Guest Post by Willis Eschenbach
Did you know that one watt per square metre is equal to one kilogram per cubic second?
I sure didn’t know that, and at first I didn’t believe it, but it’s true.
(Yeah, yeah, I know it’s a second cubed and not a cubic second, but a metre cubed is a cubic metre, so I had to find out just what a cubic second might look like when it stepped out of the shadows … but I digress …)
The thing I like best about climate science is that I am constantly learning new things. For example, I came across that fascinating fact because against my better judgement I decided to take a look at the recent paper, charmingly yclept “Emergent Model for Predicting the Average Surface Temperature of Rocky Planets with Diverse Atmospheres”, by Den Volokin and Lark ReLlez, paywalled here. It has been gathering attention on some skeptical websites, so I thought I’d take a look even though it is just another in the long string of fitted models purporting to reveal hidden truths. As it turns out, it is a fascinating but fatally flawed paper, full of both interesting and wrong ideas.
The Abstract and Highlights say:
Highlights
• Dimensional Analysis is used to model the average temperature of planetary bodies.
• The new model is derived via regression analysis of measured data from 6 bodies.
• Planetary bodies used for the model are Venus, Earth, Moon, Mars, Titan and Triton.
• Two forcing variables are found to accurately predict mean planetary temperatures.
• The predictor variables are solar irradiance and surface atmospheric pressure.
Abstract
The Global Mean Annual near-surface Temperature (GMAT) of a planetary body is an expression of the available kinetic energy in the climate system and a critical parameter determining planet’s habitability. Previous studies have relied on theory-based mechanistic models to estimate GMATs of distant bodies such as extrasolar planets.
This ‘bottom-up’ approach oftentimes utilizes case-specific parameterizations of key physical processes (such as vertical convection and cloud formation) requiring detailed measurements in order to successfully simulate surface thermal conditions across diverse atmospheric and radiative environments. Here, we present a different ‘top-down’ statistical approach towards the development of a universal GMAT model that does not require planet-specific empirical adjustments.
Our method is based on Dimensional Analysis (DA) of observed data from the Solar System. DA provides an objective technique for constructing relevant state and forcing variables while ensuring dimensional homogeneity of the final model. Although widely utilized in other areas of physical science to derive models from empirical data, DA is a rarely employed analytic tool in astronomy and planetary science.
We apply the DA methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the Solar System, i.e. Venus, Earth, the Moon, Mars, Titan (a Moon of Saturn), and Triton (a Moon of Neptune). Twelve prospective relationships (models) suggested by DA are investigated via non-linear regression analyses involving dimensionless products comprised of solar irradiance, greenhouse-gas partial pressure/density and total atmospheric pressure/density as forcing variables, and two temperature ratios as dependent (state) variables. One non-linear regression model is found to statistically outperform the rest by a wide margin.
Our analysis revealed that GMATs of rocky planets can accurately be predicted over a broad range of atmospheric conditions and radiative regimes only using two forcing variables: top-of-the-atmosphere solar irradiance and total surface atmospheric pressure. The new model displays characteristics of an emergent macro-level thermodynamic relationship heretofore unbeknown to science that deserves further investigation and possibly a theoretical interpretation.
Well, that all sounded quite fascinating ,,, except for the part where I didn’t have a clue what dimensional analysis might be. So I went to school on that question. Here’s what I found out.
As we generally know but rarely stop to consider, the various special units that we use in science, like say watts per square metre, can all be expressed in the fundamental SI “base units” of mass (kilograms or kg), length (metres or m), time (seconds or sec or s), temperature (kelvins or k), and the like.
Dimensional analysis is a method of combining the variables of interest to make new dimensionless variables. Let’s say we have N variables of interest, we’ll call them x(1), x(2), x(3), x(4) … x(N). Dimensional analysis combines them in such a clever way that the fundamental dimensions cancel out, and thus what remains are dimensionless variables. This ensures that whatever we do with the variables the units will be correct … because they are dimensionless. Nifty.
Next, I found out that there is a mathematical theorem with the lovely English-sounding name, “The Buckingham Pi Theorem”, which sounds like it should calculate the appropriate dessert amounts when you have tea with the Queen. Anyhow, it states that if you have a system defined by a function involving N dimensioned variables, f(x(1), x(2), x(3), x(4) … x(N)), you can reduce the number of variables. The theorem states that by using dimensional analysis to combine the N dimensioned variables into dimensionless variables, you end up with N – m variables, where “m” is the number of SI base units involved (e.g. kg, m, etc).
So that sounded like a most promising theoretical method, worth knowing. It would seem that almost any model could be simplified by that method. However, at that point, they take their dimensionless sports car out on the autobahn to see how it performs at speed … and that’s where the wheels come off.
They applied dimensional analysis to the modeling of planetary surface temperatures. They decided that the following variables were of interest (sorry for the “MANUSCRIPT” across the page, it’s a samizdat copy):
Since there are six variables and four fundamental units, the Buckingham Pi Theorem says that they can be reduced to two dimensionless variables. A neat trick indeed. Then they used twelve different combinations of those dimensioned variables converted into dimensionless units, and tried fitting them to the data from six rocky celestial bodies using variety of formulas, including a formula of the form:
y = a exp(b x) +c exp(d x)
Out of all of the possible combinations of variables, they looked at 12 different possibilities. After trying various functions including the dual exponential function above, they picked the best function (the dual exponential) and the best combination of variables, and they produced the following graph:
Note that they started out with six celestial bodies, but at the end they couldn’t even fit all six with their model, so they “excluded” Titan from the regression. This is because if they left it in, the fit for Venus would really suck … in scientific circles this is known as “data snooping”, and is a Very Bad Thing™. In this case the data snooping took the form of selecting their data on the basis of how well it fit their theory. Bad scientists, no cookies.
Once they’ve done that, hoorah, their whiz-bang new model predicts the “thermal enhancement” of six celestial bodies with amazing accuracy … well, it does as long as you ignore the celestial body it doesn’t work so well for.
In any case, “thermal enhancement” is defined by them as the actual planetary surface temperature Ts divided by the temperature Tna that the planet would have it were an airless sphere. So “thermal enhancement” is how much warmer the planet is than that reference temperature. And here is the magic equation used to derive the results:
In the formula, P is the atmospheric pressure. Pr is the pressure at the triple point of water, 611.73 pascals. Pr is not important, it is a matter of convention. All that changing Pr does is change the parameters, the answer will be the same. As such, it seems odd that they include it at all. Why not make Pr equal to 1 pascal, and cancel it out of the equation? I have no answer to that question. I suspect they use 611.73 pascals rather than one pascal because it seems more sciencey. But that may just be my paranoia at work, they may have never considered canceling it out.
So there you have their model … what’s not to like about their analysis?
Well, as it turns out … just about everything.
