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.

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.

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.”

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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.

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

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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!

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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.

Robert, you seem like you don’t understand this topic very well, nor do you understand statistics.

1) You’re using an independent variable that is a function of the dependent variable. Seriously? Where did you go to school? This is statistics 101…

2) Your “study” found a perfect fit with your “predictions”. A perfect fit is only logical if you’re suggesting that air density is 100% of the greenhouse effect. Either you think air density is the ONLY determining factor of the greenhouse effect, or you messed up somewhere (see #1).

“However, that does NOT mean that there is any net atmospheric warming arising from it!”

A forcing by definition effects energy balance….

You really need to elaborate on this. How does a forcing not affect temperature? I don’t even know where to start with this.

“…you don’t understand this topic very well..”

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Yes, I’m a total dummy; that’s why my grades are in the top 1% across the entire university, and I am a member of Golden Key – they love dummies!

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“How does a forcing not affect temperature? ”

.

Let me try to think using my idiot brain….

How about where there is 100% negative feedback of that forcing?

In conclusion, if the gravity, the amount of gas and the sun irradiation remain the same, the temperature should not change, the CO2 beaing negligeable will keep a negligeable effect even if it doubles in concentration.

is it right?

Yes.

No. The author has made some very fundamental and elementary mistakes. See Ned’s comment above.

This paper is about the ideal gas law, not about climate prediction. This law writes PV = (m/M) RT, with P the pressure of the gas, V its volume (here the volume of some well-identified “domain of gas”, say some open barrel), m its mass, M its molar mass, and T its absolute temperature. (R is a constant number.) It writes equivalently P = (ρ/M) RT with ρ = m/V the density.

This is just the state equation that turns out to apply quite accurately to many gases in “normal conditions”, including the atmospheric air. It depends on the chemical species only through its molar mass M (the mass of one mole of the gas). Actually the air is a mixture of several gases: dinitrogen N2, dioxygen O2, carbon dioxid CO2,… and accordingly one should replace m/M by sum_i (m_i/M_i), or equivalently ρ/M replaced by sum_i ρ_i/M_i with ρ_i = m_i/V.

So in the first place it is not true that the chemical composition of the air plays no role in this law.

Secondly, it seems rather absurd to try to explain the temperature field of the Earth’s atmosphere just from the state equation of the air that composes it. The ideal gas law just tells us that IF we know the pressure and the density (and the composition) at some place, then we know the temperature at that place. But the theoretical problem is then to compute the pressure and density fields! To do that one uses models based on fluid mechanics. These models, when runned over short time intervals, do the weather prediction. When runned over longer time intervals, roughly the same kind of models (though differing in important points) do the climate prediction. Incidentally I am a climate sceptic, too, in particular I am not convinced at all that the current models for climate prediction, which include a “forcing” on temperature as function of the CO2 content, are physically correct – and we can only observe that they are very inaccurate in their predictions, by comparing the current climate with what was predicted one or two decades ago.

If instead the subject is considered from the purely experimental point of view, then it’s quicker to measure the temperature than to measure both the density and the pressure!

Thanks – you explain that well and I then realised I had not updated it from a “it maybe” to a “it definitely is” just a restatement of PV=nRT.

“This paper is about the ideal gas law, not about climate prediction.”

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“it definitely is” just a restatement of PV=nRT.”

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“it’s quicker to measure the temperature than to measure both the density and the pressure!”

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I wonder if you guys have actually read the paper. If you have, you certainly did not understand it.

What the paper is about is trying to find the climate sensitivity by another means.

Yes, Formulas 5 and 6 are another form of the ideal gas law – as I clearly pointed out in the paper. But there is a reason for this, now we can see that it is the interplay between density and pressure which causes all temperature changes in the troposphere on short-time scales. (With the exception of molar mass changes due to water vapour).

This formula cannot tell you what causes a temperature change; but it can be used to to rule out what did not cause a temperature change. This is the real importance of this paper – it disproves that there is any net warming from the greenhouse effect on any planetary body.

Regards

Robert Holmes

“but it can be used to to rule out what did not cause a temperature change.”

No. It can’t. You’re using circular logic.

Even if the climate sensitivity to Co2 was 1000x what it currently is, you would still reach the same results in your “analysis”.

The ideal gas law derives temperature from pressure and density. Any amount of radiative forcing from the greenhouse effect would impact both pressure and density. The ideal gas law would still be able to predict temperature from just pressure and density.

Steve,

“The ideal gas law derives temperature from pressure and density. Any amount of radiative forcing from the greenhouse effect would impact both pressure and density. The ideal gas law would still be able to predict temperature from just pressure and density.”

