Traveling Through Other Dimensions

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.

watts per metre square kg cubic seconds(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):

volokin table 1Since 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:

volokin figure 4Note 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:

volokin equation 10aIn 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:

oxbow lakesNotice 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.

volokin equation 4aSo 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.

lunar surface temperature

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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September 2, 2015 6:16 am

It is probably disconcerting to many to discover that the explanation of global climate change is simple and that CO2 has nothing to do with it. (Ockham would not have been surprised).
Engineering science proves CO2 has no significant effect on climate.
The proof and identification of the two factors that do cause reported climate change (sunspot number is the only independent variable in the resulting conservation-of-energy equation) are at http://agwunveiled.blogspot.com (now with 5-year running-average smoothing of measured average global temperature (AGT), the near-perfect explanation of AGT since before 1900 of R^2 = 0.97+ ).

Reply to  Dan Pangburn
September 3, 2015 8:15 am

Dan Pangburn: You said: “Engineering science proves CO2 has no significant effect on climate”.
On the contrary, one can use the same emissivity curves that are used in many fields of engineering to derive a forcing curve that is nearly identical to q=5.35ln{[CO2f]/[CO2i]}.

Reply to  John Eggert
September 3, 2015 4:18 pm

It is so easy to get mired in unreliable minutia. The proof that CO2 has no effect on climate is very simple. You only need to be aware that CO2 has had to be above about 150 ppmv for life on land as we know it to have evolved and that a forcing needs to act for a time to have an effect.
The proof is described two different ways in the agwunveiled paper. Here is a third way, in steps:
1) Atmospheric CO2 has been considered as a possible climate change forcing. Forcings, by definition (and according to usage by the ‘consensus’ and the IPCC), have units of J s-1 m-2.
2) A thermal forcing (or some function thereof) acting for a time period accumulates energy change, J m-2.
3) If the forcing varies (or not), the energy change is determined by the time-integral of the forcing (or function thereof).
4) Energy change, in units J m-2, divided by the effective thermal capacitance (J K-1 m-2) equals average global temperature (AGT) change (K).
5) Thus, if CO2 is a forcing, the time-integral of the atmospheric CO2 level (or some function thereof) times a scale factor must closely equal the average global temperature change.
6) When this is applied to multiple corroborated estimates of paleo CO2 and average global temperature (such as extant examples from past glaciations/interglacials ice cores, and proxy data for the entire Phanerozoic eon), the only thing that consistently works is if the effect of CO2 is negligible and something else is causing the temperature change.
The equation used to identify the cause of climate change includes a provision for including the contribution from CO2 as C/17*ln(CO2f/CO2i). Setting C to zero produced R^2=0.905. Optimum C produced R^2=0.906 which demonstrates that considering CO2 or not made no significant difference which is consistent with the proof.
Many folks seem to be unaware that, if CO2 is a forcing, its effect on temperature must be according to the time-integral of the of the CO2 level (or the time-integral of a function thereof). Are you aware that, for most of the life of the planet, CO2 has been higher, usually several times higher than now?
Any analysis that concludes CO2 has an effect on climate is faulty.

September 2, 2015 6:18 am

E = M * c^2 M = mass, c = meter/s
kJ = kg * m^2 / s^2
W = kJ/s = kg * m^2 / s^3
W/m^2 = kg / s^3
Congratulations Einsteins. Maybe this matters at the nuclear/quantum level.
Einstein was awarded the Nobel prize for explaining the photoelectric effect which is essentially how fluorescent light bulbs and lasers work. Paraphrasing: when an atom or molecule absorbs a photon of a given frequency/energy the target atom/molecule will emit a photon of frequency/energy minus the work function of the atom/molecule.
For example: a ruby is a compound of aluminum and silica. The work function of aluminum is such that when it absorbs higher energy UV photons it emits lower energy visible red light.
So CO2 molecules that absorb LWIR can only emit lower energy microwaves, not 90% of the incident LWIR, which are good for heating water molecules and not much else, certainly not at 2 W/m^2.

Gary Pearse
Reply to  Nicholas Schroeder
September 2, 2015 6:31 pm

The mineral corundum is Al-oxide and it comes in a variety of colors: Rubies are red corundum, sapphires are blue corundum and there are also colorless, green, etc. The different colors are due to the presence (or absence) of trace ‘colorant’ impurities. I beleive the red is from Cr. So, you can’t get any mileage from this idea.

