A Greenhouse Gas Planetary Temperature Formula to Put Nikolov and Zeller’s Pressure Formula in Context

Guest Post by Bob Wentworth

Ned Nikolov and Karl Zeller (N&Z) have written about their “discovery” of an interplanetary pressure-temperature relationship (e.g., in their 2017 paper). They offer a formula, developed via a curve-fitting process, which relates planetary Global Mean Annual near-surface Temperature (GMAT) to a function of solar irradiance and the average near-surface atmospheric pressure.

Their formula fits their version of the data quite well. They tried to fit their temperature data with formulas based on measures of greenhouse gases, and couldn’t achieve a convincing fit.

Based on a pressure formula fitting planetary temperatures, and greenhouse gas formulas not fitting, N&Z argue that they have discovered new physics, and that their formula establishes that:

“The ‘greenhouse effect’ is not a radiative phenomenon driven by the atmospheric infrared optical depth as presently believed, but a pressure-induced thermal enhancement analogous to adiabatic heating and independent of atmospheric composition”

There are plenty of reasons to be skeptical of this conclusion, at various levels: fundamental, procedural, and at the level of interpreting the significance of curve fitting.

At a fundamental level, there are simple thermodynamic arguments put forth by Willis Eschenbach in 2012 (and which I’ve spelled out in much more detail) which say that it’s impossible that the “pressure-induced thermal enhancement” hypothesis could be right.

At a procedural level, N&Z’s formula is built on top of their calculation of a planet’s “no atmosphere” temperature. For Earth, their calculated “no atmosphere” temperature is 90 K colder than the observed temperature. Yet, N&Z’s “no atmosphere” calculation doesn’t agree with anyone else’s (e.g., Smith 2008 or Spencer 2016). It appears the reason N&Z’s calculation (published under pseudonyms) doesn’t agree with others’ likely relates to an erroneous conclusion that the rotation rate of a planet doesn’t matter, and possibly also to their failure to take into account the heat storage capacity of the oceans. (Although oceans wouldn’t survive the absence of atmosphere, omitting their influence entirely and insisting that atmospheric effects alone must account for whatever effects oceans are responsible for seems logically suspect.) In any event, if N&Z’s “no atmosphere” temperature calculation is wrong, then that calls into question how meaningful any formula could be that purports to explain atmospheric warming relative to that wrong temperature.

However, today, I’d like to mainly focus on the significance (or lack of significance) of N&Z’s curve-fitting.

Essentially, N&Z argue that their formula fits the data so surprisingly and uniquely well that it must be more that a statistical coincidence—their formula must reflect real physics.

That argument hasn’t been convincing to me personally. After all, correlation doesn’t imply causation and there are plenty of examples of spurious correlations. But, I could argue all day long, at a philosophical level, about whether N&Z’s discovered correlation is spurious, and it likely wouldn’t convince anybody of anything.

If I think that N&Z’s formula only reveals a chance correlation, could I perhaps find another chance correlation? I set out to see if I could discover another formula that fits the data just as well as N&Z’s formula.

I succeeded. Once I had gotten to a point of being able to reproduce N&Z’s curve fitting, it took just a few hours of experimentation to discover another formula (or family of formulas) that fits N&Z’s data just as well.

The formula(s) I discovered depend on measures of the amount of greenhouse gases, not on total atmospheric pressure. The main difference from what N&Z tried is that I consider each greenhouse gas separately, rather than lumping them together as if their effects were indistinguishable.

Before I go into the details of the new formulas, let’s look at the results.

For each celestial body, the chart plots the ratio of the observed global mean annual temperature (GMAT) to N&Z’s calculated “no atmosphere” temperature for that body. For each body, I’ve plotted the actual observed temperature (using N&Z’s data), the predictions of N&Z’s pressure-based formula (which involved 4 tunable parameters, i.e., regression coefficients), and the predictions of three variants of my greenhouse gas formula. One variant, GH6, involves 6 tunable parameters, while the other two variants, GH4a and GH4b, each involve 4 tunable parameters.

It’s easier to assess the significance of the fits by looking at the residual errors (difference between observed and predicted values), as charted below.

I have normalized the residual errors relative to the uncertainty in the temperature data (as estimated by N&Z).

Note that I suspect N&Z have significantly underestimated some uncertainties. In their paper they repeatedly point out variability and lack of consensus in available data, and then proceed to offer a specific value for which they assign an uncertainty only modestly larger than the uncertainty associated with planets for which there is a strong consensus and vastly more data. So, I suggest taking the uncertainty values with a large “grain of salt.”

As the charts indicate, overall, all four models fit the data quite well. The NZ4 model is a little off for Titan, and the GH4a and GH4b models are a little off for Triton. The GH6 model matches the temperatures for all celestial bodies very well.

Note that the excellent fit of the GH6 model was not automatic, just because there were 6 tunable parameters. Closely related 6-parameter models, involving slightly different independent or dependent variables, were completely unable to fit the data and produced terrible fits.

I imagine that this experience, of slight variations in the model leading to terrible fits, is likely similar to the experience that led N&Z to believe that the fit of their model must be significant, must be due to more than chance.

Only, now we have two distinct formulas, depending on different variables, which offer comparably good fits to the data.

This strongly undermines N&Z’s argument that “such a good fit must mean it says something about the underlying physics.”

* * *

So, what’s this new formula of mine, and what motivated its form?

I wanted my formula to have at least some hint of a relationship to underlying physics. Different greenhouse gases absorb and re-radiate longwave radiation in different wavelength bands, with different strengths. Different gases are not the same, and it seems questionable to develop a model under the assumption that they are. So, I wanted to consider each primary greenhouse gas, CO₂, CH₄, and H₂O, separately.

Then there is the question of what metric to use to represent the amount of each gas. N&Z tried curve fitting using the total partial pressure or density of greenhouse gases near the surface. It made more sense to me to ask, “How much gas does longwave radiation need to pass through to make its way from the surface out to space?” So, the metric I use for the amount of gas x is the number of moles of gas x in a column of gas extending from the surface out to space, denoted Uₓ. (This is computed as Uₓ/Aᵣ = L⋅ρₓ/Mₓ, where Aᵣ=1 m² is a reference area, ρₓ and Mₓ are the near-surface density and molar mass of gas x, and L is the nominal scale height of the atmosphere, given by L = P/(g⋅ρ) where g is the surface gravity, P and ρ are the total atmospheric pressure and density at the surface, and g is the gravitational acceleration. Further details are available. All data was taken from N&Z.)

Another thing that we know about the underlying physics is that the radiative impact of greenhouse gases changes as their concentration increases. For a small amount of gas, we might expect the impact to vary linearly with the amount of gas. But, for higher concentrations, the impact of CO₂, for example, is said to be logarithmic in concentration. To reflect this, I assumed that the impact of gas x has the form aₓ⋅ln(1 + Uₓ/bₓ), where aₓ and bₓ are unknown parameters.

Altogether, the form I assumed for the ratio of overall temperature, T, to no-atmosphere temperature, Tₙₐ, is:

T/Tₙₐ = 1 + a꜀ₒ₂⋅ln(1 + U꜀ₒ₂/b꜀ₒ₂) + a꜀ₕ₄⋅ln(1 + U꜀ₕ₄/b꜀ₕ₄) + aₕ₂ₒ⋅ln(1 + Uₕ₂ₒ/bₕ₂ₒ)

(Note that I tried using (T/Tₙₐ)⁴ on the left, as might seem to make sense if we’re balancing energy flows. And I tried using greenhouse gas near-surface partial pressure or density. Each of these variations were terribly unsuccessful at fitting the data. Similarly, trying to introduce real albedo values also broke the fit.)

The models whose values were charted above corresponded to the following parameter values:

  • GH6: a꜀ₒ₂=2.47461964e-01, b꜀ₒ₂=3.46821712e+03, a꜀ₕ₄=2.52997123e-02, b꜀ₕ₄=1.49966410e-03, aₕ₂ₒ=1.81685678e-01, bₕ₂ₒ=7.97199109e+01
  • GH4a: a꜀ₒ₂=2.47085039e-01, ꜀ₕ₄=1.16558785e-01, aₕ₂ₒ=1.99513528e+00, b꜀ₒ₂=b꜀ₕ₄=bₕ₂ₒ=3.42189402e+03
  • GH4b: a꜀ₒ₂=a꜀ₕ₄=aₕ₂ₒ=2.47283033e-01, b꜀ₒ₂=3.44616690e+03, b꜀ₕ₄=3.36453603e+04, bₕ₂ₒ=1.67913332e+02

For model GH6, all six model parameters were allowed to vary independently. For model GH4a, all the bₓ parameters were assumed to be equal, and for model GH4b, all the aₓ parameters were assumed to be equal. Thus, model GH6 had 6 tunable parameters, but models GH4a and GH4b had only 4 parameters each. Thinking about the underlying physics, I would really want many parameters to describe each greenhouse gas. But, to prove my point, I wanted to show I could fit the data with as few parameters as N&Z had used.

* * *

What does all this mean?

Do I think my formula represents the “real physics” of atmospheric warming of planets?

No, not at all.

My formula, like N&Z’s formula, neglects albedo, which we know must have an effect on planetary temperature.

Both formulas assume the atmosphere accounts for the temperature difference between N&Z’s “no atmosphere” formula and what is observed. Yet, I’ve argued that it is almost certainly wrong to attribute that full temperature difference to atmospheric effects, when some of the effect is due to planetary rotation rate and the heat capacity of oceans.

Also, the temperatures of the celestial bodies involved vary from 39 K to 737 K. That means the wavelengths of thermal radiation on each body will be quite different, and will interact with different absorption bands of greenhouse gases. Without accounting for the impacts of absorption bands at different temperatures, it seems implausible that we could be accurately accounting for the real physics.

So, in terms of corresponding to underlying physics, I expect my formula is basically nonsense. But, it has at least as much correspondence to the underlying physics as is the case for N&Z’s formula based on atmospheric pressure. (I’ve omitted some relevant physics. N&Z omit relevant physics and, in addition, had to hypothesize new physics to justify their model. That hypothetical “new physics” is easily falsified.)

* * *

Let’s look at the logic of N&Z’s argument one more time.

They used curve fitting to find a model that “predicts” planetary temperature. The only model they were able to find that fit the data well depended on total atmospheric pressure, without regard to the presence or absence of greenhouse gases.

Because of the uniquely good fit of their empirical model, they argued that their model must correspond to actual physics.

Yet, based on the work I’ve presented here, we now know that the fit of N&Z’s model is not uniquely good. A model that relies only on amounts of greenhouse gases, without regard to total atmospheric pressure, fits the same data just as well.

N&Z’s pressure-causes-temperature model has no justification in terms of known physics (and is falsified by known physics).

If the pressure-causes-temperature model also does not offer a uniquely good empirical fit to the data, why should we believe that it signifies more than a chance, spurious correlation?

We shouldn’t.

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April 10, 2021 6:47 am

That neatly sets out certain limitations of the N&Z work which I have previously considered to be flawed on a similar basis.
Now, do me a favour and have a go at deconstructing the alternative proposal set out in previous contributions to this site by myself and Philip Mulholland.
No new physics required, just a proper acknowledgment of adiabatic processes within a convecting atmosphere.

Gary Ashe
Reply to  Stephen Wilde
April 10, 2021 2:09 pm

up vote from me steven, both you and phil’s work was great, these down votes just prove the gate-keepers of the RGHE that swim amongst the wuwt crowd are still as pissy as ever worthless treachorous luke warmer b@stards.

Last edited 1 year ago by Gary Ashe
Reply to  Stephen Wilde
April 10, 2021 5:45 pm

I know how Earth’s surface temperature is controlled so if you provide a link to your thoughts I will check it out and advise if you are correct or not.

Reply to  RickWill
April 13, 2021 8:55 am

Earth surface temperature is controlled by the majority of it’s surface, which is the ocean.
Venus surface temperature is controlled by it’s clouds, which acts as it’s surface.

Jim Whelan
Reply to  Stephen Wilde
April 11, 2021 10:07 am

If I understand, to put it in simple terms:

In a planet with an atmosphere, adiabatic movement (for example the adiabatic rise of hot from the surface and the adiabatic downflow of cold air) raises the average radiative surface (for lack of a better term). Due to the pressure temperature differential this, of necessity, means the temperature at the surface exceeds any nominal radiative temperature.

Calculations left to others 🙂

Last edited 1 year ago by Jim Whelan
Bob Wentworth
Reply to  Stephen Wilde
April 13, 2021 10:18 pm

Now, do me a favour and have a go at deconstructing the alternative proposal set out in previous contributions to this site by myself and Philip Mulholland.

Hi Stephan, thanks for asking. I’m curious.

First, I’d like to check and see if I’m looking at the right material. I see your Lungs of Gaia blog post, and the referenced articles An Analysis of the Earth’s Energy Budget and Return to Earth: A New Mathematical Model of the Earth’s Climate. Are these the proposals you’d like me to take a look at?

Second, I’d like to test the waters a bit, and see what kind of response I might be setting my self up for, if I try to engage with your materials.

To that end, I’d like to name an apparent issue that jumped out at me immediately upon looking at “An Analysis of the Earth’s Energy Budget.” You write:

The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled. 

You go on to say “Because the intercepted energy flux is being recycled this feed-back loop is an endless sum of halves of halves.” You sum the infinite series and conclude, “we must double the energy flux within the atmosphere.” You apparently conclude that this is the maximum that the energy flux can be boosted via the energy recycling process.

Did I follow you correctly?

If so, the conclusion you’ve reached is erroneous. There is almost no limit to how high the recycled energy flux can become, given an atmosphere with appropriate long-wave absorption properties.

(If necessarily, I could do some math to demonstrate what I’m talking about. In principle, the ultimate limit on atmospheric heating is that if the planetary surface gets too hot, it will start radiating short-wave radiation rather than long-wave, and that short-wave radiation will experience less absorption by the atmosphere. This mechanism guarantees that the planetary surface could never, under any circumstances, get as hot as the Sun.)

It appears that where you go wrong is in interpreting Figure 4 as if it is a model for the radiative effects of the atmosphere as a whole. The way the diagram is intended to be understood is as a model of the radiative effects of a single layer within the atmosphere. To properly use the model to compute the overall radiative effects of the atmosphere, you need to partition the atmosphere into many horizontal layers, each one of which has the radiative behavior shown in the diagram. There will be feedback cycles between layers, as well as a feedback cycle between the surface and the atmosphere.

When you do this multi-layer analysis, you will find that, although a single layer might direct half the radiation out towards space and half towards the surface, the atmosphere as a whole can end up sending more radiation to the surface than it does to space. (On Venus, the atmosphere as a whole sends perhaps a hundred times as much radiation towards the surface as it does towards space. On Earth, the effect is less dramatic, but there’s still more radiation going to the surface than to space.)

So, I’m wondering—is this sort of feedback useful and wanted?

Last edited 1 year ago by Bob Wentworth
Bob Wentworth
Reply to  Bob Wentworth
April 13, 2021 10:39 pm

Stephen, not Stephan. Apologies. (Embarrassing because I value both getting the details right, and being respectful.)

Last edited 1 year ago by Bob Wentworth
Carlo, Monte
April 10, 2021 6:48 am

The links all have a mailto: protocol tag in front of the https tag.

Reply to  Carlo, Monte
April 10, 2021 10:09 am

Fixed. That’s one item that got past my filters BOB

Bob Wentworth
Reply to  Carlo, Monte
April 10, 2021 12:03 pm

Yes, I hope that will get fixed. In the meanwhile, the main link not already familiar to many readers would be the one to my related essay.

April 10, 2021 6:55 am

If I’m understanding correctly you are using gas law incorporating parameters necessary to calculate pressure, this is not a departure from NZ. What you have done is to just decompose different constituents into partial pressures. NZ argue that it is only total pressure that seems to matter, regardless of the composition. In your formulae it wouldn’t seem to make any difference what the ratios of gases are because you just add them up. This agrees with the findings of NZ.

Bob Wentworth
Reply to  JCM
April 10, 2021 12:30 pm

Your understanding is incorrect in several respects. (1) The formula I offered includes only greenhouse gases, ignoring other gases. The total partial pressure of greenhouse gases is not the same as the total pressure of all gases. (2) The formula I offered does not “just add up” the amounts of the different greenhouse gases. It weights amounts of different gases differently, and assumes that the effects of different gases saturate separately (which is a nonlinear effect). So, the effect is not at all the same as just adding up individual partial pressures to calculate a total pressure. The result in no way “agrees with the findings of NZ.”

Reply to  Bob Wentworth
April 10, 2021 4:13 pm

The number of gases included just wash out in the coefficients, as do the weightings. I suppose your argument is with statistics in general but it does not address any problem with the hypothesis or data presented by NZ. I believe the quarrel is with the perceived arrogance of the authors.

Bob Wentworth
Reply to  JCM
April 12, 2021 10:51 am

While I might not enjoy arrogance, what I am more concerned about is lack of rigor and sound logic.

Last edited 1 year ago by Bob Wentworth
Reply to  Bob Wentworth
April 10, 2021 4:56 pm

Specifically, the analysis presented here has total pressure baked into the parameters such as density or U. The remaining gases not mentioned would simply result in an offset to the intercept.

Bob Wentworth
Reply to  JCM
April 12, 2021 10:50 am

As described in a comment below, no, total pressure is not “baked into” Uₓ (despite superficial appearances to the contrary). Total pressure and Uₓ are independent variables, and one can be changed without altering the other.

The “remaining gases not mentioned” would not “simply result in an offset to the intercept.” There is no “intercept” involved (this isn’t linear regression), and there is no information about the “remaining gases” present which would allow any sort of “equivalence” to work out in the manner you’re suggesting.

Reply to  JCM
April 10, 2021 6:44 pm

Essentially this analysis has demonstrated that the partial pressure of a gas can be calculated using temperature and the parameters involved in U. It has been shown that for a given pressure the temperature quotient is tied to the sum of U; ie mass and density of n gases. It seems reasonable this would fit the same curve; it is not arbitrary.

Bob Wentworth
Reply to  JCM
April 12, 2021 10:21 am

On Venus, greenhouse gases comprise 95% of the atmosphere. On Earth, they comprise under 1%. You appear to be arguing that the numbers related to the amounts of greenhouse gases somehow implicitly, magically, tell you about total pressure. They really don’t.

I may have used total pressure in calculating Uₓ, but that’s not inherently necessary. I only did that to transform the raw data from the form in which it was given. If I’d been given the raw data in a more suitable form, I wouldn’t have needed to reference pressure at all. Ultimately, Uₓ and total pressure are entirely independent of one another.

On Venus, you could make the total pressure 10 times higher by adding a lot of nitrogen, and it wouldn’t change U꜀ₒ₂ at all. On Earth, you could remove nitrogen and oxygen to reduce the total pressure by a factor of 10 or more, and again, it wouldn’t change U꜀ₒ₂ at all.

The greenhouse gas U values and NZ’s total pressure are independent variables. The value of one does not predict the value of the other.

Therefore, a function of one set of variables fitting temperature is not equivalent to a different function of a different, independent set of variables fitting temperature.

Last edited 1 year ago by Bob Wentworth
Reply to  Bob Wentworth
April 12, 2021 11:10 am

You misunderstand your own implementation of the gas law. Density of your chosen gasses is naturally a function of total pressure, mass, and temperature. You have provided all parameters necessary to calculate the pressure proportion of your gasses as a function of total pressure by including the mass contribution of your chosen gases, density of your chosen gases, total density, total pressure, and temperature. You cannot separate one from the another. This is what your models shows. This is why it is a gas law. I am uncertain why you have included total pressure in your equation if the point of your claim is that total pressure is irrelevant. The model supports the opposite conclusion of your claim. Perhaps you are fooling yourself, or there is some cognitive dissonance on this matter by confusing gas law principles with radiative effects.


Reply to  JCM
April 12, 2021 1:30 pm

The easiest way to test this would be to do the same analysis for random combinations of any gases. I am happy to do this if you can provide a sheet with the specific form of your calculation, input parameters and units used, and the empirical method to derive coefficients. This is not clear from your articles.

Bob Wentworth
Reply to  JCM
April 12, 2021 5:35 pm

“The easiest way to test this would be to do the same analysis for random combinations of any gases.”

