Plass and the Surface Budget Fallacy

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.

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