.

This statement of yours is correct if molar mass is added too.

Yet I am also still correct when I said that we can use the results from this formula to determine that the GHE does not cause a net change in temperatures.

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“Even if the climate sensitivity to Co2 was 1000x what it currently is, you would still reach the same results in your “analysis”.”

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Let’s agree on three postulates first, then I will show you how I am right;

Postulate 1:

The molar mass version of the ideal gas law is correct.

Postulate 2:

For Earth to become ~3⁰C warmer with a doubled CO2, then the extra CO₂ must change one or more of the three gas parameters very significantly and anomalously – i.e. there has to be a large and an anomalous effect in one or more of these three gas parameters.

Postulate 3:

If the presence of the extra CO₂ does not change one or more of the three gas parameters very significantly and hence anomalously, then the greenhouse gas hypothesis must be incorrect.

Noticed a mistake in my post;

“Any amount of radiative forcing from the greenhouse effect would impact both pressure and density. ”

should be;

“Any amount of radiative forcing from the greenhouse effect should impact both pressure and density. “

I am sorry, you can’t “disprove that there is any net warming from the greenhouse effect on any planetary body” just by using the state equation of the air (the ideal gas law). I maintain that this paper really is about the ideal gas law: your Table 1 and your (equivalent!) Figure 2 really are a check of the accuracy of that law for different planets, and for different places ((averaged) Equator and South Pole) on the Earth.

The rest of the paper is secondary, e.g. your short discussion about “auto-compression” is just a digression. The formula you write is well-known indeed, though things are more complex in reality than just discussing a “column”, because the atmosphere is a 3-D gas with exchanges that are not confined to just the vertical direction. Anyway that discussion is really a digression from your main argument which is, I repeat, merely to verify that the ideal gas law does allow one to compute the temperature when the pressure and the density (and the composition) are known.

Let me also add this: the state equation of the air does belong to the equations used in the climate models and in the weather models — but there are several other equations in these models, e.g. Newton’s second law applied to a fluid (Euler’s equations or the Navier-Stokes equations, depending on whether the viscosity is accounted for or not).

I agree. However, it is clearly a very good demonstration of how easy it is to get the causal relationship the wrong way around. However, that is also a possibility with the present concept of how IR active gases work.

But it’s also possible the relationship is a necessity of the way surface pressure is calculate. Surface temperature can be measured indirectly by IR, molar gas by spectrum, gravity can be assessed, then …. just guessing … the “height” of the atmosphere can be used to give a volume of gas … that in turn can be used to estimate surface pressure.

So, in a sense temperature is being used to calculate pressure.

Yes, perhaps the pressure-height curve on the distant planets is being estimated precisely in the way you outline: from a 1-D (vertical) pressure gradient model assuming equilibrium under gravity, using the ideal gas law and measured estimates of the temperature and the composition. (I do not claim to be a planetologist.) Thus, the calculations by Holmes would be reverting the order between the measured variables and the calculated one!

(However, there have been spacecrafts on many planets now, perhaps some have got a few direct pressure measurements?)

The direct measurements may cause more problems than they solve. I suspect that may be why Mars is so far off. Rather than using the planet-wide radiative temperature, someone’s thought it a smart idea to quote the actual temperature from the probe. Neither is wrong – but they may give very different results due to the issues of averaging temperatures.

I agree, the inhomogeneity is a problem.

We understand that the pressure is linked to the temperature when the mass and composition remain the same. The increase of the small concentration of CO2 does not impact much. The visible sun light is absorbed by the ground and the sea water. The IR emission of the sea as well as ground is reabsorbed by the GHG particularly H2O in atmosphere and by other gaz including CO2. The two IR bands of CO2 at 4.3 and 16 microns absorb totaly within less than 1 m of path and convert this radiation in heat. If the concentration rose from 400 PPM of today To 800 PPM in future, then the IR light would be converted in heat within 60 cm.. The Green house effect of CO2 remains invariable at the différence of H2O which is not saturate and variable in space and time. Its effect of GHG is largely superior to CO2. When I asked people of ICCP or GIEC about H2O he replied:” yes you are right water is much more important than CO2 but we do not monitor moisture and we can nothing about it so we do not speak of water! “.

In conclusion the amount of CO2 remains négligeable for the composition of air and its GHG effect being already saturated cannot heat more the atmosphere even if it doubles.

“I am sorry, you can’t “disprove that there is any net warming from the greenhouse effect on any planetary body” just by using the state equation of the air (the ideal gas law).”

