Does Climate Science Assume the The Earth is Flat?

On Facebook I recently came across a character by the name of Joseph Postma. I had come across some of his ideas on YouTube in the past and had quite a laugh at some of the nonsense that he puts in his videos, but recently Postma started participating in a group that I participate in, so I've interacted with him personally. For those of you unfamiliar with him, his ideas should best be understood as coming from the lunatic fringe of contrarian thinking. In fact, I'm seriously tempted to think that he doesn't actually believe what he says, but he's basically seeing how absurd he can be and still get people to believe him. To be sure, he has not yet convinced even the most radical of people blogging on some of the most popular contrarian sites. I mean, WUWT has posted criticisms of his views, Willis Eschenbach has publicly disagreed with him, and Roy Spencer has devoted at least one post to responding to his claims. Even David Burton has taken issue with Postma. In other words, Postma is not someone that even fringe contrarians take particularly seriously. Which makes me wonder why I'm giving his views my attention, but I guess I'm a sucker for this kind of thing, so I'll give it a go.

I don't have time to go into everything he says, but I think it's good to divide this into two parts: first, his criticism of climate science, and second what he uses to replace climate science. In effect, I'm going to look at the right hand side of the chart below and then the left.

Postma's Criticism of Climate Science

As you can see from the right hand side of the diagram above, Postma has essentially taken a heavily simplified diagram used to illustrate some equations governing the greenhouse effect and imagined that because some of these diagrams use straight lines (he doesn't show you diagrams that use curved lines) that climate science is based on the assumption that the earth is flat. He seems to be under the impression that the theory of the GHE was generated by assuming that the diagram on the right represents a flat earth, and so the greenhouse effect is based on "flat earth " model.

However, he does show the formula for incoming solar radiation as F*(1-A)/4, where F is TSI and A is albedo. The /4 part of the equation is there because the Earth is a sphere. Let's think about this a moment to see why. Imagine that that there's a flat disk in tidal lock orbiting the Sun, such that the same face of the disk always faces the Sun (this is technically impossible, but we're imagining here). The area of that disk would be πr^2. Let's give this flat disk an albedo of 0.3, equivalent to that of the Earth. With a TSI of 1370 W/m^2, then the radiative forcing received by this flat disk would be 1370*(1-0.3) = 959 W/m^2. Since the area of that disk is πr^2, then this flat disk would receive 959*πr^2 J/s of energy from the Sun. But since the Earth is a sphere, not a flat disk, there is much more surface area to the earth than πr^2. But how much more? Well, that's pretty easy to figure out. It's the ratio of the surface area of a sphere to the area of a circle of the same diameter: that is, 4πr^2/πr^2 = 4. So a sphere has 4x the surface area as a circle of the same diameter. That means that the same quantity of energy from the Sun is spread out over 4x the surface area, so each m^2 will receive 1/4 of the energy as a flat disk would receive. This means that the actual equation should be 1370*(1-0.3)/4 = 240 W/m^2. Now of course this is a global average. At any given time, half of the spherical earth is facing away from the Sun, but over the course of a day, month, year, etc. this equation accurately describes the average amount of J/s each m^2 of the Earth receives.

The diagram on the right is a highly simplified diagram used as a heuristic device to explain the basics of climate science to college students. It contains a single atmospheric layer and shows straight lines from the perspective of an observer at the surface of the Earth. Professors using these diagrams I think correctly assume that their students realize the Earth is rotating on an axis giving us night and day and that even though the horizon looks flat at the surface, the earth is a globe. And the diagram above is far more simplified that the models created by climate scientists to simulate climate. Actual climate models are built with a 3D grid system to simulate climate around the globe as well as at various elevations above the surface of the Earth. Furthermore, it should be obvious to anyone that the GHE is not the result of any of these diagrams. Our understanding of the is the result of observational evidence dating back to the 19th century. We could begin with Fourier noticing that the Earth's surface is warmer than its effective temperature and proposing that the atmosphere contains some property that causes it to slow down the rate at which heat escapes the planet's surface towards pace. We could continue with the work of Tyndall who identified greenhouse gases as that property of the atmosphere that slows down the escape of heat to space. These diagrams are just heuristic devices used to explain how the equations work, assuming a spherical earth. There is nothing about the straight lines used in these diagrams that generate any of the equations used to describe the greenhouse effect.

