I read that reference in detail. Author's quotes are boldfaced.
The author uses curve-fitting models. The word model occurs 152 times throughout the text.
Thus, our working hypothesis was that a general physical model should exist...
He uses 7 physical variables to define a set of 12 dimensionless variables, as would be required in empirical dimensional analysis, and engages them as models (see Table 5.)
Based on the current state of knowledge we identified seven physical variables of potential relevance to the global surface temperature
...
The second step of DA (after the construction of dimensionless products) is to search for a functional relationship between the [12] variables of each set using regression analysis.
...
The following four-parameter exponential-growth function was found to best meet our criteria:
y = a exp(bx) + c exp(dx)
In short, the author defined a menu of 12 dimensionless variables to be used to compute 4 parameters to fit the data from 6 planets. That kind of empirical liberty makes good curve-fitting an almost certainty.
After heuristically fitting curves he gets to the physical significance of the formulas starting at the bottom of page 11. He finds a close similarity to the adiabatic Poisson formula derived from the ideal gas law. However his conclusion is quite limited according to his statement,
while qualitatively similar, Equations (10a) [the author's curve fit] and (13) [Poisson formula] are quantitatively rather different. . . .[they] describe qualitatively very similar responses in quantitatively vastly different systems.
His results, (equation 10a) could neither be analytically deduced from known physical laws nor accurately simulated in a small-scale experiment.
That is to say it is unreproducable, and unphysical.
His conclusion: To our knowledge, this is the first model accurately describing the average surface temperatures of planetary bodies throughout the Solar System
I would word it that his model fits the 5 planet data points rather well, but has no further significance. His further conclusions sort of renege his disclaimer of physical significance and more directly relates it to Poisson's formula. Go figure.
The author is quite knowledgeable about physics except for one thing: adiabatic systems are very fleeting in nature and have no long term effect. I have no quarrel with his mathematical technique - what he did and how he did it - but I do think his rampant use of fudge factors in his curve fitting effort did not carry much significance, and as he admits, his result is vastly different than what he physically attempted to show.
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