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:

Planetary body | Calculated temperature Kelvin | Actual temperature Kelvin | Error |

Venus | 739.7 | 740 | 0.04% |

Earth | 288.14 | 288 | 0.00% |

South Pole of Earth | 224 | 224.5 | 0.20% |

Titan | 93.6 | 94 | 0.42% |

Mars (low pressure) | 156 | 218 | 28.44% |

Jupiter | 167 | 165 | 1.20% |

Saturn | 132.8 | 134 | 0.89% |

Uranus | 76.6 | 76 | 0.79% |

Neptune | 68.5 to 72.8 | 72 | 1-5% |

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.

## Discussion

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.

## ADDENDUM

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.

This is already covered by Nikolov and Zeller. See interview here, plus links to papers.

https://tallbloke.wordpress.com/2017/10/23/wcc4-rome-interview-with-nikolov-and-zeller/

I see RT has tweeted accordingly

This paper reaches the right conclusion about the Greenhouse effect being “caused by adiabatic auto-compression”, but uses a faulty circular reasoning to do it.

The author employs the Ideal Gas Law to calculate planetary average surface temperatures using the

air densityas an input (independent) variable. This is physically incorrect because, in an isobaric system such as a planet, air density is afunctionof pressure & temperature. This is demonstrated by the fact that air density is lower at the equator and higher near the poles for nearly the same surface pressure. The independent variables determining surface temperatures are atmospheric pressure & solar radiation! That’s because pressure depends on atmospheric mass, planet surface area and gravitational acceleration, while solar radiation comes from the outside. Also, reported air densities for other planets are oftentimes calculated from the Gas Law rather than independently measured, so they are not independent!Bottom line is this: One cannot use the Gas Law to conclusively prove the lack of a radiative GE. One can only point out the fact that the Gas Law does

notcare about the chemical composition of a gas.I wonder how this paper passed peer review, because the methodological mistake made by the author is pretty basic!

Yes – you seem to have reached pretty much the same conclusion as I came to (after a bit of thought) – but it’s still a bit of a brain teaser. I think temperature is affecting the other parameters as determined by the ideal gas law, so rather than temperature being determined, temperature is determining.

As you say pressure is determined by atmospheric mass, surface & gravity (I always forget gravity!!). So, in a sense pressure combines all the planetary variables into a nice “package”. That means we’re left with density and molar mass. Again molar mass is pretty much a constant, implying the relationship is between density and temperature.

Second point – the oddity was that the Mars value was so different. Again, on reflection that may be because of imperfect circulation such that the various “average” values do not perfectly match each other with respect to the ideal gas law.

I agree… The average temperature for Mars (218 K) used in the paper as “measured” quite incorrect! The global average surface temperature of Mars is ~191 K. This is explained in Appendix B of our 2017 paper:

https://www.omicsonline.org/open-access/New-Insights-on-the-Physical-Nature-of-the-Atmospheric-Greenhouse-Effect-Deduced-from-an-Empirical-Planetary-Temperature-Model.pdf

Standard atmosphere: pressure and density curves are pretty much identical.

http://www.digitaldutch.com/atmoscalc/graphs.htm

“As you say pressure is determined by atmospheric mass,”

Yes, and what determines atmospheric mass?

How hot the surface is, right? The lower the temperature, less evaporation, and not just water evaporation. All gases increase from rising temperature at the surface. The heat flow carrries the atmosphere, inflating it. Therefore the atmosphere cannot determine heat flow. Only two things can increase temperature, heat and work. So, gravity and solar heating must be the cause.

“temperature is determining.”

Exactly!

Ned,

“..air density is a function of pressure & temperature. This is demonstrated by the fact that air density is lower at the equator and higher near the poles for nearly the same surface pressure.”

.

My paper shows that air density at the South Pole is 1.06kg/m3 in other words, only slightly below the global average – yet the pressure is a very low 68kPa. It’s the low pressure which mainly results in the low average temperature of -49C.

.

“One cannot use the Gas Law to conclusively prove the lack of a radiative GE.”

.

I realize that, and I did not even try to do this! The radiative GHE certainly exists in our atmosphere; the forcing from it has even been measured and quantified. However, that does NOT mean that there is any net atmospheric warming arising from it!

.

On Earth, temperature is determined by the interplay of pressure and density, with some influence from molar mass via;

T=PM/Rρ

Pressure, density and molar mass are mainly determined by insolation and auto-compression.

I think that we are in broad agreement.