Objection the First—If the formulas don’t fit, you must acquit
Let me start at the most fundamental level. The problem lies their assumption that the surface temperature of a planet with an atmosphere can actually be modeled by a simple function of the form:
Surface Temperature = f(x(1), x(2), x(3), x(4) … x(N))
I find the idea that the climate is that simple to be laughable. As an example of why, consider another much less complex system, a meandering river in the lowlands:
Notice the old river tracks and cutoff oxbows from previous locations of the river. Now, we have variables like gravity, and the slope of the land, and the density of the soil, and the like. But I would challenge anyone to successfully combine those variables in a function like
Average position of river mile 6 = f(x(1), x(2), x(3), x(4) … x(N))
and make the formula work in anything but special situations.
This is because a) the location of the river is always changing, and more importantly, b) the location of the river today is in very large measure a function of the location of the river yesterday.
In other words, the only hope of modeling this system is with an “iterative” model. An iterative model is a model that calculates the river’s position one day at a time, and uses one day’s results as input to the model in order to calculate the next day’s values. Thus, an iterative model MAY be able to calculate the ongoing state of the system. And this is exactly why climate models are iterative models of just that type—because you can’t model such constantly evolving systems with simplistic equations of a form like
Surface Temperature = f(x(1), x(2), x(3), x(4) … x(N))
So that is my first objection. The formula that is at the root of all of this, a simple dual-exponential, is extremely unlikely to be adequate to the task. The surface temperature of the earth is a result of a host of interactions, limitations, physical constraints, inter- and intra-subsystem feedbacks, resonances, thermal thresholds, biological processes, physical laws, changes of state of water, emergent phenomena, rotational speed, the list is long. And while you might get lucky and fit some simple form to some small part of that complexity, that is nothing but brute-force curve fitting.
Objection the Second – Von Neumann’s Elephant
John Von Neumann famously said, “With four parameters I can model an elephant, and with five I can make him wiggle his trunk”.
As near as I can determine there is one parameter used in the calculation of Tna, the hypothetical and unknowable “no atmosphere temperature”, and another four parameters in Equation 10a, for a total of five parameters.
It gets worse … when a parameter has either a very small or a very large value, it indicates a very finely balanced model. When I see a model parameter like 0.000183, as occurs in Equation 10a, it rings alarm bells. It tells me that the model is applying very different formulas to small and large numbers, and that’s a huge danger sign.
Next, they had full choice of formulas for their model. There was nothing limiting him to a double exponential, they could have used any formula they pleased.
Next, they tried no less than twelve different combinations of dimensioned variables before finding this particular fit.
Finally, there are only five data points to be fit. I can guarantee you that when the number of your model’s tuned parameters equals or exceeds the number of the data points you are using for your fit, you’ve lost the plot and you desperately need to trade up to a new model.
So my second objection is to Von Neumann’s elephant, with five parameters fitting the formula to the pathetically small number of only five data points, augmented by twelve variable combinations, and a free choice of formulas. That kind of fitting is not a model. It’s a tailor shop designed to make a form-fitting suit.
Objection the Third—Variable Count
The authors make much of the claim that they can calculate the temperature of five planets using only two variables. From their conclusion:
Our analysis revealed that the mean annual air surface temperature of rocky planets can reliably be estimated across a broad spectrum of atmospheric conditions and radiative regimes only using two forcing variables:TOA stellar irradiance and average surface atmospheric pressure.
But then we look at the calculations for Tna, which is a part of their magic equation 10a, and we find three other variables. Tna is defined by them as “the area-weighted average temperature of a thermally heterogeneous airless sphere”. Here is their equation 4a, which calculates Tna for the various celestial bodies.
So we have as additional variables the albedo, the ground heat storage coefficient, and the longwave emissivity. (Volokin et al ignore the cosmic microwave background radiation CMBR, as well as the geothermal flux.)
In other words, when they say they only use two variables, “TOA stellar irradiance and average surface atmospheric pressure”, that is simply not true. The complete list of variables is:
TOA stellar irradiance
Surface atmospheric pressure
Albedo
Heat storage coefficient
Longwave emissivity
So my third objection is that they are claiming that the model only uses two variables, when in fact it uses five.
Objection the Fourth: Data Snooping
They say in the Abstract:
We apply the DA methodology to a well-constrained data set of six celestial bodies representing highly diverse physical environments in the Solar System, i.e. Venus, Earth, the Moon, Mars, Titan (a Moon of Saturn), and Triton (a Moon of Neptune).
But then they have to throw out Titan, because it doesn’t fit, which is blatant data snooping … and despite that, they claim that their model works wonderfully. And of course, the “six planets” from the Abstract is the number quoted around the blogosphere, including by WUWT commenters.
Objection the Fifth: Special Martian Pleading
While they use standard reference temperature values for five of the six celestial bodies, they have done their own computations for the temperature of Mars. One can only presume that is to give Mars a better fit to their results—if it fit perfectly using the canonical values, there would be no need for them to calculate it differently. Again, data snooping, again, bad scientists, no cookies.
Objection the Sixth: The Oddity of Tna
Immediately above, we see the complete equation 4a for Tna, the area-weighted average temperature of an airless sphere. It depends on three variables: albedo, how much heat the ground soaks up during the day (heat storage fraction), and the emissivity. The authors actually use a simplified version of that formula. After showing the entire formula, they note that they will reasonably ignore the geothermal flux and the cosmic background radiation, because they are quite small for the bodies in question. OK, fair enough, that’s common practice to ignore very minor variables. But then they say:
Since regolith-covered celestial bodies with tenuous atmosphere are expected to have similar optical and thermo-physical properties of their surfaces (Volokin and ReLlez 2014), one can further simplify Equation [4a, see above] by combining the albedo, the heat storage fraction, and the emissivity using applicable values for the Moon to obtain:
Tna = 32.44 S^0.25 (4c)
Equation (4c) was employed to calculate the ‘no-atmosphere’ reference temperatures of all planetary bodies in our study.
I find that to be an unwarranted and incorrect simplification. I say this because it is clear that the reason the temperature of the moon is so low is because it rotates so slowly. It has two weeks of day, then two weeks of night. This increases the day-night swing of the temperature, because it lets the moon’s night-time temperature drop to a rather brisk -180°C or so.
And for a given solar input, whatever increases the surface temperature swings decreases the average temperature. With a day-night temperature swing of 270°C, the average lunar temperature is much, much colder than the S-B blackbody temperature.
But those huge temperature swings are NOT characteristic of the Earth, or Mars. Even without an atmosphere, the surface temperatures of those planets wouldn’t swing anywhere near as much as the moon because they all rotate much faster than the moon. With faster rotation, the days can’t get as hot, and the nights can’t get as cold. This means that their average temperature would not be depressed anywhere near as much as the moon, because the swings are smaller. As a result, while Equation 4c is accurate for the moon, it says that an airless earth rotating once a day would have the same temperature as the moon, and that’s simply not true. And for Venus, the opposite is true. With a rotation period of 116 days, its average surface temperature would be correspondingly lower, again leading to an incorrect result.
