There is apparently a paper from a couple of years ago that is currently doing the rounds and that argues that the Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity. The suggestion is that it is difficult to determine the surface atmospheric temperature but that it can be done with
a gas constant and the knowledge of only three gas parameters; the average near-surface atmospheric pressure, the average near surface atmospheric density and the average mean molar mass of the near-surface atmosphere.
and, given this, no one gas has an anomalous effect on atmospheric temperatures that is significantly more than any other gas and 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.
The problem is that the method the paper is applying is the ideal gas law. It’s simply a relationship between pressure, density, temperature and molar mass that essentially applies anywhere in an Earth-like planet’s atmosphere. It’s a truism; if you know the values for three of these terms, then you can determine the fourth. It doesn’t tell you anything about why these terms have these values. That you can use it to determine the surface atmospheric temperature from the density, pressure and molar mass doesn’t imply that there is no greenhouse effect, because the greenhouse effect doesn’t imply that the Earth’s atmosphere would no longer satisfy the ideal gas law.
In the case of an Earth-like planet’s atmosphere, the surface atmospheric pressure is essentially the weight of the atmospheric column; this is fixed. The molar mass depends on the composition, so is also fixed. The only two that can vary are the density and temperature. So, should we regard the temperature as depending on the density, or the density as depending on the temperature? The ideal gas law – by itself – can’t tell us, but we can consider other physics.
The density profile in the atmosphere depends on the scale height, which is the vertical distance over which the density decreases by a factor of (). The scale height is set by the atmospheric temperature; if the atmospheric temperature is high, the scale height will be large, the atmosphere will extend to large heights, and the density (mass per unit volume) will be low. If the temperature is low, the scale height will be low, the atmosphere will be compressed near the surface, and the density will be high.
So, if the surface temperature is low, the atmospheric density will be high, and if the surface temperature is high, the atmospheric density will be low. This is simply a consequence of the ideal gas law; we still haven’t determined why an atmosphere has a certain set of properties. For example, why is the surface atmospheric temperature on the Earth around 288K (15oC)? Well, that’s a consequence of the greenhouse effect.
In the absence of an atmosphere, energy balance would require that surface temperature were 255K; the presence of an atmosphere enhances this by about 33K. Having done so, the atmosphere still satisfies the ideal gas law, so if you know the surface pressure, density, and molar mass, you can certainly determine the surface atmospheric temperature. This does not mean, though, that there is no greenhouse effect, or that climate sensivity is low.
I thought I would end with the relevant part of the poem that gave us the phrase a little knowledge is a dangerous thing:
A little learning is a dang’rous thing;
Drink deep, or taste not the Pierian spring:
There shallow draughts intoxicate the brain,
And drinking largely sobers us again.