Yirgach
September 2, 2015 6:38 am

The moon is cold because it is made of cheese.
If it wasn’t cold, then it would go bad and everyone knows that the moon is not bad.

September 2, 2015 6:43 am

“The Buckingham Pi Theorem”… “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.”
I always wondered how the AGW crowd could determine the temperature of a whole geographically diverse region by using 1 urban located temperature station. Now we know.

Editor
September 2, 2015 7:03 am

Dimensional analysis should be taught in high school physics. Like steveta_uk said, if the dimensions do not match, then you are wrong. Vital as part of checking one’s work. Caveats/Notes:

1) Thanks, Dad, for making sure I appreciated dimensional analysis.
2) There was an article in Science News several decades ago that said it should be taught better.
3) Dimensional analysis involving temperature and heat messes with your head.
3a) So do the units of some fundamental constants, like G above.
4) Dimensionless constants are a scourge, but you can often create non-fundamental units to help out. E.g. the circumference of a circle is π × radius. You’re expected to know that even though both the circumference and radius are lengths, they aren’t equal. However, if you create units like circumferential meters and radial meters, then π is 3.14159+ circumferential meters per radial meters, and things work out nicely.
5) It’s really neat how units, especially mass tend to fall out of basic orbital analysis. It’s to be expected, as an astronaut inside the space station needs to travel at the same velocity as the space station to be in the same orbit. Duh. But it’s neat.

OTOH, one relationship I came up with while looking into the possibilities created by jumping off Deimos was that, in simplified terms, the period of a low orbit was a function of the large body’s density and that diameter doesn’t apply. So a satellite orbiting Earth has about a 90 minute period, as would a person orbiting Deimos, if Deimos had the same density. (At the time, back in pre-web days, I was having trouble finding Deimos’ density. Not surprisingly, it’s less than Earth’s.) At the time I had never heard of that relationship.
The result, first on USENET’s sci.astro, and currently at http://wermenh.com/deimos.html remains one of my favorite writings.

BillK
Reply to  Ric Werme
September 2, 2015 7:58 am

“the circumference of a circle is π × radius”. Really?

Reply to  BillK
September 2, 2015 8:10 am

How ’bout PI() * D or PI() * 2*r

Editor
Reply to  BillK
September 2, 2015 1:34 pm

Yes, that would work better…. 🙂

Editor
Reply to  BillK
September 2, 2015 4:10 pm

Oh, and of course, I wanted to demonstrate that dimensional analysis is no panacea, you still have to think and use reliable sources. 🙂

September 2, 2015 7:04 am

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. love is love quote

Itocalc
September 2, 2015 7:13 am

Did I miss something?
(Kg*meter^2/sec^2)/(sec/meter^2) = (kg*Meter^4)/sec^3
not kg/sec^3

Itocalc
Reply to  Itocalc
September 2, 2015 7:14 am

Nevermind

Gary Pearse
Reply to  Itocalc
September 2, 2015 7:00 pm

I thought you were correct with kg*meter^4/sec^3. Where did you go wrong? I looked at that and thought:
1/2/1/2= 1/2*2/1 =1 that seems to be correct.

itocalc
Reply to  Itocalc
September 5, 2015 8:41 am

It’s all in the parenthesis, which are not clear enough in the way it is written in the second to last term.
Try it this way (kg*m^2/sec^2)/sec = (kg*m^2/sec^3)
Now we can divided by m^2. (kg*m^2/sec^3)/m^2 = (kg*m^2)/(sec^3*m^2) = kg/sec^3

September 2, 2015 7:23 am

It’s the water/water vapor cycle that moderates/modulates the atmospheric climate. CO2 is about as meaningful as a bee fart in a hurricane.
The popular GHE ignores water vapor. Water vapor isn’t caused nor controlled by man. Without water vapor a greenhouse becomes an oven. It’s water that makes earth different from Venus et. al. and comparisons interesting yet irrelevant.

Kevin Kilty
September 2, 2015 8:22 am

The thing I like best about climate science is that I am constantly learning new things…

Which is so unlike the guys who get paid for it.

Zek202
September 2, 2015 8:24 am

What Institution do the authors work at ? I followed the link and could not determine this fact?