CONCLUSIONS:
Well, my conclusion is that this model fails a number of crucial tests. The equations are not physically grounded and are of doubtful simplicity. It is a Von Neumann trunk-wiggling monstrosity with a free choice of formulas, five tunable parameters, and 12 combinations of variables. They have done their fit to a ridiculously small dataset only six planets, and failed at that, only fitting five. As a result, they removed one of the six from their fit, which is blatant data snooping. They claim only two variables when there are actually five. They have calculated their own temperature for Mars. And finally, they erroneously calculate the reference temperature Tna as if the Earth, Venus, and Mars rotate once every 28 days. This last one is critical to their actual result. Their model results report the surface temperature Ts divided by Tna … and since Tna is badly wrong for at least three of their five data points, well, it’s just another in the long list of reasons why their results do not hold water.
You’d think we’d be done there. But nooo … in a final burst of amazing hubris, they use their model results as a basis to claim that they “appear” to have discovered a new unknown thermodynamic property of the atmosphere, viz:
Based on statistical criteria including numerical accuracy, robustness, dimensional homogeneity and a broad environmental scope of validity, the final model (Equation 10) appears to describe an emergent macro-level thermodynamic property of planetary atmospheres heretofore unknown to science.
I’m sorry, but what the authors describe is merely a simple dual-exponential multi-parameter curve fitting exercise that after trying an unknown number of formulas, no less than twelve different variable combinations, and five tunable parameters, finally got it right an amazing five out of five times … by using the wrong values for Tna, re-calculating the temperature of Mars, and throwing out the one data point that didn’t fit. Which is impressive in its own bizarre manner, but not for the reasons they think.
However, who would have guessed that such a curve-fit had such a strong scientific capability that it could reveal a new “emergent macro-level thermodynamic property” that is “heretofore unbeknown to science?
Dang … that’s some industrial-strength trunk-wiggling there.
However, at least the part about dimensional analysis was fascinating, I need to look into it more, and it revealed unknown dimensions to me … a watt per square metre is a kilogram per cubic second? Who knew?
My regards to everyone,
w.
As Always: Let me request that if you disagree with someone, please have the courtesy to quote the exact words you object to. That way, we can all understand the precise nature of your objection.
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The climate models have far more trunk wiggles than this. It is sad that skeptics use the same failed techniques as the CAGW-ers.
The best part about this is to point out how much BS most modeling of complex systems is…
I have a pink noise model that models historical GISS temperatures. It even predicts the future! It only took a couple of hours of compute time to find the magic state for the random number generator. I wrote it to demonstrate the absurdity of it all, by being very absurd.
Peter
You have to admit though, that the paper makes the Drake equation look exceedingly accurate regardless the variables used.. 🙂
Venus does not rotate faster than the moon.
My bad … but it doesn’t change the problem, just changes the direction. Venus rotates much more slowly than the moon and so would be proportionately colder …
w.
Venus rotates so that it always presents the same face to earth at closest approach. This observation flies in the face of those that suggest that forces between planets are too small to affect climate.
Venus is unique in having a length of day measured in hundreds of earth days. If earth for example rotated once every 200 days, our climate would be fantastically different than our current climate. Daytime temperatures would be much hotter than current and nighttime temperatures much lower.
What is fascinating about Venus is that daytime and nighttime temperatures are almost identical. None of the radiative GHG theories about surface temperatures are able to explain this. Unless and until we have a successful theory that can predict observed Venus temperatures we are unlikely to have a successful theory that can predict Earth temperatures.
Since Venus’s atmosphere is not transparent to a rather large spectrum, I would be more concerned about the movement of the air rather than the ground. Minor in regards to the scope W’s analysis.
But Venus has a retrograde rotation to consider as part of the calculation? Irrelevant I suppose in the overall analysis. Rotation is tricky business when comparing 2 objects orbiting different primary bodies.
Earth’s daytime and nighttime — and even equatorial and polar — temperature is remarkably constant . . . at the surface of the lithosphere/bottom of the hydrosphere. At least as constant as Venus’s surface-of-the-lithosphere temp, I should imagine. 🙂
The capacity of Venus’ atmosphere to transport heat would seem to negate the thermal effects of slow planetary rotation.
Why are the planets in the graph arranged by Ts / Tna results? Of course using anything else would make a travesty of the whole thing. Thus, one could make a chart of how many grams of food we each ate for supper last night + our shoe size, and arrange it so it makes a nice graph.
Some people use a system of units where e = c = h (or is it h bar ?) = 1
So they view energy and mass as identical ( E = m = nu (or f) )
George,
It’s h-bar, but c is not 1 in those units.
Willis
You have a set of dimensional relations at the top but just because the dimensions are all the same it does does mean the values are all the otherwise you would be able to say that e.g. miles = kilometres. There is a scalar constant in the conversion e.g. 1 mile =1.8 kilometre and likewise for you other relations
Sorry, I was too hasty there. Willis’ relationship does work numerically. Dimensional analysis is very useful, but you need to watch out for dimensionless factors in expressions – I remember seeing somewhere a whole heap of pseudoscience resulting from someone equating the gravitational force with the electromagnetic force, because they have the same dimensions (both forces) and, hey, they must be equal numerically. Not Willis’ example however – that does work
jimmi_the_dalek September 2, 2015 at 3:04 pm Edit
Thanks for that, Jimmi. I’m not any kind of expert in dimensional analysis, but I do know how to carry units through and cancel them.
However, I also do know how to make foolish mistakes, so your vigilance is entirely appropriate.
Regards,
w.
ferdberple wrote:
About your first paragraph: yes, if rotation of the Earth took 200 days, daytime temperatures would be much hotter and nighttime temperatures much colder. However, the differences would be smaller than in the moon, despite this one rotates faster than every 200 days. The reason is we have an atmosphere and an ocean, and both would circulate and redistribute heat between the two “faces” of the Earth.
And this leads to your second paragraph: this phenomenom is why Venus daytime and nighttime temperatures do not differ too much. Because it has a super dense atmosphere capable of redistributing an enormous ammount of energy at great speed. So it seems that the “succesful theory that can predict observed Venus temperatures” is there in plain sight.
The only question I want answering is whether or not the temperature is related to atmospheric pressure and the obviously correct answer is that it is. So, whilst I doubt that atmospheric pressure on its own determines the temperature, it certainly plays a huge part in setting the “greenhouse” temperature.
So, sorry, your conclusion which fails to mention this is rather like Obama talking about receding Alaskan Glaciers and failing to mention they’ve been receding since the 1800s.
Scottish Sceptic September 2, 2015 at 12:38 am
We have no evidence showing that the surface temperature is related to total atmospheric pressure. What we have is a bogus model claiming that it is related. Oh, plus you making the same claim.
So, sorry, your conclusion which fails to mention this is totally unsupported by the facts. You are free to believe what you want, and to babble about how my actions are like those of Obama … but when people start comparing me to totally random people like the president, I know they’ve lost the plot. The only reason a man like you starts slinging mud is because you’re out of real ammunition …
w.