I don’t understand what you are proposing.

“I am happy to do this if you can provide a sheet with the specific form of your calculation, input parameters and units used, and the empirical method to derive coefficients. This is not clear from your articles.”

All raw data is taken from N&Z’s 2017 paper, aside from surface gravity figures and molar mass for each gas, which are readily found elsewhere. For each celestial body, and each greenhouse gas, I calculated Uₓ as I have described. The specific Uₓ values I calculated are given in the appendix of my longer essay. For each celestial body, the data included a value of the temperature (GMAT) divided by N&Z’s calculated “no atmosphere” temperature (all provided in their paper), plus the values of U꜀ₒ₂, U꜀ₕ₄, and Uₕ₂ₒ. T/Tₙₐ was the dependent variable, and U꜀ₒ₂, U꜀ₕ₄, and Uₕ₂ₒ were the independent variables. I assumed the formula for T/Tₙₐ as described in my blog post (above), with unknown aₓ and bₓ parameters. I used the Python scipy.optimize.curve_fit method to identify the aₓ and bₓ parameter values that best fit the formula (a function of Uₓ values) to the temperature data for the 6 data points associated with the 6 celestial bodies. This yielded the parameter values shared in the blog post. Using these parameter values, I compared the values produced by the formula to the actual values of T/Tₙₐ.

What else would you like to know?

Last edited 1 year ago by Bob Wentworth
Bob Wentworth
Reply to  JCM
April 12, 2021 5:13 pm

The only thing my model needed to do, in order to prove my point, is to be different than N&Z’s model and still fit the data.

You seem to be making a baseless claim that the two formulas are equivalent.

If you believe the models are equivalent, please show me how you would transform one formula into the other, without cheating by including any data outside of what is explicitly present within the two formulas.

* * *

“I am uncertain why you have included total pressure in your equation if the point of your claim is that total pressure is irrelevant.”

I have not included total pressure in my equation. I included only the Uₓ values. These are not inherently dependent on pressure.

I could have calculated Uₓ as (total mass of gas x)/(molar mass of gas x)/(surface area of planet), if I had had the appropriate data. This form has no dependence whatsoever on the total pressure at the surface of the planet.

* * *

There is a relationship (in part associate with gas laws) between different values in the data preparation phase, in which one knows all the values, including temperature (that which is to be “predicted”). At that phase of the process, various data and relationships are helpful in computing certain other data.

But, when it comes to do modeling temperature as a function of some independent parameters, one needs to pretend that temperature and the values of all those other variables are unknown. It is in this context, in which all those things are unknown, in which one must assess whether variables are dependent on or independent of one another.

Given only U꜀ₒ₂, U꜀ₕ₄, and Uₕ₂ₒ, it is not possible to deduce the total pressure P. Conversely, given only P, it is not possible to deduce the various Uₓ values.

They are independent variables, not deducible from one another, in the context of “predicting” temperature.

* * *

Suppose I tell you that for some planet, U꜀ₒ₂=1e4, U꜀ₕ₄=2, and Uₕ₂ₒ=3e3. Tell me, what is the total pressure P that you believe is encoded in these values?

You can’t tell me, unless I tell you the temperature T, but I can’t tell you that, because that’s what we’re trying to predict. Even if I told you T, you couldn’t tell me, because you don’t know anything about the other gases that may or may not be present.

Or, if I tell you the pressure on a planet is 80 bar, can you tell me what the Uₓ values are? You can’t.

Yet, these are ultimately all that is known when the time comes to apply N&Z’s formula, or mine.

The independent variables in the formulas are not equivalent, and neither are the formulas.

Reply to  Bob Wentworth
April 12, 2021 5:47 pm

From your article:

“Uₓ/Aᵣ = L⋅ρₓ/Mₓ, where Aᵣ=1 m² is a reference area, ρₓ and Mₓ are the near-surface density and molar mass of gas x, and L is the nominal scale height of the atmosphere, given by L = P/(g⋅ρ) where g is the surface gravity, P and ρ are the total atmospheric pressure and density at the surface, and g is the gravitational acceleration”

Ux is a function of L. L is given by total atmospheric pressure and total density.

The form of the expression Uₓ/Aᵣ = L⋅ρₓ/Mₓ makes Ux directly proportionate the ratio of total pressure and the pressure property of gax x.

I fail to understand if the argument is:

1) about the validity of gas law equations?
2) that you deny using the exact parameters used in gas law?
3) a problem with NZs observation of the relationship of planetary atmosphere regardless of composition?


Bob Wentworth
Reply to  JCM
April 12, 2021 6:37 pm

Your interpretation is deeply misguided. Maybe offering an analogy might help?

Suppose we are trying to predict height, based on data about 6 children. N&Z do some curve fitting, and conclude that height, H, is a function of the number of freckles, F, that a child has. They offer a formula for calculating H from F: H = g(F).

I have a different idea. I suspect that height would be more naturally predicted based on the age of the child, A.

But, the data that N&Z have provided does not directly include the age of the children. Fortunately, the data includes some related information: the number of moles each child has, M, and the “blemish density”, D, (freckles plus moles) per (year of age of the child). So, I use the data N&Z have provided, calculating A = (F+M)/D. Now I have the age of each child.

Given this data, I develop a formula to predict height, H, as a function of age, A: H = q(A).

N&Z offered a formula for height as a function of number of freckles. I offer a formula for height as a function of age. They both happen to fit the data pretty well.

Are these formulas “equivalent”? No, they are not.

And, it’s totally irrelevant that at one point a calculation was done to figure out age that relied on knowing number of freckles. That was only an artifact of the form in which the original data was offered.

* * *

“I fail to understand if the argument is”

Do you mean (A) the “argument” that I tried to make in my blog piece?
Or (B) the “argument” between you and me?

If you are talking about (A), I am not trying to make any argument that has anything whatsoever to do with the gas law. I am arguing that the curve fitting technique N&Z used does not lead to results that mean anything when so little data is used. And that being able to fit more than one unrelated formulas to the same data is one way of demonstrating this.

If you are talking about (B), I regret I am unable to make enough sense out of what you are saying to understand what the argument is.

Last edited 1 year ago by Bob Wentworth
Reply to  Bob Wentworth
April 12, 2021 6:33 pm

“But, when it comes to do modeling temperature as a function of some independent parameters, one needs to pretend that temperature and the values of all those other variables are unknown.”
Can you explain how you ran scipy.optimize.curve_fit without supplying data values?

Reply to  JCM
April 12, 2021 6:54 pm

“If you believe the models are equivalent, please show me how you would transform one formula into the other, without cheating by including any data outside of what is explicitly present within the two formulas.”

Yes, you provided all necessary data.

Gas density is directly proportional to the pressure and molar mass, and inversely proportional to the temperature.

density = pressure x molar mass / gas constant x Temperature

This is the molar mass version of gas law. You provided all of these value. Each value is proportional to one another, it never fails..


Bob Wentworth
Reply to  JCM
April 12, 2021 7:16 pm

You provided a valid formula. It in no way shows my formula is equivalent to that of N&Z. Maybe it’s time to accept that we each have no idea what the other is talking about.

Reply to  Bob Wentworth
April 12, 2021 8:24 pm

I would only like to clarify that the U in your equation simply represents the values in gas law I mentioned. Reducing the gas law values to the letter U does not render it independent from T.

This is why you, like NZ, have demonstrated that the temperature effect of atmosphere has a simple relationship to its pressure (or density and mass) properties. You have both used the variables of gas law to demonstrate this relationship. This includes density, pressure, mass, and temperature. To me this represents the same model framework and the same variables for input. Using your analogy, you have both used the same variables in “predicting” the variable of interest. However, in this case we know that each variable is proportional to the other (or not independent).

My view is that you, like NZ, have used this relationship to demonstrate the simple curve of T vs P observed in real atmospheres.

I admit that in your case the inclusion of only 3 gases in proportion to the total mix does result in a different equation structure, but it’s the same model. NZ have simply reduced it to total pressure. You have broken it down into units of U derived from density and mass. Same model, same variables, different calculation structure. You have effectively solved for pressure of gasx by including the variables of T, partial mass, density, and total pressure in T/Tₙₐ = 1 + a꜀ₒ₂⋅ln(1 + U꜀ₒ₂/b꜀ₒ₂) + a꜀ₕ₄⋅ln(1 + U꜀ₕ₄/b꜀ₕ₄) + aₕ₂ₒ⋅ln(1 + Uₕ₂ₒ/bₕ₂ₒ)

Last edited 1 year ago by JCM
Bob Wentworth
Reply to  JCM
April 12, 2021 11:18 pm

Thanks. I think I might (finally) have a glimpse of the argument you’re making.

It sounds like you’re arguing that both N&Z’s formula and mine are trivially correct because both just secretly reproduce the ideal gas law. Is that it?

If that’s the argument, then maybe I now have enough clarity to express why I disagree with your analysis.

The ideal gas law is P⋅V = n⋅R⋅T. Does that mean it’s trivial to predict T, given P? It would be if you knew n and V. However, N&Z’s formula predicts T without using any information whatsoever about n or V! That’s not the ideal gas law.

In the case of my formula, Uₓ is more or less nₓ integrated from ground level out to space. My formula predicts T without using any information whatsoever about P or V. Nor does it include any information about the vertical distribution of gas, so one doesn’t even have a value of n near the surface to work with. So, again, that’s not the ideal gas law.

Reply to  Bob Wentworth
April 12, 2021 8:57 pm

Your form could be simplified to dT = fn(total P) for planetary atmosphere considering total P is an input in your equation. This matches NZs observation.

Bob Wentworth
Reply to  JCM
April 12, 2021 7:14 pm

scipy.optimize.curve_fit was given the temperatures as the target data to fit, and the U values as independent variables. All other data was omitted.

The point I was trying to make is regrettably difficult to express clearly. I was trying to say that, at the level of what goes into the final model, there is insufficient information available to allow one to deduce total pressure.

Reply to  Bob Wentworth
April 12, 2021 11:38 am

It seems apparent from the outside that once you found the NZ fit you muddled around with the parameters and ultimately found your own way of representing the same relationship by introducing partial pressure of your gases as a proportion of total pressure. You then go on to claim that the relationship is arbitrary and that using derived coefficients one could use any set of inputs to find the same result. Then you invalidate your own claim by admitting that other sets of non logical parameters in the gas law equation breaks the fit.

Bob Wentworth
Reply to  JCM
April 12, 2021 5:40 pm

In what way is it the “same” relationship? I’d like you to present some math, because your vague assertions are so unclear as to seem meaningless.

Mike McMillan
Reply to  JCM
April 10, 2021 7:27 pm

Yet another shot at Nikolov-Zeller, one among over a hundred shots here at WUWT.

The bottom line I take from N-Z is that it is the mere presence of an atmosphere that makes for warmer, not what the atmosphere is made of. Greenhouse gases can make a difference only at the margins. N-Z ignored most of what really doesn’t make much of a difference.

The presence argument boils down to the adiabatic lapse rate, constantly shuffling what heat is in the air downward, yet many at WUWT are skeptical of ADL’s abilities.

Nine years ago, before N-Z, Professor Robert Brown (rgbatduke) took aim at the ADL in this <a
href=”http://wattsupwiththat.com/2012/01/24/refutation-of-stable-thermal-equilibrium-lapse-rates/” target=”_blank”>WUWT post</a>, which posed a perpetual motion-type paradox supporting his contention.

With apologies to Willis and other ADL unbelievers, I solved Professor Brown’s paradox in this non-WUWT post, <a href=”https://rockyhigh66.org/stuff/adiabatic_lapse_rate.html” target=”_blank”>In Defense of the Adiabatic Lapse Rate/</a>.

(shure hope my html works 🙂

Reply to  Mike McMillan
April 10, 2021 11:39 pm

thanks Mike

Bob Wentworth
Reply to  Mike McMillan
April 11, 2021 1:05 pm

There seem to be two distinct issues here:

  1. Does the existence of an adiabatic lapse rate imply an ability of atmospheric pressure alone to warm planetary surfaces?
  2. In a thermally isolated column of gas with no heat sources, would the column reach equilibrium in an isothermal state (same temperature at all altitudes) or in an isentropic state (temperature varying with altitude in accordance with the lapse rate).

As best I can tell, these are independent questions. As far as I can tell, the answer to the second seems irrelevant to the answer to the first.

I believe the answer to the first question is unambiguously “no.” An atmosphere with no radiative absorption must tend to cool a (thermally uniform) planet (or be neutral in effect), rather than warm it. This follows from simple thermodynamics arguments that don’t seem to have much room for any loopholes.

Regarding the second question, the issues involved are quite subtle, and I can understand why there might be disagreement. However, after spending some time thinking about Professor Brown’s arguments, your arguments, doing some background reading on issues like potential temperature, and thinking through some thought-experiments of my own, I am largely coming down on the side of Professor Brown.

As I understand it, the adiabatic lapse rate limits how much heat from below can warm the air above through convection. However, it does not limit how warm the air above could become through other means. And, there doesn’t appear to be any “restoring force” through which an isothermal situation (same temperature at all altitudes) would shift towards an isentropic situation (characterized by the lapse rate).

(It seems suggestive that on Earth, near the poles, the temperature profile appears to be closer to isothermal than isentropic, but I will readily admit that the Earth’s atmosphere is complex enough that this observation doesn’t remotely prove anything.)

To me, it’s helpful to modify Professor Brown’s thought experiment. Instead of using a solid conductor, put a black-body radiator at the top and bottom of the gas column (and assume the gas is transparent to radiation). If there were a thermal “restoring force” trying to make the gas column isentropic rather than isothermal, this would set up a perpetual-motion-like cycle in which heat would flow radiatively from the bottom to the top of the gas column, but then some mechanism in the gas would cause heat to flow from the top of the gas column to the bottom. This would seem to be clearly contrary to the Second Law of Thermodynamics. To me, this seems to establish, pretty definitively, that there can be no thermal “restoring force” trying to create an isentropic temperature profile (despite any intuitions that might seem to support the idea of such a tendency).

Last edited 1 year ago by Bob Wentworth
Reply to  Bob Wentworth
April 11, 2021 2:13 pm

Bob 1:05 pm, for your number 2., if you read Prof. Brown’s earlier post many years ago closely, find he merely assumed the tall column equilibrium temperature would be isothermal in the assumptions. Because of that assumption he takes T(z) as a constant out from under eqn. 5 integration over dz. So, his isothermal conclusion simply follows from his assumption of isothermal T(z) = constant at equilibrium.

This isolated gas column theoretical setup has been much discussed in the literature as far back as Gibbs 1867, Maxwell 1888, Exner 1925, Emden 1926. Those earlier authors defined the problem somewhat confusingly at times & Exner tried to set that straight with Emden attempting to end it. Turns out, in modern history, the isothermal solution for a tall isolated column of Earth’s atm. air T(z) = constant is not the maximum entropy solution after a higher entropy solution for T(z) being non-isothermal at equilibrium was found and published in Dr. Craig Bohren’s ‘Atmosphere Thermodynamics’ 1998 text book Chapter 4.4. 

Bob Wentworth
Reply to  Trick
April 11, 2021 6:44 pm

I’ve refined my thought experiment in a way that I find compelling. (I attached a diagram, which I hope will show up as I hope.)

Imagine a thermally isolated system, perfectly insulated from its environment. On the left is a vertical column of gas in a gravitational field. On the right is a vertical vacuum chamber, with black-body radiators at the top and bottom (and sides that are perfectly reflective). Heat exchangers at the top and bottom of the system connect the gas column to the radiative heat-exchange column. Between the top black-body and the top heat-exchanger we place a heat engine, which can use any temperature differences to generate work. The bottom heat-exchanger is at temperature T1, corresponding to the temperature of the bottom of the gas column. The top heat-exchanger is at temperature T3, corresponding to the temperature of the top of the gas column. The black-body just below the heat-engine is at temperature T2.

Start the system in an isothermal state, with T1=T2=T3. In this state, there is a radiative balance between the black-bodies, and zero net heat flow on the radiative side of the system.

Suppose it is true that there is a tendency in the gas to revert to an isentropic state in which the temperature of the gas obeys the adiabatic lapse rate. If this is the case, then the temperatures will shift towards a state where T3 < T1. The top of the gas column will become, at least to some degree, cooler than the bottom of the gas column.

Given that the heat-engine has some thermal resistance, it follows that we will find T3 < T2 < T1.

Net radiative heat will flow from the lower black-body at T1 to upper black-body at T2. The only way this heat can be eliminated is by flowing through the heat engine and to the top of the gas column.

There will be a temperature difference (T2-T3) across the heat engine. The heat engine will be able to perform work.

Therefore, if there is a tendency for the gas to revert to an isentropic temperature profile, we will have successfully built a perpetual motion machine, doing work without any external energy input.

This seems to definitively argue against the possibility of such a tendency.

* * *

Regarding Prof. Brown’s post… As I understand it, Brown considered the hypothesis that the state of the gas was isothermal, then he showed (eq. 5) that, given an isothermal temperature state, the density profile showed no evidence of convective instability (as would be the case if gas less dense was below gas that was more dense). I don’t see anything improper in what he did.

I’d be interested in seeing Craig Bohren’s argument, if you had some way of offering that. Unfortunately, his textbook currently sells for $60, which I’m not prepared to pay. The reviews don’t inspire confidence in me, regarding Bohren’s temperament. And sometimes questionable temperament and questionable logic go together. So, I’m interested, but feeling cautious.

Reply to  Bob Wentworth
April 11, 2021 8:47 pm

Bob 6:44 pm, Bohren’s text book can be obtained on loan for free from your nearest college library. Dr. Bohren and collaborator(s) present a detailed mathematical proof maximizing the entropy in the isolated tall earthen air column to find the equilibrium T(z) that does so.

To do that, they write out the eqn. for entropy in the column then maximizes that entropy eqn. subject to the constraint total energy (including PE per unit area) being a constant. It is interesting to note that thermodynamics by itself is powerless to predict when that equilibrium occurs.
As for your isolated setup in a gravity field, a tiny universe all to itself, the system will produce entropy until it reaches a maximum entropy temperature profile and stop; it is not a perpetual heat engine nor is Prof. Brown’s isolated system with rod. To find yours or prof. Brown’s T(z) at equilibrium (heat death) follow the same logic as Bohren, write out the system entropy eqn. subject to the constraint of constant total energy and maximize that eqn.  

Bob Wentworth
Reply to  Trick
April 12, 2021 12:30 am

It makes sense that entropy needs to be maximized, and it also makes sense that the energy at the top and the bottom need to end up the same, or else there would be a perpetual motion machine involved. The only way to reconcile these would seem to be if entropy is maximized by an isothermal gas column.

I get that you’re saying Bohren’s text calculates the energy maximizing solution as involving an adiabatic lapse rate. But (a) that leads to a contradiction (via the thought experiment above) and (b) that disagrees with Feynman’s analysis of the situation. Feynman asserts that gravitational potential affects the spatial distribution of molecules, but does does not make the temperature at different altitudes anything other than isothermal.

I haven’t seen Bohren’s analysis. But, it seems hard to see how it could yield an adiabatic lapse rate in the absence of a heat source and convection and still be thermodynamically consistent.

Reply to  Bob Wentworth
April 12, 2021 7:08 am

Bob, Dr. Bohren’s analysis will be hard to see until you see his solution laid out thermodynamically consistent. Once you understand the work, it will make sense the max. entropy equilibrium temperature at top and bottom cannot be the same in a gravity field.

Your physics background will enable you to understand Bohren’s work in a beginning textbook and find that Feynman’s treatment is too vague to be defensible. The gravity field introduces PE which has to be accounted for in the total isolated system energy as does Dr. Bohren but PE & entropy are not accounted in Dr. Feynman’s high-level pass-by.

There is an absence of convection at equilibrium (but not an absence of mixing) because the isolated air column is nowhere heated from above in a gravity field which seems counterintuitive. At thermodynamic equilibrium, i.e. entropy max. “heat death”, the PE gain downward must balance the KE increase and vice versa.  

Bob Wentworth
Reply to  Trick
April 12, 2021 5:45 pm

I’m having a lot of trouble getting access to Bohren’s book, so far. The libraries I have access to don’t have a copy and they aren’t doing InterLibrary Loans now. Still working on it.