September 2, 2015 8:48 am

willis,
I saw hockeyschitck link to Volokin junk on judiths.
I want to thank you for being even handed and debunking junk on both sides of the climate wars.

ossqss
Reply to  Steven Mosher
September 2, 2015 6:33 pm

Why do you call it climate wars?
It isn’t. We are all in the same boat for a bit.
Just think,,,,, 156 years ago around this time, a major solar event was happening. The same event on our earth today would have been real trouble in real time.
Not something 85 years away.
Just sayin, perspective is important in the, so called, climate wars…?
http://www.history.com/news/a-perfect-solar-superstorm-the-1859-carrington-event

Gary Pearse
Reply to  Steven Mosher
September 2, 2015 7:35 pm

Steven, I think your insinuation that thinking sceptics support garbage if it is on the ‘supportive’ side is straw-manish. It is certainly a charge that can be leveled at the activist CAGW scientists and ideologue green men. Using unthinking contrarians as a proxy for sceptics is beneath you. Having that off my chest, yes I also like the way Willis wields his sword – nice aliteration huh?

ferdberple
Reply to  Gary Pearse
September 3, 2015 5:44 am

but claiming that gravity can heat the surface in an ongoing manner isn’t one of them.
===================
gravity cannot heat the surface except by cooling the upper atmosphere via conversion between PE/KE. this provides a net warming at lower levels and a net cooling at higher levels, as compared to an isothermal atmosphere. this increases surface temps over those predicted for an isothermal atmosphere. this cannot happen without vertical circulation. some sort of external energy source is required to maintain the vertical circulation. gravity alone cannot provide this.

hanelyp
Reply to  Gary Pearse
September 3, 2015 10:40 am

“gravity cannot heat the surface except by cooling the upper atmosphere via conversion between PE/KE”
As I’ve already described, this can happen on individual molecules without bulk fluid flow.

September 2, 2015 9:10 am

Sorry I don’t even have time to read this interesting looking post right now , but want to make 2 observations .
0 ) Hadn’t thought about cubic seconds , but — of course .
Had a fruitless volley with David Appell over a comment I make somewhere about the equivalence of radiant energy flux , W % M^2 and energy density J % M^3 by dividing by a light*second . His incomprehension of the interchangeability of time and space thru this basic relationship made me find it incomprehensible that he actually had a PhD in quantum under George Sterman at Stony Brook . BTW , a cubic second is pretty big , 300k km on a side .
1 ) It’s not the pressure which “causes” the higher temperature lower in atmospheres ; as I have been enlightened in discussions here , it’s the gravitational energy well — of which the density of the atmosphere is a factor . I have often pointed out when the “it’s pressure” argument comes up that ( static ) pressure , per se , is not in any temperature equations . If it were , we could just pump up scuba tanks and then suck perpetual energy from them . HockeySchtick has equations I plan to examine , ie : implement , after I get a general release of 4th.CoSy releasable .

hanelyp
September 2, 2015 9:49 am

It is arrogance to say that 2, and only 2, factors determine planetary temperature, and everything else doesn’t matter. That the graph doesn’t match perfectly also hints at some factor or factors not in the model. Still, the degree of match between this solar input + pressure model and actual planetary temperature suggests that those 2 factors are a very large part of the picture. Known gas dynamics, allowing for gravity potential, also come to a very similar model, though adding Cp/Cv as a factor.

September 2, 2015 9:59 am

Willis: fun post, always something to learn: the proper serving size of bunting at tea with the queen! Love it

Martin Mason
September 2, 2015 10:03 am

Bob, you’re correct but they don’t claim that it’s only pressure that determines the temperature but pressure plus solar insolation. I think that the DA thing has hidden the important things in their papers. This is that average surface temperature and lapse rate on any planet with almost any atmosphere can be found without recourse to radiant properties, that is an Atmospheric rather than the Greenhouse effect. I would have thought that this was important?

Kristian
September 2, 2015 10:20 am

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.”

Willis,
What are the “canonical values” for the average global surface temperature of Mars, and how were they arrived at?
They discuss this, among other things, in their Appendix B (pp.47-52).

