Can Atmospheric Pressure or Density Explain the Earth's Temperature?

In my last post, I responded to the claim that the greenhouse effect contradicts the second law of thermodynamics. When people make this claim, I often ask what it is that makes the Earth's temperature warmer than its effective temperature if there's no greenhouse effect. The response I get back usually has to do with what can only be described as an ill-informed, "crackpot" theory arguing that this is due to atmospheric pressure or density. Using the ideal gas law, critics of science calculate the temperatures on planets like Venus, Earth and Mars from other known quantities in the ideal gas law, and then assert that this means planetary temperature is due to density or pressure instead of the GHE. There are multiple versions of this, all of which claim either that there is no greenhouse effect or that the greenhouse effect has nothing to do with greenhouse gases and everything to do with atmospheric pressure and/or density.

To my knowledge the original version of this comes from Ned Nikolov and one of his colleagues Karl Zeller. A later iteration of this comes from Robert Holmes. For no particular reason, I'll respond to the Holmes first and then Nikolov and Zeller.

Robert Holmes

In 2017, Robert Ian Holmes published a paper claiming that he can show that climate is largely insensitive to CO2 concentrations using the ideal gas law. Holmes claims to show that

no one gas has an anomalous effect on atmospheric temperatures that is significantly more than any other gas. In short; there can be no 33°C ‘greenhouse effect’ on Earth, or any significant ‘greenhouse effect’ on any other planetary body with an atmosphere of >10kPa. Instead, it is a postulate of this hypothesis that the residual temperature difference of 33°C between the S-B effective temperature and the measured near-surface temperature is actually caused by adiabatic auto-compression.[1][2]

In these papers Holmes claims to be able to predict the average near surface temperature of several planets using the molar mass version of the ideal gas law:

T = MP/(Rρ) where,

T = near-surface atmospheric temperature in Kelvin
M = near-surface atmospheric mean molar mass gm/mol⁻¹)
P = near-surface atmospheric pressure in kPa
R = gas constant (m³, kPa, kelvin⁻¹, mol⁻¹) = 8.314
ρ = near-surface atmospheric density in kg/m³

Of these, R is a constant while M and P are largely unchanging on planetary basis. The molar mass of the atmosphere depend its molecular composition, and this doesn't change much on Earth-like planets. Atmospheric pressure is simply a function of gravity and the mass of the atmosphere above the planet's surface. This also doesn't change much. While increasing CO2 concentrations will increase the partial pressure of CO2 of the surface, the atmospheric pressure as a whole is essentially fixed at 1 atm (101.325 kPa). The only real variables here are temperature and atmospheric density. Holmes simply plugged in values for M, R, and P with ρ and solved for T for various planets and moons. And since the temperature value he calculated usually agrees with the values on one of NASA's fact sheets, he believes he demonstrated that the Earth's surface temperature is ~33°C warmer than its effective temperature because of adiabatic auto-compression, not the greenhouse effect. 

Except that's not at all what he showed. What he actually showed is that atmospheres on other planets obey the ideal gas law, a rather trivial observation that should surprise nobody who has passed high school physics and chemistry classes. He does not show what causes planetary temperatures to change or why planetary temperatures are higher than their effective temperature. The only two variables that are significant here are atmospheric density and temperature. If one changes, the other must change with it while the other values are largely unaffected. In climate science, increasing greenhouse gas concentrations increases tropospheric temperatures and decreases stratospheric temperatures. Consequently the troposphere is expanding (atmospheric density decreases) and the stratosphere is contracting. This is all observable by satellites and agree with predictions from Manabe & Wetherald 1967, and yes these observations agree with the ideal gas law.

What Holmes' alternate proposal requires, though, is that changes in atmospheric density determine changes in temperature, but what changes atmospheric density? Holmes offers no proposal for this. He just wants us to believe that he's come up with an alternative to the greenhouse effect, even though the greenhouse effect is essentially an observable dynamic of the climate system. In reality, atmospheric density changes vertically with scale height, which is the height over which some quantity decreases by a factor of e - that is, the base of the natural log (ln), where e = 2.718. But this scale height is set by and increases with temperature. As temperature increases, scale height increases, and therefore density decreases. In other words, density is generally determined by temperature, not the other way around.