You say that the “higher entropy solution” Bohren found is “non-isothermal at equilibrium.” Out of curiosity, does it involve the adiabatic lapse rate, or is it something else entirely?

Reply to  Bob Wentworth
April 12, 2021 7:31 pm

Yeah, these are trying times for personal interaction. Normally I’d suggest going to see the college librarian and give them the chance to ply their trade which I have found they are waiting & eager to do. Nowadays that may be difficult. I cannot begin to cover Dr. Bohren’s ~8 textbook pages of “Entropy Maximization in the Atmosphere” thermodynamics here. I’ll note it is restricted to the lower layer several hundred mb thick and dry. A few teaser quotes to incent your search for a copy:
Bohren text p. 109: “The significance of the dry adiabatic lapse rate is …it demarcates the boundary between statically stable and unstable atmospheres.” Then the result p. 167: “Of all linear potential temperature profiles, a constant potential temperature maximizes the entropy of an isolated layer (several hundred mb thick) of the atmosphere in hydrostatic equilibrium…. Entropy maximization requires the equilibrium temperature of an isolated atmospheric layer subjected to mixing with no condensation or evaporation of water to decrease with height at the dry adiabatic rate.”

Bohren goes on to ask the obvious Q: “This result might appear to be at odds with our everyday experiences. Why isn’t the equilibrium profile isothermal?”

 A: “If a solid is isolated from its environment and initially has a nonuniform temperature, conduction eliminates all temperature gradients. But in the atmosphere, energy transfer in an isolated layer is dominated by convection rather than conduction (Lord Kelvin 1862)…. Energy transfer in the atmosphere and other fluids differs fundamentally from energy transfer in solids, in which mass motion is absent… Thus the example of conduction in solids can impede our understanding of atmospheric convection.” Dr. Bohren (and collaborator(s)) then go on for a page supporting that contention eliminating everyday impediments to understanding atm. convection.

NB: the last sentence of my 7:08 am substitute more accurately “PE loss” for my “PE gain”. That was my captcha to prove I’m human. 

Bob Wentworth
Reply to  Trick
April 12, 2021 10:54 pm

Thanks very much for that added detail. I also found it helpful to look at the Verkley & Gerkema (2004) paper suggested by Ed Bo.

Part of what I take from all this is that the different solutions—isothermal vs. isentropic—result from solving the entropy maximization problem under different assumed constraints.

In retrospect, the arguments I perceive to be happening about whether “the” equilibrium is isothermal or isentropic now seem a bit silly. The answer can be either, depending on what boundary conditions you assume for the problem.

I thought we were talking about equilibrium in a constant-energy context in the absence of convection.

But, both the extracts from Bohren and V&K’s gloss on Bohren & Albrecht seem to indicate that Bohren’s solution arises from assuming constraints that are closely tied to the idea of convection being the dominant heat transfer mechanism. (And V&K imply this doesn’t maintain a constraint of constant energy or enthalpy.)

So, it seems we’re not talking about what I had imagined we were talking about.

V&K derive maximum entropy profiles under a variety of different assumed constraints, yielding an isothermal profile, an isentropic profile, and an intermediate profile (which they say “agrees almost perfectly with the tropospheric part of the Standard Atmosphere”).

Bottom line: it’s all about the assumed constraints.

I feel like I’ve learned something. I appreciate that.

Reply to  Bob Wentworth
April 13, 2021 7:13 am

The V&G treatment leaves out much clarifying discussion of the natural solution for equilibrium max. entropy T(z) and thermodynamic equation development found in the Bohren book. As a somewhat famous physicist once implied nature does not play dice, so there is only one set of natural constraints, meaning there aren’t two (or more) natural solutions to equilibrium T(z). V&G point out mathematically there is more than one set of constraints, and don’t fully develop which set is selected by nature.
Bob: ”V&K imply this doesn’t maintain a constraint of constant energy or enthalpy.”

That implication is not accurate. Gas enthalpy does not include PE which is included in total column energy in a gravity field. If & when you are able to obtain Bohren’s book, you will find the text’s thermodynamic development adds PE(z) to column enthalpy(z) for total column energy and that IS the natural constraint eqn. held constant when integrating (total energy(z))dz over the restricted column height in the entropy maximization process.

Unfortunately, V&G use words with different meanings & they do not quote Dr. Bohren text exactly while crediting him with reviewing their early manuscript. So far as I know, Dr. Bohren hasn’t written a response to the final version. There is only one set of natural constraints: those used in the Bohren book which are an advancement over the classical solution constraints. Dr. Bohren develops in a lengthy essay details showing where the classical constraints are lacking of nature.

NB1: another issue is V&G do not restrict their work to the lower several hundred mb that is shown as a simplifying eqn. restriction in Bohren’s book eqn.s 4.149 to enable 4.150. V&G simply jump to their answer in eqn.s 15-17 without showing their work that is shown in Bohren text. It would be interesting to look into what difference, if any, that simplification causes in the two treatments but I’ve not spent the time.

NB2: V&G intermediate solution is just their curve fit to the standard atm. 

Last edited 1 year ago by Trick
Bob Wentworth
Reply to  Trick
April 13, 2021 4:40 pm

I take your point that “V&G intermediate solution is just their curve fit to the standard [atmosphere].”

And that, V&G don’t much address the question of what constraints are “natural” to analyzing the atmosphere. They more focus on unpacking the implications of different constraints. (This would likely explain why they don’t restrict their work to the lower atmosphere. I’m guessing the position in the atmosphere affects what constraints would seem to be most appropriate.)

Regarding energy being held constant… What V&G assert is that, given a 1st constraint of constant mass, an isothermal maximum entropy has been proven to result from assuming either of the following constraints:

  • (constraint 2) constant total energy (including gravitational potential energy)
  • (constraint 2′) constant total enthalpy (which does not include gravitational potential energy but does account for work done in compressing or expanding gas parcels)

V&G report that, instead of using constraint 2 or 2′, Borhen uses:

  • (constraint 3) constant total potential temperature

V&G say that there is some (potentially controversial) approximation involved in arriving at constraint 3. Unfortunately, their gloss doesn’t describe the approximation involved.

I gather from your comments that constraint 3 is meant to reflect what happens if one factors gravitational potential energy into an enthalpy constraint (possibly with some approximation involved, perhaps one which explains why Bohren’s model is restricted to the lower layer of the atmosphere)?

Hmmm…. the nuance is getting a little too fine for me to parse without more work. Guess I’ll need to mull it over some more.

Reply to  Bob Wentworth
April 13, 2021 6:57 pm

Because V&G don’t show their detail work eqn.s 15-17 to arrive at Bohren’s result, I can’t figure out what they mean mathematically by: “constancy of the integrated potential temperature as a single additional constraint 3”. This wording is not found in Bohren’s treatment so I can’t verify that Bohren does what they claim.

Dr. Bohren (and collaborator(s)) expose all details of their work and the approximation I noted. V&G don’t discuss this well enough – they are not writing a text book & keep details hidden so it is an open issue to mull as you note.

Mike McMillan
Reply to  Bob Wentworth
April 11, 2021 3:08 pm


Your two issues:

1. Does the existence of an adiabatic lapse rate imply an ability of atmospheric pressure alone to warm planetary surfaces?

The atmosphere does not warm the surface. The sun does that. Contact with the surface warms the atmosphere. This causes convection cooling of the atmospheric column down to the ADL temperature, where the gravity mechanism takes over and the only cooling is from radiation.

The existence of an atmosphere and atmospheric pressure implies gravity and the gravity mechanism, which creates the ADL.

2. In a thermally isolated column of gas with no heat sources, would the column reach equilibrium in an isothermal state (same temperature at all altitudes) or in an isentropic state (temperature varying with altitude in accordance with the lapse rate).

In your example it would, in the absence of gravity. With gravity, the mechanism starts shuffling the available heat downward until an ADL is established, even without a heat source.

The basic argument is whether the gas column has uniform thermal energy or rather uniform total energy (thermal + gravitational potential). I have all the atmosphered planets on my side.

comment image


Mike McMillan
Reply to  Mike McMillan
April 11, 2021 4:52 pm

I note that Titan has a shallower lapse rate than Earth. It has 4 times the atmospheric density but 1/7 the gravity of Earth, which indicates (though does not prove) that gravity is the determining factor in ADLs.

Bob Wentworth
Reply to  Mike McMillan
April 12, 2021 12:11 am

The standard formula for adiabatic lapse rate is g/C_p, so, yes, the result you point out about Titan is expected. Was someone asserting that gravity doesn’t play a role in the adiabatic lapse rate?

Bob Wentworth
Reply to  Mike McMillan
April 11, 2021 7:07 pm

The planets all have heat sources in the form of absorbed sunlight, and in some cases, internal energy. So, they tell us about the extent to which adiabatic temperature profiles naturally occur in the presence of a heat source—which is something that everyone agrees on.

I don’t see planetary data as having any relevance to the question of what temperature profile would result if there were no heat sources, which is the only part of the issue regarding lapse rates where there appears to be any controversy.

(Also, I note that on each planet there are portions of the atmosphere which do not adhere to any lapse rate. This too, is the result of heat sources, in the form of radiation absorption in the upper atmosphere.)

* * *

I asked the question:

Does the existence of an adiabatic lapse rate imply an ability of atmospheric pressure alone to warm planetary surfaces?

It sounds like you found that question ill-posed. Let me try again:

Does the existence of an adiabatic lapse rate on actual planets imply that on a planet without any IR-absorbing gases, atmospheric pressure could warm the planetary surface relative to the temperature the surface would be at in the absence of an atmosphere?

That’s the core non-physical assertion that I read into N&Z’s work.

This is the question I’m most interested in engaging with.

* * *

I think I agree with most of what you say about ADL, except that I don’t know what you mean by the term “gravity mechanism”, so I don’t know if it refers to something I would agree with or something I would disagree with. I’d be curious if you’d like to try to clarify this.

Reply to  Bob Wentworth
April 11, 2021 9:08 pm

Bob 7:07 pm, your rephrased question 2. contains a singularity as all gases are matter thus are IR absorbing on a planetary scale. Also, you need to add in to your question a way to control for the same surface optical properties without an atm. which presents a difficulty.

But I think you are getting at, yes, any reasonable atm. will increase the global multiannual avg. temperature of a solar illuminated planetary surface over no atm. against the cold of deep space due the IR absorbing gas opacity that isn’t present without an atm. given the same surface optical properties.  

Bob Wentworth
Reply to  Trick
April 14, 2021 5:13 pm

Trick 9:08pm: “your rephrased question 2. contains a singularity as all gases are matter thus are IR absorbing on a planetary scale.”

(I think it was actually a rephrasing of my question 1.)

I’m unable to find data on IR absorption of non-polar gases like nitrogen, oxygen, argon, so it appears that absorption is very, very low. I’m imagining that the short-wave optical depth of an atmosphere made only of these gases would be much less than one. If that’s the case, that’s sufficient to match what I’m talking about.

If we assumed no water, and an inert gas atmosphere, then I would think surface optical properties likely wouldn’t be strongly affected.

* * *

What my “rephrased question” was trying to address was an apparent contention by N&Z (and some others) that IR absorption is not necessary for planetary warming, that atmospheric pressure even in the absence of greenhouse gases could achieve warming.

Maybe they are not actually saying this. But, if not, their hypothesis becomes more ambiguous and less falsifiable.

Last edited 1 year ago by Bob Wentworth
Reply to  Bob Wentworth
April 14, 2021 6:06 pm

Bohren 2006 on Planck radiation: “All matter – gaseous, liquid, or solid – at all temperatures emits radiation of all frequencies at all times, although in varying amounts, possibly so small at some frequencies, for some materials, and at some temperatures as to be undetectable with today’s instruments (tomorrow’s, who knows?). Note that there is no hedging here: all means all. No exceptions. Never. Even at absolute zero? Setting aside that absolute zero is unattainable (and much lower than temperatures in the depths of the Antarctic winter or in the coldest regions of the atmosphere), even at absolute zero radiation still would be associated with matter because of temperature fluctuations. Temperature is, after all, an average, and whenever there are averages there are fluctuations about them.”

As far as reduction in earthen OLR in the IR bands from N2,O2 see:


Noble gas (i.e. Ar) radiation from quantized atomic spin was a viable research topic in the 1930s or earlier when quantum stuff was all the rage in laboratories – you can google all that for yourself. I had to visit the local college stack archives to read up on it as I found it interesting. IIRC the testing went into the early 1950s and is mostly forgotten now.  

Bob Wentworth
Reply to  Trick
April 16, 2021 9:03 am

Thanks for that reference on absorption of long-wave radiation by N₂ and O₂. Very interesting.

Mike McMillan
Reply to  Bob Wentworth
April 12, 2021 6:02 am

By gravity mechanism, I meant the slowing/cooling of molecules going up and the speeding/warming of molecules headed down under gravity. The energy they transfer when they bump into other molecules is less in the upward direction and more downward, thus the sorting out of temperatures.

Your radiative transfer example is much better than rgb’s silver wire, but in your case the air column won’t be doing any perpetual motion, just stabilizing with slightly different temperatures, while rgb’s wire will just assume the same temperature locally as the air.

An atmosphere doesn’t add warmth to the planet. It just helps the planet retain what heat it has or acquires, so yes, it will be warmer than it would be without the air.

Reply to  Mike McMillan
April 12, 2021 7:17 am

Mike 6:02am, well written. Intuitively, dropping a silver wire into an isolated air column cannot create perpetual motion, a proper thermo. analysis will so demonstrate.

Bob Wentworth
Reply to  Mike McMillan
April 14, 2021 5:20 pm


the air column won’t be doing any perpetual motion, just stabilizing with slightly different temperatures

Yet, if there are “slightly different temperatures” across a heat engine, then work will be getting done. That means that either energy is coming from somewhere (violating any assumption that the system is fully isolated) or there is “perpetual motion.”

I’m having a hard time seeing a way around this logic. If you don’t agree, what do you see as wrong in the logic?

Reply to  Bob Wentworth
April 14, 2021 6:16 pm

“Yet, if there are “slightly different temperatures” across a heat engine, then work will be getting done.”

The logic is: not at maximum entropy in a universe, no more heat engines can exist at that point as no more entropy can be produced. Which is why they call it “heat death”.

Ed Bo
Reply to  Bob Wentworth
April 11, 2021 6:21 pm


Robert Brown’s example on WUWT is exactly the same as Richard Feynman’s in his famous Lectures on Physics from the 1960s (Vol 1 #40):


I think a slight variation on their configuration makes the point more obvious. Putting a heat engine like a thermoelectric generator in the middle of the metal link, producing work from the temperature difference. If the otherwise isolated gas column has a mechanism to restore the lapse rate, then it is steadily producing work without rejecting any heat to a lower temperature reservoir, an obvious 2nd Law violation.

In the 1800s, James Clerk Maxwell posed a similar thought experiment with two otherwise isolated columns of gases with different Cp values tied well together at the bottoms so their bottom temperatures are the same. Their tops are connected by a much more slender conductor with a heat engine in between. This was a key analysis for him in deriving what we now call the Maxwell-Boltzmann distribution of gases.

Bob Wentworth
Reply to  Ed Bo
April 11, 2021 11:43 pm


Very helpful, thanks.

I’ve been trying to reconcile the thought experiment of Feynman and Brown (and my similar thought experiment with a radiative rather than conductive connection) with Trick’s and Bohren’s assertion that entropy in an isolated gas column is maximized by a temperature profile associated with the adiabatic lapse rate (rather than an isothermal temperature profile).

The thought experiments are very compelling to me, as is the argument that entropy must be maximized. So, if these are in conflict, that presents a dilemma.

After reading Feynman, my suspicion is that the claim that a temperature profile associated with the adiabatic lapse rate maximize entropy is simply wrong. Based on Feynman, it seems that the density variation with altitude being exponential is what maximizes entropy with respect to the distribution of molecules, while the entropy of molecular energy modes is maximized by all molecules being at the same temperature.

I’m curious if this matches your sense of things? That the assertions about what maximizes entropy in this situation being something other than an isothermal state are simply wrong?

Reply to  Bob Wentworth
April 12, 2021 7:23 am

The assertions that an isolated column of earthen air is maximum entropy isothermally were proven inaccurate when the non-isothermal T(z) solution was found to have a higher entropy and there is no possible higher entropy solution. 

Bob Wentworth
Reply to  Trick
April 12, 2021 8:18 pm

Is that non-isothermal higher entropy solution associated with the adiabatic lapse rate, or is it yet another temperature distribution? Edit: From a review of the subject (as offered by Ed) I see that the answer is isentropic, but that the result of maximizing entropy depends entirely on the constraints one assumes.

Last edited 1 year ago by Bob Wentworth
Ed Bo
Reply to  Bob Wentworth
April 12, 2021 8:38 am


Yes, I do think the density change with height is the key factor many people are missing, whether in “hand wave” analysis (which we all do) or something more formal.

In a vertical gas column, it is the isothermal case (whether equilibrium or not) that provides the exponential profile. An important thing about an exponential profile is that it has a constant relationship between a variable and its derivative.

Thinking at the molecular level, some people argue that, taking a horizontal plane in that column, since the molecules crossing from below are decelerating and those from above are accelerating, these will only balance (equilibrium) when there is a temperature gradient.

But these people ignore the density difference. There are fewer molecules crossing the plane from above than from below. So even if those from above have higher KE, their total KE is the same.

Some years ago, I stumbled on an article discussing what a struggle it was for Maxwell to derive an equilibrium velocity distribution that did not lead to these 2nd Law violations, but he finally did derive it — what we call the Maxwell-Boltzmann distribution. Unfortunately, I did not bookmark it and have not been able to find it since.

You may enjoy this paper that reviews the arguments pro and con:


BTW, I think we may have overlapped in grad school in the 1980s — I was in engineering there.

Mike McMillan
Reply to  Ed Bo
April 12, 2021 8:55 am

“But these people ignore the density difference. There are fewer molecules crossing the plane from above than from below. So even if those from above have higher KE, their total KE is the same.”

No, once the column is temperature, density, and pressure stable, the number of molecules crossing the plane up and down will be equal. More in one direction would change the density at that level.

Ed Bo
Reply to  Mike McMillan
April 12, 2021 9:50 am

Mike: You believe the density of a vertical column does not vary with height? Seriously?

Mike McMillan
Reply to  Ed Bo
April 13, 2021 7:46 pm

No. I do seriously believe that density is constant at any given altitude, and to keep it constant, the number of molecules passing through it in the up direction must equal the number going in the down direction.

Bob Wentworth
Reply to  Ed Bo
April 13, 2021 2:27 pm

Thanks for the link to the journal article by Verkley & Gerkema (2004). I found it very informative.

The biggest insight I got was realizing that the disputes that exist are not about the answer to a particular problem, but about what is the “right” problem to solve. Different constraints, representing significantly different versions of the problem, yield different results.

With regard to arguments that, at a molecular level, higher layers should heat lower layers if they are at the same temperature… Given the dependence on constraints, it appears that this argument may be valid in the context of some boundary conditions but not under others. So, the answer is quite subtle.

It’s clear that, under some constraints, an isothermal solution is valid. And that, in this case, an upper layer does not gravitationally warm a lower layer when both are at the same temperature.

I think you’re right that the “density change with height” is part of why such gravitational warming does not occur in the stable-isothermal-profile case.

Yet, I don’t think you’ve quite nailed where others’ reasoning goes wrong. As some have noted, in equilibrium, the total number of molecules crossing a horizontal surface in the upwards and downwards directions must be equal.

I think that Feynman’s explanation of Fig. 40-4 is more to the point. The answer seems to have to do with an interaction between density profile, energy distribution, and the ways that more and less energetic molecules move.

If you consider the population of molecules at slightly lower and higher planes, only the more energetic molecules from the lower plane will reach the higher plane, which results in reduced pressure at the upper plane, but also turns out to yield the same distribution of molecular energies at the upper plane as at the lower plane, once the change in potential energy is accounted for.

Similarly, it is less energetic molecules from higher up that are preferentially somewhat more likely to end up lower down, so that when you account for gravitational acceleration and density differentials, they end up maintaining an isothermal kinetic energy distribution.

But, ultimately, when you get quantitative, it all comes down to the assumed constraints (or boundary conditions).

