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The carbon dioxide theory of Gilbert Plass

Filed under: — gavin @ 4 January 2010

Gilbert Plass was one of the pioneers of the calculation of how solar and infrared radiation affects climate and climate change. In 1956 he published a series of papers on radiative transfer and the role of CO2, including a relatively ‘pop’ piece in American Scientist. This has just been reprinted (as an abridged version) along with commentaries from James Fleming, a historian of science, and me. Some of the intriguing things about this article are that Plass (writing in 1956 remember) estimates that a doubling of CO2 would cause the planet to warm 3.6ºC, that CO2 levels would rise 30% over the 20th Century and it would warm by about 1ºC over the same period. The relevant numbers from the IPCC AR4 are a climate sensitivity of 2 to 4.5ºC, a CO2 rise of 37% since the pre-industrial and a 1900-2000 trend of around 0.7ºC. He makes a lot of other predictions (about the decrease in CO2 during ice ages, the limits of nuclear power and the like), but it’s worth examining his apparent prescience on these three quantitative issues. Was he prophetic, or lucky, or both?

To understand if Plass should get full credit, we need to see his workings. These are mainly outlined in two more technical papers in Tellus and QJRMS earlier that year. In today’s parlance, Plass calculated the change in top-of-the-atmosphere (TOA) radiative fluxes given a doubling (or a halving) of CO2 while everything else stayed the same. He then took that number and using someone else’s estimate of the sensitivity of the TOA radiation to the surface temperature, he calculated the temperature change that would be necessary to compensate. Converting from the units he used, the radiative flux values for a doubling of CO2 were 8.3 W/m2 and 5.8 W/m2 for clear-sky (no clouds) and averagely cloudy conditions (all-sky) respectively (and slightly larger and of opposite sign for a halving). The sensitivity of the TOA flux to surface temperature he used was around 2.3 W/m2 per ºC (equivalent to a temperature sensitivity of 0.4 ºC/(W/m2)). However, this is a ‘no-feedback’ estimate (allowing only the surface temperature to change with a constant lapse rate, but with no changes to water vapour, albedo or clouds).

Today, our current best guess for the forcing due to 2xCO2 is around 4 W/m2, and the ‘no-feedback’ sensitivity is around 0.3 ºC/(W/m2), giving an expected no-feedback temperature change of about 1.2 ºC, a factor of 3 smaller than the number Plass quoted, though since our number is for ‘all sky’ conditions, it would be a little better to compare it to his averagely cloudy number 2.5 ºC (so a factor of two higher). Note that Plass was a little casual in how he described his numbers and the ‘clear sky’ designation for the 3.6ºC number was not always made clear. However, Plass was well aware that the ‘no-feedback’ case was unrealistic and estimated that the water vapour, cloud and ice-albedo feedbacks would be amplifying, although he was not able to quantify them.

Moving now to the rate of change of CO2 in the atmosphere, Plass made a very good estimate as to how much human emissions of CO2 were increasing. His estimate was (again, in modern units) that then-current emissions were 1.5 GtC based on earlier estimates from Callendar, which actually was an underestimate. Our current best estimate for the anthropogenic emissions in 1956 is about 2.2 GtC. Given the increasing nature of the emissions, Plass then estimated that concentrations would rise about 30% by the end of the 20th Century. This however needs an estimate of how much of the emissions would be absorbed by the oceans and biosphere. Here, Plass has another impressive insight that the ocean chemistry would prevent quick uptake of the human CO2, a concept that wasn’t fully worked out until Revelle and Suess’s paper in 1957 (though possibly he may have been aware of some informal communications earlier). Plass actually assumed that none of the CO2 would be taken up in the short term. So his 30% growth estimate (the actual rise was 36%) was derived from an underestimate in emissions (and emissions growth) combined with an overestimate of the ‘airborne fraction’ (which is roughly 40% of total emissions).

Finally, his estimate of temperature rise of about 1ºC by the end of century follows from the two previous numbers, along with two further assumptions – that the climate is always close to equilibrium with the forcings and that of course, there aren’t any other factors changing. The first assumption affected by the substantial lag in the system because of the thermal inertia of the oceans, and of course, there are many more factors driving climate change over the 20th C. Plass can of course be forgiven for not knowing about the greenhouse impact of rises in CH4, N2O and CFCs (not realised until 1974), or the role of aerosol emissions (1970s), and indeed, he was fortunate that the net effect of all non-CO2 drivers is close to zero (though with significant uncertainties).

So Plass was correct about all of the big issues, but lucky that, in his quantitative estimates, the errors went both ways and end up pretty much cancelling out.

Eli has described this using Isaiah Berlin’s Hedgehog and the Fox metaphor – Plass being the Hedgehog who knows one big thing, and for whom the details are more incidental. I think this is a reasonable take, as long as it is realised that Hedgehogs are not always right, even though in this case he was.

The Fox in this case was another big name in atmospheric physics, Lewis Kaplan. He published a counter to Plass’s 1956 work in Tellus in 1960 (vol. 12, p204-208), and there was a “spirited” exchange of letters in 1961 (vol. 13, p296-302) (references for those of you with libraries – for some reason, none of the old Tellus volumes are online). His calculation used a different methodology, more up-to-date spectra but was different enough in approach and specifics to make a fair apples-to-apples comparison between the results hard to do. Nonetheless, Kaplan declared that “Plass’ estimate of a temperature drop of 3.8ºC due to a halving of [CO2] appears to be too high by a factor of two or three” and that “it would seem, then, that CO2 variations could not play a role in the ice-age cycle unless the changes were by an order of magnitude”.

