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Nikolov & Zeller have published a paper concerning what they call The Unified Theory of Climate.
Please read the paper in full and then answer my question.
Personally I can see no areas in which the new theory is compatible with the current theory of the Greenhouse Gas Effect and Anthropogenic Global Warming however there are some extremely knowledgeable participants on this site so I welcome their input but only, please, if you have read the whole paper.
The paper you linked lists as its first reference Volokin and ReLlez, 2014; a paper that addresses the magnitude of the Earth's greenhouse effect. The validity of the paper you found largely hinges on the reputation of the Volokin and ReLlez, so we will investigate that one first.
The traditional way to determine the 'greenhouse effect' of a planet is to compare actual planetary temperatures with Stefan-Boltzmann blackbody temperature based on the luminosity of the star, distance from star, and the albedo and emissivity of the planet. This calculation is done in Volokin and ReLlez and can also be found on Wikipedia.
Volokin and ReLlez are arguing that the actual greenhouse effect should be measured using the albedo of a bare planet stripped of its clouds. The Earth's albedo is 0.294, but they propose a bare albedo of the Earth of between 0.122 and 0.13. They then make an argument that simple albedo calculations are not very accurate, and that a use of Holder's Inequality should be used to integrate the effects of albedo and radiation incidence angle over the exposed surface of the bare planet. Redoing the Stefan-Boltzmann expected temperature calculations with this new method, they then calculate that actual 'greenhouse effect' of the Earth is more like 90 K, instead of the 33 K normally cited. This is significant because temperature magnitude of the Earth's greenhouse effect affects the climate sensitivity factor of global warming models.
I actually think this paper is pretty interesting. The core of its mathematical arguments seems valid (though I didn't try to work any of it out myself) However, the conclusions are not very good, and not very related to much of the mathematical arguments in the body. While there is an argument to be made that calculating expected surface temperature should assume a bare planet, the authors are basically concluding that all temperature differences between the bare planet and the observed Earth should be assigned to the greenhouse effect. That just isn't supported by the information they present. The Earth's actual atmosphere and biosphere are much more dynamic than the bare model they are presenting; the formation of high-albedo clouds by equatorial rainforests,and the presence of high-albedo sand in the sunniest places on Earth are just two non-greenhouse related effects that account for temperature differences between the author's ideal bare Earth and the real Earth.
While they consider a lot of interesting factors, I think Volokin and ReLlez are guilty of making too much of a spherical cow estimate. The author's make an argument for one thing, then make some huge leaps to an unsupported conclusion. All in all, I don't think that the author's conclusion of a 90 K greenhouse effect is valid.
Whatever its scientific merits, the paper doesn't look very good upon meta review. First off, the authors used fake names to publish the paper in an open access site. In fact, it is the same two authors of the paper you linked, except that they spelled their names backwards (Nikolov -> Volokin; Zeller -> ReLlez). Ummm...what? Also, they later retracted the paper. Also also, the journal they published in is now defunct. All in all, this is not a sign that the paper is good science.
So the paper that you are asking about (Nikolov and Zeller, 2017) is based on a paper by the same authors which has not-very-good conclusions, and was generally published in a shady manner. That's a big black mark at the very outset.
This paper is pretty long and detailed, and I admit I did not read all of it. But the kill shot for me was on the very first page:
We began our study with the premise that processes controlling the Global Mean Annual near-surface Temperature (GMAT) of Earth are also responsible for creating the observed pattern of planetary temperatures across the Solar System. Thus, our working hypothesis was that a general physical model should exist, which accurately describes equilibrium GMATs of planets using a common set of drivers.
That is great, but we have already gone over how these authors are attempting to oversimplify a bare planet approach for predicting expected temperatures. The predictor variables they are using are stellar irradiance, blackbody reference temperature, greenhouse gas partial pressure and density, atmospheric pressure and density, and reference pressure for greenhouse fluids. We can see the authors are once again ignoring the effects of cloud formation and the way the biosphere affects albedo, amongst other things.
On a methodology note, the authors use a regression model to try to get some useful results. As a statistician (not a planetary scientist), this strikes me as a poor choice. Regression analysis of complex systems is a good way to get insight into what factors are important in affecting this system. I think they can be very useful for predicting trends, but I do not believe they are good for providing predictions that are accurate by physical science standards.