Kristian
Reply to  Willis Eschenbach
September 2, 2015 10:45 am

It does matter. If the “canonical values” were just numbers ‘thrown out’, then why use them? Why go by them? Why not rather try to look into the matter a bit more closely and see if you can figure something out for yourself? Which is exactly what they did. I’m not saying that their derived number is necessarily correct. But they do at least provide a reasonable argument for why it might be. I have NEVER seen, say, the 215K “canonical value” justified in any way through actual global, annual data. It’s only ever ‘stated’. A suggestion. A guesstimate. A finger in the air.

Kristian
Reply to  Willis Eschenbach
September 2, 2015 1:11 pm

Willis, we’re talking about the actual, globally/annually averaged SURFACE temperature of Mars, aren’t we? Then why do you feel the need to state and quote the following?

… the earliest estimates of Martian temperatures I can find are from about 1950, and the work has gone on since. For example, the temperature of Mars can be measured from the earth, with the scientists finding:
“At the date of these observations, r=1.402 AU, so the correction factor from observed brightness temperature to average temperature is 0.959, yielding TB,Mar8,Ave(9G.11Z) = 212±15 K. This value is higher than the value reported by Rudy (1987) at 2 cm, 193 ±10 K, averaged over the whole Mars disk and corrected to the average temperature at the mean Mars orbital radius.”

‘Estimating Martian temperatures’ and ‘measuring it from Earth’ is NOT the same as determining the actual, globally/annually averaged surface temperature of Planet Mars. Your source calls it “apparent temperature”. No empirical measurements of the surface temperatures are performed. It’s all computations and extrapolations.
Further:

Did you think that scientists were just waving their hands and making up the Martian temperatures? Of course the canonical values are scientifically based, they didn’t just watch the movie “John Carter on Mars” and pick a number.

Willis, read what I write. I do not say that “scientists were just waving their hands and making up the Martian temperatures”. Nor do I imply it. I say they ‘threw out some numbers’. As guesstimates. Educated guesses of course BASED ON computations such as the ones above. I say that a number like 215K (one of several ‘suggestions’ or “canonical values” as you call them) is never given a proper data-based explanation or justification. It is just stated. Naturally it will be in the general ballpark. But we’re not interested in the general ballpark. We’re interested in the actual value. As averaged from direct global measurements over a full Martian year (or preferably, several of them). There are no actual global/annual data to support it (the stated 215K value). It is based on calculations, extrapolations and – importantly – on certain assumptions about what a planetary surface such as the Martian one, beneath a radiative atmosphere such as the Martian one, should experience.
Finally:

Plus, of course, we’ve had satellites in orbit around Mars, viz:

Yup, now we’re getting somewhere. The MGS and the MRO obviously have enough data collected for us to determine at least the average brightness temperature of the global surface of Mars. And yet we have never seen such a figure presented. Why? Shouldn’t that be a pretty straightforward thing to accomplish …?

Kristian
Reply to  Willis Eschenbach
September 3, 2015 2:49 pm

“Before, you claimed that YOU have “NEVER seen, say, the 215K “canonical value” justified in any way through actual global, annual data.”
Now, having had some actual data pointed out to you, both data from measurements from earth and from measurements from satellites, you claim that WE have never “seen such a figure presented” as the brightness temperature of Mars.”