The subsequent comment and reply are actually very reminiscent of recent disputes in climate science. Plass complains that not enough information was provided to replicate the analysis, that Kaplan used unjustified precision, that he wasn’t comparing like-with-like (all-sky with clear-sky), that he made unjustified technical assumptions, and that his overall conclusion was ‘misleading’ because of the neglected feedbacks (that neither of them had quantified). Kaplan responds that of course there is enough information to check his workings (in another paper), that it was Plass’ fault he compared the all-sky and clear-sky numbers, and that he has exaggerated the impact of the technical criticisms. Notably, Kaplan did not respond on the issue of feedbacks.

Looking over the exchange with a 50 year perspective, a number of things stand out. First, Kaplan does seem to have been closer to modern values in his calculation – Plass was out by a factor of two for the all-sky no-feedback case. I’m not really familiar enough with the details to be be able to tell why (perhaps someone can enlighten us in the comments). However, Kaplan was wrong about everything that has ended up mattering – CO2 does play a big role in ice age cycles (with a magnitude of change close to what Plass anticipated) and its growth today is climatically significant. Significantly, I can find no trace in the literature of any resolution of the technical issues raised in the letters. Resolution in Plass’ favour of the big questions came with further independent efforts as computers got fast enough to do the more complicated feedback problem, better observations, better spectral data and better paleo-climate information (particularly from the ice cores). In some sense, resolution of their technical differences would have been moot because that wasn’t the real issue. Of course, that would have been difficult to see at the time.

So, to summarize, Plass did have some key insights and in many respects was well ahead of his time. But he was also lucky.

Update: Stay tuned, it looks like there is another little wrinkle to this story…

158 Responses to “The carbon dioxide theory of Gilbert Plass”

  1. 151
    Hank Roberts says:

    > Edward Greisch [corrects my mistaken history] 8 January 2010 at 4:06 AM
    Thank you. I found a better source, saying the design choice came from Rickover but for propulsion.

  2. 152

    Hank Roberts #120:

    Now this gets interesting if you use the oxygen as well, in combustion, instead of using atmospheric air. That avoids the nitrogen oxides problem (with excess nitrogen being a huge biological problem nowadays). And produces a waste gas stream that’s almost entirely CO2, ready to sequester or resell to the fizzy water companies.

    Let’s look at some ballpark numbers (industry figures are hard to come by without paying for expensive reports, and carbonations levels vary significantly between types of drink).

    Worldwide consumption of fizzy drinks is about 327 billion litres. Allowing 5g per litre of CO_2 (I couldn’t find an accurate source but this is probably a fair estimate), soft drinks worldwide use about 1.6 million tonnes of CO_2 per year, less than a tenth the output of one dirty coal power plant.

    Don’t raise your hopes too much of selling “clean coal” detritus to the fizzy drinks industry — even if I’m out by an order of magnitude.

  3. 153
    CM says:

    sidd (#65),
    belated thanks.

  4. 154
    Roger says:

    Amazingly informative. Shirly, and others, thanks for taking time from your other work to comment here. There is so much to learn…yet Nature’s clock ticks…and the question remains: will we ACT to save ourselves before the big scoreboard in the sky lights up with “GAME OVER?”

  5. 155


    No, almost certainly we will not. Humans don’t prevent crises; they wait until the crisis happens and then react (cf World War II). Only this time that will be too late.

  6. 156
    Ray Ladbury says:

    Stuart @146, Given the many problems already pointed out with the B&B site, why do you persist in using it, I wonder? Surely, some of the resources on the Start Here page are more informative. B&B is climate denialism with the spittle mopped up.

  7. 157
    Hank Roberts says:

    > fizzy drink industry
    Philip, yep; my point being that industry would much rather spread their waste around and get paid for it than absorb the cost of sequestering it.

    Sewage sludge is toxic waste unless it’s sold as fertilizer.

    Coal tar is toxic waste unless it’s sold as asphalt parking lot sealant.

    When I was a kid, in the 1950s in the American south, the timber industry marketed its waste polychlorinated biphenyls (those not sold as transformer oil, anyhow) by soaking the stuff into sawdust, and selling the resulting purple stuff by the 55-gallon drum as a dust collector — for janitors to throw on floors and push around with dust mops to produce a clean, shiny, dust-free floor.

    Thus fizzy drinks …. urp. I shouldn’t try sarcasm, I can’t do it.

  8. 158
    Richard S. says:

    I am currently reading David Archer’s book “Understanding the Forecast”. I’ve also read parts of Jarred Diamond’s book “Collapse”. Human activity forcing major changes in their environment has happened many times in the past. Many civilizations on this Earth have faced adaptation of elimination because of changes to their environment. What could save us, is that, unlike past civilizations, we have scientific method. And through scientific method we can discern what happened in the past and what the future is likely to hold for us. What is so amazing about global warming is that we have the technology and resources to begin to deal with this situation now. But just like past civilizations, we have protection of the status quo, a sort of societal inertia.
    I wish somebody would print in a newspaper a step by step journey of the science behind global warming, why atmospheric scientists believe what they do about global warming, and in a separate, and adjacent column, show the scientific basis for the rebuttal. Where is the science behind the Hoaxers!? I need to see it. I want everyone to see the scientific research behind why the Hoaxers believe what they believe vs. the pro global warming science.
    But I already suspect that the Hoaxer’s column will be empty.