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.
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.
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.
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.)
Y’all might also enjoy my post “The Mystery of Equation 8” …
w.
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.
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.
Bob:
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.
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.
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.
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.
Australian climate prognosticators are not alone in this nonsense. Attached is the UK effort.
The effort from a couple of the US groups.
And Europe.
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.
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.
http://web.ihep.su/dbserv/compas/src/einstein17/eng.pdf
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.
http://www-das.uwyo.edu/~geerts/cwx/notes/chap01/diurnal.html
http://articles.adsabs.harvard.edu//full/1966SAOSR.207…..J/0000001.000.html
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.
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?
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
“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:
https://www.discovery.com/science/What-Would-Happen-If-the-Sun-Disappeared
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.
Well that’s as clear as mud. Thanks.
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.
Clouds are not a gas; clouds consist of liquid and solid water. Water vapor in the atm. is not visible.
Correct.
But the pseudo science of the greenhouse effect theory:
https://en.wikipedia.org/wiki/Greenhouse_effect
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.
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.
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.
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.
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.
Here is the relevant paper, from 1959. Gavin Schmidt uses Plass as his touchstone, though Kaplan in this paper kneecaps Plass.
Dennis,
Have you checked the reference to the Kaplan paper on Google Scholar?
The main PDF entry there appears to link to a letter by Plass in 1961 and not the 1960 paper by Kaplan.
Philip, exactly. If you look into Gavin Schmidt’s background and what he uses as a touchstone, it is Plass. I have researched this a lot and what happened was that the USAF did their “upper atmospheric research” to figure out what wavelengths in the atmosphere were most transparent to IR radiation vs the exhaust temperature of jet engines. This is where the design of IR seeking missiles research started.
By the mid 1950’s spectrometers with wavelength resolution were built that were used to fully characterize the transmission wavelengths, and conversely the greatest absorptivity in the atmosphere. Based on where Kaplan was located, he probably participated in some of these upper atmospheric studies.
From these highly precise measurements of line broadening and the shapes of the spectral broadening across wavebands, it was determined that a Lorentz transformation of a gaussian function (which is what absorption emission lines are in a QM world) and that the transformation function is dependent on both temperature and pressure.
This is illustrated in any QM optical radiation textbook. Loudon’s 1967 version of Quantum Optics provides the fundamental equations for all of these functions.
Kaplan found that Plass, who used models all the way down, came up with a temperature function for CO2 that was 2-3x higher than what the actual experimental numbers came up with. Both the MODTRAN and HITRAN ,models used by the USAF have their ultimate heritage to all this (then) classified work that Plass probably did not have access to. I twas common in that ere that scientists working on classified projects where able to publish in open scientific literature if it was of general scientific interest that would not reveal the true purpose of the work.
Here are the references for that Kaplan paper…
ON THE LAPSE RATE and GHE WITHIN IT:
Oh dear, more models with opinions from people w/o a clue about the physics that controls everything. N&Z really proved the ideal gas laws are alive and well using mindless computer curve fitting models, which was fine as a presentation of a simple reality physics already knew. There was nothing wrong with this clearly stated modelling approach except presentation and a lack of physics understanding, as presented..
They seemed to me to miss the fundamental physics point. And decline to communicate on the matters of physics fact ex post.
While basically correct in their analysis, they made two mistakes of presentation by being too arrogant. They didn’t state, maybe didn’t realise, that they had confirmed the natural gas laws dominated the lapse rate, not the GHE, so they disregarded the proven deterministic physics, that supported them so well, while also denying the relatively small contribution of GHE as a real effect at the same time, so pissing off all the dogmatic so called scientists on hobby horses on both sides of the debate at once. Brilliant PR. Good work. No friends at all.
The simple and physically self evident point is that GHE, as described as the scattering of LWIR, just isn’t most of the cause of the thermocline/lapse rate to the tropopause. Physics 101. Those who could even begin to ignore the lapse rate are also denying the proven physics of the ideal gas laws to favour something they made up in a model and believe in, without physical law or observational support.. Error. Hard of physics. Climate scientists have a minimal grasp of the joined up physical world that physics knows.
The lapse rate to space is mainly created by a combination of the ideal gas laws, PV=nRT (do the physics before you start having baseless ideas?).
For an ideal gas this is 288 deg K at 1 Bar. Any one whi is doing this work should be able to do this for themselves , its High School physics..
The NASA pictogram simply doesn’t show what causes the lapse rate, it just quantifies the radiation and convective heat flows through the reducing temperature column of air to the tropopause, whose gradient is in fact mainly defined by gravitational pressure, as above. But nobody says.
By doing this NASA allows the unknowing to deceive themselves that all their 300W/m^2 of scattered LWIR fudge factor is GHE which is the cause of the entire lapse rate, which is utterly deceitful.
The atmospheric pressure already established a lapse rate, that is slightly modified by the scattering of a small part of the radiated LWIR, mainly from the oceans, most of the scattering is by the water vapour GHE, a smaller part by natural CO2, and a smaller part by AGW. A small effect on SST that is then mostly negated by the dominant oceanic feedback..
NUMBERS: If you look to the right of the NASA diagram you will see 105W/m^2 heading for the troposphere as convected latent heat, also c.50W/m^2 of the the 70W/m^2 reflected by the atmosphere is from the clouds this evaporation forms. Both vary significantly at the rate of several W/m^2 per global SST degree, that provides strong negative feedback to any SST change, the real control of climate, since there were oceans.
Now for the GHE component itself. Of the 50% of the incoming energy that is absorbed by the surface, 2/3 mainly leaves with the convected latent heat to be emitted as LWIR in the troposphere. Not radiated from the surface. The rest, 58W/m^2, is emitted from the surface as LWIR that passes through the ideal gas plus water vapour atmosphere on its way to space, where a small proportion, 18W/m^2, IS scattered by the GHE. But what effect does this really have on the overall climate system? I suggest it is small and nobody really knows, except that it is statistically unchanged in the planetary temperature records compared to similar past cycles
Because what we do know is that this warming phase of the interglacial is very similar to the pre industrial warmings in both range and rate, so is mostly natural, and any AGW GHE change undetectable. Let’s see what we have from NASA.
41W/m^2 goes straight to space unattenuated or scattered. About 18W/m^2 of the 58W/m^2 is scattered by the GHE, and the IPCC reckon 1.6W/m^2 of this is due to AGW. THat’s 10% of all GHE and 1% of all energy returned to the Tropopause. “Not a lot” to quote the scientific pairing of Morecambe, E and Wise, E.
I suggest the evidence of observation proves that models are so badly in error on the facts because they actually underestimate the power of the natural feedback that neutralises almost all the small warming perturbations created by the small change in GHE from GGs within the overall lapse rate, that dominates the raised surface temperature effect.
In particular the cloud albedo element of this is underestimated by modellers in their hot running models. I suggest their errors on the fact are compounded by their assumed oversensitivity to CO2 by IPCC modellers, also the partial selection of causes and effects they choose to include, such as nixing the clearly demonstrated solar wind effect on cloud albedo. These are all simple problems of pay to prove modelling science, an oxymoron in itself. SCience it ain’t, as models based on observations prove no physics. While creating a presumptive model to meet the demands of grant funding rather than to reflect the laws of physics and natural observations of record is can never be science, including omitting the dominant lapse rate effect nobody mentions. But I will.
The last thing the IPCC pseudo scientists want in their fairy tale radiative climate science is deterministic physical laws and methods that account for effects they wish to assign to CO2, for entirely non scientific political purposes.