Erm, do you say ‘totally’? I agree on ‘this is bad science’ part.
We have no evidence showing that the surface temperature is related to total atmospheric pressure.
===============
please explain why Venus has almost identical daytime and nightime temperatures, with a length of day of 243 earth days, combined with very high surface temperatures. which model of planetary surface temperatures successfully predicts this?
clearly the answer cannot be radiation, because this would lead to a large difference between daytime and nighttime temperatures. an atmosphere without convection would be isothermal. the temperature of this isothermal atmosphere is determined by radiation from the sun.
however, with convection you get conversion between PE/KE and an atmospheric lapse rate. this lapse rate is a function of KE/PE, modified by phase change of the convective gasses. starting with the temperature of an isothermal atmosphere, the lapse rate increases temperatures below the midpoint of the convection, and reduces temperatures above the midpoint of the convection.
it is this lapse rate increase in temperatures below the mid-point of the convection that increases surface temperatures over what they would have been had the atmosphere been isothermal. thus the near constant surface temperature of Venus is explained by the very large mass of the atmosphere leading to a very much larger conversion between KE/PE and the resulting enhancement of surface temperatures as compared to an isothermal atmosphere. This overwhelms the effects of daytime radiation at the surface.
ferdberple September 2, 2015 at 6:59 am
Thanks, ferd. Basic answer seems to be, nobody knows for sure. However, here is a model of planetary surface temperatures which successfully explains such a small variation. Don’t know if it is correct or not, but it certainly is a candidate.
I note that their explanation has nothing to do with yours. However, you seem to have arrived at your explanation by a process of elimination (i.e., you say it can’t be radiation so it must be your explanation). To which I’d misquote the Bard by saying that there are more things in Heaven and Venus than are dreamt of in your philosophy …
All the best to you,
w.
“We have no evidence showing that the surface temperature is related to total atmospheric pressure.”
Now, that’s just silly. Of course atmospheric pressure plays a part. It plays a part in all models, including the ones the IPCC uses. The dry adiabatic lapse rate, which limits the actual lapse rate, is calculated fundamentally based, in part, on atmospheric pressure. See derivation here.
If you have TOA temperature, then you just extend it down to the surface via the lapse rate. The real question is, how does TOA temperature get set, and at what height (ERL – Effective Radiating Level) is it evaluated? The people who claim surface temperatures have nothing to do with greenhouse gases are claiming that TOA temperature and ERL can be determined independently of atmospheric composition.
I do not agree with that assessment. I agree with those who say that, in the absence of greenhouse gases, the atmosphere would become isothermal. To establish a lapse rate in the first place, there must be a heat sink at TOA. However, it does not follow that sensitivity to added GHG is monotonic. There is a point of diminishing, and possibly even decreasing, returns as convective overturning becomes significant. But, that is wandering off topic for this post.
There are a number of your points which I find underwhelming
——————-
1)
“When I see a model parameter like 0.000[0]183, as occurs in Equation 10a, it rings alarm bells.”
But, you also say
“Pr is not important, it is a matter of convention. All that changing Pr does is change the parameters, the answer will be the same.”
Well, if it is not important, multiply it by 1000, and your coefficient will become something close to 0.0183. Feel better now?
2)
“The complete list of variables is:
TOA stellar irradiance
Surface atmospheric pressure
Albedo
Heat storage coefficient
Longwave emissivity”
These are not free parameters being fitted, so they cannot be part of the tuning to fit the elephant.
3)
The exclusion of Titan may be reasonable. After all, it is not a planet, but a moon. It spends considerable time in eclipse, and OTTOMH it may receive significant radiation from its parent.
——————-
Dimensional analysis is, indeed, a powerful tool. But, it is not definitive. I think the study says only, here is a formula which fits the data to some degree. Further investigation required to determine what, if any, value it has. I don’t think your critique establishes that it is worthless, even as I doubt that it is significant.
Bartemis said “I agree with those who say that, in the absence of greenhouse gases, the atmosphere would become isothermal.”
A molecule going up against gravity loses energy. A molecule going down with gravity gains energy. Do the math.
“A molecule going up against gravity loses energy. A molecule going down with gravity gains energy. Do the math.”
The molecules are not in free fall. Upper atmosphere particles are buoyed upward by lower atmospheric particles.
“The molecules are not in free fall. Upper atmosphere particles are buoyed upward by lower atmospheric particles.”
Molecules are not in free fall for very long between collisions. But that short free path is enough for a small change in energy, multiplied over the many mean free paths between ground and upper atmosphere.
Published in Nature Geoscience last year. A common tropopause is reached at 0.1 bar atmospheric pressure on all planets with atmospheres (reaching 0.1 bar, Mars doesn’t get that high).
http://faculty.washington.edu/dcatling/Robinson2014_0.1bar_Tropopause.pdf
Now whether the common 0.1 bar tropopause temperature in all these planets and moons is equal to [Solar Irradiance * (1-Albedo) / 4] noting they are all at different distances from the Sun and have different Albedo is the question. If they are, the common lapse rates also seen would then say the surface temperature just depends on how thick the atmospheres get. The farther the surface is from the 0.1 bar pressure level, the hotter the surface will be.
Hanelyp
Properly speaking, a molecule going up against gravity, does not lose energy—–it’s kinetic energy falls and its potential energy rises, and overall energy is unchanged, minus some friction loss during the movement. Vice versa for a molecule falling with gravity—–potential energy converts to kinetic energy.
Sorry to nitpick, but important when considering energy fluxes in an atmosphere.
I keep coming across this claim, or something like it, and it is really annoying. In equilibrium, atmospheric pressure has nothing to do with temperature. If we suppose that the gravitational force of a planet is suddenly increased, then the atmosphere will be compressed, and heat will be generated by compression, but that is a temporary, one-off effect, as the heat will be dissipated through the atmosphere and ultimately radiated into space. A new equilibrium is then reached, with the resulting stable gradient of pressure generating no heat and no gradient of temperature. To suppose otherwise would violate both the 1st and 2nd Laws of Thermodynamics.
I think there is another objection – the atmospheric pressure on the moon and Triton at least are so low that the “fit” is not a test. The curve is almost vertical there. If the temperature of the moon was 10% higher, it would still fit just as well. Even Mars would continue to fit well if the temperature were reduced. There are really only two planets which test the goodness of fit. Not impressive, given the number of parameters.
This is absolutely very important thing to note.
I was pondering that as well, good point Nick.
Thanks, Nick. I suspect that is the reason for the dual exponential fit. One exponential works at very low pressures, one works at high pressures, so it covers both ends of the spectrum. Unfortunately, it’s covering both ends with bovine waste products, but we can’t have everything …
w.
“Anyhow, it states that if you have a system defined by a function involving N dimensioned variables, f(x(1), x(2), x(3), x(4) … x(N)), you can reduce the number of variables.”
This sentence is missing something imho.
Thanks for the lecture on curve-fitting. It’s amazing!
Willis Eschenbach:
Dimensionless analysis is often used in physical modelling. I write to provide a hopefully amusing anecdote which derives from an example of this.
