, it had better be a pretty darn universally important thing to know. If you’re going to be a climate hedgehog, the constraint imposed by top-of-atmosphere radiation balance would be a pretty good place to hang your hat.

230 Responses to “Plass and the Surface Budget Fallacy”

  1. 201
    Sou says:

    @186 Tom Clark
    Down in my part of the world the current El Nino has been part of the seasonal outlook report of the Bureau of Meteorology site for quite a while:

    I’m not sure it’s hugely relevant to climate change, except that it seems to be coming more often. Perhaps someone can comment on its frequency.

  2. 202
    Completely Fed Up says:

    “-There is a general 50-60 yr cycle of temps, and we were warming from roughly 1980 to 2005”

    And the causation is..?

    You need this to ascertain whether it explains the changes or not.

    What you do is you find out the strength and direction of the causation, plug in the changes as measured and find out whether, after these causes are taken out of the data, the remainder is flat.

    If it is flatter but still rising, then they are not sufficient cause. If the causations to not make the shape flatter, then they are not provable causes.

  3. 203
    Jim Bouldin says:

    Dont spend time and energy on ‘Monckton’, just concentrate on the science. The number of posts increasing on here about this guy begins to look like paranoia! Not needed….

    Bingo. Same goes for a number of other fools.

  4. 204

    182 Jianhua Lu

    Thanks for responding.

    However, if 3 W/m^2 went into the troposphere for 20 years, that troposphere would have to have warmed by about 10 degrees C over that time.

  5. 205
    Hank Roberts says:

    Jim Bullis, heat doesn’t stay in one place for 20 years to ‘add up’– the way you’re doing the arithmetic just fails.

    I’m done replying to those ideas here. Good luck with it.

  6. 206
    John E. Pearson says:

    166: Barton, I like your absorption page a lot. Yes it does help. But what I don’t see in it is this whole bit about increasing the scale height of the atmosphere by adding CO2. The climate guys have this picture they present that is pretty simple. It’s basically “add some more feathers to your down comforter and the outer liner expands a little bit and keeps you warmer”. It sounds entirely plausible but I’ve never seen it worked out in a version that doesn’t require computers but I think that such a simple picture must have an analytic formulation. I reckon this stuff is in books but I think I’ll wait for Raymond’s book to come out since Goody’s book is $115 used on Amazon.

  7. 207
    Completely Fed Up says:

    JEP: “It sounds entirely plausible but I’ve never seen it worked out in a version that doesn’t require computers”

    That’s because the detail you’re looking for requires a lot of sums to be made.

    Take those computer programs and look at the maths in it. Then work through the maths. Then you’ll have seen it worked out without a computer.

    This could take weeks, mind.

    Alternatively, you can just take the result from the computers calculations.

  8. 208

    g Lamoto: The rather poor correlation between temp trends & [CO2] over the past century or so…

    BPL: Read and learn:

  9. 209
    tom clark says:

    Thank you very much, Hank Roberts, for noticing the magnificent, if entirely unscientific, Marguerite Yourcenar line.

    And thank you, Ray Ladbury, for your lovely condescension.

    I don’t know what American Idol is. Perhaps you could inform me, Ray.

    I follow the longterm forecasts like everyone else. Plenty of hedging of bets around the longterm forecasts of a “weak-to-moderate” El Niño cycle, since last Fall.

    And thank you, too, flxible, for informing me that “any El Nino event is ‘classic'”.

    Perhaps, though, some classics are more classical than others. I’ve seen four or five big El Niño events affecting this coast. The last big one was 1998.

    We have been told that this one would be “weak-to-moderate”.

    Is it still looking that way?

    Do forgive the non-scientific source (StormSurf) and the perhaps offensive-to-some term “classic” in the following report, dated 1/14/10:

    “Sea Surface Temp anomaly data (1/14) indicates that warmer than normal waters were consolidated on the equator from the Galapagos Islands west to the dateline and even west of there, and holding. A new strong Kelvin Wave has erupted along the coast and some evidence of it can be seen with a most solid warm anomaly signature present over and just west of the Galapagos Islands. It is expected that water temps will continue to increase yet more over the coming weeks as this Kelvin Wave and a new one continues impacting the coast there. This is classic El Nino.