Willis, what are you talking about? The 215K “canonical value” has still not been justified through actual global/annual surface data. And we have still not seen the avg gl sfc temp figure for Mars as derived and estimated directly from the MGS-MRO data.
“Kristian, you seem to be confusing what YOU have seen with what has been seen.”
If you don’t understand what it is that I’m talking about, then why reply at all? It is very obvious that you have done no prior research whatsoever when it comes to the global average surface temperature of Mars. You appear simply to take the “canonical values” for granted as based firmly on actual global/annual observational data, when they’re clearly not. You throw some completely irrelevant google searches at me, that’s what you do. They don’t address the issue, Willis. I don’t need for you to do any googling for me. I’ve done it. I have a pretty good idea of what’s out there. And what’s not. That’s why I’m saying what I’m saying. No avg sfc temp figure provided for Mars has ever been explained in the sense of saying: “According to this and that dataset, globally and annually averaged, we arrive at a mean temp of so and so” … It is always just stated. Some value drawn out of a hat. And you know why? Because there were no comprehensive (multiyear, global) datasets around of the surface temperature of Mars until the MGS and MRO missions performed the task. Into the 21st century.
And still, even today, we never get to hear about the average surface temperature of Mars as derived from these MGS/MRO data. Even though, by now, these should obviously be the ones, the only authoritative ones, to refer to. The gold – the only – standard. Even though we actually do have the answer now. Somewhere. If only we want to know it … It is not presented. Never referred to. Even today. We’re still only ever served the old assortment of ‘educated guesses’ based on computations, extrapolations and a priori assumptions from the past. I can see why this would be a pretty frustrating situation for someone with an interest in the exact figure, not in any “it’s probably something like this” kind of figure.
What I wonder is why the authors of the paper in question didn’t consult the MGS and/or MRO datasets. To find out what they reveal. But I also wonder why NASA haven’t officially published the MGS/MRO avg global figure for the Martian surface. Why haven’t we seen any announcements? Such a figure would certainly have interesting implications for the whole rGHE hypothesis. I suspect it might be the “210K” figure now mostly used by NASA, for instance here: http://mars.jpl.nasa.gov/allaboutmars/facts/
But it’s hard to say for sure if they won’t actually come out and confirm it.
Willis, my initial comment to your critique of this study was not meant as a direct criticism. Your objections are likely for the most part legitimate. I was simply curious about your take on the “canonical values” of the Martian sfc temp. My approach to this subject is via a different route, namely the one about T_sfc vs. T_eff (which in a way defines the rGHE). Since the Martian T_eff is ~211K, then any T_sfc below this value would point directly to the non-existence of an rGHE on Mars (or rather a ‘negative’ one!), as defined by the “raised ERL” concept. Suggestions of a T_sfc of 215K or 218K (two common stated values) seem very much based simply on the preconceived assumption that there must be an rGHE on Mars, albeit small. After all, its atmosphere is 95% CO2. The funny thing is, even if the actual physical temperature of the global Martian surface, as opposed to its brightness temperature (as measured by the MGS TES and MRO MCS instruments), turned out to be in the 215-220K range, this would only mean that the small warming of the actual solid surface over that of the planetary effective radiating level is entirely due to a ground emissivity below unity (~0.95), not to any DWLWIR. In fact, as a blackbody, the surface would then be slightly colder than the conceptual ERL.

Science or Fiction
September 2, 2015 10:27 am

Anyone know how they measured temperature, pressure and composition of the atmosphere for these planets? (If they did.)

eyesonu
September 2, 2015 10:58 am

WUWT University at it’s best. Many thanks to all the commenters here.

September 2, 2015 11:48 am

FWIW Wikipedia calls it data dredging, but lists data snooping as a synonym. See https://en.wikipedia.org/wiki/Data_dredging
Interestingly,Google shows that data fishing, another synonym, is even more popular, as shown by the number of pages found with the following search phrases enclosed in quotes:
“data fishing” 85,300 results
“data snooping” 64,500 ”
“data dredging” 32,900 ”
Wikipedia also offers p-hacking as a synonym. The idea is that you conduct statistical analyses over a relatively large number of variables and select one relationship that shows a p-value (probability) of less than 5%. Of course you don’t mention how many variables you started with, because someone might figure out that in 20 relationships from a table of random numbers, at least one would likely show up with a p < 0.05.
The weird thing about this is how few journal referees, especially in the so-called "social sciences," are seemingly either unaware of this problem or perhaps just don't want to rock any boats. (A survey of the level of statistical knowledge and practices of reviewers might actually be much more of a contribution to knowledge than a lot of other things that get published.)

Reply to  Willis Eschenbach
September 3, 2015 12:22 am

Thank you for the clarification, Willis.
This might be kind of nit-picking, but is data snooping then either synonymous with or conceptually somewhat overlapping with cherry-picking?

James at 48
September 2, 2015 12:30 pm

We’ve had lots of discussion about missing heat. One of my suspicions is that it exited as physical work, some sort of mass displacement or dynamic energy dissipation involving mass motion.

Editor
Reply to  James at 48
September 2, 2015 3:22 pm

I hadn’t thought of that before. In general, energy winds up being heat. Kinetic energy -> friction -> heat. Acoustic energy -> absorbed -> heat. Light -> absorbed -> heat.
The only way it could turn into moved mass is if the mass moves upward. Wouldn’t it be ironic if Trenberth’s missing heat turned out to be in the Antarctic and Greenland ice caps?