Whatever the net result after feedback, the GHE/AGW perturbation itself should be quantifiable. Is 1.6W/m^2 what the IPCC think is the net effect after feedback by the controlling feedback, or a gross effect? Whatever, they clearly have the net effect wrong by a factor of more than 2, given the observations made to test their predictions by the UAH satellite and balloon data. And anyway, observed change is not significantly anomalous with past warmings, so where is this problem anomaly the modellers say they prove. In their virtual reality?
nb: while Most of the Lapse rate is simply pressure related, by real physical laws, I have as yet been unable to get the lower more closely representative average figure (than 288K for an ideal gas mixture) that using a higher global average R value for damp air would give. But a meteorologist could………….
Anyone here care to have a go and let me know the numbers.?
It’s empirical seaweed waving in science terms, but better than anything else, especially people who don’t understand the physics guessing it with a model.
So NIkolov and Zeller did a great job of supporting the physical laws and the physical reality of the lapse rate with their crude model, laws that they seemed not to know about. But their approach to presenting it and denying all GHE was a disaster, when they had the laws of physics behind them as regards the cause and scale of both effects, but seemed not to know and prefer to deny it? As a one time marketing guy between my STEM work, this amounted to self harming to me. Modelling 10/10, Communication 0/10. IMO. CPhys, CEng.
CAVEAT LECTOR:Your climate may vary. E&OE, correction of errors of fact and physics most welcome, with the facts. No opinions sought, or welcome, without the improved physics and facts.
Actual damp air surface temperature for lapse rate, before GHE, EVER so welcome, with working 🙂
“…also denying the relatively small contribution of GHE as a real effect at the same time, so pissing off all the dogmatic so called scientists on hobby horses on both sides of the debate at once. Brilliant PR. Good work. No friends at all.”
That about sums it up.
“My formula, like N&Z’s formula, neglects albedo, which we know must have an effect on planetary temperature.”
No! Neglecting albedo (accidentally) deals with the most profound mistake in determining the GHE. So it is a good thing to do. Why?
It is extremely simple. There is an albedo with regard to visible light, or SW radiation in general. In the LW range the albedo does not simply disappear, it is still there. So we have a SW albedo AND a LW albedo. The first impacts absorptivity, the latter emissivity, and both are required to calculate a GHE.
Of course in the end SW and LW albedo tend to cancel each other out, but that is just a tendency. So the most accurate approach is to precisely account for SW and LW albedo. In case you do not know LW albedo, the second best approach is to ignore both of them (again: they tend to cancel out each other).
The worst approach however would be, to only allow for SW albedo and assume there was no LW albedo. That will always give you a temperature which is too low and thus an erroneous GHE. As I have shown before, you even get a GHE on the moon. And of course it hugely overstates the GHE of Earth as well.
https://notrickszone.com/2020/09/27/plenty-of-physics-flaws-accumulate-into-a-huge-ghe-hoax-the-dark-secret-behind-surface-emissivity/
It is a logical error on the part of Mr Wentworth to suggest an albedo parameter should be added to his gas law calcs. It is already baked into the temperature pressure relationship in the equation presented, and so adding this redundant term results in a squaring effect.
It can’t possibly be true that albedo is “baked into” the formula. N&Z’s pressure formula would lead to a prediction that a planet like Earth, with water vapor and clouds, should have exactly the same temperature as a similarly-situated planet with a pure argon atmosphere, no water, and no clouds.
These different planets would absorb very different amounts of solar energy. Yet, N&Z’s formula predicts that, somehow, seemingly magically, this should make no difference.
You have used the gas law equation to confirm that d temp is proportional to d pressure across planetary bodies with varying atmospheric composition. The gas law model you used has no parameter to account for radiative effects. It is important to not over complicate the interpretation. For example, you have demonstrated that for a difference in mass-density of gases there is a proportionate difference in temperature. In this model there is no need to account for radiative effects of varying gases. It is deceptively simple, and almost unbelievable! This is the point of NZ observation; there is a fairly straightforward relationship between pressure difference and temperature difference across planetary bodies (when normalizing for solar input), no matter the atmospheric composition. There is no dispute that solar input differences between planetary bodies is required to compare long term mean annual temp. The point of suggesting albedo is “baked” into the temp pressure relationship is that it is not a parameter of your model and, yet, the model works. I’m sure you can find it by thinking in terms of the chosen model framework. It is important to consider that this, alone, does not validate or invalidate anything to do with greenhouse effect. However, it can be used as a framework for the discussion.
regards,
JCM
The error may stem from not recognizing that the analysis presented is a rearrangement of gas law to solve for the partial pressure of the gases listed (obfuscated in the coefficients arbitrarily i.e. representing the the 3 in relation to total pressure). Naturally it fits the same curve as NZ merely adjusted to a theoretical no atmosphere temp datum, an inconsequential detail from gas law perspective. Nothing is presented here to do with radiative input or energy balance.
I should add that the log adjustment to the parameters may simply be an element of calculation needed to offset the redundant mixing of molar mass and volume formula versions of gas law in the equation. This should be reduced – it is an important aspect to the discussion that molar mass version is used.
There is a clue in the admission that the model fit is broken when adding additional parameters to the equation, such as albedo. This speaks to the validity of the gas law relationship. It is only in the mind of Mr Wentworth that he has presented GHG based model, it is in fact based on pressure-temperature relationship in the math.
So, roughly, water absorbs as blackbody and emits 1/2 as much as blackbody?
Hmm. Greenhouse gases do 10 C?
I tended to think around 15 C.
One thing I was wondering about is scatter/diffusion/ect of IR longwave in regards to N2,O2, or with most of mass of the atmosphere.
Not quite, cause I was wrong ;). In the article I mentioned that the text book hemispheric emissivity was 0.91, while my own precise calculation gave me 0.934. This contradiction is solved by now and it was my mistake.
The mistake I made was to ignore the excinction coefficient in the Fresnel equation. I back-checked my results and they looked perfectly fine. Indeed the extinction coefficient does not make any difference in the SW range, and there the results matched. However in the LW range there was a substantial deviation, which I overlooked. My bad!
After fixing this issue I get 0.908 now, which is consistent with the text book. I mean given the precision is only down to 2 demical places and there are still factors not accounted for (different water temperatures, waves..).
So absorptivity remains unchanged at 0.934, but emissivity is actually lower, ~0.91. With that we get a temperature of (0.934/0.91 *342 / 5-67e-8)^0.25 = 280.5K
(Note: with a blackbody both terms are 1/1 and the temperature then is 278.7K)
In other words, I overstated the GHE. It is not 10K, but only about 7.5K.
And no, that does not mean GHGs would do a 7.5K. The problem is, clouds are net warming the planet and hold a significant share of those 7.5K. GHGs as such hardly cause any GHE. By now I also know why satellite data on CF are completely wrong. Real, empiric data however show the warming effect of clouds.
I know this will sound very confusing to anyone not having my highly advanced knowledge, so let me give you a hint: water is doing the same thing to the surface of Earth as it is doing to your body. If you sweat it cools you. Vapor is constantly transporting latent heat from the surface to the atmosphere, from where it gets radiated into space. This effect is a lot stronger than what vapor otherwise contributes to the GHE, which makes it an “anti-GHG”. This largely neutralizes the GHE of other non-condensating GHGs if we put them all into one basket.
“This effect is a lot stronger than what vapor otherwise contributes to the GHE, which makes it an “anti-GHG”. This largely neutralizes the GHE of other non-condensating GHGs if we put them all into one basket.”