From here, Postma makes the nearly equally preposterous claim that the Greenhouse effect violates the laws of thermodynamics. He asserts that the Greenhouse effect assumes that a cold atmosphere both cools the Earth's surface and warms it, and so this violates the thermodynamic principle that heat flows from hot to cold. I've already responded to this objection in another post. I'll just note here that Postma appears to deny the fact that all objects with a temperature emit thermal radiation in all directions. This means necessarily that cold objects can and do emit thermal radiation towards warm objects, but the net flow of heat is from hot to cold. The atmosphere is colder than the surface, but the atmosphere contains GHGs that absorb and emit IR light in all directions, about half of which heads back towards the surface. This has the effect of slowing down the rate at which the Earths' surface can cool, and since the Earth also constantly receives thermal energy from the Sun, it can't cool to its effective temperature; its equilibrium temperature will be above its effective temperature. The more GHGs are in the atmosphere, the slower the Earth's cooling rate and the warmer the Earth's equilibrium temperature. The net flow of heat is always from hot to cold, and there's no violation of the laws of thermodynamics.

Postma's Alternative to the Greenhouse Effect

So then why is the Earth's surface warmer than its black body temperature - the temperature it should be given its distance from the Sun? In this video (in which he attempts to mimic a college class), he asserts that this is due to adiabatic lapse rate. He spends a considerable amount of time trying to derive from first principles that the lapse rate is -6.5 K/km. None of this is necessary, and it has nothing to do with explaining why the temperature of the Earth is warmer than its black body temperature. Let's skip to the punch line. He ends up with the following equation:

T(h) = -6.5 K/km * (h - h0) + T0

From here he plugs in observed values for h0 and T0 in the Earth's atmosphere with a greenhouse effect. He plugs in the Earth's effective temperature of -18 C and the height at which the atmosphere currently has that temperature, 5 km. Then from here he solves for the temperature at the surface and comes up with 14.5 C, which is remarkably close to the actual surface temperature of 15 C. What has he demonstrated with this? Absolutely nothing. The Earth's effective temperature at the surface would be -18 C without a greenhouse effect. With a greenhouse effect it's ~15 C. Given that we observe a lapse rate of -6.5 C/km, we'd expect 5 km to be -18 C. He never even attempted to explain why the Earth's surface is ~15 C and not -18 C. If there were no greenhouse effect, the surface would be -18 C, and 5 km above the surface (assuming the same lapse rate) would be 6.5*5 = 32.5 C cooler, or -50.5 C.

From here Postma appears to think he can explain planetary temperatures at the surface using the ideal gas law. In another post, I examined a couple versions of this from others, one from Robert Holmes and another from Ned Nikolov. I see no need to go over the details of this again here. Suffice it to say here that all these papers do is take some some unknown quantity in the ideal gas law and solve for it given known quantities, then assert that this somehow explains planetary temperatures without a greenhouse effect. But this is simply foolish. The GHE exists on all planets with an atmosphere and greenhouse gases, and the ideal gas law generally works. So the fact that you can solve for some quantity using the ideal gas law on a planet with a greenhouse effect doesn't show that there is no greenhouse effect. It simply shows that the ideal gas law generally works. On a planet where GHG concentrations increase, temperature increases, and atmospheric density will decrease because of the ideal gas law. This is actually an observed feature of the Earth's climate system. The height of the troposphere has been increasing with global warming.

In reality, Postma's model requires that energy be created in the climate system to elevate the temperature of the Earth's surface above it's effective temperature, in violation of known laws of thermodynamics. He's pretty much denying a large quantity of known physics since Fourier, whose observations led to the understanding of the greenhouse effect.

Conclusion

There's a term that physicists use to describe those people who email them with quacky, fringe "theories" that violate basic physics and are based on the assumption that the person with this fringe theory is a genius Galileo that has discovered what's wrong with what virtually all physicists on the planet understand. They're called "cranks." Postma seems to think that he's discovered that climate science is based on a flat earth model - something that no physicist on the planet ever thought before he informed them. Then he asserts that the greenhouse effect, which is an observable feature of the climate system (see here and here), is impossible. Then he attempts to replace the greenhouse effect with a math trick. He simply back-calculated surface temperature given the observed lapse rate and the temperature at 5 km in which the greenhouse effect is operable. His views appear to be so laughably ridiculous that I really have a hard time believing that even he believes what he says. It's almost like he's trying to see how ridiculous he can be and still get people to believe him.