Science or Fiction
Reply to  Ric Werme
September 3, 2015 8:17 am

Or in space.

September 2, 2015 1:30 pm

Those who wander are not lost.
The imbalanced heat’s not “missing” simply because we/they have no idea where it went. Besides 2 W/m^2 in the global heat balance would be easy to lose track of, somewhere in the third or fourth decimal place.

Will Nelson
September 2, 2015 2:50 pm

When I got into engineering I thought: “(Plastic) Section Modulus, (Z) S, in units of in^3, great I can handle that”, until Moment of Inertia, I, and Torsional Constant, J, came along, which are units of in^4 and we went along in that strange dimension until, what!? the Warping Torsional Constant, Cw, in units of in^6. And modern art still doesn’t make any sense.

Richard M
September 2, 2015 2:53 pm

This looks to be another version of the Jelbring hypothesis and ties in with work of Nikolov and Zeller. All of these are variations on the theme there is a relationship between the atmospheres of various planetary bodies.

Michael J. Dunn
September 2, 2015 3:59 pm

I have a hard time getting excited over this critique.
For one thing, the skeptical comments (in this thread) about dimensional analysis are simply ignorant. The technique has a long and productive history. The science of aerodynamics would be largely nonexistent if it were not for the use of non-dimensional parameters developed from dimensional analysis. It is a sophisticated tool, and not for sophisticated fools.
For another thing, equation 10a is really of the form
y = exp (a x^m) * exp (b x^n)
(since addition of exponents is only multiplication of the exponential terms) which leads me to think that Willis knows less about what is going on than he propounds.
And the graph seems interestingly reasonable. Ferment over Mars, Triton, and the Moon is misplaced because the errors are aligned with the vertical portion of the curve (as a previous commenter has already mentioned). It doesn’t matter. Similarly, the decision to use Earth as an anchor point was defensible on grounds of error, and the fact that the curve doesn’t pass PRECISELY through Titan (a complicated environment, as already noted) should not raise the hackles of anyone who ever compares theoretical prediction to observed data. What are the error bars? Use both Earth and Titan and the results would show little practical difference. What is surprising to me is the degree of fidelity shown by the model. It provokes thought.
Oh, I think someone was declaiming against the existence of isothermal atmospheres? They might be interested to know that while the Earth’s troposphere is isentropic (lapse rate, convection), its lower stratosphere is isothermal (constant temperature). Temperature increase at higher altitudes is an artifact of high-energy chemistry going on, but the air is so thin that it is probably better than vacuums drawn in high-school bell jars.
Venus’s atmosphere is optically thick and thermally insulating. No surprise that there is little diurnal variation, especially if it is isothermal.
Maybe this paper is not the Cat’s Pajamas after all, but I don’t think it is the Devil’s Hoofprint, either. It suggests that the presence of an atmosphere results in a predictable increase in surface temperature relative to an airless body. Hmmm. Either the relationship derives from correct physics (which is goodness), or it does not—in which case someone needs to explain why it has seeming validity. Simply accusing the authors of technical mendacity is not an explanation.

richard verney
Reply to  Willis Eschenbach
September 3, 2015 3:10 am

What an extremely venomous response to what was not a particularly venomous comment by Michael.
Whilst Micheal did remark ” (since addition of exponents is only multiplication of the exponential terms) which leads me to think that Willis knows less about what is going on than he propounds”, I suspect that this is a remark that could be fairly levelled at all: it is human nature to give the impression that one is more knowledgeable than one truly is, it is human nature to shun giving the impression of ignorance and accepting that one knows little and understands even less.
Willis, whilst you cannot control what people say about you, you can control what you say about others. There is no need to drag yourself down to the level of others. So if you feel that someone has been rude to you, there is no need to respond in like tone. It adds nothing to the merits of the points that you wish to make, and if anything detracts from them.
Whilst I have no intention of telling you how you should lead your life, an objective reader may conclude that it may be better for you to simply let the science behind your response do the talking.