Well, just because you sweat and cool down, it doesn’t mean guy next you is cooled by your sweating. But anyhow, you don’t think this is correct:
“As we can see water is an excellent vertical emitter, with an emissivity of 0.986. This number so close to 1 that you could say the difference was indeed negligible. But that is only part of the truth. With flatter angles the picture changes dramatically and finally turns to 0 emissivity towards the horizon.”
Because a lot emission occurs below 30 degree angle.
Or radiation is going into a hemisphere, and below 30 degree angle is where 50% of emission goes. Or very little goes straight up.
And ocean has more sunlight reach when sun is nearer zenith, and very little sunlight when sun lower than 30 degrees above horizon {or 60 degrees or more from zenith}
Not quite. You will need to include Lambert’s cosine law. If you take a hemisphere it is true that 50% of its surface is below 30° so to say. However ANY surface emits less towards “flatter” angles, and that is a seperate entity from the Fresnel curve.
So 50% of emissions go below a 45°(!) angle. The geometry is actually the same for a surface emitting into a hemisphere, as for a source of light shining onto a hemisphere.
Oh, after looking it a bit seems it’s rather narrow angle around 10 degree with a still surface- though with waves on ocean surface reflects in broader range- so from about 0 about 30 degrees
N&Z formulas are derived from data. At a basic level: they are just formalized empirical findings – like the Gas Laws. We should be skeptical of N&Z if we can make real world observations which falsify their formula(s). That’s called science. Sitting in our armchairs and supposing things which could make N&Z wrong is called fake science. If anyone here wants me to take them seriously on greenhouse gas formulas then describe the real world experiments done attempting to falsify GHGE. If you cannot do that then at least tell me what was done to validate the GHGE; and how well those validations went.
As far as I’m concerned the greenhouse gas effect, GHGE, is completely falsified. Its believers are reality deniers. GHGE is falsified by N&Z, Connollys (2014), Gerlich-Tscheuschner (2007, 2009), Ferenc Miskolczi, Ambika & Mishra (2020), the failure of reality to match model predictions wrt: the tropical hotspot, specific humidity mismatches, its violation of the 2nd law of thermodynamics.
PS: Ambika and Mishra 2020 Environ. Res. Lett. 15 124060 – found that: The Indo-Ganges plain cooled 0.8C during 1979–2018 while experiencing increased irrigation which led to a 2% increase in relative humidity. In GHGE: with increased humidity, temperature is suppose to rise – not fall. Reality does the opposite of what GHGE modelers order it to do.
Excellent review of opposing data.
Here’s some more recent experimental data failing to find CO2 radiative warming:
https://notrickszone.com/2021/04/01/physicists-lab-experiment-shows-a-co2-increase-from-0-04-to-100-leads-to-no-observable-warming/
“We should be skeptical of N&Z if we can make real world observations which falsify their formula(s).”
Ok, then. I hypothesize that “climate change on Earth during the modern era is actually exclusively determined by the rate at which pigeons flap their wings when flying at altitudes of over 20 meters. My “proof” is that I saw two pigeons on two different days, counted their flapping rates and it offered a great fit to the air temperature. A friend made a third observation of a pigeon in Brazil that was similar.
Apparently, you should be skeptical of this hypothesis only if you can make real world observations which falsify this hypothesis. Theoretical arguments are not welcome, only empirical falsifying evidence.
As with my pigeon hypothesis, N&Z’s hypothesis has no substantive affirmative evidence to suggest that it’s true. If you apply a chi-squared test to N&Z’s curve-fitting, there is literally a normalized chi-squared value of infinity, where normalized chi-square values less than about one or two are indicative of significance.
Science does not work by accepting hypotheses that are put forward on the basis of data with no statistical significance, and then requiring that these hypotheses be disproved.
(N&Z’s subsequent “validating” work hasn’t actually confirmed their pressure-causes-temperature hypothesis at all. If you examine the details of the that work, it turns out what N&Z have been validating have been side-calculations that are actually completely independent of their pressure-causes-temperature hypothesis.)
“the greenhouse gas effect, GHGE, is completely falsified… GHGE is falsified by N&Z… Gerlich-Tscheuschner (2007, 2009)”
I’m not familiar with all the sources you cite. But, if you include N&Z and Gerlich-Tscheuschner in your list, you appear to have an extremely low bar for quality of logic.
For what it’s worth, I’ve written a detailed critique of Gerlich-Tscheuschner (2009).
like you, N&Z have demonstrated that planetary atmospheres have pressure that is proportional to temperature. There is no cause and effect implied. The variables of temperature and pressure are proportional, this is known as gas law. This neither validates nor invalidates anything to do with GHGE. They have also demonstrated that rocky planets have a simple curve relating the temperature and pressure profiles between their atmospheres. Deriving this curve does not require any information about the radiative properties of the gases. You have shown this by inputting density, mass, and pressure (U) related to T. This too does not validate or invalidate anything to do with GHGE. We know that the properties of pressure and density will vary proportionately with temperature and mass. This is what your T vs U relationship shows. PV = nRT is the standard form of the equation, but we can substitute in molar mass, which you have done, to show the same relationship without need to account for V.
JCM
I’m glad you agree that “This [N&Z’s model and mine] neither validates nor invalidates anything to do with GHGE.” That’s my core thesis.
Beyond that, the “logic” you are applying is wrong. Or, more precisely, it seems to be so muddled that it’s “not even wrong.” I feel at a loss as to how to usefully engage with you any further.
That’s too bad and I’m disappointed it is muddled. Good luck to you and thanks for the discussion.
regards,
JCM
This model of thinking provides a common foundation to discuss mechanisms which may lead to changes to variables of ideal gas state equation in an atmosphere, such as gravity effects, albedo effects, GHG effect, direct solar effects, and other unknown effects.
For example gravity effects may impact density, pressure, and temperature. Albedo may affect density, pressure, and temperature. GHGE may affect density, pressure, and temperature; direct solar effects may impact density, pressure, and temperature. This line of thinking also opens the door to think about how changes to total mass may impact the other variables, and how it might relate to gravity. It also opens the door to the possibility that albedo in the form of ice and cloud is the result of ideal gas law variable states, a novel hypothesis. It is an interesting way to think about the relationship between the variables in a way that is not in dispute.
I’m not convinced by N-Z. There is nothing in their theory that explains why the effective temperature of Earth is at 0.5 bar. Or for that matter why the balance of any other planet is where it is.
I have calculated the pressure at the ERL for every planet with an atmosphere. They all lie in a narrow band with Venus at 0.05 bar at one extreme and Titan at 0.8 bar at the other. The rest have a balance in the range 0.3-0.4 bar.
Thinking about this I would expect the balance for a world with no GHGs to be at the surface. It would still have a lapse rate but the only source of heat for the atmosphere would be from contact with the surface so that would be the maximum.
Adding GHGs would move both absorption and emission upwards thus increasing the altitude of the balance point and therefore, by the effect of the lapse rate, increasing the surface temperature.
Comparing Earth, Venus and Mars and assuming the driver is CO2 results in a sensitivity of 3.2 per doubling of CO2. Another approach assuming that 15% of Earth’s emission is from CO2 and assuming increased CO2 moves that emission up proportionally gives 4.5. Both of these are on the high side but within the usually accepted range. I suspect the actual value is significantly lower due to other effects such as the proposed cloud
What we need is a theory that gives the ERL, as a pressure, for any atmosphere. I think such a theory would include the chemistry of the atmosphere.
their theory
What theory? How many times can you fail to understand that N&Z is an observation. Not a theory. Read the paper. Plot surface pressure and insolation in a 2d phase space. Observe them line up according to a fitted formula. That’s just observing the real world. That’s still allowed.
The “theory” is your interpretation of the observations.