Hand-waving arguments are unreliable, and it seems a shame that so much energy often seems to be get wasted on pointless arguments at that level.

It’s fun to think we might have been on the Stanford campus at the same time. Thanks for pointing that out.

Last edited 1 year ago by Bob Wentworth
Ed Bo
Reply to  Bob Wentworth
April 13, 2021 6:55 pm


I agree that you must be very careful in describing the constraints of the problem. But if gravity ALONE creates a negative lapse rate, then it must be able to maintain it in a thermodynamically isolated column. And top physicists from Gibbs and Maxwell on to Feynman believe that yields a 2nd Law violation. Of course, the earth’s atmosphere is not remotely thermodynamically isolated.

Some years ago I found an article describing Maxwell’s struggles in deriving his kinetic theory of gases. (Unfortunately I forgot to bookmark it, and my google-fu has not been good enough to find it again.)

According to the article, one of his biggest challenges was coming up with a theory that would not lead to violations of the 2nd Law. In the 1860s, his equations led to a solution for an isolated column with a negative lapse rate, which he considered a 2nd Law violation, and he wrote to William Thomson (later Lord Kelvin), who was also working on the problem, as Trick has noted, to ask for assistance. Many of Maxwell’s letters are now collected and published, so I hope to track that down one day.

If memory serves, his next solution yielded a positive lapse rate for an isolated column, which also created a 2nd Law violation. After that, he came up with a solution that yielded an isothermal solution. Boltzmann later derived the solution separately, using what we now call statistical mechanics, so we call this the Maxwell-Boltzmann distribution. Maxwell was very clear on his stance in The Theory of Heat.

So why is it not in accord with the intuitive solution that KE (and so temperature) go down as PE goes up? As we have discussed, I believe it lies in the reduction in density with height. I have seen it phrased this way: that the important thing is that equal VOLUMES of the column have the same overall energy (KE + PE) when they have the same temperature, because the higher volume has a lower density, so even though it has a higher (KE + PE) per unit mass, the lower mass per unit volume compensates for this.

However, without cranking through the math, this is just another “handwave” argument. If you want to tackle some serious math, here’s what I think is going on, although I have never seen it stated exactly this way:

Consider a horizontal plane in such a column. For it to be in hydrostatic equilibrium, the total momentums (m*v) of the molecules crossing the plane in both directions must match.

For it to be in thermodynamic equilibrium the total kinetic energies (0.5*m*v^2) of the molecules crossing the plane in both directions must match. This is why the distribution of velocities is so important, and was to Maxwell.

I have not tried to crunch through the math to see if this idea is correct, as it is far from trivial. I may try to cut loose some time soon.

Regardless, even if there is a gravitationally induced lapse rate, it does not (as you have noted) set the level of the temperature — due to that pesky constant of integration. And it cannot provide the necessary hundreds of watts per square meter needed to make the surface energy balance even out.

Reply to  Bob Wentworth
April 13, 2021 2:12 pm

“Regarding the second question, the issues involved are quite subtle, and I can understand why there might be disagreement.” – no they are not. Thermal conduction works to equalise temperature and unless you have a flow of energy through the column greater than the thermal conduction, the temperature difference along the column will collapse.

Reply to  Mike McMillan
April 11, 2021 11:03 pm

Yes Mike, It appears that some here do not understand dimensional anlaysis (dimensionless numbers) which chemical engineers have used for over a century and the 5th postulate of (chemical) engineering thermodynamics ie the relationship between pressure, volume and temperature. Further, many do not understand the 4th postulate (ie the 2nd law of thermodynamics). Radiation absorbing gases within a path in the very short term (may be seconds) change can the rate of heat flow but not the absolute temperature of the of surfaces emitting of absorbing. I read one of Willis’s evaluation of the Z&K paper. To me it was clear he had no understanding of dimensional analysis.

Reply to  Mike McMillan
April 13, 2021 9:25 am

“The bottom line I take from N-Z is that it is the mere presence of an atmosphere that makes for warmer, not what the atmosphere is made of. Greenhouse gases can make a difference only at the margins. N-Z ignored most of what really doesn’t make much of a difference.”

Well, the “margins” causes glacial and interglacial periods.
And why we been in an ice age for 34 million years.
And we been this ice age because the entire ocean {not skin temperature of oceans]
is cold. The surface of our ocean has average temperature about 17 C, and average global land surface is about 10 C, but entire ocean is about 3.5 C.

And the 34 million years we been in the icehouse climate, is due to having a cold ocean. And this time period is called Late Cenozoic Ice Age or Antarctic Glaciation:

Mike McMillan
Reply to  gbaikie
April 13, 2021 7:48 pm

Darn, can’t argue with Wikipedia. 😉

Reply to  Mike McMillan
April 13, 2021 8:37 pm

Wiki, again:
But you got any graph of temperature for last 100 million year
And I rather they didn’t splice into present, like some of above.
Just apples to apples
Even Micheal Mann said splicing was bad. {before he went ahead and did it}
Or look at say 5 million year, for last couple million it been down treading
How about the longest ice core record.
How about NOVA:

Reply to  Mike McMillan
April 13, 2021 2:08 pm

It’s a big target and not difficult to miss.

Nick Schroeder
April 10, 2021 6:59 am

PV=nRT is a state equation and does not explain why the surface is warmer than ToA.

Q=1/R A (Tsurf – Ttoa) is a process equation used daily by HVAC engineers all over the world that does quantify that difference.

Earth Heating PPt Video 021518.jpg
Reply to  Nick Schroeder
April 10, 2021 7:19 am

The difference being that the process equation involves convection.
The thing is that a static atmosphere would, via conduction, involve an isothermal outcome with the temperature the same at the surface and top of atmosphere.
The only way to set up a thermal gradient from surface to space is to introduce large scale convective overturning of atmospheric mass.
The gradient is then caused by the conversion of KE to PE and back again as mass moves up and down within the gravity field and so expanding then contracting in the process.
Work is done in both directions and cancels out in a stable system so that energy is conserved but energy is transformed between thermal
and non thermal energy instead.
N&Z are correct in terms of their observations but didn’t appreciate the significance of the well established mechanical process that leads to the observed outcome so they proposed some ‘new’ physics.
Thus that ‘new’ physics is just as wrong as the radiative theory.
Both wrong theories can be expressed in equations that are equally wrong as the above author points out.

Reply to  Stephen Wilde
April 10, 2021 8:38 am

Nick and Stephen,
Temperature reduction with height increase is a characteristic of gases in a gravitational field (needs lots of height to become apparent). Molecules moving upward as a result of their random collisions gain potential energy and slow down, thus reducing their temperature….no different than why a cannonball fired straight up will result in its velocity reducing with altitude. For gases, a reduction in velocity is a reduction in temperature. The net answer integrated over zillions of molecular collisions isn’t any different than one gets by moving a parcel of air adiabatically by the much quicker process of convection.

Hope this explains for Nick why TOA is colder than surface, and for Stephen why a static atmosphere would not be isothermal. Good thinking to all !

Reply to  DMacKenzie
April 10, 2021 9:13 am

It isn’t the slowing down in the vertical plane that causes the observed amount of conversion of KE to PE for gases around a sphere. The amount of energy involved in the vertical plane alone is miniscule. Thus the cannonball analogy is incorrect.
It is the exponential decline in density with height due to the exponential increase in available space that allows the molecules to move further apart with height so that there is less and less thermal energy contained in any given volume as one moves linearly upward. That is what makes the temperature fall.
If one reverses the process then as one descends again the increasing amount of thermal energy in any given volume also increases and the temperature rises again.
In other words gases held in a large volume of space at height are cold but they have the potential to generate that energy as heat again as they descend and contract. Hence the term potential energy for higher locations.
At the surface KE is at its maximum and at the top of atmosphere PE is at maximum. Each molecule of an atmosphere carries the same total of KE plus PE wherever it is situated in the vertical plane.
If there were no convective overturning the atmosphere would become isothermal from conduction alone.

Reply to  Stephen Wilde
April 10, 2021 10:33 am

Sorry Stephen, your interpretation is not quite OK. Conduction is molecules bumping into each other, on average at the same elevation, and adiabatic lapse rate is the result of them being bumped up or down hill. Yes, warmer when they end up downhill of their starting reference point. That’s what “potential temperature” is about in climatology texts. This topic is improperly covered in even 3/4 of university undergrad textbooks, but should be in high school textbooks as a learning tool for the basic molecular theory of gases.
Assuming the temperature drop is the result of expansion, which offsets the temperature increase of the displaced downward parcel results in the “isothermal” answer, which isn’t correct.

Last edited 1 year ago by DMacKenzie
Reply to  DMacKenzie
April 10, 2021 11:23 am

Adiabatic changes are a consequence of expansion and contraction and not bumping up or down hill. Any other method involves diabatic energy transfers.
That is why the Gas Laws are relevant.
If the atmosphere were static with no convection up or down then energy would be transferred between molecules by conduction or radiation and all else remaining the same a static atmosphere would become isothermal over time.
In reality, a static atmosphere is impossible due to the inevitability of temperature and density variations arising in the horizontal plane when a sphere is illuminated from a point source.

Reply to  Stephen Wilde
April 10, 2021 11:41 am

Adiabatic lapse rate due to molecular motion in a gravitational field is completely derivable from gas laws and basic physics. So is the amount of cooling resulting from expansion resulting from a piston that has moved to change the volume. I’m not saying anything that Boltzmann would disagree with.

Bob Wentworth
Reply to  DMacKenzie
April 12, 2021 12:03 am

Yet, Feynman considers “molecular motion in a gravitational field” and comes to a conclusion that this does not yield an adiabatic lapse rate, but rather corresponds to an isothermal solution. (See Feynman Fig. 40–4 and associated discussion.)

Fred Souder
Reply to  Stephen Wilde
April 10, 2021 11:45 am

I set up an air track in our lab to evaluate just this phenomenon. As long as there was a small energy input (I put it at the surface), then you do indeed see a temperature gradient. I used a small energy input to simulate solar energy input. There are tiny frictional losses that “may” correspond to radiative losses. In any event, there was always a thermal gradient, and the temperature of the surface depended on how much mass of “atmosphere” was in the system. I.e., if I added a few more “molecules” of air, then let the system reach equilibrium, then the temp at the bottom was higher.

Gary Ashe
Reply to  Fred Souder
April 10, 2021 2:19 pm

Ofcourse it was warmer if you added more volume, thats compression.

To bed B
Reply to  Stephen Wilde
April 10, 2021 2:35 pm

“Adiabatic changes are a consequence of expansion and contraction ”

No. That is PV work. It is the assumption so that you don’t have to calculate PV work but just assume that gravitational potential energy gained is heat energy lost*. It’s why you get 9.8 °C per km instead of 6.4°C per km.

That is what you are taught. Thinking for yourself, a gas should show a temperature gradient even without convection. Your isothermal argument is like insisting the atmosphere should be isobaric. Radiative heat transfer is why it’s not 9.8 and you need to show it is enough to make an atmosphere isothermal if there is no convection. The above argument is like a net convection of heat downwards until equilibrium due to a temperature gradient.

*I know you also calculate PV work when it adiabatc. The point of using the label is …

Last edited 1 year ago by Robert B
To bed B
Reply to  To bed B
April 10, 2021 4:29 pm

“The above argument is like a net conduction of heat downwards”. Sorry, written in a rush on a phone. A bit hard to make a good argument in 100 words or less.

Expansion and contraction are the reason for cooling and warming, although not specifically referred to in calculation of the theoretical adiabatic lapse rate.

There is no convection of adiabatic packets of air. Heat coming into or out of the packets of air is only slow enough to observe phenomena like foehn winds.

In the absence of convection and radiative heat transfer, conduction of heat should be downwards is the argument, creating a temperature gradient. Not something that seems to have been investigated since not close to anything real. It doesn’t mean you argue that the atmosphere would be isothermal if there was no convection.

Reply to  DMacKenzie
April 11, 2021 1:27 am

They become warmer at a lower level due to compression and thus contraction.
I think there is some terminological difference between us because we both agree that the Gas Laws are in control.

Reply to  Stephen Wilde
April 11, 2021 10:54 am

The extra space at the top of the atmosphere (say 32km) is a miniscule addition compared to the surface.

Bob Wentworth
Reply to  DMacKenzie
April 11, 2021 11:51 pm

The Feynman Lecture on this topic says that the result of molecules interacting with gravitational potential is an exponential density variation with altitude, not a temperature variation with altitude. (See Feynman Fig. 40–4 and associated discussion.)

Last edited 1 year ago by Bob Wentworth
Joseph Zorzin
April 10, 2021 7:20 am

The bottom line is that “the science” is not “settled” and therefore we shouldn’t be planning to spend trillions to fix the climate.

April 10, 2021 7:32 am

What is the purpose of this post?
is it to show that the gas laws are wrong?
That there is no relationship in a gas between temperature and pressure?
That any apparent such relationship is in fact caused by greenhouse gasses?

So Boyle’s law is wrong.
Charles’law is wrong.
Gay-Lussac’s law is wrong.

Only CO2 determines gas temperature and pressure, even in atmospheres where there is no CO2 present.

Got it.

Last edited 1 year ago by Hatter Eggburn
Kevin kilty
Reply to  Hatter Eggburn
April 10, 2021 8:57 am

I agree. I can’t figure out what these accomplish.

Bob Wentworth
Reply to  Hatter Eggburn
April 10, 2021 11:24 am

You’re assuming a false linkage between the reality of the gas laws and the assertion that atmospheric pressure alone could warm planets.

The gas laws predict things like what will happen to the temperature of a gas if you change its volume or pressure. That’s a relative relationship between a start state and and end state. The relationship doesn’t say anything at all about what the absolute temperature of a gas would be, in steady state. If you drop an atmosphere into a gravity well and the gas compresses, the change in the state of the gas would initially lead to some heating. But, that heating would be a one-time thing, not anything that affects the ultimate steady-state temperature.

Similarly, an adiabatic lapse rate sets a rate at which temperature changes with altitude in an atmosphere, but says nothing about absolute temperature.

The logic involved reminds me a bit of the logic of some meditators who assert that that a video of people jumping offers evidence of a human ability to levitate. Relative, temporary effects cannot be extrapolated to absolute, ongoing effects.

Reply to  Bob Wentworth
April 11, 2021 3:20 am

and the assertion that atmospheric pressure alone could warm planets.

Pressure alone does warm.
What else ignites stars?

That pressure comes from gravity.
The existence of both pressure and gravity are denied in CAGW orthodoxy.

It is absurd nonsense.

I only have to see just one star to understand this.

Bob Wentworth
Reply to  Hatter Eggburn
April 11, 2021 1:25 pm

You seem to be failing to distinguish between one-time events and steady-state. As matter is gravitationally drawn together to form a star, there is a one-time heating event, as gravitational potential energy is converted into kinetic energy and heat.

That’s not a steady-state process. If it weren’t for fusion being ignited inside a star, the initial heat from gravitational collapse would dissipate over time. Eventually, the un-ignited star would reach thermal equilibrium with the 3 K microwave background radiation.

Pressure changes can produce transient heating. Pressure alone does not produce ongoing heating.

Last edited 1 year ago by Bob Wentworth
Jim Whelan
Reply to  Bob Wentworth
April 12, 2021 2:48 am

You are right but with a planet the steady state involves a constant input of energy from the sun. That warms the surface and the atmosphere to some temperature. Convection then churns the atmosphere and the pressure differential of the atmosphere means that the upper atmosphere is cooler than the lower atmosphere. Energy is radiated into space from all parts of that atmosphere and the temperature differential means that the surface will be warmer than the “black body” temperature.

Last edited 1 year ago by Jim Whelan
Bob Wentworth
Reply to  Jim Whelan
April 16, 2021 9:35 am

As I’m tracking things, the reason we are talking about pressure and lapse rates is because some people believe these are an alternative explanation for planetary warming–an alternative to longwave-absorbing gases (i.e., greenhouse gases) being important.

So, to me, when a statement says “when you’ve got an adiabatic lapse rate AND longwave-absorbing-and-radiating gases, you get a warmer planet” that statement doesn’t appear to shed much light on the point that is controversial.

“Energy is radiated into space from all parts of that atmosphere” means to me that you are assuming the presence of significant quantities of longwave-absorbing gases. If so, that muddles the issues together, and doesn’t clarify if a lapse rate could warm a planet in the absence of longwave-absorbing gases.

In the situation you’re talking about, if one could somehow prevent convection (e.g., via hypothetical impenetrable but radiation-transparent horizontal membranes in the atmosphere), then there would still be a temperature differential, with higher parts of the atmosphere being colder and lower parts being warmer, just from radiative effects associated with those longwave-absorbing gases. The planet surface would still get warmer, despite the absence of convection and any convection-induced lapse rate.

So, the argument that the planet would be warmer in the scenario where convection is allowed does not establish that the convection is causing the warming of the planetary surface. In contrast, in every scenario that I can think of, having longwave-absorbing gases present does cause warming of the surface.

Brian R Catt
Reply to  Bob Wentworth
April 11, 2021 8:18 am

This is plain wrong. The temperature of an ideal gas will always try to be that determined by PV=nRT. It won’t stop obeying the law after a bit.

Which means to me that gravity, hence the space time distortion that creates that acceleration in matter, does work on things, like atmospheres and stars, which starts a whole other thought process in other areas of physics.

Bob Wentworth
Reply to  Brian R Catt
April 11, 2021 1:33 pm

Yes, an ideal gas will always obey PV=nRT. But, that doesn’t in any way fix temperature as a function of pressure! Gas density (the number of molecules relative to volume) can change to accommodate any pairing of pressure and temperature.

Absolutely any temperature profile in the atmosphere would be consistent with the ideal gas law. And, absolutely any surface temperature would be consistent with the ideal gas law.

To figure out temperatures, one needs to consider the dynamics of what is happening and look to other additional laws of physics.

Last edited 1 year ago by Bob Wentworth
Jim Whelan
Reply to  Bob Wentworth
April 12, 2021 2:59 am

Hence “adiabatic”. With heat energy constant, an increase in pressure as a volume of the atmosphere descends causes a decrease in volume and an increase in temperature. But, of course, the energy that causes atmospheric movement doesn’t come from gravity but from the sun. Gravity and the weight of the atmoshere does cause the pressure differential.

Stephen Richards
Reply to  Hatter Eggburn
April 10, 2021 11:26 am

You forgot Dalton’s law. :))

Robert W Turner
Reply to  Stephen Richards
April 10, 2021 5:24 pm

And Kinetic Theory and Quantum Theory of Radiation.

Stephen Lindsay-Yule
Reply to  Hatter Eggburn
April 10, 2021 2:12 pm

That’s funny Hatter, 430 (quadrillion) joules in the atmosphere while only 173 trillion watts strikes the earth. 340 per square meter. And you sarcastically say CO2 does determines gas temperature. A mole of air 28.96 has 0.287 Joules per gram 8.314 (mole constant). Multiple by pressure for whole earth and you have 430 (quadrillion) joules. Also 170.36^4 then divide by 1000 and pressure. You have mole constant. It seems models has CO2 as another sun. Complete fiction just like you humor. .

Bob Wentworth
Reply to  Stephen Lindsay-Yule
April 11, 2021 1:42 pm

You’re talking about the seeming “magic” of energy recirculation. Yes, it’s counter-intuitive, particularly if one is unwilling to consider the math. But it’s physics that is very real and which applies in many different situations, not just in climate science. It can be observed in situations a simple as a room with walls that reflect sound to create strong reverberations. (For an unpacking of this topic, see Section 7.)

April 10, 2021 7:32 am

I question any statistical curve fitting model that includes more than four unrelated parameters other than time.Even more so when only two or three parameters can accout for most of the variability. You can get a near perfect (but meaningless) fit by including too many perameters.
The IPPC’s modeling is an example of averaging a bunch of meaningless models to get a meaningless average.

Trying to Play Nice
Reply to  Fred Haynie
April 10, 2021 4:04 pm

You forgot Mann’s Law: Two wrongs don’t make a right, but averaging a bunch of incorrect models always gives the correct answer.

Reply to  Trying to Play Nice
April 10, 2021 11:46 pm

Just about the most succinct comment you have EVER contributed, thanks for the smile.

