Observation on a "Unified Climate Theory"

In the past week, a so-called "Unified Theory of Climate" has been excitedly debated on a number of climate blogs. The introductory paper can be found here. That theory has been compared by some to the procedure I used in my Venus/Earth temperatures comparison, which disproves the consensus "greenhouse effect". I want to make just a few simple observations here of the "Unified Theory of Climate", to distinguish my own, factual position, and my professional concern for physical cause and effect relationships, from that theory.

My blog is not about climate science per se, and my aim in my relatively few climate science posts has been to clearly point out the simplest, definitive evidence, which reveals an entrenched incompetence in the current, consensus theory, which is basically that of the supposed "greenhouse effect", claimed to cause an increase in the average global surface temperature with increasing atmospheric carbon dioxide (supposedly due to mankind's ever-increasing burning of fossil fuels).

First, I do not claim to have a theory of climate, and I consider my Venus/Earth analysis to be a simple presentation of fact, not theory. While my mathematical procedure involved a usage of the Stefan-Boltzmann "blackbody" equation that seems to be widely derided by current climate scientists, it was a usage that was taught to me as fact in my earliest days as a university physics major (and which I physically understand as motivated by the traditional description of a blackbody as a cavity inside an object maintained at constant temperature, with only a small hole to allow radiation -- but neither convection nor conduction of heat -- to pass into and out of the cavity). And of course, the results of my Venus/Earth analysis, which are mathematically precise, confirm my usage as correct, and thus the fact I always thought it to be; in contrast to that clear confirmation, defenders of the "greenhouse effect" are not able to explain my amazingly simple finding -- that the Venus/Earth temperature ratio, outside of the Venus cloud layer, is due only to the ratio of the planets' distances from the Sun, nothing else -- within their own theory. They are all reduced to dismissing it as a "coincidence"; and they don't even stop to realize that it is a "coincidence" piled upon even more unlikely coincidence, that I just "happened" to learn (at a well-respected university, the University of Colorado at Boulder) just the wrong physical "fact" that allowed me to effortlessly uncover that "coincidence", of the Venus/Earth temperature ratio being precisely and solely explained by the planets' distances from the Sun -- in perfect mimickry of a coherent physical reasoning that (in my scientific judgment) corrects and simplifies our understanding of basic atmospheric warming by the Sun.

In looking to apply my procedure more widely, by comparing temperatures in Earth's troposphere with temperatures in other planetary atmospheres, I found detailed temperature and pressure data on only one other body having pressures in the range of Earth's troposphere: the Saturn moon, Titan. The stipulation of that range of pressures is due to the fact (!) that for atmospheres equal to or greater than Earth's, the atmospheric mass is enough to impose a quite general hydrostatic condition, exemplified by a negative temperature lapse rate throughout the range of Earth tropospheric pressures. Scientists over many years developed the Standard Atmosphere model of our atmosphere, based upon the hydrostatic condition, and my Venus/Earth comparison confirmed that model as the stable state which the atmosphere is constantly trying to attain and maintain. This of course is directly counter to the modern idea of "runaway climate", which has enmeshed climate scientists in ever-more complicated "explanations" for the observations that continually challenge, rather than confirm, their theories.

I will not try to give a complete critique of the "Unified Theory of Climate", since I have not paid particular attention to the recent debates over it, nor given it any sustained study in the few days it has been in the climate news. In the following, I will assume the reader has the above-linked article relating the theory at hand, and is familiar with its basic contents.

The following illustration shows the basic equations developed in the theory.

The theory puts forth a relationship between 1) the surface temperature (Ts) of a planet or moon with an atmosphere, 2) the temperature (Tgb) of a so-called "gray body" reference body, at the same distance from the Sun as the planet or moon, but having no atmosphere, and 3) the surface pressure of the planet or moon being considered. The first equation above gives the definition of Tgb, according to the authors of the Unified Climate Theory (Nikolov and Zeller).

