Some recent attention has recently been going around the web concerning a new “paper” done by Joseph E. Postma (PDF here) which claims to “…physically negate the requirement for a postulation of a radiative atmospheric greenhouse effect.” It has been echoed particularly by some of the more crackpot web sources like climaterealists.com, and of course is spreading around various "skeptic" blogs.
The claims are of course extraordinary, along the lines of Gerlich and Tseuchner’s alleged falsification of the atmospheric greenhouse effect. As is often the case with these types of “skeptics,” the more extravagant the claim, the more obscure the publishing venue; in this case the host is Principia Scientific International, which according to the website “…was conceived after 22 international climate experts and authors joined forces to write the climate science bestseller, ‘Slaying the Sky Dragon: Death of the Greenhouse Gas Theory.’” Most rational people would stop here, but this is the Americanized age where we need to glorify everyone’s opinion and must provide rebuttals for everything, so here it goes:
I ask that the reader have the paper open in a new window so they can follow along with this article.
The Foundations
Most of Postma’s first 6 pages are actually correct. He describes the greenhouse effect through the so-called layer model, which is a simple way to break up the planet into a “surface” and an “atmosphere,” with outer space overlying the top layer. This model is described in many climate books such as Dennis Hartmann’s Global Physical Climatology, David Archer’s Understanding the Forecast, Marshall and Plumb’s Atmosphere, Ocean and Climate Dynamics, and radiation books like Grant Petty’s First Course in Atmospheric Radiation. I will say that I do not particularly like this model as a suitable introduction to the greenhouse effect. It is useful in many regards, but it fails to capture the physics of the greenhouse effect on account of making a good algebra lesson, and opens itself up to criticism on a number of grounds; that said, if you are going to criticize it, you need to do it right, but also be able to distinguish between understood physics and simple educational tools.
The atmosphere in Postma’s paper is just a single slab, so he has two layers (atmosphere+surface), but in general you can have many atmospheric layers of varying emissivity. He goes on to solve for the energy balance of each layer (see equations 11-14). RealClimate derived the same result in less than a page here.
Figure 1: Layer model is Postma's paper. Click to Enlarge
Postma actually doesn’t get the atmospheric radiative flux right. The emission is not σTa4, it is fσTa4, where f is the atmospheric emissivity/absorptivity (following his notation). The emissivity is a unitless factor between 0 and 1 descrbing how good of an absorber/emitter the object is relative to an ideal body. f = 1 describes a blackbody. By Kirchoff's law, the absorptivity of a layer must be equal to the emissivity (at the same wavelength), Both right hand sides of equations 11 and 12 are thus wrong, but it turns out that those errors cancel each other out and he gets equation 14 right. The factor of 2 in Equation 12 comes about because the atmosphere emits both up and down, although Postma clearly doesn't know how to derive this result formally, based on later statements he makes about this. Toward the end of page 14 he says this is invalid since the atmosphere radiates in 3-D, not just up and down. In fact, the quantity σT4 refers not only to the total power output of an object (the rate of energy emission), but it also refers to isotropic (equally intense in all directions) radiation. The result σT4 is obtained if one assumes that a plane radiates uniformly over a hemisphere (for example, the domed "half sphere" field of vision that a human can see when you stand outside," with the base of that half-sphere being the surface you sre standing on; the other hemisphere is invisible (see this image).
So far, it is simple textbook stuff with not much promise.
Geometry of the Global Energy Budget
Postma then goes on to describe fictitious “boundary conditions.” In particular, he seems to have serious objections to the averaging of the solar radiative flux over the Earth. In essence, he would prefer we had one sun delivering 1370 W/m2 of energy to the planet, with a day side and a night side, noon and twilight, etc. instead of the simple model where we average 1370/4=342.5 W/m2 over the planet (so that the whole Earth is receiving the appropriate "average" solar radiation). The number becomes ~240 W/m2 when you account for the planetary albedo (or reflectivity).
The factor of 4 is the ratio of the surface area to the cross section of the planet, and is the shadow cast by a spherical Earth. It is therefore a geometrical re-distribution factor; it remains “4” if all the starlight is distributed evenly over the sphere; it is “2” if the light is uniformly distributed over the starlit hemisphere alone; with no re-distribution, the denominator would be 1/cosine(zenith angle) for the local solar flux.
In simple textbook models, we like to prefer explanations that get a point across, and then build in complexity from there (see Smith 2008 for descriptions on a rotating Earth). Of course, students who use this model are probably educated to the point where they know that day and night exist, and certainly GCMs have a diurnal cycle. The radiative calculations are done explicitly by accounting for the temperature distribution and absorber amount that is encountered at each grid box. Postma is simply tackling a non-issue, just as how people criticize the term “greenhouse effect” for not working like a glass greenhouse. Postma objects to teaching this simple model because it is not real. All that is done, however, is to use a brilliant and sophisticated technique, taught only to the geniuses among us, called averaging! And of course, simple models are used in any classroom...it is how we learn.
But, in actuality, the globally averaged solar re-distribution approximation is not bad when we use it to describe the temperature for planets like Earth or Venus. These planets have an atmosphere or ocean that transport heat effectively, especially Venus with virtually no day-to-night or pole-to-equator temperature gradient. The atmosphere and/or ocean help smooth the diurnal temperature difference very well. Therefore, when coming up with a temperature estimate, it is a great first approximation. If you want the local equilibrium temperature for an airless body like Mercury or the Moon (that does not transport heat), then you want to use the no-redistribution or hemisphere only solar factor. This is well-known (see e.g., Selsis et al 2007). On Mercury, there is no heat distribution and very little thermal inertia; before the sunrise the temperature on the surface is somewhere near 100 K (-173 °C) and by noon the temperature on the surface of Mercury rises to about 700 K (427 °C). This may also be relevant for tide-locked planets (very slow rotation since one side is always facing the host star, the other in perpetual darkness). Earth does not experience any such changes of the sort. On Venus, the variability is even less and most of the planet is at around 735 K.
Summary
To summarize Part 1, Joseph E. Postma did not like a simple model of Earth’s radiative balance where we approximate the Earth as a sphere with uniform solar absorption. Of course, this is never done in climate modeling or in more detailed analyses appropriate for scholarly literature, so it is more an exercise in complaining about undergraduate education than an attempt to correct what he calls a “paradigm” in climatology. Nonetheless, the 0-D energy balance model is a useful approximation on Earth when coming up with an average emission temperature (~255 K), since air circulations and oceans tend to even out the diurnal temperature gradient on Earth, in addition to the thermal inertia provided by the system.
In Part 2, I will examine several of the other claims in the paper.
These posts comprise the Advanced rebuttal to Postma disproved the greenhouse effect
Posted by Chris Colose on Wednesday, 17 August, 2011
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