Joe Born
April 10, 2021 7:45 am

Lubos Motl cleaned up Tony Heller’s view on the subject to result in a concise summary. Basically, surface temperature would depend only on insolation and not atmospheric mass in the absence of greenhouse gases, but, beyond some minimum level of greenhouse gases and atmospheric mass, it’s mostly atmospheric mass that determines surface temperature.

Richard M
Reply to  Joe Born
April 10, 2021 8:46 am

You do need “enough” GHGs to allow the effective radiation level to be raised above the surface. This allows the lapse rate to start at a higher temperature. The amount of warming then depends only on the solar energy input (radiation minus albedo) and the atmospheric mass (which defines the pressure gradient).

Without any GHGs the effective radiation level can only be the surface. This is the part N&Z are missing in their claims.

So, it turns out the temperature is based on a combination of GHGs and atmospheric mass. However, once you have enough GHGs to absorb all the surface radiation, adding more GHGs have no effect. This is because GHGs are also emitters. Once all the energy is absorbed a new absorber is also a new emitter of the same quantity of energy.

On Earth all of the surface radiation is absorbed very near the surface except for what is called the radiation window. This is the only place where additional energy is available to enhance the surface temperature. It turns out CO2 will expand into this window due to the physics of pressure broadening as CO2 levels increase.

Does anyone else not find this interesting? The only gas that can add more energy just happens to be the same gas that can add to the quantity of living organisms. This same gas also just happens to be of such a weak energy level that it also enhances evaporation which will enhance the convective water cycle.

It is almost as if these processes were designed so that as CO2 increases all the requirements for growing the biosphere also increases. And, as the biosphere increases it uses up the extra energy provided by the very nature of life itself.

I think this is the part climate science has completely missed. The extra energy from increases in CO2 simply goes into the enhanced biosphere. Nothing is left to provide any significant warming.

Reply to  Richard M
April 10, 2021 9:22 am

Adding more GHGs reduces the speed of convective overturning by trying to alter the lapse rate slope. They always fail because such overturning will always adjust to enable enough thermal energy to be returned to the surface to keep the surface at a high enough temperature to both maintain continuing overturning AND match energy in from space with energy out to space.
Adjustments to convective overturning will always neutralise radiative imbalances. Failure would result in a loss of the atmosphere because hydrostatic equilibrium would be lost whereby the upward pressure gradient force would no longer balance the downward force of gravity.

Richard M
Reply to  Stephen Wilde
April 10, 2021 11:17 am

Stephen, don’t see it, sorry. GHGs slow the movement of energy from the surface to space. That delay provides energy used to add warmth to the atmosphere. The lapse rate is a function of gravity and has little to do with convection. Convection is a net cooling process where energy is removed from the surface and taken higher in the atmosphere. It does not heat the surface.

The higher heating of the lower atmosphere is due to the lapse rate, but the energy provided is by slowing down outgoing radiation. This takes GHGs. Without them the surface energy goes straight to space except for some conduction which requires the atmosphere to be cooler than the surface.

Last edited 1 year ago by Richard M
Reply to  Richard M
April 10, 2021 1:20 pm

“GHGs slow the movement of energy from the surface to space.”

H2O….. yes..because of specific energy, latent heat and changes of state

CO2….. NO !! If anything it speeds up the rate of convection while acting as a radiative pathway.

Robert W Turner
Reply to  Richard M
April 10, 2021 5:29 pm

Einstein proved this silly idea wrong once and for all in 1917.

It wasn’t picked up again until generation LSD.

Philip Mulholland
Reply to  Robert W Turner
April 11, 2021 1:12 am

I love the way he writes a paper without a single reference.

Bob Wentworth
Reply to  Robert W Turner
April 11, 2021 7:19 pm

What “silly idea” do you think Einstein proved wrong? There is nothing in Einstein’s model that contradicts greenhouse gas warming models.

Richard M spoke informally in some ways, and perhaps you’re taking issue with his informal way of describing something. It’s not clear what.

The most easily misunderstood item in Richard’s description related to the idea of “slowing down outgoing radiation.” Technically, greenhouse gas absorption and re-radiation effectively redirects radiation, so that some of the radiation which was initially directed towards space gets redirected in other directions. This is entirely consistent with Einstein’s radiation model. The net effect is a reduced flow of radiative energy between the Earth’s surface and space.

Richard M
Reply to  Bob Wentworth
April 14, 2021 2:39 pm

Bob is correct. The energy is physically redirected. It just turns out when you average out all those redirections you end up with an accelerating flux from the surface to space. That’s why I say GHGs “slow” the radiation. On average, it still moves relentlessly towards space.

Once you realize the way it works “on average”, you can also see the greenhouse effect requires no downwelling IR. The concept of downwelling IR warming the planet is a fiction. The fact it is measured as 3.7 w/m2 is meaningless nonsense. That in itself has no warming ability since we already know it all ends up in space.

The only important question is how much of the slowdown in the outward flux occurs as a result of increasing GHGs? Will more GHGs slow this flow? As I stated earlier the answer for our atmosphere is yes only if you start slowing down additional amounts of energy that are not already absorbed.

Bob Wentworth
Reply to  Richard M
April 16, 2021 9:59 am

The energy is physically redirected. It just turns out when you average out all those redirections you end up with an accelerating flux from the surface to space.

Huh? I can’t imagine what you could mean by this that would actually be true.

On average, the net effect of those redirections is more radiant energy being directed towards the surface than towards space.

This happens because upper layers of the atmosphere are colder than lower layers. Upper layers emit relatively little radiation to space, while the warmer lower layers emit a lot of radiation to the surface.

Once you realize the way it works “on average”, you can also see the greenhouse effect requires no downwelling IR.

No, I’m afraid I can’t see that. Of course, I don’t agree with you about how things work “on average.” I’d need you to unpack what you mean by that, for it to make any sense at all.

The concept of downwelling IR warming the planet is a fiction. The fact it is measured as 3.7 w/m2 is meaningless nonsense.

Are you saying you don’t believe “downwelling IR” exists? Or that you don’t believe it warms the planetary surface?

If you don’t believe it exists, then how do you explain the measurements?

If you believe that it exists but doesn’t warm the planetary surface, how do you explain energy absorbed by the surface not warming that surface?

That in itself has no warming ability since we already know it all ends up in space.

That’s like saying “We all end up dead, so what happens before we die doesn’t matter.”

Consider a house with and without insulation. In both cases, all the heat generated by a furnace ends up outside. But, it still matters whether or not the house has insulation.

“It all ends up in space” is a specious argument.

The only important question is how much of the slowdown in the outward flux occurs as a result of increasing GHGs? Will more GHGs slow this flow? As I stated earlier the answer for our atmosphere is yes only if you start slowing down additional amounts of energy that are not already absorbed.

It’s not clear what you mean by “slowing down additional amounts of energy that are not already absorbed.”

I’m also worried that the metaphor of “slowing down” energy is vague enough that it may be leading you to faulty reasoning.

Gary Ashe
Reply to  Richard M
April 10, 2021 2:27 pm

You’ve nailed it richard in one short paragraph, the heat energy is converted to calorific and then mechanical energy in an expanding biosphere created by the same molecule..

Last edited 1 year ago by Gary Ashe
Reply to  Richard M
April 10, 2021 5:50 pm


I agree with you that both convective overturning and a radiative absorber/emitter component in the atmosphere are essential elements for creating the temperature gradient in planetary atmospheres. Without both there will be no temperature gradient. I also think that dust and aerosol particles and clouds and latent heat effects contribute to the process.

I prefer to think of atmospheric radiative absorber/emitter effects as a resistance to radiative heat transfer rather than a slowing effect. This resistance is analogous to thermal conductivity (or its inverse resistivity) in solids and liquids in that it enables the existence of temperature gradients in a radiative heat transfer environment.

Peta of Newark
April 10, 2021 7:47 am

I promised my spreadsheet ‘formula’ recently.
lets put it here

OK. Consider;
Spherical Earth
Standing with its axis perpendicular, as it is ‘on average’
Albedo. In 10 equal ‘parts’…
3 parts that of the Moon (0.1) and 7 parts that of liquid water (0.0)
Combined/Average Albedo = 0.03

Consider 1 degree latitude to be 111 kilometres
Consider Earth to be 40,000 km circumference

Emissivity. Give 10 parts again,
7 out of 10 are that of water (0.99)
3 out of 10 are ‘same as the dirt’ or 0.9
Combined/Average Emissivity = 0.93

No atmosphere

Incoming solar power = 1372 Watts per square metre.
From here

The sums:
Put yourself on the Equator with a Solar Power Meter
You will see the sun rising and setting and your power meter will see a Sine-Wave.
The actual ‘average power’ will be the Root Mean Square of the Peak Power, as seen at Solar Noon.
i.e.1372 divided by square-root of 2

But half the time is night, so actual average power will be half of that.
I get 484.4 Watts per sqm

Now multiply that by Albedo, strictly (1 minus albedo) so…
Average power absorbed at Equator is 469.8 Watts per sqm

Hope you’ve got that so we now move (lets say) North by (lets say) 5 degrees
It don’t matter, just saves vast pages full of numbers when you build the

At 5 degs latitude, Peak Solar Power will be that of the Equator multiplied
by Cosine (5 degs)
Calculate an average there.
Move 5degs further, multiply Peak Power by Cosine 10degs and calculate

Carry on up as far as 85 degrees North

For each strip (5 degrees wide) use Stefan’s Formula to get a temperature
Make sure to use the emissivity figure

Ah now you all scream, the Earth is spinning. That will wreck your
Now we all need to go and look at the thermometer data-loggers we’ve put outside,
especially the one we buried under some dirt.

Look at its graph of daily temperature and it patently does not ‘see’ the sun.
From the data-log of a buried thermometer, night and day are totally
12″ or thereabouts of dirt perfectly averages the sun.
If earth were spinning more slowly, night and day might be visible from underground.
But its not. Earth spins fast enough to average the solar power as seen by its surface.

Now then, for each strip, calculate its area.
Thus at Equator we get 5 times 111 times 40000 equals 22.2 million square
Double that because we also have a Southern Hemisphere
Remember another cosine function.
The figure of 111 stays the same but the circumference (40,000) goes down by Cos(latitude)

Radians and degrees are a total pain
To turn degrees into the default Excel radian usage, divide degrees by 57.27

Do that for all the latitude strips
Sum them. And check.
You should get circa 500 million square kilometres

For each strip, multiply its area by the temperature you calculated for that
Do all the strips and sum them

Then, this should blow your mind as a figure very close to one we all
Divide the (Temp-times-Area) sum by the (Total Area) sum
Whaddya get?

Earth doesn’t need an atmosphere to be the temperature it is.
Thus, it doesn’t need a Green House Effect or Green House Gases

While looking at your crop of numbers, see that the Equator strip is about
what is The All Year Round Annual Average for a Rainforest.

See also the Polar temp, about minus 100 Celsius – don’t we recall something like
that number for the Antarctic recently (as an all time record yes, could it
ever go any lower?

See also where the temp goes from positive to negative
A latitude of circa Central France. Where the grapes are freezing right
now. ah diddums.

It was The Grapes, consumption thereof and similar, that played a very large part in creating this colossal train-wreck.

As I have learned from numerous online courses, that is the closest the ice
ever gets to the Equator during Ice Ages. Certainly Southern France or about 40 degrees latitude

Interesting huh
So what did I get wrong?
This is surely a proper (re) working of the very basis of the Green House
Statement which states that Earth is 33 Celsius warmer than it should be.

No. it is exactly at the temperature it should be, by their very own
authority (Jozef Sfefan) and their very own calculations.
When done properly on a spherical spinning globe.

A screenshot of spreadsheet is at Dropbox

Last edited 1 year ago by Peta of Newark
Peta of Newark
Reply to  Peta of Newark
April 10, 2021 8:01 am

Quite sensitive to solar power eh
Maybe The Sun Did Do It After All

Also Albedo
That is my Pet Rave = the businesses of Tillage and de-forestation
also UHI of course.

That figure for power in the UV surprised me, somehow I never thought it would be that high.
Learn something new innit………

Why all this matters is..
How did Stefan, when trying to calculate the power and temperature of El Sol (using ‘Laminae‘), get those things up to a temp of nearly 2,000 – just by exposing them to the sun?
Also, why does a UK renewable energy forum have a section on Solar Cooking..
Where they use one/more of the ‘evacuated tubes’, normally for Solar Hot Water Heaters,for running a barbecue.
Never mind frying eggs on the pavement, the technology is here to grill burgers and steaks.
Just using the sun.

The atmosphere cools the Earth.
It does not warm it

The GHGE is Total Garbage and Utter Nonsense

Last edited 1 year ago by Peta of Newark
Reply to  Peta of Newark
April 10, 2021 10:41 am

The deep subsurface temperature is the long term average of daytime heating and nighttime cooling. Tha fact that temperatures are constant if you go deep enough doesn’t mean that there’s no nightime cooling, there obviously is and the fact that the earth rotates does cause the average amount of solar heating on any given spot to be less, duh. How many times have we all awoken on a clear morning to find the ground covered with frost? Where in the world do you think frost comes from? The deep subsurface’s temperature is what it is because the heat diffusion rate through solid earth is slow and as you get to deeper depths the temperature from daytime heating and nighttime cooling approaches the yearly average. That’s why permafrost in the polar regions a couple of meters down can survive a whole summer of surface temperatures well above freezing (that’s why they call it permafrost). In addition, you obviously don’t know that the moon is much darker than terrestrial land – the lunar marias are as dark as coal. You probably made other fundamental errors but I stopped reading after the first two stupid mistakes. Don’t get me wrong as I’m the first to say that climate crisis is a scam, but for real reasons. Don’t bother logging on under a different name to defend your stupidity- we’re on to you.

Gary Ashe
Reply to  Meab
April 10, 2021 2:40 pm

You are not onto anything, you are just another worthless luke warmer, another worthless gatekeeper of your worthless RGHE fantasy, pretending to be sceptic you are just astroturfing.

And if anyone is likely to have several alias’s it is you.

Last edited 1 year ago by Gary Ashe
Rich Davis
Reply to  Gary Ashe
April 10, 2021 4:14 pm

Referring to other skeptics as worthless lukewarmer gatekeeper bastards is definitely not helping you win any arguments Gary. Makes you look like a crank who can’t make the case for your claims.

Philip Mulholland
Reply to  Peta of Newark
April 10, 2021 8:43 am


Philip Mulholland
Reply to  Peta of Newark
April 10, 2021 8:56 am

If you are looking for subsurface temperature values for the Antarctic Icecap search for Dome Argus.
Here are some example data from 2008

Philip Mulholland
Reply to  Philip Mulholland
April 10, 2021 12:12 pm

A while we are on the subject of the comparison of planetary temperatures, here is something curious about the atmosphere of Mars.

Possibly the one thing that all can agree upon is that due to its low surface atmospheric pressure Mars does not have a radiative greenhouse effect, and the standard vacuum planet equation when applied to Mars effectively computes the annual average surface temperature of 210 Kelvin.

Now the average surface pressure for Mars is 610 Pascal (6.1 mbar) and so the question is if we drilled an open hole on the surface of Mars, and assuming that there is no geothermal gradient (I know it’s a big ask but just tag along and see where we get to), at what depth would the air pressure in the open hole be one Earth atmosphere?

Using Mars atmospheric pressure data and applying a curve fitting pressure equation (tut tut) using depth in Km to give the pressure in hPa
P subsurface = (4.5024*EXP(1)^-(0.08*D1))+(0.0057*D1^2- 0.1817*D1 + 1.4803)
Depth to reach 1 atmosphere is -67.2 Km

Now here is the fun bit. Using an environmental lapse rate for Mars of 1.11 K/Km what will the temperature be at a depth of -67.2 Km?

Temperature at -67.2 Km is 210 + 1.11 * 67.2 = 284.6 Kelvin or 11.4 Celsius

Two main caveats:
1. The exponential pressure equation is corrected by the extrapolation down of an unconstrained 2nd order polynomial difference equation.
2. The pressure calculation assumes a constant gravity and so ignores Newton’s Law of Gravity Shells.

Good enough for government work. YMMV

Tim Gorman
April 10, 2021 7:54 am

The thermodynamic system known as the Earth is a conglomeration of multiple components. All those components sum to an overall system response. If you can accurately predict the overall system response then it is really a non sequitur to say that the prediction doesn’t accurately represent all the physics of the system.

It’s like saying you can’t predict the acceleration of a car based on observation without knowing all the physics details about the engine, the drive train, the mass of the car, and the aerodynamics of the car.

It’s what’s wrong with the climate models. They try to predict the overall system response by describing all the multiple components – and they fail to meet their goal of accurate prediction of the overall system response. Mostly because of the unknown components they fail to include as well as the inaccurate representation of the components they think they know.They then turn around and ignore all the uncertainties with what they are doing by claiming all the uncertainties will cancel out.

The N&Z model provides a good baseline matching observations. If there is something they are missing then modify the model in while maintaining the accurate overall system response.

It’s hard to argue with success. If there are other models which provide the same success then work toward modifying them while retaining the success. it’s no different than analyzing any black box. You can model the output and then start taking the box apart to find the components creating that output. The climate models try to build a black box first without worrying about if the output matches reality.

Bob Wentworth
Reply to  Tim Gorman
April 10, 2021 10:50 am

The approach you describe might be an interesting one if we had the data of thousands of planets to work with. But, we don’t. Curve-fitting with a number of tunable parameters comparable to the number of data points available tends to be meaningless, and that’s what N&Z’s model demonstrates. It may be a “good fit”, but it’s a trivial fit. It’s not much better than simply copying the observations to another column and then saying “Here are my predictions!” I don’t think it’s defensible as a “good baseline” to use for building a deeper understanding.

John Shotsky
April 10, 2021 7:58 am

For another alternative explanation of how the atmospheric temperature remains as it is, consider the following…
Everyone has seen a hunk of meat on an open fire on a rotisserie. Everyone knows that the surface temperature of the meat is ‘normal’ at the time the meat is placed on the rotisserie. As time goes on, the whole of the meat warms, from the surface toward the center. If you raise the spit further from the fire, it takes longer to ‘cook’ the meat. At some point, it won’t cook, it will simply come to a static temperature, above the ambient temperature. If the spit is tilted, the heat will be unevenly distributed across the meat.
Consider the sun as the fire. Consider the earth as the meat. Consider that as the earth changes its tilt, is is as if changing one side of the spit, so that one end is closer to the fire (sun).
The earth spins once per day. Where the sun is present, there is heating. As a given point spins away from the sun, it begins to cool. It continues to cool until it spins back toward the sun. When the sun is shining, the temperature can rise rapidly. When turned away from the sun, radiative cooling occurs, just as with the meat. That continues at a rate dependent on the temperature of the ‘point’ at the time, and the emissivity of that point. But cooling does not happen as rapidly as heating can occur. The atmosphere closest to the surface is heated the most, and convection occurs. The rising air warms the whole atmosphere. Rising air causes sinking air to replace it. That air is then heated by the surface and the cycle is established. As long as the sun is present, the cycle continues, ignoring for the moment intervening clouds, which could be thought of as the smoke from the fire.
As seasons occur, it has the effect of making the earth closer to, or further from the sun (fire).
You don’t NEED a more complicated mechanism to explain the temperature of the earth. We all know the sun is our heat source, and the received heat is ALL radiated away, every day. If it weren’t, earth’s temperature would not be stable. We can SEE this, every day.
Consider what earth’s temperatures would look like if the earth rotated only once in 48 hours…it would get FAR hotter in the daytime, and FAR cooler in the nighttime.
The earth has a remarkably stable temperature history. How has it never run away, regardless of the gas makeup of the atmosphere? Co2 has been hundreds of times higher, before oxygen began to be created. How did that not burn earth to a cinder? Because CO2 has nothing to do with the earth’s temperature, any more than nitrogen does.
We need to learn to stand back and look at the whole process, not simply deduce that a trace gas is responsible for earth’s climate and then spend trillions of dollars trying to ‘control’ that trace gas. SMH…

David Blenkinsop
April 10, 2021 8:19 am

This ‘N and Z’ claim about detailed atmospheric composition having no importance has been debunked here on WUWT before. I get a bit concerned however, that maybe a powerful partial truth in the most basic idea here might be lost. What if there are lots of practical situations where planetary albedo, atmospheric mass, spin rate of the planet, plus any other relatively gross factors, actually determine most of what you need to know about temperature? As long as you can assume an atmosphere that’s IR absorptive enough to plausibly drive convection, maybe that’s all it takes to have a PV=nRT based lapse rate in temperature, wth net surface warming, etc.