N&Z offer an observation in the form of a correlation which has no statistical significance (a normalized chi-squared value of infinity), plus an unsubstantiated hypothesis that their formula describes actual physics.
Agree that N&Z curve fitting is far from physics.
I do however think they have a point when they talk about a planet with and without atmosphere.
A stone planet will be in local radiation equilibrium (since heat can not be transported).
With an atmosphere- heat can be moved from hot areas to cold areas. The radiation balance will be more “global”.
Redistribution of heat over a planets surface will increase the planets average temperature at radiation equilibrium.
This is straightforward math based on Stefan Boltzmanns law.
The amount of heat that can be transported is dependent on the heat capacity of the atmosphere, which is proportional to the mass, which is proportional to the pressure.
I agree that an atmospheric pressure can be expected to correspond with ability to transport heat laterally, thereby reducing global temperature variations and raising the mean global temperature to be closer to the radiative effective temperature. So, in that sense, atmospheric pressure can warm a planet.
But, it’s important to keep this effect in perspective.
At most, this temperature-smoothing can account for raising a planet’s temperature up to the radiative “effective temperature” given by a radiative equilibrium calculation involving the Stefan-Boltzmann law.
So, in particular, atmospheric temperature-smoothing cannot account for the 33 K warming above the no-atmosphere S-B radiative effective temperature on Earth, or the 505 K warming above this on Venus (cf., Smith 2008).
In principle, atmospheric temperature-smoothing could account for some of the 90 K in warming that N&Z claim is needed on Earth. However, Spencer 2016 showed that most of the warming this atmospheric effect could potentially account for is already explained by the temperature smoothing associated with the Earth’s fast 24-hour rotation period.
So, in the case of Earth, atmospheric temperature-smoothing might account for at most a few degrees of warming. But, it cannot account for the majority of atmospheric warming of Earth.
Appreciate that you share the basic ideas.
A globe with uniform temperature distribution would be around -18 C (glabal radiation balance)
A globe without heat redistribution would be around -80 C (local radiation balance).
The difference between local and global is definitely more than a few Centigrade.
Heat distribution over earths surface is a major factor regarding earths average temperature.
I do definitely think that N&Z are saying something important in this context.
Yes. However, what I asserted is that the atmospheric contribution to “the difference between local [low heat-retention] and global [temperature distribution]” is no more than a few degrees Centigrade.
Temporal temperature-smoothing turns out to be sufficient to account for most of the shift in radiative balance, even without any spatial heat-transport.
Spencer 2016 and Smith 2008 both compute that most of the temperature-smoothing shift from from local to global radiative balance is accomplished by other factors (the rapid rotation of the Earth and high surface heat-retention) even in the absence of any heat redistribution by the atmosphere.
So, while the total difference between local (without much heat retention) and global is large, the amount of this difference that atmospheric heat transport is responsible for seems to be quite small.
Yes, I agree with that. Sort of. What I actually agree with is that temperature-smoothing over the Earth’s surface is a major factor regarding Earth’s average temperature. Much of this temperature smoothing seems to be due to heat retention (due to heat conductivity and high rotation rate) rather than to heat transport between different locations.
I disagree with this, on two levels.
The moon is a stone “planet” and it receives the same amount of sun-radiation as earth (per square meter)..
My understanding is that the average temperature on moon is something like -80 to -90 C.
That is the equilibrium temperature for a stone “planet” at our distance from the sun.
The Moon is a stone “planet” that has a “day” length of 29.5 Earth days. According to calculations by Spencer (2016), simply speeding up the rotation of the Moon to match an Earth day would be expected to warm the average temperature of the Moon by roughly 55ºC.
So the mean temperature of the Moon (-76ºC according to N&Z) is the equilibrium temperature of a stone “planet” at our distance from the Sun if that planet has a 29.5 day rotational period.
But, the equilibrium temperature of a stone “planet” at our distance from the Sun with a 24-hour rotational period would be perhaps 55ºC warmer than that, i.e., perhaps -21ºC.
The rotation rate of a planet matters!
* * *
A planet has a an “effective” temperature Teff which may be computed using the Stefan-Boltzmann law. But, if the temperature of the planetary surface varies in time or in space (over the surface of the globe), then these variations result in an actual temperature lower than Teff.
The reason that the Moon is so much colder than Teff is, according to my sources, primarily because of temperature variations in time, and only secondarily due to variations in space. As Willis Eschenbach said, “The low average lunar temperature is a consequence of the size of the temperature swings.”
A faster rotation rate greatly smoothes out temperature variations in time, substantially warming a planet, holding all other conditions unchanged.
(N&Z assert that rotation rate doesn’t matter. But, they are clearly mistaken. N&Z’s predictions in this regard don’t match what anyone else calculates, and are not consistent with the observed time variations of temperatures on the Moon.)
* * *
Does the relevance of rotation rate make sense to you?
I’ve made the same point several times, and it seems as if it’s not making an impression. I wonder where the disconnect might be? Is there something about what I’m saying that doesn’t make sense to you?
Bob, there are a couple issues causing disconnect here that I see but can’t summarize easily.
1) N&Z, Willis are right in that rotation rate doesn’t matter for radiation energy budget balance. Willis’ piece also points out the moon multiannual energy balance is around 304 in and 304 out in W/m^2 terms (albedo 0.11) which won’t vary with rotation speed. The issue enters in that global temperatures cannot properly be added or divided (intensive property) and that process has to happen to get an average diurnal and global temperature.
2) Another issue is what is meant by equilibrium? Clearly temperatures varying from 390K to 190K per day (diurnal) are not in equilibrium and properly shouldn’t be averaged. Dr. Spencer finds moon equilibrium temperature on avg. about 0.05m deep but again that is from averaging diurnal temperature. Vasavada 2012 finds equilibrium depth about the same using avg. diurnal temperature and 0.25m deep without averaging daily temperature (no-diurnal cycle found that deep).
My view is the no-diurnal cycle thermometer derived temperature of Vasavada is more compelling for lunar equatorial global equilibrium temperature around 240K being the better lunar physical near surface equilibrium temperature. Don’t have a quick resource to extend that for lunar global equilibrium temperature as I haven’t found one.
[Only after finishing this comment did I realize I was talking to Trick, rather than Jonas.]
I’m glad we’re getting to the issue, namely, that you don’t believe rotation matters. That helps clarify what’s worth talking about.
Willis’s piece does not say that “rotation rate doesn’t matter.” It says the opposite.
So, Willis is in the camp of those who say that rotation rate matters. Of the sources we’ve talked about, N&Z are alone in their position.
It should also be obvious that, at some point, rotation rate is going to matter. What if the Moon rotated once per hour? Once per minute (and was strong enough to not fly apart)?
If a planet rotates fast enough, the planetary surface won’t have time for the temperature to vary much during the course of a rotation. And if temperature doesn’t vary as much, the planet must be warmer.
So, it’s definitely wrong that rotation rate never matters. That can’t possibly be right.
The only question is, how much does a change in rotational period from 29.5 days to 1 day matter? Willis, Spencer, and Smith all calculate that it makes a big difference.
* * *
Much of the result of your comment leads me to believe that you’re confused about issues that need not be confusing.
Yes, that’s what allows one to calculate the effective radiative temperature, Teff, using S-B.
I agree that won’t change with rotation speed. But what rotation speed changes is how much colder the actual temperature will be, compared to Teff.
When they say temperatures can’t be added, that means that adding them doesn’t yield any physically meaningful state variable. But that doesn’t mean you can’t add them, if you just want to compute a statistical metric, like “mean temperature.” Adding them for statistical purposes is entirely legitimate.