In the 1980s and 1990s the UK’s Coal Research Establishment (CRE) developed novel power generation methods that used fluidised beds. The systems used air blown, high temperature (i.e. ~1000°C), fluidised bed reactors with a variety of designs. Full scale and true temperature examples of these fluidised beds were constructed, operated and studied.
Optimising designs of the reactors required observation of the behaviours (e.g. flows and mixing) of gases and particles within the fluidised beds. To that end ‘cold models’ of the fluidised beds that operated at ambient temperature (i.e. ~20°C) were used. But parameters (e.g. viscosities and densities) are very different at 1000°C and 20°C and, therefore, dimensionless analysis was used to determine how the ‘cold models’ could be constructed.
The dimensionless analysis determined that particles of wheat had the required density to represent silica particles when doing the cold modelling. And the models were full-scale so used many tons of these grains.
Unknown to us, mice discovered that the grain store was a rodent version of paradise. Thousands of them were displaced from the grain store when the modelling finished and the grain was removed.
In the subsequent weeks it was impossible to find a lab. or an office that did not have mice wandering around in plain sight. People with musophobia were too terrified to come to work, and this situation existed until the pests were exterminated.
Richard
Great story.
Does make me wonder: did the presence of mice in the modeling medium affect results?
ticketstopper:
Probably not. At least, there was no detected affect.
Mouse droppings would have contaminated the grain but no mice were observed to be fluidised in the models probably because the grain passed through a sieve on removal from the grain store (but perhaps they did not like theme park rides). Indeed, this size selection is why the mice remained when the grain was completely removed after the modelling was ended.
Richard
I doubt it, the viscosity of a mouse at 1000 degrees is negligible 😉
Titan and Triton – why?
Of all the rocks in all the solar system, why those?
It just seems so arbitrary. And then they exclude one anyway. It seems so strange.
Titan is interesting because the dominant greenhouse gas on that moon is nitrogen. Well, I find that interesting.
Actually, its Methane.
The dominent “greenhouse gas” on Jupeter is hydrogen. It is pressure creates the high temperatures on Jupeter.
Actually, its nitrogen. Why didn’t you check it out first Ed?
https://geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdf
What’s also interesting is that Titan has an anti-greenhouse effect. An atmospheric layer that blocks sunlight coming in and allows infrared out.
pressure creates the high temperatures on Jupeter.
=====================
pressure alone cannot explain the high temperatures, because statistical thermodynamics predicts that due to conduction all atmospheres will be isothermal.
however, when you add convection to the mix the situation changes. convection allows for the introduction of a lapse rate, where the conversion between PE/KE leads to warmer temperatures at the bottom of the convection and colder temperatures at the top of the convection.
thus, it is actually the mass of the atmosphere coupled with the gravitation force of the planet that provides PE/KE increase in surface temperatures, with the energy from the sun (along with radioactive decay within the planet) being the driving force to create the convection.
ferdberple September 2, 2015 at 7:12 am
Convection does cause a thermal gradient. However, it doesn’t make the surface warmer and the upper atmosphere cooler. It just makes the upper atmosphere cooler. We can prove this by contradiction. Suppose we have a very fast-rotating planet with an atmosphere with no greenhouse gases of any type.
Like all planets at equilibrium, that planet would be radiating the exact amount of energy that it receives. And since the surface is the only thing on the planet capable of radiating energy (no GHGs in the atmosphere), its surface temperature is such that it emits the precise amount that it gets from its sun.
Now, suppose there is some mysterious effect of gravity that could warm the surface, as you claim. How much energy would the surface be constantly radiating at that point?
Well, it would be constantly radiating more energy than it is getting from the sun … which as we all know is not possible.
Q.E.D.
w.
ferdberple @ur momisugly September 2, 2015 at 7:12 am
“… convection allows for the introduction of a lapse rate…”
It’s the other way around. Convection requires a thermal gradient to flow from hot to cold. You’ve got to have a heat sink at TOA in order to establish a persistent gradient.
“You’ve got to have a heat sink at TOA in order to establish a persistent gradient.”
I think everyone is somewhat right here. Yes, you have to have a heat sink somewhere to drive convection. But the cold polar region at surface will do fine, because it radiates to space. Once you have gas motion with gravity, then as ferd says, that forces a lapse rate. Vertical motions, with adiabatic heating on compression, pumps heat down, as long as the temperature gradient is below the DALR.
And as Willis says, the surface temperature is fixed by the radiative balance requirement. I use the following analogy. Vertical motion creates a temperature difference, like the voltage of a battery. But the surface balance “earths” one end, and that completes the fixing of temperature.
All this works with or wothout GHGs. But with GHG’s, the “earthing” tends to happen at TOA, where the radiative balance is enforced.
Willis wrote:
Thanks a lot for that Willis, it is the nicest way to demonstrate the absurdity of the Dragon Slayers’ theory that I have seen so far. No possible response. I will memorise it and repeat the next time that I face one of them.
Willis — why would a pressure differential only cool the upper atmosphere and not warm the lower?
I imagine a box with gas in, receiving whatever energy it receives from the nearest star, so its temperature is X throughout. If I apply a gravitational field on the side away from the star, the gas thickens on that side and thins on the star side. With the total energy the same, seems as though the temperature (which I’m thinking of rather as “density of motion”) must increase at the “bottom” and decrease at the “top” — with the average remaining the same, so the whole system still radiates just as much as it receives.
It’s clearly the case that, however hot it is today in my home town, if I go straight up to, say, 29000 feet at the same latitude and longitude, it’s going to be colder. When people speak of “the” temperature of the Earth, I assume they mean some average.
Where the average temperature itself comes from, I have no idea.
??
“Willis — why would a pressure differential only cool the upper atmosphere and not warm the lower?”
Indeed. The potential difference warms the surface by making the upper atmosphere cooler. The upper atmosphere then radiates less heat.
Willis may be assuming the ground or lower troposphere in radiative equilibrium with space, instead of a layer in the upper atmosphere.
mellyrn September 3, 2015 at 9:26 am
This is the illusion, that gravity alone can create a persistent temperature difference. It cannot. If it could, all we’d have to do is thermally isolate a tall column of the atmosphere. Then gravity would make the lower end hotter and the upper end cooler … and we could run a heat engine on the temperature difference forever.
But that is a perpetual motion machine, and those are not possible.
w.
“This is the illusion, that gravity alone can create a persistent temperature difference. It cannot. If it could, all we’d have to do is thermally isolate a tall column of the atmosphere. Then gravity would make the lower end hotter and the upper end cooler … and we could run a heat engine on the temperature difference forever.
But that is a perpetual motion machine, and those are not possible.
w.”
I’m a bit rusty with advanced thermodynamics, but how are you proposing to dispose of waste heat other than transporting it to the top of the column, subject to the same rules?
Nylo September 3, 2015 at 1:20 am
Thanks, Nylo. You might enjoy a full post I wrote using the example, called A Matter Of Some Gravity.
