Plass and the Surface Budget Fallacy

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.

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