Ned Nikolov (aka Den Volokin)

Ned Nikolov is an ecologist with the USFS. He and one of his colleagues Karl Zeller have collaborated on several papers. They have published papers with a very similar proposal to Holmes,[3] sometimes published under the fake names Den Volokin and Lark ReLlez,[4] apparently because they believed it would help them get their papers past peer review. Their paper published under fake names was retracted, probably due to this ethical violation. Their papers were published prior to Holmes' papers; in fact, I'm suspicious that Holmes possibly just lifted his own "work" from Nikolov. But I digress.

Here's how Nikolov and Zeller explain the greenhouse effect in the paper that used their real names:

A key entailment from the model is that the atmospheric ‘greenhouse effect’ currently viewed as a radiative phenomenon is in fact an adiabatic (pressure-induced) thermal enhancement analogous to compression heating and independent of atmospheric composition. Consequently, the global down-welling long-wave flux presently assumed to drive Earth’s surface warming appears to be a product of the air temperature set by solar heating and atmospheric pressure. In other words, the so-called ‘greenhouse back radiation’ is globally a result of the atmospheric thermal effect rather than a cause for it. Our empirical model has also fundamental implications for the role of oceans, water vapour, and planetary albedo in global climate. Since produced by a rigorous attempt to describe planetary temperatures in the context of a cosmic continuum using an objective analysis of vetted observations from across the Solar System, these findings call for a paradigm shift in our understanding of the atmospheric ‘greenhouse effect’ as a fundamental property of climate.[3]

As you can see, this paper's argument is very similar. Using the ideal gas law, Nikolov and Zeller wrongly claim that the greenhouse effect actually a "pressure-induced" thermal enhancement. He does calculations for several planets and moons in our solar system: Venus, Earth, the Moon, Mars, Titan, and Triton.

But as we've already seen, surface pressure is largely determined by gravity and the mass of the atmosphere above the surface, and surface pressure itself does not determine temperature. Whatever surface pressure is, there are multiple combinations of temperature and density that will be consistent with that value for pressure. When temperatures increase due to the greenhouse effect, the troposphere expands, lowering atmospheric density, while the Earth's surface pressure remains constant at 1 atm.

Conclusion

I think this can be pretty well illustrated with a thought experiment. Let's begin with the Earth as a simple black body. Assuming an albedo of 0.3, the Earth's effective temperature without an atmosphere at the surface would be ~255 K. That's the temperature at which the energy radiated directly from the Earth's surface to space would match incoming solar radiation. Now let's add an atmosphere that is 100% transparent to heat radiated from the planet's surface. With no greenhouse effect, the atmosphere lacks the ability to slow down the rate at which heat escapes the surface to space. So the temperature of the atmosphere can't increase above the Earth's effective temperature. If we keep this atmosphere's surface pressure at 1 atm, its temperature can't exceed ~255 K at the surface, and you can solve for the value of atmospheric density that would satisfy the ideal gas law. In fact, let's do it. First let's take the equation above and solve for density.

ρ = MP/(RT)

Now let's add the values used by Holmes for M, P and R, with 255 K for T.

ρ = 101.3*28.97/(8.314*255) = 1.38 kg/m^3

As expected, since T is smaller than our current temperature, the calculated density is a bit higher than the 1.225 kg/m^3 we normally experience, but the ideal gas law is satisfied. You need greenhouse gases in the atmosphere to increase temperature above the Earth's effective temperature. These papers simply can't use the ideal gas law to replace the greenhouse effect with atmospheric density or pressure.

These proposals understandably have earned near universal rejection from climate scientists, even those that are strongly contrarian. These proposals have been conclusively debunked on multiple blogs, even on Roy Spencer's blog, a post that was actually taken up by Watts Up With That. You know a contrarian idea is in trouble when even WUWT takes it to task for its quackery. No version of these proposals makes any compelling case against the greenhouse effect.

References:

[1] Robert Ian Holmes. Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity, Earth Sciences. Volume 6, Issue 6, December 2017 , pp. 157-163. doi: 10.11648/j.earth.20170606.18

[2] Similar paper is published here. Robert IH. Thermal Gradients on Planetary Bodies and the Molar Mass Ideal Gas Law. J Phys Astron. 2018; 6(1):134
www.tsijournals.com/articles/thermal-gradients-on-planetary-bodies-and-the-molar-mass-ideal-gas-law.pdf 

[3] Nikolov N, Zeller K (2017) New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model. Environ Pollut Climate Change 1:112.

[4] Den Volokin, Lark ReLlez. WITHDRAWN: Emergent model for predicting the average surface temperature of rocky planets with diverse atmospheres, Advances in Space Research, 2015. https://doi.org/10.1016/j.asr.2015.08.006.