Regards,
w.
You said
Now, suppose there is some mysterious effect of gravity that could warm the surface, as you claim. How much energy would the surface be constantly radiating at that point?
Well, it would be constantly radiating more energy than it is getting from the sun … which as we all know is not possible.
Q.E.D.
This is not right, in the absence of an energy input the ke+pe = 0 and the atmosphere is isothermal, well actually the gasses would be solids and the KE = 0 and the PE will be minimum possible (mgh where h = 0) given the planet does not implode. But introduce energy into the air mass (without energy flow) and that energy will be split between potential and kinetic energy forming the gradient. That atmosphere will have a gradient otherwise the atmosphere would collapse in on the planet as a solid. It has to because the molecules neither gain nor lose total energy. Now if we allow energy to flow then it must flow from the warmer molecules at the bottom to the colder ones at the top, reducing the gradient from theoretical.
This really is just an application of the ideal gas law, PV=nRT.
I was introduced to dimensional analysis in the first year of University physics. It was suggested as a first-order method of seeing whether any physical equations make sense. If the dimensions do not match, then you are wrong. If they match, then continue. Since this involves no quantification of anything as yet, then it cannot be used to ‘prove’ diddly-squat.
Yes, it is used for checking equations
That’s the best use of it: if your answer has the right units, you *may* be correct; if not, you’re surely wrong. But I’ve seen profs trying to derive equations using dimensional analysis. You’ll get the right order of magnitude unless there are constants with units floating around, but if there are, and you don’t know those constants a priori, you’re sunk.
Correct.
Reminds me of the proof showing one equals zero…
If you used
Energy=1/2 m.V.V
Then wouldn’t 1W/m.m=0.5kg/s.s.s. ?
It’s been a since I went to school.
V.v should be (v.v) and s.s.s should be (s.s.s)
No. 1W = 1kg/s³. The half is an unrelated multiplier.
Funny me. 1W/m² = 1kg/s³ as said.
Thanks Hugh,
The penny dropped. I’m back on track.
If temperature isn’t related to atmospheric pressure then why is it hotter in Jericho than Jerusalem or why is death valley so hot? Why does temperature decrease with pressure in the atmosphere and why is a snow line so well defined at a given elevation (pressure)? Surface temperature and atmospheric lapse rate can be calculated with no reference to radiation only physical properties of the atmosphere, does this not indicate that it is the atmosphere that is critical rather than the concentration of GHG’s?
Thanks, Martin, but as far as I know, nobody said temperature wasn’t related to atmospheric pressure. In any case, that’s not the question.
The question is whether average planetary surface temperature is a function of atmospheric pressure, solar input, and nothing else. The study says yes. I say whaaaa?
w.
Willis,
Dimensional analysis is a very useful tool when considering equations such as the Potential Energy formula (m*g*h) which has dimensions M*LT^-2*L = M*L^2*T^-2 and the Kinetic Energy formula (1/2m*v^2) which has dimensions M*(LT^-1)^2 = M*L^2*T^-2 (as expected).
Starting with the basic equations:-
Velocity equals distance travelled divided by time elapsed i.e. L/T or LT^-1
Acceleration equals the rate of change of Velocity with Time or Velocity divided by Time i.e. (LT^-1) / T = LT^-2
Force equals Mass (M) times Acceleration (A) i.e. M * (LT^-2) = MLT^-2
Remember that gravity is acceleration.
Work Done equals Force times Distance moved i.e. (MLT^-2) * L = ML^2T^-2, so work done has units of energy and is measured in Joules.
Power measured in Watts is the rate of doing Work which is the amount of energy delivered per unit time and so has the equation Work Done per Second i.e. (ML^2T^-2) / T = ML^2T^-3
We can also establish that because a Watt is a unit of Power (Joules per second) then Watts per square metre will have dimensions (ML^2T^-3) / L^2 = MT^-3
Which can be described as a “kilogram per cubic second” as you correctly deduced.
the increase in surface temperature is due to the lapse rate due to convection as compared to an isothermal atmosphere. this lapse rate is not simply a function of pressure (gravity and mass) it also is modified by phase change of the convective gasses.
as such, one must account for this phase change in the convection as it reduces that temperature increase at the surface as compared to what would be calculated for solar radiation and pressure alone.
On earth this changes the lapse rate from 9.8C/km (as predicted by earths gravitational force) to 6.5C/km, which reduces the enhancement in surface temperatures predicted for atmospheric pressure.
As Phillip says Dimensional analysis is a useful tool. It has been around and used by engineers since 1914 and was fully proved in 1951. Engineers get actual measurements then with dimensional analysis formulate an equation with the measured data to allow modelling or extend the data outside the measured range. The relation of friction with the Reynolds number (Re) is one such relation, another in heat transfer is the relation between the Nusselt number (Nu), Reynolds number (Re) and the Prandtl number (Pr). This is the opposite of science where Feynman said guesses are made of relations or functions which should then be experimentally tested or falsified (except that with so-called “climate science” no one wants to accept that the hypotheses are false)
Willis that paper is based on experimental data of planets and moons obtained by various probes. The paper states that the data for Titan could be inaccurate. There are three bodies which have an atmosphere which allows a comparison of temperatures at the surface (greater than100 kPa absolute pressure) , at 100 kPa abs, and at a point about 10 kPa where the lapse rate is no longer linear. Therse are Venus, Earth and Titan. There is considerable information about pressure, temperature, gravity and atmosphere composition about earth and Venus but limited data on Titan. The atmospheres on Mars, Triton and the moon are very slight (but some has been measured). The paper used the Diviner orbital data for temperature for the moon.
I suggest that firstly you read some more about dimensional analysis. Then look at the actual data used in the paper, then finally see if you can come up with a relation or functions that explain the data. particularly the temperatures on the three bodies at 10 kPa atmospheric pressure.
“nobody said temperature wasn’t related to atmospheric pressure”
I’ll say it. Temperature is not related to atmospheric pressure. As of a few minutes ago, the temperature at McMurdo station was -9 C and at Naples, FL is was 33 C. Both places are close to sea level, so the pressure is very nearly the same. Clearly, no connection whatever.
Direct comparison between Hyperion and Titan proves the average planetary surface temperature as a function of air pressure and solar input is FALSE. Hyperion has no air. Titan has a thicker atmosphere that Earth. Both get the same insolation. Both have the same surface temperature.
Also false – the notion that there is such a thing as an anti greenhouse effect.
If there were such a thing, Titan would be cold relative to Hyperion. This paper is a post hoc flim flam to resus the assertion that methane is a powerful greenhouse gas (23~25 times as strong as co2, they claim).
They looked at Titan with the hairy eyeball, and discovered definitive proof the greenhouse theory is crap.
Can’t say that though, so instead they create the anti-greenhouse effect out of whole clothe.
How does Mike B describe it? “An atmospheric layer that blocks sunlight coming in.”
That’s already a well established phenomena, with it’s own name and formulas. It’s called albedo.