For example, I'm writing a paper right now that uses regression analysis to predict subway ridership at each station on a subway network. This is a very complex system (like planetary atmospheres), and our goal is to get error scores of 0.2 or so. That is great for predicting subway ridership, not so much for planetary temperatures. An error score of 0.2 is like predicting a temperature to be 300 K but it is actually 360 K. That's not good enough. So I just don't know what the authors are really trying to accomplish using a regression approach, especially with so few predictor variables. The physics behind the interaction of the predictor variables is pretty well known, so there isn't a lot of value if determining the correlations of the predictor values to the planet surface temperature; it is as if they are using the regression to test if the physics is correct. Finally, the data set is way too small to be using a regression analysis. Their only available data points are the planets and moons in our own solar system.
Well I wrote a lot there, and hopefully it is all comprehensible. All in all, there are some interesting bits to Nikolov and Zeller's approach, but I think they are over simplifying some things and are using a non-physical science applicable methodology to obtain questionable conclusions.
Honestly, I don't think that anyone should be treating their research pejoratively (I'm looking at you Andrew Jon Dodds in the comments). It is interesting, and it is certainly novel (from everything I've read). It just doesn't have great conclusions. And that's fine! Most research probably doesn't lead anywhere useful. At least they tried something. People seem to be mad at them just because the results are contrary to the general climate change consensus. Research should be appraised on its merits (or lack thereof) and not on whether its conclusions match preconceptions.
kingledion gave a great overview on the general scientific quality of the papers, but I don't think the title question has been really answered yet.
Is the Unified Theory of Climate (Nikolov & Zeller) compatible with the AGW/GHG theory in any respect?
Yes.
First, I too would comment on that preceding paper (On the average temperature of airless spherical bodies...). What it's concerned with is the equation $$ T_\mathrm{e} = \left(\frac{S_0\cdot(1-\alpha_\mathrm{p})}{4\cdot\epsilon\cdot\sigma}\right)^{1/4}, $$ which derives from the Stefan-Boltzmann law the radiating equilibrium temperature $T_\mathrm{e}$. The main point of the paper is that this temperature is not in any way physically meaningful for airless bodies. Which is completely correct: airless bodies do indeed not have a “representative mean temperature”, because the integral over a function of some quantity (here, fourth power of temperature) isn't directly related to the function value of the average of the quantity†. For a body without atmosphere like the moon, temperature varies extremely strongly over the surface, and thermal emission is completely dominated by the hot regions.
This does not really give rise to any interesting conclusions though, because $T_\mathrm{e}$ isn't of much interest for climatology anyway. Any proper climate model is well aware of the importance of locally varying temperatures, as Volokin/ReLlez themselves admit:
It should be pointed out that global climate models intrinsically account for Hölder’s inequality by virtue of being three-dimensional and explicitly resolving the spatial heterogeneity of radiation absorption and emission (as well as other energy transport processes) within the context of a spherical geometry. However, 3-D models have not historically been applied to assess the strength of Earth’s ATE (GE). Hence, our critique is strictly directed towards the effective emission-temperature formula (3) and other similar 1-D radiative-transfer models (e.g. Manabe and Möller 1961; Manabe and Strickler 1964).
One could also add here that $T_\mathrm{e}$ is not quite so meaningless for a planet with substantial atmosphere but no greenhouse gases, because here the spatial temperature variations are less pronounced, yet the surface is in radiative equilibrium with the sun/space. I'll come back to that.
Now to the paper you're asking about. It does two things:
Fit generic models without a-priori physical motivation to observed values of pressure, density, greenhouse-gas content and observed and vacuum-predicted temperatures.
Try to take new physical conclusions from the fit result.
kingledion discussed well how sensible this approach is in principle. Yes, it is sensible to just fit the available data, if that's all you have available. It can even be valid to inter- or extrapolate from that data somewhat, using the fitted models as a guide. Nikolov/Zeller emphasize that they chose models which make such extrapolation particularly robust. Ok.