    “This appears to be a late blooming ENSO event.

    “El Nino is affecting the global atmospheric weather pattern at this point in time and is expected to continue having an impact into the Summer of 2010. This suggests that not only will the winter and spring storm pattern be enhanced in the North Pacific, but also the early summer storm track in the South Pacific too.

    “A solid accumulation of warm surface water in the equatorial East Pacific and a solid pool of warm subsurface water is evidence in-favor of continued development of El Nino. As long as there continues to be WWB’s [Westerly Wind Bursts], then warm water will be migrating east, and the warm water pattern will hold if not build, and the atmosphere above it will respond in-kind to the change (towards El Nino). We expect one last shot at another Kelvin Wave from the current Active Phase in-play now (Jan 2010) and then the slow degradation will begin in the ocean. But the atmosphere is already be strongly influenced by the warm water buildup over the past 6 months, and it will not return to a normal state for quite some time. This El Nino it is already larger and stronger than any other in the past 12 years.”

    By the way, it’s raining cats and dogs and blowing hard this morning. (He said very unscientifically.)

  10. 210
    CM says:


    #188 (“+ has been added”) — that’s the weirdest arithmetic I’ve seen since a certain viscount calculated climate sensitivity.

    #189 — Why would the atmosphere need to be “simple”?

    #207 (“magic molecule”) — You may well be right. Raypierre’s inline reply to you in another context at #141 is relevant.

  11. 211
    Ray Ladbury says:

    Tom Clark, I’m sorry the world is not as simple as you would desire. However, in a system as complicated as the coupled ocean and atmosphere, a 5 month prediction or a 5-day storm track are pretty goddamned good. The fact of the matter is that everyone seems to be demanding that they be able to understand the science. Well, the science can only be dumbed down so much, so the only solution is for people to wise up.

    If people want better forecasting: Great, ask your legislators to increase your tax rate so we can afford more research. If they want to understand the science: Great, there’s a wonderful “Start Here” page on this very site. People need to stop expecting reality to comform to their prejudices. Then they need to stop expecting to be spoonfed reality.

  12. 212
    CM says:

    Tom Clark,

    Forgive me if I misread you, but judging from your strident asides you seem to think non-scientists are frowned on here, or that one has to express oneself somehow “scientifically” to pass muster. This simply is not the case, and any issues you may have with not being a scientist really are your own. But if you start out with confident assertions about the scientists getting this or that wrong, you’d better have your facts straight.

  13. 213
    flxible says:

    tom clark – It’ll be another few weeks before the Jan data is added to the chart, but currently El Nino is running neck n neck with 2002, and while it’s “weaker” than ’97/’98, the El Nino in ’82/’83 was also stronger than current while winding up quite the same as ’98

    It’s also currently pouring and blowing a gale way north of you, nearly identical to conditions here in Jan ’98, so again, old news to folks who’ve been paying attention – like South American fisher folk

  14. 214
    Completely Fed Up says:

    “that’s the weirdest arithmetic I’ve seen since a certain viscount calculated climate sensitivity.”

    Only because it’s an extremely simple analogy.

    2 + 5 = 7

    change one thing: add a 0:

    20 + 5 = 7


    So when rod or yourself say “well, what if we changed just one thing: convection”, that isn’t changing one thing. It’s changing a whole raft of things.

    Because convection isn’t a single thing: it’s a result of multiple processes.

    Removing that means changing each and every one of those processes.

  15. 215
    Completely Fed Up says:

    “And thank you, Ray Ladbury, for your lovely condescension.” tom says, condescendingly…

    When someone turns up and states something categorically as true, then they’d better be enough of a speci alist in it to be able to use authority to carry the statement.

    There is no royal road to education. And blank statements are the opposite of erudition.