As some indication of what I’m talking about here, instead of just debunking this one questionable paper, try looking at*all* the publishied papers that relate to estimating the temperatures of any exoplanets that have been discovered, or that may be discovered. How many planetary scientists are concerned in the least with greenhouse gas composition versus those who just use things like Bond albedo to estimate what a planet’s temperature ought to be?

Reply to  David Blenkinsop
April 10, 2021 10:01 am

— I get a bit concerned however, that maybe a powerful partial truth in the most basic idea here might be lost. What if there are lots of practical situations where planetary albedo, atmospheric mass, spin rate of the planet, plus any other relatively gross factors, actually determine most of what you need to know about temperature?–

I would say it was known before the ‘N and Z’ claim.
As in what would the temperature be if mediterranean sea dried up:
{which it did}
In the empty Mediterranean Basin, the summertime temperatures would probably have been extremely high. Using the dry adiabatic lapse rate of around 10 °C (18 °F) per kilometer, the maximum possible temperature of an area 4 km (2.5 mi) below sea level would be about 40 °C (72 °F) warmer than it would be at sea level. Under this extreme assumption, maxima would be near 80 °C (176 °F) at the lowest points of the dry abyssal plain, permitting no permanent life but extremophiles.”

Reply to  gbaikie
April 10, 2021 11:19 am

So, also the empty Mediterranean Basin is a “warming effect” {using lingo of cargo cult “greenhouse effect theory”}. It increases the average global land temperature, due it’s extremely high surface air temperature over land during daytime, and because of extremely high night temperature. And Mediterranean basin is pretty big chunk land area. Let’s see area of Mediterranean ocean is 2,500,000 square km, well actually that is not very big actually, a bit more than 1% of total global land area, but it would be definitely the hottest 1% of land area.
Currently the average temperature of global land area is about 10 C, and add to it 1% which averages around +40 C. So I guess only it’s some fraction of degree added to the global land average temperature. Oh, though when this occurred it was in glaciation period, so might add as much as 1 degree to the far lower and colder global land average.
But this 1 degree added to average does not make other land warmer.
So might have average without it being say, 2 C, but warmer and isolated Mediterranean Basin, could allow to one say global average land was 3 C, and having an illusion of warmer global average land area of +1.
It’s same type illusion with 15 C average global air temperature.
The ocean surface average is 17 C, and no one lives on ocean, and everyone lives on land and on the land average is about 10 C. And we have largest countries in world {Canada and Russia] well below a yearly average of 0 C- and somehow global warming is considered a problem. And, there could currently be lots Canadians and Russians worried their frozen wastelands could warm up.

Come to think about, living slightly below the present Mediterranean Basin coastline, would be sort like living on tropical island paradise with the grand view of the dead basin floor.

David Blenkinsop
Reply to  gbaikie
April 10, 2021 12:12 pm

Interesting link! It makes you wonder, doesn’t it, what conditions over most of the Earth’s surface would have applied if the whole atmosphere were that much heavier, so 10 degrees C hotter would apply everywhere?

Reply to  David Blenkinsop
April 10, 2021 2:01 pm

Well, our world has 10 tons of air per square meter, and you talking about making it 12 to 13 tons per square meter.
Or you talking only increasing atmosphere by about 25%.
I usually think of 1/2 or doubling it, which have uncertain results.
But I think 25% would definitely increase global air temperature.
But start with tropical ocean, average of about 26 C, would it, could it
increase to 36 C?
It couldn’t due to water vapor pressure relate to surface temperature of water, but few degrees might be possible.
And it seems biggest effect would be to make a more powerful tropical ocean heat engine in terms it’s effect on global air temperature.
Also you allowing more atmosphere to be warmed, which generally means less difference between day and night air temperature.
Basically you going to get a more uniform temperature.
But a more uniform global temperature is what global warming is.
Global warming causes less hottest day and less coldest days.
I don’t think you could day high air temperature of anything warmer than 50 C
And highest was ever recorded was 56.7 C
But terms global average surface air temperature it could about 25 C rather than about 15 C.

Reply to  gbaikie
April 11, 2021 11:25 am

More about this. Trying out a 1.1 atm Earth:

1 atm: “At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg”
sea level: 15 C density: 1.225 kg
-1000 : 21.50 C at density of 1.347 kg per cubic meter

Roughly: 1.225 + 1.347 = 1.286 kg per cubic meter average 
and 1 meter square by 1000 meter column: 1286 kg
And 1 km square is 1286 million kg of air
Total surface of Earth: 510067420 square km {wiki-Earth}
510 million square km times 1286 million kg = 
510 * 1286 = 655,860 or 6.5586 x 10^5 x 10^12 = 6.5586 x 10^17 kg
Or 6.5586 x 10^14 tonne or 655.86 trillion tonne
{Hmm, less than I thought it would be, 510,000,000 x 1,286,000,000 = 655,860,000,000,000,000 kg
or 6.5586e+17 kg or 6.5586e+14 tonne. Hmm.}
So amount of CO2 in present atmosphere, …oh right, it’s hundreds of billion of tonne, ie, “During 1987–2014 we 
emitted 758 billion tons of CO2.” -and the total in atmosphere is few trillion tons. 
And, of course, converting O2 into CO2 is not added to the atmosphere.
But if added 655.86 *billion* tons of CO2 {mined it from someplace] it would add 1 meter height to our atmosphere
and…add about 120 ppm to CO2 global , see: https://tinyurl.com/48bhwwn7
Anyhow so going add 655.86 trillion tonne of the same composition of earth air, to Earth- 1 atm going to 1.1 atm.
In simple terms that should add 6.5 C to 15 C = 21.5 C, but don’t think adding height 1 km to atmosphere would give that simple result.
But good news is adding .1 atm has less complicating factors involved as compared to adding .25 atm.
And roughly what happens is you get less warming {of the 6.5 C} in tropics and more of increase average temperature in polar region- or in terms increasing average temperature, you mostly are getting polar amplification. 
But also Earth should reflect a bit more sunlight and globally less sunlight will reach the earth surface.
Or Earth is lousy place to harvest solar energy, and it would get a bit worse.
And adding more up .25 atm, makes Earth surface
even dimmer, and makes Earth have an even more uniform global temperature. But it some point of continuing to add to the atmosphere, 
it’s going to make Earth have lower average temperature.
And if added until Earth average surface temperature returns to 15 C, then Earth would feel {and be} much colder than it is now.
In terms of analogy it would similar being in 15 C water- and 15 C {59 F} water is cold water {for a human}. Though having cities in sky should be easier.
{and part of more uniform temperature is not having as much difference between ocean and land average temperature, and it’s diminishing effects of high mountain ranges- or comparatively, land gets flatter/more uniform in terms of moving air masses, or weather effects.}
{I got a bit over excited with idea 1.25 Atm, as it seemed much easier than wondering about 1/2 atm or 2 atm or more worlds. But 1.1 atm is better though there so many factors- and it’s just a rough idea. ie, Cloud levels and how much of them??}
Not really interested or do climate, but I think modeling 1.1 Atm world could be useful. As I think modeling world entirely covered ocean would be useful.

Bob Wentworth
Reply to  gbaikie
April 10, 2021 6:07 pm

I’m curious what you think this example demonstrates? Nobody that I know of is arguing against the existence of a lapse rate.

In your example, if the Earth’s surface overall warmed or cooled by a few degrees, the empty Mediterranean would likely also warm or cool by a few degrees.

This lapse rate influences the relative temperatures of parts of the world that are at different elevations, as your example of an empty Mediterranean illustrates.

But, the lapse rate does not have much relevance to determining the absolute temperature of the Earth’s surface.

It is faulty reasoning to infer from a relationship between relative pressure and relative temperature, that there is also a fixed relationship between absolute pressure and absolute temperature. A gas at a given pressure can be at any temperature. In general, these are independent variables, except under certain specific circumstances.

Reply to  Bob Wentworth
April 10, 2021 9:27 pm

Bob Wentworth

–Reply to 
 April 10, 2021 6:07 pm
I’m curious what you think this example demonstrates? Nobody that I know of is arguing against the existence of a lapse rate.–

Right, and that what I said- it’s common knowledge.
Or if dig a very deep hole, it will have warmer air temperature at bottom of hole.
You can have both the geothermal gradient and lapse, but with the large dried up ocean basin, it’s just all due to the lapse rate.
As article indicate it needs warmer air surrounding it- it is the air temperature surrounding ocean basin, in which the lapse rate is based upon. And even in a glaciation period it can get pretty warm at this latitude. And with all that air mass of the basin, it will remain warmer at night.

Bob Wentworth
Reply to  gbaikie
April 11, 2021 1:50 pm

Again, so what?

Yes, there is a lapse rate. Yes, it results in air being warmer at lower altitudes. All agreed.

You seem to be repeating this information as if there is some unspoken implication.

Are you believing that, because there is a lapse rate, this makes it plausible that atmospheric pressure alone is able to warm a planetary surface beyond the temperature it would have with no atmosphere?

If so, that’s where there is a disagreement, and that’s what we could be usefully talking about. Simply repeatedly offering examples of the lapse rate existing doesn’t advance the conversation.

Reply to  Bob Wentworth
April 11, 2021 3:20 pm

“Are you believing that, because there is a lapse rate, this makes it plausible that atmospheric pressure alone is able to warm a planetary surface beyond the temperature it would have with no atmosphere?”
I think having a ocean make Planet Earth have higher average temperature. And that has little to do pressure.
So I would say that is big picture. Or with Earth, atmosphere is secondary aspect in terms it’s average temperature.
But I think Earth’s atmosphere is greenhouse effect, a greenhouse as analogy. But huge real greenhouse doesn’t get very warm, whereas car with windows rolled up can can quite hot. But huge real greenhouse could retain more heat, and if put lake into it, it will retain even more heat.
Or put huge real greenhouse with lake in it on Mars, and it would keep warm, a lot warmer than -50 C – and without the lake, not as warm. And that would have pretty low air pressure- say, 2 psi. And structurally as high 2 psi is a bit of challenge- would need lots structural material. Or one could put same thing on Moon.
But anyhow, in terms of troposphere, the average velocity of N2 molecule are going around same velocity. And what make difference in measured air temperature is related to density of air- or more molecules in cubic meter means more mass times around 500 m/s squared. So got more to due air density rather than pressure, but lower elevation air has more pressure and density- though warmer the air temperature has less density [but same pressure}- but lower elevation air has have lower density. So as day warms, low elevation air density lessens but the air density above it likewise lessens as it warms. And as day cools, the air densities increases.

Jim Whelan
Reply to  Bob Wentworth
April 12, 2021 3:08 am

If air is warmer at low altitudes then there is no question tha the surface WILL be warmer than if there were no atmosphere for the simple reason that radiative cooling will take place at all levels of the atmosphere. The questions isn’t WHETHER the surface will be warmer. the question is how much?

Reply to  Jim Whelan
April 12, 2021 12:06 pm

–If air is warmer at low altitudes then there is no question that the surface WILL be warmer than if there were no atmosphere for the simple reason that radiative cooling will take place at all levels of the atmosphere.–

If air is warmer at low altitudes [[ *low* being say, about 3000 meter elevation?]] then there is no question that the surface WILL be warmer [[*surface* being surface air- couple meter above ground- or the ground or water surface]] than if there were no atmosphere [[this seems suggest *surface* –above– is land/ground surface.]]

When sun is near zenith and land surface is dry, it will be about 60 to 70 C if surface air is say 40 C or more, surface will closer to 70 C. If ocean then the surface is limited to about 30 C, and if 30 C, the air 2 meter above will be 30 C and partial pressure water vapor will be 0.0419 atm pressure [or 0.61593 psia, 47.3730 kPa]. Or each square meter has 10,000 kg of air and about 400 kg of 10,000 is H20. Or if only say 200 kg of water per square meter, the surface would evaporate quicker, which would cool surface and air above it.
And if land ground surface is wet, similar ocean but it can be warmer. Or with clear water, sunlight not warming the surface of
water but rather the meter depths of water. Or muddle puddle can get much warmer than 30 C.
But if atmosphere- it’s like the Moon, and surface temperature can heated to 120 C.
But the intense sunlight reaching surface, is when the sun is closer to zenith and at any given time this a very small portion of planet and part reason the Moon has very low average global temperature. And because ocean retain heat much more than a land surface {though wet land does better than dry land}, ocean make global air temperature, warmer.

Reply to  Bob Wentworth
April 13, 2021 11:36 am

Let me address this:

“You seem to be repeating this information as if there is some unspoken implication.”

What I am saying is what is known.
The conflict, seems to be due to the endless amounts pseudo science which does as pseudo science does- create more nonsense.
And most people, ignore it.
It’s like food fads, or wokism.
But it seems more people pay attention as the dead bodies, start to pile up- because of the nonsense.
Or stupidity seems to have an exponential aspect to it.
But I would say there has some aspect about say, wokism or whatever ism is “somewhat” true, but I say an important aspect about it, is all the confusion.
I think water vapor does make earth warmer. And I am on side, that a doubling of CO2 levels warms, rather than cools.
Though appears to me, that people who imagine CO2 has an even larger “warming effect” {than I do} , also believe CO2 has a lot cooling in upper part of the troposphere.
I would guess 50% or more of people, agree that CO2 gas in upper troposphere account a large part of the average of about 240 watts per square meter of Earth’s cooling or emission into space.
So going over the basic facts, and I very interested in any kind disagreement about them. So I think CO2 in upper troposphere or or any where in atmosphere, causes very close to zero cooling.
And planet Venus is my proof. As is planet Mars.

Bob Wentworth
Reply to  David Blenkinsop
April 10, 2021 1:04 pm

As long as you can assume an atmosphere that’s IR absorptive enough to plausibly drive convection, maybe that’s all it takes to have a PV=nRT based lapse rate in temperature, wth net surface warming, etc.”

The problem is that “a PV=nRT based lapse rate in temperature” does not lead to “net surface warming,” but only to net cooling at the top of the region where there is convective mixing (i.e., at the tropopause). If you could somehow have convection and a lapse rate without any greenhouse gases, you’d end up with no net surface warming. See Willis Eschenback’s argument or my arguments to this effect.

“How many planetary scientists are concerned in the least with greenhouse gas composition versus those who just use things like Bond albedo to estimate what a planet’s temperature ought to be?”

It depends on the interests of the particular planetary scientist. For many purposes, yes, it’s sufficient to work with the Bond albedo and bolometric emissivity to characterize the net effect of solar irradiance and atmospheric effects, without worry about the details of what affects albedo and bolometric emissivity.

But, those details potentially become important if one is trying to understand changes in planetary temperature and climate.

David Blenkinsop
Reply to  Bob Wentworth
April 10, 2021 2:13 pm

You said “problem is that “a PV=nRT based lapse rate in temperature” does not lead to “net surface warming,” but only to net cooling at the top of the region where there is convective mixing (i.e., at the tropopause). If you could somehow have convection and a lapse rate without any greenhouse gases, you’d end up with no net surface warming.”

If this were really true, then the top of Jupiter’s atmosphere would have to be very cold indeed? Instead we see something that is mostly just a big ball of hydrogen, with the temperature steadily increasing all the way down to who knows where! You may say that Jupiter still has IR absorptive molecules in it’s atmosphere, but this is just typical, all real planets have that?

Bob Wentworth
Reply to  David Blenkinsop
April 10, 2021 4:47 pm

Since I was making an assertion about the effect of an atmosphere without greenhouse gases and Jupiter has greenhouse gases, Jupiter doesn’t seem like a very helpful test case. Jupiter is also a poor test case insofar as it is believed to derive much of its heat from internal sources, rather than from the Sun.

Yes, most atmospheres seem to include some IR absorptive molecules. But some arguments seem to assert that that doesn’t matter.

In examining the merits of such arguments, it’s useful to do thought experiments about the physics that would apply on such a hypothetical planet. In such thought experiments, simple arguments lead to a conclusion that an atmosphere without greenhouse gases would be unable to warm the planet (except to the extent that horizontal heat transfer in the atmosphere contributes to keeping the surface of the planet more uniform in temperature thereby leading to a mean temperature closer to the radiative effective temperature).

David Blenkinsop
Reply to  Bob Wentworth
April 10, 2021 6:22 pm

When I try to do a thought experiment on some sort of atmosphere with no IR processing ability,(pure argon, maybe), I am not at all sure where that should take me. It’s like trying to imagine an impossible ideal — although it *may* be that argon gas or other things fulfill the idea of gases with no IR effect? I do, however, have some affinity for conventional Arrhenius-like GHG theory. For instance, I know that adiabatic lapse is an important part of the IR emission balance that they try to visualize as applying in the upper atmosphere, etc. It’s complicated, but not necessarily implausible, so conventional theory *might* be realistic in the end.

What’s odd is that something as intricate and as complicated as regular GHG theory should be taken as confirmed in some way, when nothing definitive has really taken place to corroborate that shifts in CO2, say, would have any particular warming effect. We don’t have a mini planet to experiment with, and gases sealed in closed containers in the lab just don’t have the weight or convective properties of the open atmosphere — so sorry, there’s no benchtop engineering analog there! So it’s all formula assumptions, or computer games, from beginning to end. In the case of Jupiter, say, do we get to define an arbitrary “flight deck” level, treat it as though it were “ground, and apply the implications of lapse rate looking up or down from there? Why, or why not?

Bob Wentworth
Reply to  David Blenkinsop
April 11, 2021 2:40 pm

These topics mix together some questions which are complicated and some questions which are simple.

I keep seeing the complications of the complicated questions leading to people getting the answers wrong, even with regard to the simple questions.

What the exact climate impact of increasing CO₂ levels will be is a complicated question.

Whether or not greenhouse gases warm the planet is a simple question. The answer is “yes,” based on any number of first-principles arguments with seemingly no possibility of a loophole. (See Section 5 of my big essay on N&Z, for one such argument. Some clarifications of things that puzzle some people about the GH effect are offered in Section 7. Another essay of mine offers another simple argument.)

I believe that thought experiments about an atmosphere with no IR-processing also render it a simple question as to whether atmospheric pressure alone can increase the temperature of a planetary surface. It can’t.

I think the conversations about more complicated questions would get a little easier, if we could at least agree on the answers to the simple questions.

* * *

In the case of Jupiter, I think you could start with any layer of the atmosphere, and use energy balance arguments to determine the temperature of that layer. You’d need to know about the energy flows to and from that layer to be able to do that. Alternatively, you could just take the temperature of that layer as an empirical fact. But that means you wouldn’t reach any conclusions about the reasons for the absolute temperature of the atmosphere; you’d just be looking at relative temperatures between parts of the atmosphere.

Once you’ve done that, then looking up, you can assume that convection will ensure that the layers of atmosphere above will be no colder than what the lapse rate would imply. (If the layers were colder than that, gas would rise and warm things to the level associated with the lapse rate.) However, the lapse rate will not act to cool upper layers that are for some reason (perhaps associated with absorption of solar or thermal radiation) warmer than what the lapse rate would dictate.

Looking down, the lapse rate would provide an upper limit on how warm layers below you could be. If they were warmer than what the lapse rate calls for, then convection should reach your reference layer and change its temperature, to bring it into alignment with the lapse rate. However, if the layers below you are colder than would be suggested by the lapse rate, you simply need to accept that. It’s a stable situation with respect to convection. Convection doesn’t provide a mechanism whereby an upper layer at the same temperature as a lower layer can heat the lower layer. (The fact that this configuration of temperatures is physically allowed is demonstrated on Earth, near the poles, where the Earth’s atmosphere does not cool with altitude as quickly as the lapse rate would suggest.)

Does this way of thinking about things make sense to you?