Michael J. Dunn
Reply to  Willis Eschenbach
September 3, 2015 11:22 am

Wow, what a thin skin. In order, because I don’t have much time:
1) I’m not “busting” your critique, I’m just failing to get excited over it. That’s my reaction and I’m stuck with it.
2) Comments on the thread are appropriate, particularly if they are accurate. Your own attitude toward dimensional analysis was hard to discern, so I didn’t remark.
3) I was commenting on equation 10a, which you were elaborating. Did I know about equation 5? Of course not. My ESP is totally undeveloped. If there was an internal discrepancy, you should have addressed it…or not brought it out. I was relying on your account of that paper to be free of inconsistencies. So, I’m not going to comment on your turgid explanation for why you introduced the wrong equation to the discussion.
4) I am not a “nasty little man.” For one thing, I am 5’11.5″ and 250 lbs, so I am definitely not “little” (alas). And I have a sense of humor…
5) “Ignorance of the subject matter”: I have three degrees in aeronautics and astronautics, with an emphasis in aerodynamics, gas dynamics, gas physics, and astrophysics. My two theses were concerning an experiment designed to study the refractive index environment of Venus. I spent a good part of my career designing weapons based on the physics of propagating infrared power beams through the atmosphere (check out the YAL-1A). I recently was granted a patent for a method of orbital debris clearing by the use of tenuous gas clouds. I guess, according to you, I should be playing checkers.
6) I see you have no dispute with the remainder of my comments, which were scientific in nature, so I’m glad to know that I’m “your man” in principle. I still think the match between the data and the theory is intriguing.
7) Get over it, Willis. You get a lot of adulation on this site and that’s fine, but you don’t get much from me. You are a talented amateur. I am a professional, verging on dinosaur. It’s nice to see what you do. But your lack of background occasionally shines forth. You ought to learn to laugh at it, and not get bent out of shape when someone points at your loose shirttail. It’s only a loose shirttail, easily tucked in. Life goes on.
8) Keep it up. Just because I’m not excited doesn’t mean that I want you to stop, shrivel, and blow away. You do good work, consistently, and with some elan. I can see that, as easily as I can see a shirttail.

September 2, 2015 4:14 pm

It………does……..not……..matter!!

Reply to  Willis Eschenbach
September 2, 2015 5:36 pm

What matters:
1) IPCC AR5 has no idea how much of the CO2 increase between 1750 and 2011 is due to industrialized man because the contributions of the natural sources and sinks are a massive WAG.
2) At 2 W/m^2 the “unbalanced” RF IPCC AR5 attributes to that CO2 increase between 1750 & 2011 is lost in the magnitudes and uncertainties of the major factors in the global heat balance, e.g. ToA. clouds, reflection, absorption, etc. A third or fourth decimal point bee fart in a hurricane.
3) IPCC AR5 admits in text box 9.2 that their GCM’s cannot explain the pause/hiatus/lull/stasis and are consequentially useless.
All of this is just pointless wandering in the weeds. Stay on target, Luke.
To…accentuate…my…point!!