What is in equilibrium is the total energy budget over the course of a rotation. If you integrate 𝜀𝜎T⁴ over the the time of a rotation, that rigorously gives you the number of Joules/m² radiated by a portion of the surface during a rotation, and that needs to balance the amount of solar irradiance absorbed during that same period.
There’s nothing improper about doing such a calculation. Do you perceive a problem with it?
Well, the temperature 0.05m deep is what is likely to be relevant for calculations of 𝜀𝜎T⁴, since radiation occurs at the surface.
The temperature 0.25 m deep is useful for assessing the diurnal mean, for use in calculating the global mean temperature. It’s not particularly useful with regard to calculating 𝜀𝜎T⁴.
So, the different measurements have different purposes.
I’m not clear what your concern about this issue is.
As I understand it, the procedure is: you use 𝜀𝜎T⁴ to do radiative balancing, and then you use T (possibly T deeper down to help diurnal averaging) to compute the global mean temperature.
It sounds like you’re feeling uneasy about the process, and suspicious of some of the approaches?
Bob! Read my statement more carefully: “N&Z, Willis are right in that rotation rate doesn’t matter for radiation energy budget balance.”
Willis & Dr. Spencer are also right that rotation rate does matter for diurnal surface temperature averaging. This means your whole comment needs a rewrite.
Willis does not write about temperature at depth as does Dr. Spencer. At a depth of roughly 0.25m (per Apollo thermometers), the diurnal temperature swings are ~zero so no temperature averaging is necessary. That depth provides a more physical lunar equatorial equilibrium temperature of 240K as shown in Vasavada 2012 Fig.7.
I’m sorry if I misinterpreted.
There are two distinct versions of what I imagined the phrase “radiation energy budget balance” might mean:
From your wording, it wasn’t clear to me if you were talking about #1 or #2. I guessed #2 (apparently incorrectly), because I couldn’t imagine why you would bother saying rotation doesn’t affect #1.
If you’re saying rotation rate doesn’t matter for #1, calculating Teff, then of course that’s true. It’s true by definition, and doesn’t require any evidence or citing of who agrees with it. I’m not clear on why it is worth saying, or what it adds to the conversation?
N&Z asserted that rotation rate doesn’t matter with regard to the outcome of calculating #2. That’s an interesting, and false, assertion.
That’s what I have assumed the conversation was about.
More “physical” than what?
More physical than the average temperature computed at a depth of 0.05 m? As Vasavada Fig. 7 indicates, averaging temperature at a depth of about 0.05 m should yield just about the same result as averaging at 0.25 m. The former requires averaging over a rotation, while the latter does not, but so what?
More physical than Spencer‘s 212 K figure? But, 240 K is a mean equatorial temperature and 212 K is a mean global temperature, so they are not comparable.
So, I’m not clear on what point you are making.
* * *
I confess I feel rather lost as to why you’re talking about what you’re talking about.
Do you see these issues of somehow having relevance to the question of whether or not N&Z’s conclusion (that rotation rate doesn’t impact the result of calculating GMAT) is correct?
If so, would you be willing to spell out the connection you are perceiving? I’m afraid I don’t get the significance of the things you are writing.
”More “physical” than what?”
Averaging an intensive property like temperature. Eliminating that diurnal temperature averaging process over even a rotation in the 0.2m subsurface is more natural for lunar equilibrium thermometer temperature.
N&Z in their 2014 publication analyze rotation rate effect on subsurface temperature of a lunar regolith covered Airless Spherical Celestial Object to find: “the annual mean temperature of the subsurface is not impacted by ω” and “The heat storage fraction can only be altered by a significant change in the apparent thermal conductivity of the regolith, which requires the introduction of a qualitatively different environment such as adding atmospheric pressure to the surface.” This is at least consistent with Dr. Spencer: “This (0.05m deep) is the thickness of soil assumed to be uniform in temperature”.
I agree N&Z analysis is likely correct for their specific airless regolith subsurface case thus is limited as it tends to agree with their ref. Vasavada 2012 Fig. 7 & Dr. Spencer. N&Z give other references to read for a deep dive down the rabbit hole for anyone interested.
The equatorial Vasavada thermometer 240K subsurface equilibrium probably means the global brightness temperature ~200K or ~212K is too low due unknown global lunar surface emissivity and surface powder diffraction issues. I am unaware of any further research papers on the subject.
N&Z’s calculation (p. 16-17) to analytically relate their ad hoc heat storage parameter η to actual heat conduction is somewhat convoluted and appears to me to contain serious logical errors. I’ll need to go though it more carefully to be certain.
In contrast, Spencer’s calculation showing that the results do depend strongly on rotation rate involves a more straightforward calculation.
N&Z’s calculations and Spencers reach very different conclusions, and one needs to decide which one to believe.
Willis also believes that rotation rate would affect the Moon’s temperature, though his logic is less rigorous.
N&Z are totally alone on this issue.
* * *
N&Z’s assertion also violates any reasonable intuition about how things must behave at the limits of the parameter space.
N&Z conclude that “the annual mean temperature of the subsurface is not impacted by ω”, but this cannot possibly be true for a planet with high thermal conductivity. For sufficiently high thermal conductivity, it’s clear that fast rotation will result in smaller temperature swings than slow rotation. And the size of those temperature swings affects the resulting temperature calculation.
It might be true that for some range of rotation rates, and some range of thermal conductivities, the temperature results are insensitive to rotation rate. But, that’s not what N&Z assert. They assert insensitivity to rotation rate as a blanket truth. This is clearly false and unphysical.
Smith analyzes a rotating airless planet and in his parameterization (p. 5, see definition of 𝝀) finds it natural to introduce a tradeoff between heat capacity and rotation rate; increasing one is equivalent to increasing the other.
N&Z only validate their analysis for the Moon. They don’t check its validity for any rapidly rotating body.
* * *
It is beyond me why you would believe N&Z’s results regarding the impact of rotation rates when this disagrees with Smith, Spencer, Willis, and common sense regarding what must happen in the limit of high rotation rates.
“N&Z are totally alone on this issue.”
N&Z are discussing only real subsurface brightness temperature equilibrium & are not alone. By “this” you are unclear what issue you mean: surface or subsurface temperatures.
Dr.s Spencer, N&Z 2014, Vasavada 2012 Fig. 7 in some of their own words I clipped discuss real SUBSURFACE temperatures which they all agree DO NOT depend on planet rotation rate (diurnal illumination avg.s) at some depth.
Willis & Smith are only discussing SURFACE brightness temperatures which they show DO depend on diurnal illumination rotation rates as Smith and Spencer demonstrate mathematically
.
Appears to me you have mixed up surface and subsurface discussions by the various authors.
Sure, you can idealize a planet with “high thermal conductivity” but that is not real. In my reading of the works there is no physics disagreement between N&Z, Vasavada, & Spencer as they all agree real SUBSURFACE temperatures DO NOT depend on celestial object rotation rate at some small depth less than 0.5m depending on assumed soil properties.
We seem to be somehow talking about entirely different subjects. I’m not sure how to cross the gap.
I find no indication that Vasavada 2012 considers varying the rotation rate. To come to the conclusion that temperature “does not depend on rotation rate”, they would need to run their models for some rotation period other than the Moon’s actual period of 29.5 days. Could you point our where they do this?
All authors (and I) agree that at some depth beneath the surface, temperature will not depend on “time of day”. That’s what Fig. 7 (which you repeatedly reference) shows.
But, that has nothing whatsoever to do with whether the average temperature changes if you change the rotation rate of the celestial body. Which is the issue that I am talking about.
