By a strange path (reading adverse comments by alarmists in a paper I don’t mention) I came across this paper by Robert Ian Holmes which on the face of it would seem to disproves the Greenhouse effect as commonly stated:
Molar Mass Version of the Ideal Gas Law Points to a Very Low Climate Sensitivity
Stunningly it suggests a climate sensitivity for the doubling of CO2 of about 0.03C.
The change would in fact be extremely small and difficult
to estimate exactly, but would be of the order -0.03°C. That
is, a hundred times smaller than the ‘likely’ climate
sensitivity of 3°C cited in the IPCC’s reports,
The approach is brazenly simple. It starts with the ideal gas law:
PV = m/M RT
If converted to density this becomes:
ρ = P/(R T/M)
rearranged this becomes:
T = P /(R ρ/M)
The author then uses the figures from NASA (space) of surface pressure (P), the gas constant R, near surface atmospheric density and the near surface mean molar mass to calculate the Greenhouse temperature for the following:
||Calculated temperature Kelvin
||Actual temperature Kelvin
|South Pole of Earth
|Mars (low pressure)
||68.5 to 72.8
The correlation is excellent as shown by the following actual versus calculated greenhouse effect:
The only substantial error is with the Greenhouse Temperature of Mars.
Although this paper does not refer to them, this confirms the finding by Nikolov and Zeller in which they show that atmospheric pressure is the largest factor affecting Greenhouse temperature. But it then expands on their work to show that several other factors are alos important as well these being the molar mass and density.
One caveat I would have, is that these different parameters may not be independent, and particularly for the less well known planets & bodies some of the parameters may be back calculated so that a match is certain. However this argument will not apply to the better known planets.
Another caveat is that the formula clearly fell down with Mars, but the author rightly highlights that Mars is the body with the lowest pressure.
Taken at face value, the suggested 0.03C greenhouse effect for a doubling of CO2, does does seem to drive a cart and horse through any idea that CO2 could be a problem. However it may not be so simple. I need to think about it and do some analysis.
But at the very least, I will be very surprised if this paper doesn’t cause waves.
After a bit of thinking, I’m wondering whether what we have here is that the temperature is setting other parameters. Pressure is set by the mass of the atmosphere divided by planetary surface area, however it may be that in effect the density and molar parameter are being affected by temperature. In which case it should be a perfect fit.
In other words it’s just a restatement of PV=nRT in the form P=ρ (R/M) T (where ρ is density & M molar mass). In other words the ratio of pressure to density (P/ρ) = (R/M) T.