Frank
Reply to  Nicholas Schroeder
September 2, 2015 7:38 pm

Nicholas wrote: 1) IPCC AR5 has no idea how much of the CO2 increase between 1750 and 2011 is due to industrialized man because the contributions of the natural sources and sinks are a massive WAG.
The C14 released by atmospheric testing of atomic bombs gave us a reasonable idea of how big natural fluxes of CO2 are. More importantly, we know from ice cores that CO2 levels changed only slightly during the last 100 centuries of the Holocene compared with 100 ppm change in the last century. So the large fluxes of CO2 emitted and taken up were in BALANCE before the Industrial Revolution began and the observed increase can be attributed mostly due to burning fossil fuels. After the Industrial Revolution, the rate of uptake by natural processes has increased with the increasing concentration of CO2 in the air. This enhanced natural uptake has removed about half of the CO2 released by burning fossil fuels. Today we burn enough fossil fuel to raise CO2 by about 4 ppm/yr, but the observed increase (after enhance uptake) is only about 2 ppm/yr. These aren’t WAGs.
“2) At 2 W/m^2 the “unbalanced” RF IPCC AR5 attributes to that CO2 increase between 1750 & 2011 is lost in the magnitudes and uncertainties of the major factors in the global heat balance, e.g. ToA. clouds, reflection, absorption, etc. A third or fourth decimal point bee fart in a hurricane.”
2 W/m2 is about 1% (two decimal points) of the 240 W/m2 of LWR that needs to escape to stay imbalance with incoming post-albedo SWR. According to the S-B equation, a blackbody at 255 degK (the temperature that emits 240 W/m2) needs to warm about 0.5 degC to emit an additional 2 W/m2. The earth isn’t a blackbody – feedbacks modify the blackbody response. Since absolute humidity will rise and surface albedo will fall with rising surface temperature, temperature probably will need to rise more than 0.5 degC for an additional 2 W/m2 to reach space. Cloud feedback is the big unknown, but summer has less cloud cover than winter. GCMs fail to reproduce seasonal changes in OLR and reflected SWR observed from space AND they also disagree with each other. These easonal changes are large and not overwhelm by noise and uncertainty: 3.5 degC in GMST and about 10 W/m2 in OLR. So: radiative forcing is real, feedbacks can be observed from space and are real, but there is no need to believe that GCMs get feedbacks and climate sensitivity correct.
3) IPCC AR5 admits in text box 9.2 that their GCM’s cannot explain the pause/hiatus/lull/stasis and are consequentially useless.
“All models are wrong, but some models are useful.” The inability to reproduce the hiatus means that GCMs fail with respect to climate sensitivity or unforced variability (chaotic behavior) or both – a critical flaw for projecting climate change. They also fail to hindcast decadal climate variability. These failures doesn’t mean radiative forcing and associated feedbacks don’t exist. To make computations practical, AOGCMs are forced to make compromises and use parameters to represent many phenomena. These compromises allow the models to reproduce some, but not all, aspects of our climate. If you want to know how the jet stream changes with the seasons, model output is very realistic.

Reply to  Frank
September 3, 2015 8:14 am

Frank,
“These aren’t WAGs.”
IPCC AR5 Table 6.1 CO2 balance uncertainties = WAGs and a few really big ones like +/- 50%!
IPCC AR5 TS.6 A page and a half of WAGs several of them substantial like the magnitude of CO2 feedback aka climate sensitivity. Yes, in our puny perspective mankind produces a lot of CO2, but in the enormous overall natural ebb & flow of global CO2 how much gets sequestered, how much remains, cannot be quantified with reasonable certainty.
“Cloud feedback is the big unknown, but summer has less cloud cover than winter.”
No kidding although IPCC AR5 assigns clouds an RF of -20 W/m^2 ten times the cooling of CO2 heating and admittedly subject to wide natural fluctuations. Also WAG’d in TS.6.
“The inability to reproduce the hiatus means that GCMs fail with respect to climate sensitivity…”
Climate sensitivity is the foundation of the CAGW theory. If that fails it all fails. That means RCPs 3.0, 4.5, 6.0, and 8.5 and their hysterical projections for ice melting and sea levels all go in the dumpster. See “Climate change in 12 Minutes.”

Frank
Reply to  Frank
September 3, 2015 5:51 pm

Nicolas: Let me repeat: The natural emission rate and uptake rate of CO2 are irrelevant because these processes were stable and in equilibrium for 100 centuries before the Industrial Revolution! That kept CO2 stable near 280 ppm for 100 centuries. If the natural emission rate and uptake rate were both 10-fold bigger or both 10-fold smaller than they are, it wouldn’t make any difference – these natural processes would still be in balance and CO2 would remain near 275 ppm. Since these natural process have been stable for a 100 centuries and since CO2 began rapidly rising only when man started burning lots of fossil fuel, the reason for the rise is obvious.
Cloud radiative forcing (measured in W/m2) and cloud feedback (measured in W/m2/K) are two different things. Cloud radiative forcing is important for getting today’s climate correct – for models to have the correct GMST. It would be important if we geo-engineered more clouds to cool the earth. When we are talking about GHG-mediated GW, however, cloud feedback is the critical unknown. For every degK of surface warming, will clouds change so as to further increase the radiative imbalance by reducing OLR or reflecting less SWR? This is the greatest source of uncertainty in ECS.
The THEORY of AGW is comprised of forcing and feedbacks, but not a particular value for ECS. Experimental evidence for forcing and feedbacks is highly persuasive. The HYPOTHESIS that AGW will be catastrophic if emissions aren’t seriously reduced requires that ECS be high (roughly 3 degC or higher for 2XCO2).