Con artists from the top to bottom. Every point in between.
“Hyperion has no air. Titan has a thicker atmosphere that Earth. Both get the same insolation. Both have the same surface temperature.”
Citation please?
Martin: Basically, no. The examples you give are not only the points in the atmosphere where GHG’s deliver their promised effects.
The temperature of the atmosphere decreases with an increase in altitude, until it doesn’t. Then it starts to rise with altitude to a temperature well above the surface temperature.
So how is this reality like some general law stating that the temperature rises as the air pressure rises? It doesn’t. It’s all over the place.
It is often stated that the temperature on Venus is the same as the Earth’s at the same Earthly surface pressure. OK, so what? What is the comparison at 1/4 of the surface pressure? 1/8th? 1/16th? 1/32nd? If it is a ‘law’ then it should hold for all pressures and atmospheric compositions. It doesn’t so it is not a law. At best it is is fluke. The universe is full of them. Further, that is not really the claim. The real claim is that the temperature at one Earth pressure is the same when compensated for the distance to the Sun. So there is a second factor, actually.
Why doesn’t the Earth’s air temperature always drop constantly with increasing altitude? GHG’s. Specifically ozone.
Um, I thought it was the absorption of EUV and UV dumping extra energy into the thermosphere… CO2 is a strong radiator in the Stratosphere, so GHG is not the magic heater…
https://chiefio.wordpress.com/2014/06/01/le-chatelier-and-his-principle-vs-the-trouble-with-trenberth/
Em Smith
Your point is agreed but what then is the definition of a GHG? If a gas captures radiation, heats up and thermalises the energy, is it not a GHG? Just because there is a preponderance of UV and EUV from above doesn’t matter. H2O works both ways, CO2 ditto. Same with Ozone. There just isn’t much UV coming from below. Oxygen is also sort of vaguely a GHG. Not very efficient, but there is a heck of a lot of it.
I hope this doesn’t distract from my point that the temperature doesn’t always drop with altitude which is the basis of the (false) meme.
“H2O works both ways, CO2 ditto.”
Crispin, H20 yes, CO2 barely.
wordpress.com/2014/01/drawing.png
Water is blue and CO2 green for absorption in the incoming spectrum. Yes, I forgot to color blue the far right water resonance. Water works a triple shift in the day; incoming near IR from the sun, and both outgoing and “downwelling” recycled IR over a very broad range of earth spectra. CO2 is pretty much limited to outgoing spectra.
One interesting thing I learned recently is that liquid water and Ice differ significantly from atmospheric water in resonance.
Green is atmospheric water, blue is ice, and red is liquid water.
Also, you can forget about visible light warming the oceans.
gymnosperm September 2, 2015 at 10:35 pm
Thanks, gymnosperm. I take it you don’t spend much time diving or swimming in the ocean …
In any case, your claims might be understandable if you would provide CITATIONS TO YOUR GRAPHS. As it stands, for all we can tell you just created them in Microsoft Paint.
It appears (without a citation I can’t be sure) that the lower graph is how fast wavelengths of various frequencies get absorbed in the ocean. But neither of your graphs have actual units listed, or any explanation, so I can’t really tell.
If that is the case, however, you’re misinterpreting the graph. It says that visible light penetrates the deepest (1 / 1E-2 metres, per the chart, which is 100 metres deep), and the penetration drops off on either side, with the blue/ultraviolet side absorbed deeper than the red/infrared side. This is the reason that when you dive deep, say down to sixty metres or so, as you go down the red colors are extinguished first, and down deep everything is blue-gray.
In addition, there seems to be a final misunderstanding. The absorption depth doesn’t matter in terms of warming. Whether a photon of energy is absorbed in the first millimetre below the surface or is not absorbed until 100 metres down, it still gives up all its energy to warming the ocean.
So no, we can’t forget about visible light warming the ocean. It is a main source of oceanic warming, and in addition, it penetrates deeper than either IR or UV.
w.
Why doesn’t the Earth’s air temperature always drop constantly with increasing altitude
==========================
the lapse rate can only be maintained by vertical circulation. otherwise conduction results in an isothermal atmosphere.
Death Valley is not hot just because of its altitude. The fact that its a Graben (a rift valley caused by a section of the bedrock sinking) while block faulting caused mountains to rise around it. Combined with its aridity and consequent lack of vegetation the effect is to produce a large scale solar furnace where there is little cooling from the wider environment while the valley is narrow enough to prevent major air circulations becoming established.
As Willis already mentioned, he did not state that temperature is not related to atmospheric pressure.
Pressure certainly is a very important factor, and quite likely is far more significant than CO2.
It doesn’t necessarily prove anything, but it’s interesting to consider the crude correlation between pressure, distance from the sun and CO2 concentration.
For Venus, Earth and Mars the crude correlation between distance from the sun and pressure is perfect e.g. the further from the sun, the colder it is.
But the crude correlation does not work for CO2: Mars actually has more atmospheric CO2 than Earth, and yet it’s colder.
Chris
You didn’t need to do all the work, Willis. When the planetary parameters folks don’t have rotation included, their formula may fit on paper but it can never be right.
Well it isn’t. The units of watt per square metre are the same as kilogram per cubic second, but that’s a different thing entirely. E=mc^2, not E=m(1 metre per second)^2.
I’ve always been driven half-nuts by dimensional analysis. Take the gravitational force, with units of newtons (kg m/s^2). Try getting that out of what it physically depends on, mass1, mass2 and distance. You’d spend the rest of your life looking for a dependence with seconds in it, or just give up and say there must be a constant. Either way, dimensional analysis didn’t “solve” the problem. And don’t get me started on papers where c=1 (no units) instead of 2.9979(etc)x10^8 m/s. I’ve come to the conclusion that most of the time, dimensional analysis is clever people subconsciously trying to show how clever they are.
What’s the problem?
Force = Mass * Acceleration
So, on the right we have units of mass (kg) and acceleration (metres per second per second) and so
The units of Force are Kg/m/s^2
That’s not really clever is it? More like obvious.
Whoops kg.m/s^2
F=ma works fine. But you can’t get F=G*M1*M2/r^2 unless you know about G first, is what I was getting at.
Dimensional analysis will give you the units of G
G= F.r^2/m^2
So units of G are N⋅m^2/kg^2
“I say this because it is clear that the reason the temperature of the moon is so low is because it rotates so slowly. ”
How about the ISS that has a similar temp range over 1.5 hours?
Also, as the pressure is so high on Venus and the temperature appears similar throughout the planet, is it possible that the dense atmosphere is behaving like a Newtons Cradle in transmitting heat?
In the atmosphere of Venus the heat is very effectively distributed by very, very strong winds, such that its low rotation become basically irrelevant.
Other people call this an attempt at principle component analysis.
That they find the two principal factors that determine the result (the insolation and the atmospheric pressure) is not surprising. The insolation determines the total heat flux propagating through the atmosphere, the pressure is is related to the total mass per square cm of surface, which in its turn is connected to the total optical depth of the atmosphere.