I am not bothering to specify that, because for what I’m talking about it does not matter.
As Vasavada Fig. 7 shows, the average temperature is the same, regardless of depth, once you go deeper than about 2 mm.
I am not talking about whether the temperature changes with “time of day.” I’m talking about whether the average temperature changes if you change the rotation rate.
* * *
Can you make sense of what the disconnect between us is?
“I find no indication that Vasavada 2012 considers varying the rotation rate.”
They consider just the lunar slow rotation rate and write p.7: “Because the near-surface regolith is highly insulating, heat exchange occurs only within the upper 30 cm at the equator [Vasavada et al., 1999], and diffusion of energy is slow.” Due to that consideration, Vasavada implies the lunar rotation rate doesn’t matter at that subsurface depth as shown in their Fig. 7 which is same as Dr.s Spencer and N&Z conclusions – see their comments already clipped.
“But, that has nothing whatsoever to do with whether the average temperature changes if you change the rotation rate of the celestial body.”
Rotation rate has nothing whatsoever to do with real subsurface temperatures at some depth, and with your physics accomplishments you should eventually agree with Dr.s Spencer, N&Z, and Vasavada et. al. that at some depth real subsurface temperature conditions are independent of rotation rate.
“I am not bothering to specify that, because for what I’m talking about it does not matter.”
Dr.s Spencer, N&Z, and Vasavada all disagree with you on that for real subsurface equilibrium temperatures. Depth matters for temperatures due soil physics as they write. And they are not writing about time of day issues, nor am I.
To find where you disconnect with those three, I’d search for why you feel a need to introduce “time of day” where none of the other authors use those words for their discussion of subsurface equilibrium temperature at a depth (less than 0.5m) where rotation rate doesn’t matter.
Trick, It is now 100% clear to me that you and I are talking about different issues when we refer to whether or not “rotation rate affects equilibrium temperature.”
So, we are talking “past” one another.
If you’re interested in working with me to sort through how we are using words differently, then perhaps we could find a way of having a productive conversation.
In the absence of that, I don’t think continuing is likely to be productive.
Same issue, different depths.
Real airless spherical celestial object top surface temperature is a function of rotation rate & there is no equilibrium temperature achieved though a Tmean can be found, see N&Z 2014 equatorial Fig. 5. See also Vasavada 2012 equatorial Fig. 4 for our moon.
Real airless spherical celestial object subsurface temperature is independent of rotation rate at a depth depending on soil properties & there is a diurnally unchanging equilibrium temperature achieved at that depth per Dr.s Spencer “uniform”, Vasavada equatorial Fig. 7, and N&Z 2014 p. 16 of 21.
That’s about as simple, and no simpler, as I can write it including ref.s.
Everyone (you, me, all our sources) agrees that there is a “diurnally unchanging equilibrium temperature achieved at that depth”.
No source (other than N&Z) asserts that that the “diurnally unchanging equilibrium temperature achieved at that depth” does not change if one changes the rotation period.
Nothing whatsoever about Vasavada’s Figure 7 “implies the lunar rotation rate doesn’t matter at that subsurface depth.”
You are making an unfounded inference.
Ok. Looks like you need an explanation of Vasavada Fig. 7. A simple one that can be no simpler would be best but I may not achieve it.
At 0.4m depth, the equatorial temperature is shown stable at equilibrium 240K over the entire diurnal cycle, or to use Dr. Spencer’s term “uniform”. That means temperature at this depth is independent of the diurnal cycle. As the rotation rate changes the equatorial temperature 240K does not change at 0.4m depth. Supported by N&Z detail soil physics.
At 0.01m depth, the equatorial top surface temperature varies from about 100K at night to about 390K during the day. Here no equatorial temperature equilibrium is achieved although a Tmean could be calculated and it will be less than 240K (as shown about 212K). That means temperature at top surface is dependent on the diurnal cycle. As the rotation rate changes the temperatures change at the top surface. Slower the spin, the wider the curve ends at the top and vice versa.
NB: Note how quickly in depth the Vasavada Tmean converges to its equilibrium value of 240K by about 0.05m which is consistent with Dr. Spencer’s detail solution depth.
Thanks for laying out your thinking more explicitly.
Most of what you say I agree with and have understood all along.
Where I do not agree is when you say:
As far as I can tell you offer no evidence at all of this assertion beyond saying “Supported by N&Z detail soil physics.”
I dispute N&Z’s analysis, and am looking for independent evidence. Citing N&Z doesn’t count for that purpose.
You’ve asserted that sources other than N&Z are supporting the above conclusion. Yet, I’m still waiting for the evidence of that.
Perhaps you are thinking that the observation “That means temperature at this depth is independent of the diurnal cycle” somehow implies independence of rotation rate? It so, that is in no way true.
Rotation rate affects the magnitude of the temperature fluctuations at the surface. As you observe, “Slower the spin, the wider the curve ends at the top and vice versa.”
At any location on the surface, there is an effective radiative temperature Teff which the surface would have if there were no temporal fluctuations in temperature. This is determined by S = 𝜀𝛔Teff⁴.
At the surface, the actual temperature is time dependent, T(t). It must be the case that S = 𝜀𝛔Teff⁴ = 𝜀𝛔<T(t)⁴>. We know that by Holder’s inequality, this means <T> < Teff. The more widely T(t) swings, the bigger the difference will be.
Now, suppose the temperature at 0.4 m depth is T₀. Using Newton’s cooling law, the heat transfer rate between the surface and the deeper regolith goes as dQ/dt = -h A (T(t) – T₀). We know that if we integrate over a diurnal period, the heat transfer must average to zero. This leads to <T(t)> = T₀.
But we know that T(t) varies widely and <T(t)> is lower when the rotation is slow, and and T(t) varies less and <T(t)> is higher (closer to Teff) when the rotation is fast. Therefore, since T₀ = <T(t)>, the stable temperature at depth, T₀, varies with the rotation rate.
The only way N&Z could be correct is if the magnitude of surface temperature fluctuations was independent of rotation rate. And, it’s not.
(I imagine that funny business where the average at the very surface doesn’t quite match has to do with some complexity of the thermal interactions in the irregular surface. But that sorts itself out by the time you get to the depth Spencer used, 0.05 m.)
“I dispute N&Z’s analysis, and am looking for independent evidence. Citing N&Z doesn’t count for that purpose.”
Which step exactly in the N&Z soil thermal energy analysis do you dispute? Clip that disputed step if need be. See Dr. Spencer’s post & search on “uniform” for Dr. Spencer’s independent evidence agreeing with N&Z p. 16of21 conclusion. Vasavada Fig. 7 development details from soil properties also independently support N&Z p.160f21.
“As far as I can tell you offer no evidence at all of this assertion beyond saying “Supported by N&Z detail soil physics.””
Read Vasavada explanation of their Fig. 7 development work closely where you will find the evidence you seek agreeing with N&Z soil thermal energy analysis. Way too detailed to go into here but maybe you can find something with which to dispute Vasavada Fig. 7 development and call it out too.
“You’ve asserted that sources other than N&Z”
Dr. Spencer blog post and Vasavada 2012 Fig. 7 development are independent others (though N&Z do cite Vasavada). The Smith work also implies support or at least nothing to dispute N&Z p.16of21.
”Therefore, since T₀ = <T(t)>, the stable temperature at depth, T₀, varies with the rotation rate.”
That’s hearsay. Please show a worked example. If you do it properly, as did Dr. Spencer, the equilibrium temperature at 0.5m will not vary diurnally as temperature there will be found “uniform” (Dr. Spencer term) and not a function of rotation rate. Use Dr. Spencer’s detail example work as a guide (which is not hearsay).