  16. 216
    Completely Fed Up says:

    [There is some discussion of this in Ramanathan’s paper where he rediscovers Sagan’s window-grey model without knowing Sagan did it first, but it’s not widely known. So I put it in Chapter 4 of Principles. –raypierre]

    I remember some about that proposition, Raypierre, but at the time it was in pretty much the same league as his Jovian Gas Bags (unfairly touted as crackpoterry by his detractors because he said at the time it was hugely unlikely that such a being would exist there).

    Such a place would, I think, be somewhat similar to the Discworld that T Pratchett makes, not in the fantasy books of the same series name, but in his more scifi work called “Strata”.

    Have a read if you get a chance. Hand-waving with science taking the place of magic, but still magic, just scientific magic.

    [Response: I don’t think you’re thinking of the same paper I’m thinking of . Sagan’s window-grey model wasn’t at all fanciful. It was a straightforward radiative-transfer paper employing the assumption that the absorber was a grey-gas within a limited subset of the infrared, but transparent outside. It’s an appealing model to rediscover. Rodrigo Caballero and I rediscovered it when we were writing our overly long QJRMS article on the dry Hadley cell (it was just a means to the end of getting the tropopause height more realistic in a grey model), then found that Weaver and Ram had done it. But then when writing the book I stumbled on the fact that Sagan had done it in the 1960’s. Who knows, if we look harder maybe we’ll find that Hulbert did it in the 1930’s for all I know. Whereever it comes from, it’s a good model to know, and important to have in one’s analytic toolkit. –raypierre]

  17. 217

    205 Hank Roberts,

    Of course heat does not stay in the troposphere that long. But if there is a net of 3 W/m^2 going into something, it has to warm up. My conditional statement was my way of demonstrating that the 3 W/m^2 could not be correct.

  18. 218

    I’m disturbed to see the conversation with Tom Clark start off so badly. He wasn’t, after all, making claims about science, only about his perceptions of how other people see science.

    Ray L’s response, while true in every detail

    “Great, ask your legislators to increase your tax rate so we can afford more research. If they want to understand the science: Great, there’s a wonderful “Start Here” page on this very site. People need to stop expecting reality to comform to their prejudices. Then they need to stop expecting to be spoonfed reality.”

    is unhelpful with respect to tone.

    That said, thanks all for a fascinating thread with many useful leads and clues.

  19. 219
    raypierre says:

    I will be closing this discussion soon, since I don’t like to leave threads open that I don’t have time to moderate or respond to. My thanks to everybody for their comments. Meanwhile, for fans of Hedgehogs, I heartily recommend
    Muriel Barbery’s novel, The Elegance of the Hedgehog (or the original
    Folio edition in French, l’Elegance du Herisson). Very interesting to think about where the Hedgehog is, since Barbery doesn’t clobber you with it.

  20. 220
    Completely Fed Up says:

    [Response: I don’t think you’re thinking of the same paper I’m thinking of .]

    It wasn’t a paper (as in written up etc), but more of a story.

    It may have been from a (very old) Scientific American (one of my mates loves it, and I’ve read a few), but it was that level of detail.

    Mind you, that model would still have stratification because the temperature profile and mixing level that blocks that temperature IR band change independently and so you’d still get a convective atmosphere.

    (I did work on stellar atmospheres and looked into the possibilities of a 4billion km diameter giant sun which is as close as possible to isothermal over the convective distance at that pressure. Dammed if I can remember, that example at the time was a hypothesis, there are other more reliable examples nowadays and maybe someone has done more work on the phenomena. In either case, it’s a source of power rather than a receptor/emiter)

  21. 221
    Hank Roberts says:

    Tom C.
    — nothing at all unscientific about the Yourcenar line. I intend to quote it in my end-of-life planning document, to try to avoid what I’ve seen Hospice do to several people, dosing them to “reduce anxiety” to the point of stupor when they really wanted to die with their eyes open. That’s not just poetry, it’s a medical directive.

    As to the El Nino, I’ve been here for all of them for more than 30 years, and I’ve seen much worse, but at any point on the ground it’s weather, no matter how intense. We’ll have to look back once it’s over to know.

