Making the Elephant Dance as Performed by Ned Nikolov and Karl Zeller

As John von Neuman put it

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

and, as fate would happen, along comes Ned Nikolov and Karl Zellner with "New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model".  It's basically 22 pages of word salad and Eli may later return to pointing out some of the more amusing light fingered moves, but here the Bunny will only provide a small amuse bouche with the "interesting" exercise in fitting five numbers with four free parameters, two unphysical constants and a free choice of fitting form.

So briefly, what goes on is to fit the five average surface temperatures of five plants or moons (Venus, Earth, the Moon, Mars, Titan and Triton.  Wait you say, that's six, not five, but they leave Titan out of the mix because  (Eli told you this would be yummy) to an arbitrary functional form

y = a exp(bx) + c exp(dx)

Wait you say again, ok, that is four parameters and the functional form plucked out of thin air, but what is x and y.  That's kind of interesting and more than a bit light fingered but you have to watch the moving cup.  The independent variable is a ratio of pressures (Ps/Pr).  Ps is the pressure at the surface, Pr, well that's interesting, Pr starts out as the "minimum air pressure required for the existence of a liquid solvent at the surface, hereto called a reference pressure (Pr)" but about a page further on it morphs into 

For a reference pressure, we used the gas-liquid-solid triple point of water, i.e., Pr=611.73Pa [38] defining a baric threshold, below which water can only exists in a solid/vapor phase and not in a liquid form. The results of our analysis are not sensitive to the particular choice of a reference pressure value; hence, the selection of Pr is a matter of convention.

The alert out there have noticed that the minimum air pressure required for the existence of a liquid solvent at the surface kind of depends on the temperature of the surface, and would vary widely from planet to planet. Of course worry bunnies like Eli might ask:  What liquid?  Water exists as water on the surface of the Earth, if there was any as steam at Venus and as ice at all the others if it exists there at all.  For Venus maybe CO2, but at the surface of Venus CO2 is a supercritical fluid and you can't tell the difference between liquid and gas.  At Titan, there are oceans, but oceans of methane, so any useful Pr is going to be wildly different for all of these bodies and, in the case of the Mars, and Triton some pretty fancy liquids are going to be needed.

Selection of water as the solvent of choice is then both arbitrary and unphysical.  But why do Nikolov and Zeller insist on using it? Turns out their elephantine trunk waving depends on using dimensionless variables, but restricting Pr to an inappropriate value independent of the planet is equivalent to stripping the units off of the surface pressure Ps.

How about y.  y is defined as the ratio (Ts/Tr) with some really serious trickery buried in Tr. Tr is defined as a reference temperature,

the planet's mean surface temperature in the absence of an atmosphere or an atmospheric greenhouse effect.

At this point no bunny should be surprised to find that that ain't quite that.  Whoa.  Where that come from.  Old timers may remember Eli's old friends Gerlich and Tscheuschner who were also in the business of trying to falsify the greenhouse effect, by as was pointed out, not understanding what the greenhouse effect was.  As Science of Doom put it

 Gerlich & Tscheuschner have written an amazing paper which had the appearance of physics yet failed to address any real climate science.

Eli and several distinguished bunnies had a run at G&T, but, of course, as such things go, the majicians never give up, and one may anticipate a visit from Nikolov and Zeller too.  Good times to be had.

Anyhow, one of the results was a nice arXiv article by Arthur Smith explaining how the surface temperature of a rotating planet varies with the rotational period and the heat content of the surface, which for the earth is basically that of water.

The parameter λ for the Earth is 0.04 and describes the ratio of the energy absorbed from the sun in a day to the heat capacity of the surface.  The effective temperature is the temperature determined by emission from  the surface on a non-rotating body needed to maintain thermal equilibrium.  Depending on your model Arthur showed, as was well known, that the average temperature of the surface of a rotating planet without greenhouse gases has to be less than the effective temperature.

Nikolov and Zeller reproduced Smith's results in another paper with one very strange twist.  In their model  they insist that every planet without an atmosphere will have the same surface as the moon.  (Basically λ =20 in the figure above.)  Using the bare moon Tr now Tna, is, again arbitrary, but let's go ahead and look at the fit which is all John von Neuman told you it would be

Further hand waving ensues.  Nikolov and Zellner will soon be here to entertain you.  Eli warns the bunnies they are indefatigable and will tell you to read the paper.  Eli's advice is if you want some laughs go ahead.  Scott Denning has been trapped into the endless circle, so be sure to take some survival rations for him.

It's not a fact. You've either misunderstood the physics or you're just lying about this. Hard to tell for sure anymore.

— Scott Denning (@airscottdenning) August 2, 2017