That they had to exclude Titan is not surprising either: that is the only planetary atmosphere (apart from Earth) with a volatile constituent (Methane) in at least two phases (liquid and gas) and therefore a dominant factor in latent heat transport which effectively decouples the heat transport from the radiative heat transfer, hence the optical depth. That would also affect the result for Earth (water!) but here the atmosphere is optically thinnish, which may dillute this effect, whereas Titan’s is optically thick.
Ed, do you wonder if they deducted the time there is no solar on Titan?
Saturn’s moon Titan is bigger and closer to our moon. Also it’s orbit inclination is only 0.35 degree, compare to 5 degree for earth’s moon. That means Titan is in almost same plane as of saturn’s rotation about sun. Titan completes saturn’s rotation in 16 days. Hence there is solar eclipse and lunar eclipse every 16 days due to titan.
http://www.quora.com/Can-we-see-solar-eclipse-from-any-other-planets
Might we have a strong methane based evapotranspiration thermostat on Titan skewing that moons temperature below the curve? Or at least phase change heat transport not accounted for in the simple model?
In my opinion this is the key point.
It reminds me of solving systems of independent lineal equations. If you have 2 unknown variables you need 2 equations to solve the unknown variables, If you have 3 variables, you need 3 equations, and so on…
In similar fashion, in a problem with 2 variables, if you have 2 data points, you are going to find a linear regression function that has an R² = 1.0000 The problem comes when you add more data points, you are going to lose the perfect fit if the two variables are not correlated.
My guess is that the same thing happens when you have 3 variables and 3 data points. You are going to find a function with a R² = 1.0000. In the paper case, they have 5 variables and 5 data points, so they find a perfect fit but when they add Titan (an extra data point) the perfect fit is lost, meaning that the variables are not correlated.
I wonder if this is related the mathematical notion of “degrees of freedom”
Willis thanks, and FYI I think you meant to say “lost the plot” not “plat”.
Thanks, Anthony, fixed. Like I say, I hate writing about this kind of nonsense, but the idea that gravity can somehow constantly warm a planetary surface seems to get traction each time it reappears, and it is damaging to the reputation of the skeptics.
w.
Potential wells have thermodynamic effects I haven’t seen discussed much.
A molecule going up against gravity loses energy. A molecule going down with gravity gains energy. Even without bulk gas circulation gas lower in the gravity column can be expected to be warmer. Given an atmosphere largely opaque to thermal radiation at ambient, thermal equilibrium is expected between a layer in the upper atmosphere and outer space.
Crispin, surely the temperature decreases with pressure until the pressure becomes too low for the conduction and convection effects of the atmosphere to dominate all other heat transfer effects as it does in the Troposphere. I believe that where the temperature rises again it is due to chemical reactions associated with the creation and destruction of Ozone. In both cases though there seems to be no dominant effect of the GHGs. I believe that if you can calculate a surface temperature and Tropospheric lapse rate without reference to GHG radiation then GHG radiation has no effect on either.
Ahh, the old explicit, formulaically evaluated mathematics meets implicit, iteratively evaluated maths and confusion reigns for thos who just don’t understand the difference.
Clue:- The universe is iterative.
Only in a cinema if the guy is winding the handle at a constant rate.
It’s been nearly sixty years since I studied it, but isn’t dimensional analysis used to derive useful dimensionless parameters in engineering such as Reynolds number?
A watt is a power unit not a unit of energy i.e. energy over time. One watt = 3.412 Btu/h or 3.6 kJ/h. Energy is heat or work. Be sure to use English hours with British Thermal Units and metric hours with kiloJoules.
Be thankful that the Axis and Allies were both on the same clock in WW2.
When I was making an effort to learn about the “greenhouse effect” I came across an article on an “anti-greenhouse” effect on Titan.
http://www.astrobio.net/topic/solar-system/saturn/titan/titan-greenhouse-and-anti-greenhouse/
Since Titan’s greenhouse effect from Nitrogen is temperature dependent on the behavior of the gas,
I suspect that moving Titan to different parts of the solar system would give inconsistent results for that single planetary model. In other words, a Titan at the distance of Earth, or Mars , or Jupiter, would be inconsistent with the model due to changes in the greenhouse gas effect of Nitrogen.
From your link.
The author is confusing concepts. CO2 and H2O are symmetrical molecules. CO2 is lineal and H2O is V shaped, that is why H2O has a permanent dipole moment, but CO2 does not.
CO2, like methane (symmetrical, tetrahedral shape), can have a induced dipole moment if it collides with other molecules and its shape momentarily changes producing an unequal charge distribution.
N2 and H2 are diatomic molecules, symmetrical and without dipole moment, permanent or induced.
I wouldn’t trust anything that article says.
http://teachers.henrico.k12.va.us/varina/tyler_e/funcenter/proof.jpg
Cute. But where is the “man” variable involved, and how?
Some claim that men are dimensionless. Others claim they can be measured in beers per football game.
“Woman” is related to “man” by the constant “Wo” (pronounced “double you zero” or “woe”)
Man = $$
O Mike M,
That’s much too complicated. Here is an example of a straightforward, simplified paper that is easy to understand, even by non-scientists…
There is no list…only random events seemingly connected, with a nexus at your mail box. 😉
roflmao
Willis: Excellent analysis. Two points. First, I too found this paper a bit too convenient. Particularly in that it ignores a number of fields of engineering where there really is a greenhouse effect with or without changes in pressure. If there isn’t a greenhouse effect, then combustion engineering (for one) needs to find new explanations for physical observations. My very light skimming of the paper led to (in my opinion) a wrong conclusion on my part. Second. I’m surprised you are unfamiliar with dimensional analysis. It is a powerful tool. Particularly at exam time when you need to quickly check that your derivations haven’t gone off the rails. The best practice of carrying units throughout a derivation is an example of DA.
Thanks, John. I’ve carried units through calculations all my life, it was drummed into our heads by Mrs. Henniger, my high school science teacher. However, I was unfamiliar with DA and the Buckingham Pie …
w.
Willis: There is a second, somewhat related, thing I’ve seen. It has been pointed out that the surface temperature of Venus can be entirely attributed to pressure, because it fits the ideal gas law. PV=nRT. The flaw in all of these derivations is: The reason the atmosphere has a particular density (which is n/V) is because it has a particular temperature. Change the temperature and you will change the density. Venus’ atmosphere has the density it does because it has the temperature it does, not the other way around. Temperature is a measure of internal energy. If Venus was not subject to a continual input of energy, the atmosphere would cool and the density would increase. Eventually it would condense. So of course the atmospheric temperature of Venus almost exactly matches that predicted by the ideal gas law. It has to whether the atmosphere is heated by the sun or by gnomes rubbing sticks together. The “almost” is because at the pressures of Venus, there is some deviation from an ideal gas. For those who ascribe the temperature solely to CO2, there is also a lot of SO2 there. That must be accounted for in estimating atmospheric temperature.