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We shall see; my next paper is undergoing peer-review now, and it will be far more in-depth.

Some focus will be on why the Venusian temperature at 1atm relates exactly to Earth’s at the same pressure – despite the GHG concentration being a totally different 96.5% compared to Earth’s 2.5%.

At the risk of repeating myself; you guys have failed totally to ‘get’ the main point of the paper. Could be my fault in not explaining myself well enough. Have tried to correct this in the follow-up paper.

Regards

Robert Holmes

I made enough-detailed comments on your paper. You just state that I “have failed totally to ‘get’ the main point of the paper”, without addressing my comments.

If there is no GHE on Venus how is it explained that at night which lasts 58 Earth days the surface does not cool. That would imply that the surface temperature is cause entirely by adiabatic auto-compression which would be ridiculous given the proximity to the Sun. On the other hand the greenhouse effect would explain this quite nicely.

By Ned;

“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 not care about the chemical composition of a gas.”

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Ned and I agree on many things, but here we diverge.

The thought by Ned that this gas law cannot prove the lack of a GHE is simply an assumption of his that is wrong. Many others also have wrongly assumed the same thing.

About Mars; after further investigation, formula 5 does fit Mars, as will be shown in my next paper. Not that it matters.

You guys are fixated on the IGL and all details over whether the measurements are correct or not. This is a total waste of your time; we know the gas law is correct. Instead concentrate on the main point which is the determination of the climate sensitivity.

Please reply to comments rather than making a new one.

I do not understand why you would want to respond in this fashion. Do you not know how to properly reply?

If there is no GHE on Venus how is it explained that at night which lasts 58 Earth days the surface does not cool. That would imply that the surface temperature is cause entirely by adiabatic auto-compression which would be ridiculous given the proximity to the Sun. On the other hand the greenhouse effect would explain this quite nicely.

Donald Mellon/Ned,

Yourself and others here seem to be confused about what I was saying in the paper. There IS a GHE on Earth and Venus, but there is no net (or anomalous) warming from that GHE.

The surface temperature on Venus is not “caused entirely by adiabatic auto-compression”. I have never claimed such.

Instead, it is the combination of adiabatic auto-compression and solar insolation that sets the levels of the three gas parameters which determine temperature.

Ned came close to an understanding when he said;

“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 not care about the chemical composition of a gas.”

His first sentence is correct; however, I was not trying to do this. Instead, I was trying to use the gas law to prove that there is no ‘special’ gases (i.e. greenhouse gases) which cause an anomalous warming effect.

His second sentence is the key; if the gas law does not ‘care about the chemical composition of a gas’, then it means that no gas is ‘special’ and the molar mass version of the ideal gas law must then act in this way.

As formula 5 and 6 show, a definite temperature is known when the three gas parameters are at certain levels. It is known that the same temperature can be made by changing two or more of the three gas parameters, which can be done by changing the constituent gases for others, and/or altering their concentrations. An example here is that the average temperature on Earth’s surface at 288K is the same as the average temperature in the Venusian atmosphere at 49km in height, with very different gases. Therefore, the same temperature can be reached by using a combination of different gas parameters.

Which leads to another question;

Can different mixtures of gases be made to form the exact same three original gas parameters?

Careful consideration of this question appears to bring the conclusion that the answer is probably no. The probability is that a certain mixture of gases, under the same gravitational and insolation levels, relates to a unique set of gas parameters, which cannot be replicated by a different mixture of gases. However, this does not necessarily mean that anomalous changes to gas parameters are allowed by the use of certain specific classes of gases.

Further consideration leads to the likelihood that changes in the concentration of any gas, forces the three gas parameters to change along a continuum. The nature of the ideal gas law (and its derivatives such as the molar mass version of the ideal gas law) effectively stipulate that there are no ‘special’ gases, and therefore that these changes are predictable and dependent only upon the basic properties of of all gases. It is expected that the continuum is predictable.

Greenhouse gas theory stipulates the opposite; that some gases act in a fashion which must change at least two of the gas parameters (pressure and density) in an anomalous way. And not only that; there exist a wide range in the amount of anomalous change, due to the fact that greenhouse gases have a very wide range of global warming potentials.

Yet none of these hypothetical and large changes in gas parameters are seen in nature; neither are they logical – or consistent with the known properties of the ideal gas law, which treats all gases equally. If there are no anomalous changes in any of the three gas parameters due to the presence of greenhouse gases, then there can be no net tropospheric warming due to their presence either.

Robert Holmes