The only way to get the equatorial thermometer 240K equilibrium at 0.5m (from Apollo data) to change is with insolation and surface optical property changes & not with rotation rate. The rotation rate changes simply spread the top surface temperatures to wider, or less wide, ranges from zero spin (wide) to rapid spin (narrow).
Thermodynamics by itself has nothing to say about the time to the equatorial 240K subsurface equilibrium temperature; it’s hearsay but pretty sure our moon has had sufficient time at that Vasavada analysis 0.5m soil depth to achieve equilibrium.
I wasn’t “hearsay”; it was a proof. Please tell me which step you disagree with.
“uniform” means not a function of time. It does not have anything to do with whether or not temperature is a function of rotation rate.
I disagree with your use of the word “Therefore” after which you simply jump to a physically unsupported conclusion. Show your physics work to support your contention as do the other mentioned authors. In detail.
You also need to show a worked example as did Dr. Spencer for “uniform” & Vasavada 2012 Fig. 7 global equatorial temperature equilibrium down at 0.5m. If done properly, the results will agree with those two authors.
That the equatorial global temperature ranges diurnally at the top is weather affected by rotation rate; that the temperature 0.5m down is not affected by diurnal rotation rate is climate.
Take your time searching for a step where you dispute N&Z’s p16of21 work, you will need to show your work as did N&Z.
I continues to appear that we are having a very odd communications breakdown—or perhaps you’re simply trolling me?
I already agree with those two authors.
It’s just that the things you’re pointing to have seemingly nothing to do with the question I am interested in.
That’s what leads me to believe that some sort of communications disconnect may be happening.
With respect, it’s not up to you to say what I “need” to do, unless you’d like me to start treating you in a similar way?
I don’t particular trust N&Z’s work, pp. 16-21. But, it’s not worth sorting that out because I deeply do not trust the validity of their more foundational choice of parameterizing their results using their “heat storage parameter” 𝜂. There are non-physical assumptions built into their model in regard to this parameter. They appear to assume that the heat released at night comes out at a steady rate, rather than being a function of the temperature difference, and this is profoundly non-physical. They use an “effective” value of 𝜂 to account for variations of 𝜂 over different lattitudes. This parameterization represents a non-physical representation of heat-conduction, and I have zero reason to trust any conclusions based on using it as the basis of their model.
I’m really surprised that you disagree with the most trivially true step in the proof. It’s as if you said you don’t believe in the transitivity of the “equals” relationship. It ought to be logically impossible to disagree with that step if you agreed with the preceding steps.
Maybe it will be useful if I lay things out a little more formally.
[SETUP]
[ASSUMPTION 1] Suppose that heat conduction is given by Newton’s cooling law, so that the heat transfer rate between the surface and the deeper regolith goes as dQ/dt = -h A (T(0,t) – T(d,t)). [I know this isn’t entirely accurate, but let’s see what this assumption leads to.]
[CLAIM 1] Given that 𝟂₁ < 𝟂₂/10, 𝟂₁ is a much slower rotation rate than 𝟂₂. We expect that the temperature swings in T₁(0,t) will consequently be significantly larger than the temperature swings in T₂(0,t).
[CLAIM 2] We assume energy balance, such that the solar irradiance absorbed over a day balances the thermal radiation emitted by the surface. Therefore, S = 𝜀𝛔Teff⁴ = <T₁(0,t)⁴> = <T₂(0,t)⁴>.
[CLAIM 3] Because of CLAIM 1 and CLAIM 2, we expect that <T₁(0,t)> < <T₂(0,t)> < Teff (This example illustrates an analogous situation, albeit with spatial variations instead of temporal variations.)
[CLAIM 4] Given ASSUMPTION 1, dQ/dt = -h A (T₁(0,t) – T₁(d,t)). However, we know that over a diurnal period, in steady-state, dQ/dt must integrate to zero. Or equivalently, <dQ/dt>=0.
[CLAIM 5] It follows from CLAIM 4 that <T₁(0,t)> – <T₁(d,t)> = 0. It follows that <T₁(0,t)> = <T₁(d,t)>.
[CLAIM 6] A result analogous to CLAIM 5 must also be true for rotation rate 𝟂₂. In particular, <T₂(0,t)> = <T₂(d,t)>.
[CLAIM 7] Combining CLAIM 3 with CLAIM 4 and CLAIM 5, it follows that <T₁(0,t)> = <T₁(d,t)> is less than <T₂(0,t)> = <T₂(d,t)>.
[CLAIM 8] Restating CLAIM 7, it has been shown that different rotation rates 𝟂₁ and 𝟂₂ lead to different mean temperatures <T₁(0,t)> = <T₁(d,t)> and <T₂(0,t)> = <T₂(d,t)>, respectively.
QED.
I wonder if your response to this will clarify how we are seeing things differently?
Could you clarity which CLAIMs you agree with? And which CLAIMs if any you disagree with, and why? (Would you be willing to take the SETUP and ASSUMPTION as givens, for the moment?)
I realize that CLAIMS 1 and 3 aren’t specified with full rigor. I’m wondering if you can agree with the possibility that these might be true?
Bob, you write you agree with authors I’ve pointed to Vasavada 2012 Fig. 7 and 2016 Spencer’s “uniform”:
“This (0.05m depth) is the thickness of soil assumed to be uniform in temperature that responds to solar heating and IR cooling. Of course, in reality the very top of the soil surface will get the hottest/coldest, with the temperature swings dampening strongly with depth; the model just uses a thin, uniform-temperature layer that approximates the average behavior of the real, thicker layer. “
Then you write without providing the exact question: “It’s just that the things you’re pointing to have seemingly nothing to do with the question I am interested in.” Read Dr. Spencer’s paragraph closely and determine your answer to this within Dr. Spencer’s context:
What is the question in which you are interested?
——
I’ve only pointed out what you need to do to convince me, here is another way to write a response for nth time:
“I wonder if your response to this will clarify how we are seeing things differently?”
You have left off albedo in your energy balance but I don’t think that matters. Your notation is headache inducing but at the end Claim 8 puts your d at, for example, intermediate 0.1m depth for Vasavada’s work and 0.01m depth for Spencer’s work where diurnal rotation rate omega1 or omega2 matters. Nothing wrong that I can spot though my headache may be in the way.
You agree with those two prior to complete temperature swing “dampening” (Spencer term) so you haven’t as yet addressed the T=240 equilibrium at 0.4m for Vasavada and 0.05m for Spencer due to:
“the temperature swings dampening strongly with depth”.
You need to realize there is a reasonable small depth where the surface temperature diurnal swings have totally “dampened” out from the rotational T swings thus rotation rate no longer matters as I have been writing & N&Z show p.16of21.
Read Dr. Spencer’s first sentence again, this “dampened out” totally depth is where the Vasavada soil temperature 240K only responds to “solar heating and IR cooling” meaning NO rotation rate response where any choice of omega0, 1, 2 or infinity doesn’t matter.
Why do you mention that? Yes, I agree to that? So? You must mean it believes something different than I do, because it doesn’t directly impact the question I’m interested in.
Every time I’ve tried to put it into words, there has been so little sign that you’ve understood me as I intended that I no longer think it’s useful to try to express it in any informal way.
The formal expression of my question is: Is my CLAIM 8 correct?
I’m in a similar position, waiting for you to convince me.
But, since we’re apparently not talking about the same question, I don’t know what you would be trying to convince me of.
No. You can’t work backwards from the conclusion to deduce d.
You need to determine d in accordance with the way it is defined in the SETUP.