But there's one principle that anybody using statistical methods surely must always keep in mind: correlation does not imply causation. What Nikolov/Zeller “find out” is that you get a marvellous fit when considering $\frac{T_s}{T_{\mathrm{na}}}$ as a function of $\frac{P}{P_r}$, namely $$ \frac{T_s}{T_{\mathrm{na}}} = \exp\left(0.174205\cdot(\tfrac{P}{P_r})^{0.150263} + 1.83121\times10^{-5}\cdot(\tfrac{P}{P_r})^{1.04193}\right) $$ gives a coefficient of determination $R^2 = 0.9999$. Wow!
Is this surprising?
Um, no. What they've discovered there is most of all the ideal gas law. That connects pressure and temperature in a pretty rigid way.
So far, everything is... ok. Nothing actually new (just long-known physics, re-discovered in an inefficient way). The trouble only really starts with the conclusions.
Nikolov/Zeller argue that this excellent fit, and the much worse fits of similar models relating other quantities – in particular, greenhouse-gas concentrations – mean that it's actually only the pressure which influences the surface temperature, and that GHG are irrelevant.
But that's completely and utterly fallacious!
Again: it's not surprising that the ideal gas law holds – rather, it would be extremely surprising if it didn't. So, the $T_s(P/P_r)$ fit tells up about as much as a fit of fall-times of weights from different heights in vacuum: nothing, they just reaffirm the long-known Newton laws of motion.
And it does not mean that “temperature is only influenced by pressure”. On the contrary: just as much, pressure is influenced by temperature – if you somehow lowered the mean temperature of a given planet, surface pressure would drop as well‡.
Both pressure and temperature also depend on other quantities though. Notably, yes, on greenhouse-gas concentration. But unlike the gas law, the mechanism is a bit more complex and can't be captured properly¶ by fitting such a primitive model to a few measured points. Instead, it requires 3D climatology models, which incorporate all of these quantities, and not just in a global-mean sense but in a detailed, latitude- and altitide-dependent way.
I said I'd come back to the scenario of an atmosphere of significant density but without greenhouse gases. Such an atmosphere would keep spatial and temporal variations limited, but wouldn't influence the radiation processes, i.e. this is the case where the surface temperature would actually be similar to $T_\mathrm{e}$. How is this still compatible with the Nikolov/Zeller model 12? Well, again that model is mostly just the gas equation. Such an atmosphere would still obey it. The higher reaches would be colder than the surface due to adiabatic expansion. Really, this scenario isn't very exotic in terms of fundamental physics, but it illustrates that GHG are absolutely essential for a climate like Earths. The Volokin/ReLlez paper just proves that $T_\mathrm{e}$ isn't relevant for bodies without any atmosphere at all, but that's hardly interesting for any discussions regarding Earth's climate.
†The paper specifically discusses the Hölder inequality, which is somewhat curious because that inequality actually states that there is, for power functions, a relation between mean-of-the-function $\langle f(x)\rangle$ and function-of-the-mean $f(\langle x\rangle)$, namely, the latter gives an upper bound to the former. The Hölder inequality does not actually imply that $\langle f(x)\rangle$ lies beneath that upper bound – it could just as well instead be smack on the bound; but it's true that there are quantities for which it is substantially below.
‡At that point, I am oversimplifying. There's a whole bunch of different scenarious what could happen when you alter a planet's surface temperature (even assuming you managed to do this in a way other than directly tweaking atmosphere properties). The pressure-drop case is what happens when it gets so cold that the formerly atmospheric gases condense onto the surface; this is relevant to e.g. Mars and Titan. In other planetary bodies, other mechanisms would step in; in either case however, you could be sure that the ideal gas law continues to hold.
¶Ironically enough, Nikolov/Zeller's Model 7 actually hints that greenhouse concentration does correlate to temperature, even though it lacks the quantities that would be needed to make the fit tight.
In physics, you should get the same result whichever way you calculate. As long as you do not make an error in calculations.
Calculating the greenhouse effect using radiative transfer equation, we get a result pretty close to the observed one, even if we neglect effects such as turbulent heat fluxes as long as we get Planck optical depth right. And this is why I think, even without following their derivation, that they must have made a massive error.
Another reason for that is simple intuition that airless (shortwave) albedo must be unimportant on planets with large optical depths (thick clouds) because at the surface you do not have much shortwave (solar) radiation anyway. The surface is dominated by longwave radiation (IR) which albedo is close to 0.0, anyway.