Last edited 1 year ago by Bob Wentworth
David Blenkinsop
Reply to  Bob Wentworth
April 12, 2021 1:43 pm

In essence, you seem to be saying that any net sum of heat power flows *into* any atmospheric layer must eventually be balanced by an equivalent power *outflow*, so energy has to balance, and such a basic consideration must be true for gas giant planets as much as for our own rocky/watery planet. Where things get difficult is in applying such principles to the planets as such, with all the real world complications (“real planet” complications) that apply. Accordingly, any altitude based lapse rate presumably will result in an upward power flow, and will have to be “powered in” in some way, eventually. To the extent that models at least try to answer such questions, I wouldn’t say that such and approach in itself is wrong. I just notice that something always tends to be missing or limiting, as compared to the large scale realities that nobody can really duplicate in the lab. Seemingly, a true lab test on this is not even possible, at least not as a complete scaled down kind of analog.

It is intriguing, isn’t it, to at least try to “scale up” and imagine how in the world would GHC theory apply to a gas giant like Jupiter? Somehow, Jupiter is able to generate what looks like a compression/gravity based lapse rate, without any fuss or bother about where to get the energy to support the resulting temperature gradient! Do we really know for sure that GHC content is the key to getting the needed energy for this into each layer of gas? Just say, for instance, what if Jupiter really were just a ball of pure hydrogen. Possibly this giant planet would then adopt an energy processing technique of taking in solar energy at the top, then filtering all needed power downward through actual downdrafts, you know, “derechos”, i.e., storm fronts, “plough winds” and the like. Maybe this sounds unlikely, but is it any more unlikely than espousing the more “standard” answer, that the whole planet would stabilize at the same temperature, an equilibrium temperature, throughout?

On raising the above “downdraft” scenario, I would also add that it seems presumptive to even say that a “no GHC’s” scenario like that is even *possible* in the long term stability sense. How do we even know that a pure hydrogen planet like that would be stable enough to last for millions of years and not just allow the solar wind to blow the whole thing away? Again, if the basic stability of a “no GHC’s” planet *is* a given, is uniform temperature, with no lapse gradient, then the correct conclusion, or should we be concluding something else?

Bob Wentworth
Reply to  David Blenkinsop
April 14, 2021 11:17 pm

It is intriguing, isn’t it, to at least try to “scale up” and imagine how in the world would GHC theory apply to a gas giant like Jupiter? Somehow, Jupiter is able to generate what looks like a compression/gravity based lapse rate, without any fuss or bother about where to get the energy to support the resulting temperature gradient! Do we really know for sure that GHC content is the key to getting the needed energy for this into each layer of gas?

Evidence says it has got a significant internal heat source, so it’s not all about greenhouse gases there. Does Jupiter still have left-over compressive heat from its initial coming together as a planet? That effect is only transient, but could the transient effect last that long for such a massive planet? One thing we know is that it’s not about a perpetual motion machine generating energy from nothing.

Possibly this giant planet would then adopt an energy processing technique of taking in solar energy at the top, then filtering all needed power downward through actual downdrafts, you know, “derechos”, i.e., storm fronts, “plough winds” and the like.

Well, it will only take in solar energy at the top if there is some mechanism for absorbing the solar energy there. Then, if the top layer is hottest (and consequently, least dense), the situation would be stable and the you wouldn’t expect any movement of gas downward. So, might be boring, but yes, I’d expect the whole thing to stabilize at around the same temperature, internally.

I would also add that it seems presumptive to even say that a “no GHC’s” scenario like that is even *possible* in the long term stability sense. How do we even know that a pure hydrogen planet like that would be stable enough to last for millions of years and not just allow the solar wind to blow the whole thing away? Again, if the basic stability of a “no GHC’s” planet *is* a given, is uniform temperature, with no lapse gradient, then the correct conclusion, or should we be concluding something else?

I suppose without greenhouse gases, the upper layers might be hotter, leading to faster loss of gases to the solar wind? Though, maybe not. The Earth’s Thermosphere gets hot for reasons that have nothing to do with greenhouse gases. Perhaps it would be the same on your pure-hydrogen planet, regardless?

Bob Wentworth
Reply to  David Blenkinsop
April 11, 2021 2:04 pm

I realize, in retrospect, that my statement about “net cooling” was potentially misleading. As I understand it, what the “lapse rate” actually does is set a limit on how much a heat source below can warm the atmosphere above via convection. So, it’s misleading to suggest that the lapse rate “cools” anything. If a layer of air at some altitude is warmer than is consistent with the lapse rate, what happens is that convection will not reach that layer. (The air below will not be buoyant enough to rise through that layer.) So, there is no convective cooling effect on upper layers of the atmosphere. Convection only warms upper layers of the atmosphere that are not yet warm enough to match the lapse rate.

Reply to  Bob Wentworth
April 13, 2021 11:06 pm

“As I understand it, what the “lapse rate” actually does is set a limit on how much a heat source below can warm the atmosphere above via convection.”
Nope. Lapse rate same at night as day.
Lapse rate governed by gravity and altered water vapor.
It’s altered by water vapor because water condenses in Earth’s atmosphere. Or any gas which become liquid in the atmosphere should alter lapse.
But I referring to troposphere- though there other stuff- inversion layers:
Temperature inversion, also called thermal inversion, a reversal of the normal behaviour of temperature in the troposphere (the region of the atmosphere nearest Earth’s surface), in which a layer of cool air at the surface is overlain by a layer of warmer air. .”
And what happens to the lapse rate above the troposphere.

Reply to  gbaikie
April 14, 2021 1:24 pm


Explains it.
It says 75% of the atmosphere is in troposphere.
Or mass atmosphere is about 10,000 kg at sea level and
at top of troposphere- 10,000 – 7500 = 2500 kg per square meter
above it.
Air molecules are held near the earth by gravity.” and
“The weight of all of the air above a given point in the atmosphere squeezes air molecules closer together, which causes their numbers in a given volume to increase”

Depending air temperature, but there is about 1.2 kg of air per square meter at sea level.
“The density of air at an altitude of 16 km (50,000 feet) is only about 13% of the density of air at the surface.”
1.2 kg times .13 = .156 kg per cubic meter or 156 gram per cubic meter. So less air mass above, causing less density. But atmosphere has more energy {higher temperature] the more energic atmosphere can push up higher against the force of gravity. So with higher air temperature, more air mass can be push above a fitted point such 16 km above the surface. Or you only say, about 13%. Or giving any precise numbers, require that give an air temperature of surface air as a reference point. It tends to be 15 C or 20 C. And it might assume it’s dry air, or wet lapse rate will likewise vary it. And weather in general can vary it.
Also with air density of 13% it reduces heat transfer from convection and with even further reduction of air density can reduce so air does not warm or cool anything. Or in first link the top graph is the thermosphere. And very low air density and it’s edge of space. Or it’s in low Earth orbit. the air molecules are traveling so fast that the temperature can be 2000 C, but doesn’t temperature in terms warming anything, and it’s air temperature is about the average velocity of the air molecules {all air temperature is about average velocity of the air molecules- and average velocity of air molecule increases above troposphere- and the air is cold, and higher you go up less cold [or less the air can cool something] and the air molecules are moving faster.}
Or Space has no temperature there is lack of anything which can cool or heat anything- it’s all radiant heat transfers. Though evaporative cooling works great in space and it is used in spacesuits to keep people comfortably cool.

April 10, 2021 8:26 am

One wonders if there is a generalised formula for each of the layers, taking into account its different properties; seems to me that atmospherics are all too complex to try to fit our simplified attempts at equations.
Nature does what it does & doesn’t adhere to mankind’s arbitrary but quite successful box fitting of equations, much like Black hole theory has come up with so called Black Holes that are neither Black nor Holes, but because our equations fir our simplifications which predict they ‘must’ exist.

M Courtney
April 10, 2021 8:45 am

..likely relates to an erroneous conclusion that the rotation rate of a planet doesn’t matter…

That sounds ridiculous but if you want to test it empirically, look at Uranus.

Bob Wentworth
Reply to  M Courtney
April 10, 2021 1:28 pm

N&Z’s actual assertion (see p. 17) was that for an airless planet rotation rate “cannot affect… the average surface temperature of a planet.” So, Uranus would offer a crude, off-the-mark test case, with confounding factors present that might confuse matters. But, in general, it’s an interesting case to look at.

Kevin kilty
April 10, 2021 8:49 am

I don’t understand the purpose of these “formulas” for planetary temperature. What are we trying to accomplish here? We know how to calculate temperature anywhere, and it doesn’t involve a regression analysis or the ideal gas law. Temperature is the result of an energy balance — or at least this is how engineers estimate it. Every place on every planet, surface or atmosphere, reaches a temperature based on heat and work transferred toward and away from that point by a variety of mechanisms; scores of mechanisms, each unique to the planet and specific location. This balance temporarily affects the unit internal energy at that point. Temperature is a function of this internal energy. Taking all this into account we can explain the instantaneous temperature, and averaging over time we can explain the mean temperature.

The “gas laws”, the ideal gas law specifically is not a determinant of temperature. The mistaken notion that it determines temperature is the most basic misconception that students have in introductory thermodynamics courses — well documented in the engineering education literature — and is an impediment to learning thermodynamics. And on many planets the atmosphere is not ideal gas at all. On Venus for instance the surface CO2 is above its critical point and not even a gas.

Though journalists, politicians, activists, and certain foolish scientists focus obsessively, i’d say hysterically, on mean temperature, mean temperature seems very unimportant to me. From the above paragraph it should be apparent that it depends on the balance among dozens of mechanisms, not just radiation from certain gases, and all of these mechanisms can vary. It certainly is not an indicator of “health” of the weather system.

So what are we accomplishing with these planetary temperature theories?

Rich Davis
Reply to  Kevin kilty
April 10, 2021 4:29 pm

The point seems to be to deflate one of the claims of N&Z that the fit of their formula proves that their physics must be correct. Both models can’t be correct, so it’s also logical that both models could be wrong. I don’t believe that Bob is proposing this as a real model of the atmosphere if that’s what has you objecting.

Reply to  Kevin kilty
April 11, 2021 7:56 am

Kevin you said that temperature is a function of internal energy. This is exactly opposite of Joule’s claim from his experiment.

Is this chicken egg situation?

“In 1843, Joule did this simple experiment to show that the internal energy of a gas is a function of temperature, independent of pressure or volume. When the gas in the left sphere initially flows without resistance into the vacuum of the right sphere, no work is performed and no heat is transferred.”

April 10, 2021 8:55 am

–“The ‘greenhouse effect’ is not a radiative phenomenon driven by the atmospheric infrared optical depth as presently believed, but a pressure-induced thermal enhancement analogous to adiabatic heating and independent of atmospheric composition”

There are plenty of reasons to be skeptical of this conclusion, at various levels: fundamental, procedural, and at the level of interpreting the significance of curve fitting.–

It seems the whole issue is understanding Earth’s climate in regards to the Ice Age we are living in. What causes glaciation periods and interglacial periods. When are going to return to a glaciation period. Because glaciation periods are not nice.
And there was the idea the CO2 levels caused it. And that was proven wrong. And everyone
seems to agree it’s related Milankovitch cycles. But exactly, how sort of remains unknown.

Reply to  gbaikie
April 10, 2021 9:21 am

So, we have living in a icehouse climate for about 34 million years:

And why is because our ocean is cold.
And why the ocean are cold, is due to cold water falling and filling our ocean basins.

One think of cold water falling as short term warming process, or debt borrowing.
And it’s related having saltwater rather than freshwater ocean.
Or if the ocean was freshwater, our ocean could not have average temperature of about
3.5 C, because the highest density of freshwater is about 4 C.
Or commonly said 90% of our ocean is 3 C or colder, if instead it was freshwater if would have to be 90% of our ocean being 4 C or warmer. Or one could say, saltwater allows more warming and more debt.
But if it was freshwater, Earth might be a snowball earth {much colder than it is}.

I would say the basic issue is that ocean surface area, causes a warmer average global temperature, and land area causes a lower average global temperature. Or primary reason
Earth is not so cold is because 70% of surface area is ocean and 30% of surface area is land. Or if Earth had 80% ocean, it would warmer, or if it had 60% ocean, it would be colder.

Rud Istvan
April 10, 2021 9:01 am

I am reminded of a failing beer company I once had as a client. It had a ten parameter regression model that amazingly and precisely reproduced ten years of sales data. Except it had no degrees of freedom. Fitting a 6 parameter model to 6 datapoints is the same nonsense. And fitting 4 to 6 is not much better. The 2017 paper was justly ridiculed at the time, and IMO best left forgotten and neglected.

Bob Wentworth
Reply to  Rud Istvan
April 10, 2021 10:25 am

If one examines things closely, N&Z used a 4-parameter model to fit only 4 distinct data points. The models (N&Z’s and the ones I offered) are rigged to automatically fit the Moon, almost regardless of the parameter values. And, Earth and Titan happened to have values so similar for N&Z’s variables as to not constitute distinct data points from a curve-fitting perspective. The “degrees of freedom” argument isn’t fully rigorous when when the curves involved have some stiffness to them. Yet, I don’t disagree about it ultimately being all best forgotten. My goal was to make that a bit more clear for anyone who was still wavering.

Reply to  Rud Istvan
April 10, 2021 11:26 am

So you are a believer in coincidences, aka statistical ones…
aren’t you Rud!


Last edited 1 year ago by whiten
April 10, 2021 9:50 am

OT, a nice example of researcher responding to the WUWT comments

Response from a researcher on the ‘Muon Particle’s Wobble and the Known Laws of Physics’ project:
Vuk: “Same magnet – same result,”
response from “Karen Zatz
Naperville. ILApril 7
Rubin (Vuk)Very reasonable question. It’s possible in principle, but the only thing that this measurement relies on in the knowledge of the magnetic field (I’m on the experiment) …….
for the rest of the response see:

Last edited 1 year ago by vuk
Mike Maguire
April 10, 2021 10:04 am

Climate models of the Earth energy system may contain errors of opposite signs in different spectral bands that fortuitously compensate, providing satisfactory model agreement for nonphysical reasons (Huang et al., 2007; Etminanet al., 2016). Empirical measurement by hyper spectral satellites provides a means to adjudicate between different climate model RF calculations and promote only those matching reality. Seventeen years of AIRS nighttime, clear-sky OLR measurements reveal 0.360±0.026 Wm−2additional long wave radiative forcing induced by +37 ppm atmosphericCO2. AIRS lacks measurement capability at 575-650 cm−1for complete CO2v2band characterization, therefore this empirical estimate of increased forcing was devised by presuming CO2v2wing symmetry and doubling the observed wing’s radiative forcing. The latest generation CMIP6 climate models predict 0.431-0.516 Wm−2of clear-sky longwave ERF, +20-43% greater than observed by AIRS. Current climate models may require modest revision to bring CO2forcing computations into agreement with observation.

April 10, 2021 10:33 am

to develop a model under the assumption

If you do not understand how something works, assumptions and best guesstimates are all you have.

Climate modelling tends to generate more heat than light.

Paul Penrose
April 10, 2021 10:53 am

I this so many times, people using energy balance equations to calculate delta temperature directly. The problem is that temperature is actually a measure of energy density. You simply can’t ignore the effects of pressure in your gas if you want to understand how differences in the energy-in/energy-out balance will effect the temperature. Of course, it gets even more complicated when you factor in a continuous pressure gradient and phase changes in some portion of the gas. It’s no wonder people engage in curve fitting exercises when faced with that amount of complexity, but it doesn’t make them correct.

Ned Nikolov
April 10, 2021 11:59 am

This “analysis” is physically nonsensical and erroneous. Unfortunately, I don’t have the time to write a full rebuttal paper on this now… Our model has evolved quite a bit beyond what was described in 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).

Our new extended model now predicts average temperatures for several absolute latitudes on rocky planets including Equator and the Poles while accounting for the effect of albedo changes on global planetary temperature. The implications of our extended model for a new understanding about the drivers of Earth’s paleoclimate and modern climate change have been verified against recent independent temperature reconstructions from the geological record and modern satellite observations, respectively.

The results from this new research were presented at the 101st Annual Meeting of the American Meteorological Society in January of this year. You can watch our presentations on YouTube:

Drivers of Paleoclimate: https://www.youtube.com/watch?v=DpUkPPtkPVc
Drivers of Modern Climate: https://www.youtube.com/watch?v=Gv66_mpJz-c


Aleksandr Zhitomirskiy
Reply to  Ned Nikolov
April 10, 2021 12:33 pm

The statement from the IPCC First Assessment Report (1990): “Secondly, we know the composition of the atmospheres of Venus, Earth and Mars are very different, and their surface temperatures are in general agreement with greenhouse theory”. It can be assumed that the Nikolov-Zeller theory, at least, deliberately refutes this argument in favor of the theory of the greenhouse effect

Reply to  Ned Nikolov
April 10, 2021 3:40 pm

If any ‘model’ is in any way valid, it should have predictive capability. Given that the 2017 NZ paper predicted Horizon’s measure of Pluto’s surface T very accurately and now given the extension of the same surface Ts = a function of total surface pressure and TOA solar input model, (replacing pressure with density) matches (predicts) actual paleo polar temperature amplification proxy data, any reasonable scientist worth her salt might take pause to consider how that could possibly be and if perhaps there are known physical and thermodynamic reasons/explanation other than FM or just ‘good luck’ in extracting regression constants from planetary data that work.

Bob Wentworth
Reply to  Lark
April 11, 2021 4:24 pm

Because Pluto’s atmosphere is so tenuous as to have effect on temperature no larger than uncertainties in temperature measurements, N&Z’s prediction of Pluto’s surface temperature only tests N&Z’s theory of the temperature of planets with no atmosphere.

Observations of Pluto have seemingly no relevance to validating NZ’s pressure-causes-temperature hypothesis.

(I haven’t looked at the “paleo polar temperature” work yet.)

Last edited 1 year ago by Bob Wentworth
Ed Bo
Reply to  Ned Nikolov
April 10, 2021 3:51 pm


Please provide at least a rough quantification of the contribution atmospheric pressure makes to the earth surface energy balance.

The earth and its atmosphere absorb about 240 W/m2 of solar radiation, averaged over the whole area. The earth’s surface emits about 500 W/m2, again averaged over the whole surface. We have good repeatable measurements for these values, good to within a few percent. 

So we’re about 260 W/m2 out of balance so far, and not even the worst alarmist thinks we’re actually more than 1.0 W/m2 out of balance.

You are effectively claiming that the force of atmsopheric pressure can provide this 260 W/m2 to close the gap in the surface energy budget to achieve (roughly) steady-state conditions. Let’s examine that claim, shall we?

We know from basic high school physics that the energy (work) transferred by mechanical force is:

Work = Force x Distance = Pressure x Area x Distance

In differential form, we have:

Power = Force x Velocity = Pressure x Area x Velocity

Expressed as power per unit area, we have:

Power/Area = Pressure x Velocity

(Of course, in the general case, these are integrals instead of simple multiplications, but that does not change the argument.)

So in a combustion piston, the expanding hot gas moving the piston head transfers power to the piston head and its linkages. But here the velocity is non-zero.

In the case of the atmosphere on the surface, the velocity is zero, so the power transferred is also zero.

I’d be curious to see the analysis you did on surface energy balance (the very first thing to be done in any thermodynamic analysis). Please show your work.

Reply to  Ed Bo
April 11, 2021 11:49 am

Ed, not sure what you are trying to say. Work = Force * Distance = Pressure * Area* Distance, but distance * area is volume so you have shown work = PV which is one side of gas law. dW = PdV

And at TDC or BDC velocity of piston is zero. Are you saying no power was transferred? Parcels of air are always moving up or down they don’t just sit on the ground and not move.

Ed Bo
Reply to  mkelly
April 11, 2021 2:53 pm

mkelly: Pressure-Volume work is another way of expressing the concept I was trying to get across. I figured the more basic equations of high school physics would be understood by more people.

At TDC and BDC, the velocity of the piston IS zero, so there is no power transferred AT THAT INSTANT. (Using your equation, dV is zero at these points, so dW is zero as a result.) But there was power transferred during the non-zero-velocity part of the stroke that got the piston to the end of the stroke.

(If power could be transferred with zero velocity, we could just hold the piston at that end, and not bother burning any more fuel! Which is in essence what N&Z claim the atmosphere can do.)

Yes, there are upward and downward movements in small parts of the atmosphere, but a moment’s thought should reveal that these must balance each other very precisely.