My first observation is that the equation for Tgb can be immediately simplified. This simplification is shown in the second and third lines above. The equation contains two physical parameters (the "gray body" albedo αgb, and the emissivity ε) which are in fact the same for all of the planetary bodies considered by the authors. The factor containing these parameters, which is thus a constant, can be taken out from under the fourth-root expression containing the incident solar intensity S0. Also, the parameter added to S0 -- cs -- is a constant, which is so much smaller than S0 for all of the planetary bodies considered, that it can be removed entirely, as shown in the third line above.

This simplification allows us to see that the use of a "gray body" temperature, involving the albedo and emissivity of the planetary body, is irrelevant to the theory as presented, for the same value of albedo is used for all the bodies considered in the paper, and the same emissivity. The only variable parameter is the incident solar intensity, which depends upon the distance from the Sun. (σ, of course, is just the Stefan-Boltzmann constant, a fundamental physical constant.) The fourth line above shows the definition for the temperature of a "blackbody", and thus reveals that the "gray body" temperature is just a constant times that blackbody temperature. So all consideration of possible real variations in albedo and emissivity are in fact dropped out of the theory at this point.

The fifth line above shows the empirical, ad hoc relation found by the authors to hold across all the bodies they consider in their paper. The sixth line shows that this relationship can be obtained by using a blackbody temperature (with no albedo or emissivity correction) instead of the author's gray body temperature. The indicated ratio of temperatures, which they denote as NTE, is just multiplied by a constant (about 0.554, for the values of albedo and emissivity they use). In their theory as presented, the surface temperature can be recovered from the calculated value of NTE as Tgb times NTE; but we see we can equivalently use the blackbody temperature with an NTE that is the constant γ times their NTE function.

Either way, it should be emphasized that the functional form of NTE is not motivated by any physics, but simply by an arbitrary fitting of the planetary data to that functional form. To me, the theory stops being a physical theory at this point, and is just an arbitrary mathematical model.

Nevertheless, it appears to give good results -- which is itself a problem, because, by using the blackbody temperature, as just indicated above, I would expect them to get the same results as my procedure for comparing Venus and Earth, and they do not. When my procedure, which calls for comparing the Standard Atmosphere Earth temperature at a given pressure with the temperature in another atmosphere at the same pressure, is applied to the surface of Titan (using a slightly different surface pressure I found, 1,452 mb, rather than their indicated 1,467 mb), I obtained a predicted Titan surface temperature of 99.9K, or approximately 100K, whereas the true surface temperature was 93.2K, or nearly 7K lower than my procedure predicts. But Nikolov and Zeller, the authors of this theory, claim no error at all (93.7K predicted, versus 93.7K true surface temperature). I obtained the Titan data here.

The physical data they use differs from my (limited) data, by 1 or 2% in some cases. I have just mentioned the slightly different values they used for the surface pressure and surface temperature of Titan. Their value for the surface pressure of Earth is some 2.4% lower than that given in the Standard Atmosphere, which I used, and it doesn't seem to be due to their using a slightly different surface temperature in the Standard Atmosphere equations. (They write that the surface temperature of the Earth is 287.4K, while the Standard Atmosphere, for nearly a century, has consistently used 288.15K.) So I wonder if they have effectively calculated their own version of the Standard Atmosphere rather than the presently official 1976 American Standard Atmosphere, and if so, on what basis did they see fit to do that on their own. The thought arises -- and I can only bring it forth, not as a suspicion but only a logical possibility -- that they might have done so, inadvertently or otherwise, to make the data more exactly fit their theory. I would not bring up the possibility, except that, as I already noted, their theory is not entirely a physical one, as my Venus/Earth comparison is physically reasoned -- using only known facts (or once-known, when I was a student) -- but accomplished through arbitrary mathematical modelling of a "best fit" function. Again, this is just my dispassionate consideration, not an accusation or insinuation of dishonesty on their part.