By assumption, T(d,t) does not vary at all over a diurnal period. In Vasavada that puts d at 0.4 m. In Spencer d would be 0.05 m or deeper.
Claim 8 is a conclusion that follows from that assumption, unless there is an error in the logic of the proof.
Yes. I have agreed with that all along.
No. This is a false inference.
If you can’t see that the last part of your sentence and the first part are not the same, then I understand why this conversation has been unable to progress.
“You can’t work backwards from the conclusion to deduce d”
I didn’t.
“By assumption, T(d,t) does not vary at all over a diurnal period”
At d=0, t=0 night find Vasavada Fig. 7 T(0,0)~100K
At d=0, t=+1/2day find T(0,1/2 day) ~390K
Thus your new assumption is wrong, T(d,t) varies over a diurnal period. As an exercise, repeat that at d=0.1
Then do it again at d=0.4 to prove to yourself that rotation no longer matters at that depth.
——
I understand why this conversation has been unable to progress your understanding since you have not yet actually agreed with Dr.s Spencer and Vasavada that rotation does not matter for the lunar equatorial equilibrium temperature at depth = 0.4m and only the “solar heating and IR cooling” (Dr. Spencer terms) matter at that depth. Same as N&Z demonstrate physically p.16of21.
The definition of d was this statement:
So, d ≥ 0.4 m for Vasavada.
That’s how d was defined.
T(z,t) is the general function. but d is a specific depth that satisfies the above definition.
You could talk about T(z,t), where z=0.
It’s invalid to talk about d=0, etc., because then d wouldn’t satisfy its own definition.
If T(d,t) actually varies in time, that’s NOT d.
Given the above, the proof establishes CLAIM 8: different rotation rates 𝟂₁ and 𝟂₂ lead to different mean temperatures <T₁(0,t)> = <T₁(d,t)> and <T₂(0,t)> = <T₂(d,t)>, respectively.
* * *
It’s time for me to turn my attention elsewhere.
I wish you well.
“Let z=0 denote the surface, and z=d denote a depth where the temperature T₁(d,t) and T₂(d,t) do not vary over a diurnal period; i.e., each is a constant with respect to t.”
Bob, your use of “and” in Queen’s English means both “z=0 denote the surface” AND “z=d” where “each” is a constant temperature wrt to t, meaning both surface 0 depth and at depth d being constant. I pointed out this assumption is wrong using Vasavada Fig. 7.
Perhaps you might rephrase & use proper Queen’s English for your assumptions. Dr.s. Vasavada, Spencer, AND N&Z each AND all use proper English & physics to show you there is a soil depth where lunar rotation rate doesn’t matter to lunar equatorial equilibrium temperature which I have contended all along thusly:
Airless celestial object rotation rate matters for a temperature range at the equatorial surface z=0. Rotation rate doesn’t matter for equatorial equilibrium temperature at some reasonable small soil depth – only Dr. Spencer’s “solar heating and IR cooling” matter at that depth as I have written consistently.
After the daft assertion by N&Z I developed a model for the same planetoid plus a few they conveniently omitted and within the limits of available information, the model was a reasonable fit.
I didn’t publish, because during the process of obtaining the various bits of data, it became obvious that many of the things like surface temperature were calculated using a version of my own model in reverse. In other words, the data N&Z are using is calculated using a model based on the physics which they claim is wrong.
But the simple fact, is the assertion that physics is “wrong” is utterly daft. Indeed, I’ve just created a new model which has nothing to do with climate, which again uses the same physics – it’s impossible to do without it.
“It should also be obvious that, at some point, rotation rate is going to matter. What if the Moon rotated once per hour? Once per minute (and was strong enough to not fly apart)?
If a planet rotates fast enough, the planetary surface won’t have time for the temperature to vary much during the course of a rotation. And if temperature doesn’t vary as much, the planet must be warmer.”
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Interesting comment.
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Only half the planet is receiving energy no matter how fast the planet spins.
The amount of energy received is exactly the same over exactly the same area.
Due to the SB law the amount radiated out goes up by the 4th power of the temperature?
But this is also the amount coming in.
Feynman might enjoy say that on balance energy in equals energy out.
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If trying to marry the average of two temperatures which vary at different rates dependent on rotation then the cold that a sunless side will get down to compared to the warmth that a permanently sunlit side struggles to increase means that the seeming average temperature in a rapidly rotating planet will be higher than that when it is not rotating.
This is meaningless given that the effective radiating temp is unchanged as energy in is energy out.
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The two of you are playing semantics based on flawed statements as to what the parameters of an average temperature actually mean.
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From a practical point of view extreme rotation causes other structural changes that would effect the type of atmosphere that could exist and the pressures that it would be stable under.
If N and Z ignore this then their whole model is compromised.
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From a layman’s point of view it is hard to see that pressure does not produce heat in the lower atmosphere as it certainly doesso in the earths depths. The problem of comparing air in a hypothetical glass column to air in an atmosphere with seas, gravity, wind, currents and all the friction involved renders the former a thought bubble.
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While perpetual motion machinery is impossible the practicalities of physics means that materials can appear to generate energy in a perpetual way to the unquestioning. The sun is a prime example of seemingly inexhaustible energy.
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N and Z are wrong about GHG not having an effect.
Part of their problem is not admitting that and incorporating that and rotation into their notion of pressure temperature relationship which has to exist because of physics.
It is sad to see so many bright minds and ideas so determined to destroy the vestige of GHG effects that they exclude the real effects from their work.
Just as sad to see others shoot them down for excluding GHG while excluding the role of the physics of heat and pressure.
Most of the people on both sides are quite up with the physics but have a mote in their eye due to their dogma.
.
While I can’t say that Ned Nikolov and Karl Zeller”s paper was flawless, I can say with complete certainty that Wentworth’s above speculations are, indeed, “nonsense”. The facts (NOT THE THEORIES) do bear out the possible truth of an interplanetary pressure-temperature relationship, as N&Z have claimed. But they positively do not bear out even the remote possibility that the exact composition of a planetary atmosphere affects a world’s surface temperature (when it comes to gases absorbing emitted infrared radiation — I am not considering here upper atmosphere particulate matter blocking sunlight), again, as N&Z have claimed.
One example is Mars, with over 20 times the “global-warming” CO2 in its atmosphere than Earth but with temperatures that cause that CO2 to solidify at the poles. If you look at the upper atmosphere (above 150,000 feet) of Venus, you see the same thing — the CO2 of Venus isn’t warming anything up there.
But the best example is the Earth: the spatial-temporal pattern of surface warming we have seen on Earth for the last 200 years proves, conclusively, that NOTHING in our atmosphere is the cause of it (CO2 or anything else).
Our atmosphere is a very kinetic fluid, 780 times less dense than water. It flows a lot. It moves around and mixes with itself in such a manner that in 3 months any gas below the stratosphere is guaranteed to have mixed itself uniformly throughout the entire planet. Therefore, the forcing effect on temperature of any infrared absorption of any gas in that atmosphere will even itself out over the entire planet in that same time frame. But that’s not what we observe. The facts show no such homogeneity in global warming — no way, Jose. So it can’t be anything in the atmosphere causing that warming.
Furthermore, the oceans of the Earth have gained much more heat energy over those 200 years than the atmosphere. Again, how could a warming atmosphere warm the oceans more than itself? Again, no way.
These facts of course don’t prove N&Z right. But they sure prove Wentworth and all the bevy of climate “scientists” using similar “climate modeling” methodologies dead wrong.
Theories are nice. But facts are the ultimate arbiter of whether your theories are true. They matter.
David Solan