Norfolk Constabulary Made the Wrong Charges

A few months ago the Norfolk UK police raided the home of Roger "Tallbloke" Tattersall. They found no evidence he was involved in the Climategate theft, but they should not have dropped the case, because he's guilty -- of counterfeiting.

Specifically, science counterfeiting. Alas, such an infraction does not appear in the legal code, though perhaps it should. In any case, Tattersall isn't very good at it.

An endless stream of scientific drivel pours out of his blog, all in the name of denying the science of climate change. But Tattersall isn't interested in quibbling about Arctic ice trends or the urban heat island effect. He and his contributors are busy constructing their own scientific reality.

Not surprisingly, their world does not agree with the data scientists actually measure, but that doesn't seem to matter to them -- they always finds ways of bending the theory and/or the data so it seems to, while simultaneously finding a way -- any way -- to claim that canonical science fails.

There are many examples I could point to, but the best is his marketing of the ideas of Ned Nikolov and Karl Zeller. N&Z, as they're known, claim that radiative physics has been misapplied to the Earth and that its basic greenhouse effect is not the commonly claimed 30 C or so, but would be several times higher -- or something. And so, they say, there is no greenhouse effect, but that atmospheric pressure accounts for the enhanced Earth's surface temperature. (Even Roy Spencer disagrees.)

Alas, N&Z are confused about the physics, and Tattersall is even more confused in his defense of them. (He doesn't like it when people point this out, and routinely bans people who insist on pointing out his errors. Deniers often resort to this tactic when obfuscation has failed.)

This gets a little technical, and sorting it all out can take some time, but the basics are fairly clear: N&Z adopt an unrealistic picture for a planetary body, and so their calculation gives the wrong answer.

Standard climate science says the Earth's average temperature, to first approximation, is 255 K, calculated according to the Stefan-Boltzmann law:

T_E = [S(1-α)/4σ]^1/4

where S is the Earth's solar constant (1367 W/m2), α its albedo (0.3), and σ is the Stefan Boltzmann constant. (The factor of 4 comes from a large-scale average.) Since the Earth's annual average temperature is about about 286 K, climate scientists say the greenhouse effect is approximately the difference, about 30 K.

To be sure, there are assumptions made in this calculation, the major ones being that the our Sun's light strikes the Earth as parallel rays, and that the planet's temperature is uniform over its entire surface. The latter is not such a bad approximation: the Earth's global annual mean temperature is 286 K, the equatorial annual mean is 4% above this, the north pole 10% below and the south pole 21% below.

N&Z say this is incorrect, because the radiation laws have been misapplied to a gray body. (A gray body is a blackbody with an emissivity less than one -- it does not radiate like a perfect blackbody.) They claim one must first calculate the temperature at each point on the gray body, and then average the temperature over the sphere. So they write the temperature function of a spherical gray body as



T(θ,φ) = S(1-α)cos(θ)/εσ


where θ is the zenith angle of sunlight (see their Figure 1 here). They then integrate this over the body's sphere:

where μ = cos(θ). Consequently they get a factor of 2/5 where the standard application above gives the fourth root of 1/4. So applying this to a planet's dayside (the nightside gets no solar radiation and so has T=0) they find (page 4 here) an average T of 234 K. They write:

"The take-home lesson from the above example is that calculating the actual mean temperature of an airless planet requires explicit integration of the SB law over the planet surface. This implies first taking the 4th root of the absorbed radiative flux at each point on the surface and then averaging the resulting temperature field rather than trying to calculate a mean temperature from a spatially averaged flux as done in Eq. (3)."

But think about this: their picture of an airless planetary body is one that has T=0 at certain points on its surface -- the points where the radiation comes in perpendicular to the surface, or on its nightside.

Does that sound like the planetary body you're living on? It doesn't even sound like the moon (where the nightside temperature is about 95 K) or Mercury (about 120 K).

They try to save their result by ad hoc adding radiation from the cosmic microwave background -- that's the c_s term in the above equation.

The CMB has a temperature of 2.72 K, so its radiation contributes 3.1 μW/m². Does that sound like the planet you're living on, for any point on its surface? No, it does not.

It's not even the moon, where heat is conducted through the lunar regolith, which is why its nightside temperature is so high compared to the CMB. (Vasavada et al modeled it in this 1999 paper.)

Tattersall is trying to claim that a measurement of the moon's equatorial temperature "confirms" N&Z's claim that the Stefan Boltzmann law has been misapplied to gray bodies. It does not.

Here is the data. N&Z's result for the average temperature is 39 K too low -- some confirmation!

Meanwhile, standard radiative physics gives exactly the right value for the average, and for the shape of the curve as well. Standard physics says (this is from Pierrehumbert's textbook, Chapter 3, pgs 152-153) that, on a body like the moon, with essentially no atmosphere, there is no large scale equilibrium, so the temperature on the dayside is due to its radiation at that point. Now, along the equator the solar radiation has a factor of a cosine due to its obliquity to the normal, and when calculating the average you have to average its fourth power. Radiative considerations alone can’t fix the nightside temperature — thermal conductance of the regolith must be included, so I'll just take that as a constant T_n. Then

average equatorial T = (2.7/2π)B +T_n/2 = 212 K

where B=[S(1-α)/4]^1/4, S is the Earth’s solar constant, and T_n is the nightside temperature of about 95 K (as measured by Diviner). The number 2.7 comes from the integral of the cosine to the one-fourth power from -pi/2 to pi/2:

done via Wolfram alpha.

Not only is this the right average, but this method also predicts that the peak for the lunar equatorial temperature will be B. The moon's albedo is 0.11, so this gives 382 K -- an exact agreement with the data. And it says the temperature along the equator should drop off as the 1/4th power of the longitude -- also in agreement with the measured curve.

But Tattersall's need to deny the greenhouse effect is so large that this isn't good enough, so he's sticking with N&Z, even though they're incorrect.

N&Z's real error (as physicist Joel Shore tried repeatedly to point out to Tattersall, which resulted (of course) in his getting banned) is the assumption that the temperature at each point on the surface is determined only by the balance of incoming radiation and emitted radiation. In effect, they assume (as Shore put it to me) "a body with no thermal inertia or thermal transport. For body with significant inertia and thermal transport (and especially rotation), these assumptions will be poor."

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Saul Bellow wrote, "A great deal of intelligence can be invested in ignorance when the need for illusion is deep."

Here is a perfect demonstration of Bellow's sagacity.