But N&Z are arguing (albeit with a lot of weasel words) that there is a huge unbalanced power transfer from atmosphere to earth. This would have to amount to hundreds of watts per square meter all over the earth. I have challenged them several times on this, but never get a response.

Bob Wentworth
Reply to  Ned Nikolov
April 11, 2021 4:38 pm

I look forward to a time when you might address the substantive points I’ve raised. (A blanket assertion that my essay is “nonsensical and erroneous” doesn’t really do anything to advance the conversation.) I imagine it would be helpful to me and to other readers to know what specific errors you interpret as being present in my analysis.

I watched your video on “modern climate.” Interestingly, I note that your derivation of the effect of “albedo deviations” (starting around timestamp 15:50) is entirely independent of the form of the atmospheric temperature enhancement formula. So, the results which you derived, and validated with observations, are equally applicable to my formula (involving greenhouse gas amounts) as to your formula (involving total pressure).

Thanks for your work to validate my model. 🙂

Reply to  Ned Nikolov
April 11, 2021 7:12 pm

Venus has about 4.8 x 10^20 kg of atmospheric gases
If 4.8 x 10^20 kg of atmospheric gases were added to Venus and
so therefore making the total being 9.6 x 10^20 kg. Then I would
assume a prediction would be that the surface temperature would
increase by some amount.

But my question is how quickly would it warm up.

So, therefore when adding gas, the gas added could be at any temperature, and so
the 4.8 x 10^20 kg of gas could be added at low enough temperature
in order to cause the surface temperature to remain at the same temperature.

And then after gases are all added, how long would it
take for gases to warm up to the predicted surface temperature?

April 10, 2021 12:42 pm

 it’s impossible that the “pressure-induced thermal enhancement” hypothesis could be right”

It depends. If the atmosphere is opaque for IR, the “hypothesis” is correct.
If the atmosphere is dilute and transparent to IR, it fails.
Of course, the temperature follows the adiabate. That is why the part of the atmosphere we live in is called “troposphere”.
The continuous adiabatic mixing of the atmosphere defines the temperature.

Bob Wentworth
Reply to  Alex
April 11, 2021 2:52 pm

If the atmosphere is opaque to IR, it’s not easy to untangle the effects of IR absorption and the conventional greenhouse effect. The pure form of the “pressure-induced thermal enhancement” hypothesis would seem to be one in which IR absorption wouldn’t matter, and warming would still occur with an atmosphere transparent to IR. As you say, in that case the hypothesis fails.

Interestingly, I only recently realized the atmospheric temperature does not consistently “follow the adiabate.” In particular, the Earth’s atmosphere does not cool nearly as fast with altitude near the poles as the adiabatic lapse rate would suggest. Granted, the structure of the Earth’s atmosphere is complicated. But, the lapse rate is less general, as a rule, than some might expect.

Last edited 1 year ago by Bob Wentworth
April 10, 2021 1:13 pm

The adiabatic lapse rate just maximises entropy. Fundamental thermodynamics

Philip Mulholland
April 10, 2021 1:25 pm


Am I correct in saying that your equation is being applied to atmospheres, such as Titan, where the temperatiure is so low that there is no water vapour or carbon dioxide gas present?

(Hatter Eggburn also touched on this point)

Bob Wentworth
Reply to  Philip Mulholland
April 10, 2021 4:05 pm

My equation is being applied to the same celestial bodies that N&Z considered, including Titan. And, yes, it’s true that the mix of gases varies between bodies.

I could understand why one might reasonably conclude that this difference in gas mixes means there isn’t enough data to properly validate a model that considers different greenhouse gases separately. (Though, for my model variants that use just as few fitting parameters as N&Z, that helps helps a little in suggesting that these models are formally just as significant as N&Z’s model.)

Ultimately, my point is that none of these curve-fitting models are likely to be significant. As I’ve described in another comment, N&Z use 4 fitting parameters to fit only 4 independent data points, so there is not really enough data to properly validate their pressure-based model either.

If one concludes there is too little data to validate my model, that wouldn’t support N&Z’s argument. The logic of N&Z’s argument included both the idea that (1) the data is well-fit by a pressure model, and (2) the data can’t be well-fit by a greenhouse gas model — so the pressure model “must” be significant and all greenhouse gas models “must” be false.

To refute N&Z’s argument, it’s okay if the conclusion is “There isn’t enough data to say that the good fit of a greenhouse-gas model is actually significant.”

All one needs to conclude is that a greenhouse-gas model can fit the data, and there is no justification for definitively asserting that “the data can’t be well-fit by a greenhouse gas model.”

That by itself is sufficient to undermine N&Z’s empirical argument.

Philip Mulholland
Reply to  Bob Wentworth
April 10, 2021 11:35 pm

And my point is that by fitting a curve to an atmosphere that is too cold to contain some of these gases makes your equation specious and your argument void.

Bob Wentworth
Reply to  Philip Mulholland
April 11, 2021 3:01 pm

I’ll point out that N&Z fitted their pressure formula to celestial bodies with negligible atmospheric pressure. So, I fail to see how my equation is any more specious than the one that N&Z offered.

Philip Mulholland
Reply to  Bob Wentworth
April 12, 2021 1:52 am

Because the terms that you use are meaningless at low temperatures.

“So, I fail to see how my equation is any more specious than the one that N&Z offered.”

Nice to see that you agree that your post is junk science, just like the radiative greenhouse effect.

April 10, 2021 2:14 pm

Strange how planet rotation matters to author in this article but not so much when averaging suns 120C temp worth of zenith energy over surface area. So much for spectral intensity and Activation Energy. I’m still waiiting for my moon-tan from CO2’s frigid 10um back radiation warming…all -80C of it.

April 10, 2021 2:19 pm

The so called GHG effect is not due to pressure,

it is due to the lapse rate caused by atmospheric convection. This is not a perpetual motion machine. The energy to run the convection comes from the differential heating caused by the sun, the rotation of the earth and earth’s orbit around the sun..

Prior to Hansen and the public concerns over radiation, this was not new science.
In the 50’s and 60’s this was settled science, when only the best and brightest went on to become scientists.

Without convection the atmosphere would be isothermal. Convection sets the atmosphere in motion vertically. This results in warming of the atmosphere at the surface and cooling at altitude, as compared to an isothermal atmosphere.

This added warming of the lower atmosphere at the surface due to convection raises the temperature at the surface over and above what is predicted for a black body.

How much warming? The lapse rate is about 6.5C/km and the center of mass of the troposphere is about 5 km, so we should expect to see about 6.5 x 5 = 32.5 C warming at the surface.

Which matches nearly perfectly with observations.

Bob Wentworth
Reply to  ferdberple
April 10, 2021 5:14 pm

Lapse rate sets a rate of temperature change with altitude, but it doesn’t set absolute temperature level.

You seem to be making an unfounded assumption that the place where radiative balancing to determine temperature is achieved is at the “center of mass of the troposphere.” But, there’s nothing special about that location, with respect to radiative balance. There’s no reason that location should be used as a reference level, for purposes of computing absolute temperature, as you appear to be doing.

Even in the presence of a lapse rate, it remains meaningful to do energy balancing at the Earth’s surface to compute surface temperature.

When you add an atmosphere to a planet, and that atmosphere is cooler than the surface, that introduces convection and latent heat flow away from the surface, which inherently cool the surface relative to its state without an atmosphere. The only mechanism available to actually warm the planetary surface is radiative, insofar as some of the radiant energy that previously just escaped to space can now be absorbed by the atmosphere and re-radiated back to the surface.

(The one slight complication to this analysis is that the atmosphere can also transfer heat laterally, thereby affecting the distribution of surface temperatures.)

April 10, 2021 3:08 pm

Y’all might also enjoy my post “The Mystery of Equation 8” …


Bob Wentworth
Reply to  Willis Eschenbach
April 10, 2021 4:22 pm

I agree that your post may be of interest, and want to acknowledge that it made a rather similar point, long ago. I had seen N&Z’s response to that post and was sad that I was unable to quickly disentangle the competing claims because I was working with N&Z’s more recent version of the data, which considered a different mix of celestial bodies and varied some other details.

That’s actually what set me off on looking for a fit to the more recent version of the data, and, in particular, a fit that would explicitly rely on greenhouse gas data.

I’ve got much appreciation for your work in addressing these issues.

Last edited 1 year ago by Bob Wentworth
April 10, 2021 3:56 pm

I dunno what to think, all I know is that if I hike up a mountain it gets colder even though CO2 stays the same and the hottest temperature ever recorded on Earth occurred a couple hundred feet below sea level.

Ed Bo
Reply to  Bob Johnston
April 10, 2021 4:38 pm


The earth’s atmosphere gains energy (“is heated”) mostly from the bottom, as 2/3 of (non-reflected) incoming solar radiation makes it to the surface, and loses energy (“cools”) mostly from the top, as only about 1/10 of surface thermal radiation passes clear through the atmosphere. 9/10 of the surface radiation is absorbed by so-called “greenhouse gases”>

When a body gains thermal energy at one end and (crucially) loses thermal energy at the other end, there is a temperature gradient between ends of that body. For the atmosphere, we call this the “lapse rate”, and the fundamental cause of that lapse rate is the absorption of surface radiation by these gases.

Reply to  Ed Bo
April 10, 2021 8:42 pm

People smarter and more knowledgeable than myself can’t agree on some very basic principles regarding this. Me reading and digesting all the theory on the matter ultimately isn’t going to amount to jack. What I find to be way more interesting and much more pertinent is how people react to ideas that go against their beliefs. People are saying that the N&Z hypothesis is trash because the formula was developed by “curve fitting” (I don’t even know if that’s true) rather than discussing the merits of the argument, which is ultimately more valuable.

And in the grand scheme of this none of this matters because regardless as to whether N&Z is right or the GHG hypothesis is right or neither is right it’s quite apparent that there is no climate emergency and all of the arguing will never go anywhere, because people believe what they want to believe and all the evidence in the world isn’t going to change their mind.

Now if you want to have a game changing discussion, figure out how to persuade people to set aside their preconceived notions and give all arguments a fair chance. Until we figure that out none of this amounts to a hill of beans.

April 10, 2021 4:58 pm

Earth’s maximum sea surface temperature depends on highly reflective properties of solid water in the atmosphere. The water vapour gets catapulted to as high as 220K during cloudburst and will solidify all the way down to 273K to form reflective cirrus cloud in the process. That sets the radiating temperature at an average of 255K while producing persistent cirrus cloud until the next cloudburst, which produces dense and highly reflective cumulus cloud for the duration of the cloudburst.

When SST reaches 30C, the combination of reflection of sunlight from persistent cloud and convergence of moist air from slightly cooler zones limits further rise.

The minimum SST is -2C due to formation of sea ice at this temperature.

The average surface temperature is the results of the wide distribution of water over the globe combined with the upper limit of 30C and the lower limit of -2C; to give 14C average.

The “greenhouse effect” is mythical.

Unless planets have an atmosphere that produce reflective cloud to regulate heat input, then their surface temperature is not being set in a similar process to that occurring on Earth’s surface.

Reply to  RickWill
April 10, 2021 5:11 pm

Climate models are based on a mythical process termed “greenhouse effect”. The models parameterise clouds, which are then no longer responsive to surface temperature.

It is easy to observe the fatal flaw with climate models when their output is compared with real data. For example, the tropical ocean warm pools regulate to 30C. The Nino34 region in the Pacific is close to the Pacific warm pools and is sometimes part of them. It is also an important zone for predicting weather conditions around the Pacific rim. This region provides the clearest example of climate model inability to produce credible output.

Attached shows the performance of two Australian models in the region. The models have to cool the past to sustain a warming trend where there is none while producing a temperature consistent with the date of the run.

Reply to  RickWill
April 10, 2021 5:13 pm

Australian climate prognosticators are not alone in this nonsense. Attached is the UK effort.

Reply to  RickWill
April 10, 2021 5:15 pm

The effort from a couple of the US groups.

Reply to  RickWill
April 10, 2021 5:17 pm

And Europe.

Reply to  RickWill
April 10, 2021 5:40 pm

It is worth noting here that climate models have a large number of tunable parameters and these parameters can be tuned automatically to produce reasonable hindcast on the key historical inputs; essentially curve fitting. That means it is not difficult to match a number of ups and down in a global trend. However they do not stand up to scrutiny once examined in finer detail.

The sea surface temperature in the Nino34 region is known to be significant to global weather and is carefully monitored using moored buoys. The NOAA/NCEP measured temperature is a combination of data from the moored buoys interpolated with satellite data. It appears to be the best indicator of actual surface temperature for the Nino34 region.

Robert W Turner
April 10, 2021 6:31 pm

Wow, what can’t be correct is the back radiation greenhouse gas hypothesis.

1st, Einstein completely refuted this hypothesis in 1917 even though that wasn’t at all the purpose of his work considering the hypothesis had already been dismissed.

2nd, Night time temperature inversions are a direct observation that refutes the back radiation hypothesis. Temperature inversions in a non turbulent atmosphere form because the surface of the planet and of clouds quickly radiates energy to space. The atmosphere near these surfaces conducts heat from the gas to the surface where it is then radiated away and the air near the surface is cooled quicker than the air layers above them. If back radiation hypothesis were correct this would be impossible and would never occur because the air near the surfaces would be absorbing a net positive radiation from not only the surface but also from the atmosphere above it. When there is turbulence in the atmosphere these temperature inversions do not form but the net effect is actually a more rapid cooling of the atmosphere overall from increased rate of heat transfer from the atmosphere to the radiating surfaces.

3rd, N&Zs work is less of an explanation and more of a proxy of the processes that explain thermal enhancement on planetary bodies from their atmospheres and acts as further evidence that back radiation hypothesis is based on erroneous physics which violates several established laws and theories. Atmospheres act as inherent thermal capacitors because of the latent heat of vaporization and the fact that gases radiate heat much slower than solids and liquids. The more massive the atmosphere the greater the thermal reservoir it contains (kinetic and potential energy) and the greater the thermal energy available to be fedback to the surface when it is cooling or when the surface is cooler than the atmosphere (high latitudes) and heat is transferred to those areas through work done by the convection. Another direct observation shows this, the diurnal expansion of the atmosphere during the day and the subsequent contraction at night.

Until a lukewarmer can explain how the Law of Conservation of Momentum does not apply to atmospheric gases then I will remain unimpressed of these articles promoting the backradiation hypothesis over more complete explanations of planetary atmospheres based on the laws of physics.

Bob Wentworth
Reply to  Robert W Turner
April 16, 2021 10:24 am

You assert Einstein’s theory of radiation refutes the idea of back-radiation causing warming, but offer no justification for this claim. Einstein’s theory is in no way contradictory to mainstream climate science, and his theory is routinely applied as part of that work.

You suggest that if back-radiation really warmed the surface, then this would prevent the surface from cooling at night and a temperature inversion forming. Uh, no. Why would you think that? It’s all about rates of warming and cooling. Back-radiation warming at night prevents the temperature from plunging 50 degrees every night. It’s not enough to entirely prevent surface cooling, or to prevent the surface from becoming cooler than the adjacent air.

Yes, the atmosphere provides a thermal reservoir that stabilizes temperatures spatially and temporally. Such temperature-smoothing helps bring a planet closer to its no-atmosphere radiative balance effective temperature, but can’t provide warming beyond that point. It doesn’t explain why Earth is 33 K warmer than its no-atmosphere radiative balance effective temperature.

Ok, the atmosphere expands in the day and contracts at night. The ideal gas law, PV=nRT, predicts this. So what? What bearing does this have on determination of average planetary temperature? And what is the purported relevance of the law of conservation of momentum?

Last edited 1 year ago by Bob Wentworth
April 10, 2021 7:44 pm

As an utter layman, someone please explain the following in terms I can understand.
Earth heats up during the day = energy in. That energy is also released back to space via radiation. Radiation occurs at the speed of light. Supposedly, greenhouse gases slow the release of energy. I can sort of comprehend this will theoretically occur during the day as the energy in is ”constant” (for the purposes of the question) – so added ”GHG” will further slow transfer.
BUT, although the GHG are still there at night, in-coming energy is absent. If radiation – in whatever direction – occurs at the speed of light, what ”slows down” the emission on the dark side of the planet and how does it do it?
BTW, I believe the Speed of light is 300,000 km every second in a vacuum

Last edited 1 year ago by Mike
Reply to  Mike
April 11, 2021 1:18 pm

“BUT, although the GHG are still there at night, in-coming energy is absent. If radiation – in whatever direction – occurs at the speed of light, what ”slows down” the emission on the dark side of the planet and how does it do it?”

Well, let’s try magic. Suppose on had magical machine which can cool, and say it’s big like 1 cubic km big. And starts cooling the atmosphere in some crazy fast way, you could cool an area a lot, but you would need to cool entire atmosphere, and it might take a week or two the cool the entire atmosphere with this super cooling magical machine.

Or we can disappear the sun. Sun blinks out, it takes while for entire earth to cool. It could take month to freeze the entire ocean.
One might ask which parts of Earth cool the fastest. And land area cools fastest and ocean area take awhile. And 70% of Earth is ocean.
I give link for blinking out sun {people like doing this}, Ie:
And they are roughly correct

But you have weather and a region can warmer [than normal] and take longer to cool down at
night. Or in summer it tends to warm up and stay warmer, but if have some cold weather in the summer it could take couple days to warm back up.
Or atmosphere and ocean [and land] have thermal mass- like hotwater bottle- but bigger.

Reply to  gbaikie
April 11, 2021 8:07 pm

Well that’s as clear as mud. Thanks.

Reply to  Mike
April 12, 2021 12:37 am

Well you said, “Supposedly, greenhouse gases slow the release of energy. “

And supposedly they do.
And there are various opinions about how much.
But clouds for example, can keep night times from getting colder and tend to have large effect- as compared to any greenhouse gas.
Clouds might be considered to be a greenhouse gas, in that case, then there is broad agreement that clouds and the water vapor are most significant greenhouse gases.

Reply to  gbaikie
April 12, 2021 7:29 am

Clouds are not a gas; clouds consist of liquid and solid water. Water vapor in the atm. is not visible.

Reply to  Trick
April 12, 2021 1:00 pm

But the pseudo science of the greenhouse effect theory:
claims 33 K of Earth is warmed by greenhouse gases.
And give guess of how much of each gas:
“By their percentage contribution to the greenhouse effect on Earth the four major gases are”
And below this say:
” Clouds also absorb and emit infrared radiation and thus affect the radiative properties of the atmosphere.”

And studies that indicate clouds could be adding up to 50% of the greenhouse effect. But whatever the percentage it’s known clouds and H20 vapor [though don’t why they ignore all water droplets which not clumped together in clouds}. Or imagine they old term
of water vapor [because it could be inclusive of the zillions small water droplets in atmosphere. Or when breathe, you are emitting water droplets and H20 gas, few say you exhaling water vapor or and more rarely said, small clouds.

April 11, 2021 12:47 am

I ain’t never seen so many minuses on any WUWT article! What great fun. It’s like this is an April fools’ joke, and half the world are rushing to update their investment portfolio to take advantage of the imminent increase of mosquito poop fertilising the corn fields.
A reductio ad absurdum argument taken for a thesis? A mathematical doodle criticised by people on the verge of becoming painters?
But that’s why we keep coming back, isn’t it? That grain of gold in every turd… or speck of truth in (nearly) every angry comment…
Now excuse me while I average all these comments to see how far mister Bob had his tongue up his cheek.

Reply to  paranoid goy
April 11, 2021 2:00 am

It is all very simple really.
Energy is required to maintain continuous convective overturning within any atmosphere. No atmosphere or indeed any ball of gas can avoid such overturning.
At equilibrium there needs to be as much energy radiated out to space as comes in from space.
To achieve both functions simultaneously the irradiated surface must acquire enough kinetic energy to service both requirements.
That is the greenhouse effect.

April 11, 2021 7:44 am

Anyone who has read a graduate text book on Quantum optics knows that:

The bandwidth of the absorption/emission spectra of CO2 (or any other “optical” gas is dependent on.

  1. Concentration
  2. Temperature
  3. Pressure

This was empirically proven in the 1940’s and 50’s during the USAF “Upper atmospheric research program”.

The effect can be calculated as a Gaussian to Lorentz transformation.