    Hang in here for a while, watch us non-scientists struggling to understand and explain what’s going on when we know the real answers take both an understanding of math and a good bit of computer time to do it; finding words to express something “well enough” is a major challenge. To quote myself from a long while ago, although others have said the same thing in similar words: Mathematical physics without the math is poetry, at best.

    We need people who can write the “poetry, at best” to explain the notions the physicists are trying to tell us they’ve been learning. Have a look at the infrared radiative transfer discussions for example. We barely know what a photon is, or a molecule, and are trying to explain to each other how a photon can interact with a greenhous gas molecule. The physicists describe what happens mathematically. We don’t have _words_ for all this and we desperately need them, because we have been changing the world — and need to understand what we’re doing.

  22. 222
    CM says:

    Re: hedgehogs,

    Since no one else has, let me also mention S. J. Gould’s posthumous _The Hedgehog, the Fox and the Magister’s Pox_, of particular interest perhaps to us humanities folks who like to listen in on natural scientists and wonder if we’re engaged in the same endeavor. It has a different take on “consilience” (a principle occasionally invoked on this site) from that given wide circulation by E. O. Wilson.

  23. 223

    Raypierre, I would like to understand adiabatic lapse rates of +4 or +5C/km in the lower Arctic troposphere , without heavy or no water vapour content… Are radiative transfers respunsible? Is there something replacing water vapour as reducing the value of a dry adiabatic lapse rate?

  24. 224
    tom clark says:

    Michael Tobis and Hank Roberts,

    Thanks very much for your courtesy. This thread has led me to do a bit of useful studying on a subject that matters a great deal to everyone on the planet.

    It also matters a great deal to me personally, if I may say so.

    And by the way, a final anecdotal aside: Wow, is it coming down here at the moment, an absolute monsoon, shades of 1982. Explanations are beside the point when your house is slipping down a hillside.

    Beautiful about the end-of-life planning document, Hank. I could use one of those myself. And that Marguerite Yourcenar was one tough cookie. She may even have known a thing or two Kübler-Ross didn’t.

    I would hope poetry and science will one day learn to lie down together in peaceful mutual understanding, who on earth would not benefit from that?

  25. 225


    The 6.5 K/km average for Earth’s troposphere is just that–an average. The exact rate depends on local temperature, pressure, and humidity, and ranges from about 4.75 K/km near the ground to nearly adiabatic (9.77 K/km) near the tropopause.

  26. 226

    226.. Much Thanks Barton. This 6.75 K/Km is likely including moisture , every thing. I do get 9.8 C/Km
    off the ground and near the trop. The just of my question is this, if there is no moisture at all, a dry atmosphere, in darkness, during the long night of Antarctica and the Arctic there are dry lapse rates
    of 4 C/Km , no inversion, not an Isotherm. I am particularly interested in CO2 impact on the lapse rates if any. Would Greenhouse gases affect the lapse rate? If they do, I observe this dry 4 C/KM always below mid troposphere levels, sometimes above… I am wondering if this may be caused by green house gases. Remember , pure darkness, no solar input, no ground heating. Just occasional advection from the South…

  27. 227

    Goodness BPL — it is not as if Kate used inches instead of millimeters to calculate a Mars trajectory. I’m glad someone threw the Greek in there.

  28. 228

    oh, yeah, and raypierre, congratulations on this book! sounds great!

  29. 229


    The adiabatic lapse rate is just g/cp where g is the gravity and cp the specific heat at constant pressure–but that’s only accurate for a dry atmosphere. For an atmosphere with a condensible substance in it, like water vapor, you need the much more complicated expression for the saturated lapse rate.

  30. 230
    Peter Offenhartz says:

    A question for Gavin: Will your book discuss the difference between winter and summer global warming? I gather that essentially ALL the warming effect occurs in winter, and I believe this is because of the seasonal change in water vapor concentration.

    It is also worth noting that some of the earth’s radiation escapes along the edge of the CO2 absorption bands, close to the radiative window, and the intensity of the escaping radiation in this band is quite sensitive to CO2 concentration, while intensity in the center of the CO2 band depends solely on the temperature of the lower stratosphere.