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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241 thoughts on “Traveling Through Other Dimensions

  1. 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.. 🙂

    • 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.

      • 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:

        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

        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

        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:

        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.

        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.

  2. 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

      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

      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.

      • So, sorry, your conclusion which fails to mention this is totally unsupported by the facts.

        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

        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?

        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.

  3. 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.

    • 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.

  4. “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!

  5. 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

      • 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

  6. 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.

      • The dominent “greenhouse gas” on Jupeter is hydrogen. It is pressure creates the high temperatures on Jupeter.

      • 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

        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.

        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 @ 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:

        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.

        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

        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.

        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

        Willis wrote:

        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.

        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.

        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.

  7. 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.

      • 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.

  8. 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.

      • 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.
        https://geosciencebigpicture.files.wordpress.com/2015/08/water_infrared_absorption_coefficient_large-vapor-green-ice-blue-water-red.gif
        Green is atmospheric water, blue is ice, and red is liquid water.
        Also, you can forget about visible light warming the oceans.
        https://geosciencebigpicture.files.wordpress.com/2015/09/absorption_spectrum_of_liquid_water.png

      • gymnosperm September 2, 2015 at 10:35 pm

        Also, you can forget about visible light warming the oceans.

        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

  9. 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.

  10. a watt per square metre is a kilogram per cubic second? Who knew?

    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.

  11. 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.

  12. “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.

  13. 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?

  14. So my third objection is that they are claiming that the model only uses two variables, when in fact it uses five.

    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”

    • 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.

  15. 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.

  16. 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.

  17. 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?

  18. 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.

  19. 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.

      Only the non-symmetrical molecules, like CO2 and H2O have a greenhouse effect, because they have a permanent dipole moment.

      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.

  20. 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.

  21. 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+ ).

    • 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]}.

      • 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.

  22. 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.

    • 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.

  23. 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.

  24. “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.

  25. 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.

      • 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.

      • 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

  26. 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.

  27. 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.

  28. 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.

    • Thanks, Mosh. Garbage is garbage on either side of the aisle, and I think it is a part of honest scientific behavior that the garbage on the skeptical side needs to be investigated by folks on the skeptical side.
      The same is true of garbage on the mainstream side … but they tend to just close ranks and ignore the mess. Well, they’ll diss Michael Mann in private, but in public it’s all smiles and backslapping.
      And then they wonder why nobody trusts them … funny, that.
      Best regards,
      w.

    • 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?

      • Gary, thanks for the alliterative sword wielding, always good to hear from you.
        You say:

        Steven, I think your insinuation that thinking sceptics support garbage if it is on the ‘supportive’ side is straw-manish.

        I didn’t understand Mosh as saying that at all. It’s not a question of support. Instead, I understood him as saying that there are not a lot of thinking skeptics who go out of their way to falsify skeptical garbage. It’s an understandable tendency, and no where near as prevalent as it is on the mainstream side. But it is still a real phenomenon.
        In fact, the reluctance on both sides to point out their own faults is one of the reasons that I do spend a fair amount of time trying to expose the skeptical arguments that are somewhat … mmm … well, let me call them “tenuous” to avoid calling them “ridiculous”.
        My point of view is that there are lots of very valid reasons to disbelieve the alarmism … but claiming that gravity can heat the surface in an ongoing manner isn’t one of them. I also think that people promoting nonsense in the guise of skeptical climate science is not good for the climate dialog.
        Regards,
        w.

      • 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.

      • “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.

  29. 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 .

  30. 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.

    • hanelyp September 2, 2015 at 9:49 am

      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.

      Not true in the slightest. That’s the problem with fitted models. I can design you a lovely fitted model that is very successful at relating the rise in global temperature to the rise in US postal rates.
      So, does the “degree of match” between US postal rates and global temperatures “suggest that postal rates are a very large part of the picture”?
      I don’t think so …
      w.

  31. 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?

  32. 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 September 2, 2015 at 10:20 am

      What are the “canonical values” for the average global surface temperature of Mars, and how were they arrived at?

      Doesn’t matter. The fact that they didn’t use them and decided to calculate their own is a huge red flag. If you can’t make your model fit except by adjusting the data your model is supposed to fit to, you have a problem.
      w.

      • 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 September 2, 2015 at 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.

        Thanks for that, Kristian, and in a perfect world you might be right about their actions. But in the real world, I doubt greatly that they did the work on Martian temperatures BEFORE they put their model through its paces. In other words, their adjusting the temperature of Mars after the fact is data snooping.
        Look, if they’d taken the same tack with the other planetary temperatures as well, done the exact same analysis on the temperatures of the Earth and Venus, it wouldn’t be such a concern.
        But to do it only for Mars, and to do it after finding out that Mars doesn’t fit their model is, well, odd to say the least … particularly since after their recalculation, guess what?
        Mars now fits their model perfectly!
        Who knew?
        As to the canonical value, a quick search for “average temperature of Mars” on Google Scholar returned lots of hits. So if you have “NEVER seen, say, the 215K “canonical value” justified in any way”, you might start there … 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.

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

        Abstract
        Between September 1997, when the Mars Global Surveyor spacecraft arrived at Mars, and September 1998, when the final aerobraking phase of the mission began, the Thermal Emission Spectrometer has acquired an extensive data set spanning approximately half of a Martian year. Nadir-viewing spectral measurements from this data set within the 15 μm CO2 absorption band are inverted to obtain atmospheric temperature profiles from the surface up to about the 0.1 mbar level. The computational procedure used to retrieve the temperatures is presented. Mean meridional cross sections of thermal structure are calculated for periods of time near Northern Hemisphere fall equinox, winter solstice, and spring equinox as well as for a time interval immediately following the onset of the Noachis Terra dust storm. Gradient thermal wind cross sections are calculated from the thermal structure. Regions of possible wave activity are identified using cross sections of rms temperature deviations from the mean. Results from both near-equinox periods show some hemispheric asymmetry with peak eastward thermal winds in the north about twice the magnitude of those in the south. The results near solstice show an intense circumpolar vortex at high northern latitudes and waves associated with the vortex jet core. Warming of the atmosphere aloft at northern midlatitudes suggests the presence of a strong cross-equatorial Hadley circulation.

        And since 1969 we’ve had results from the Mariner 6 & 7 fly-by’s … so for a couple of model-makers to decide to throw out all of that previous research and do their own calculations seems … well … let me call it “self-serving” on their part.
        My regards to you, thanks for the comment,
        w.

      • 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 September 2, 2015 at 1:11 pm

        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 …?

        Thanks for the reply, Kristian. 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.
        Kristian, you seem to be confusing what YOU have seen with what has been seen. I’m tired of doing your homework for you. How about you get out of your chair and find out what is actually out there? Near as I can tell, what you’ve NEVER seen is … well … a lot of stuff. Like say this paper from 1970 …

        Mars: Measurements of its Brightness Temperature at 1.85 and 3.75 cm Wavelength
        MICHAEL J. KLEIN
        Radio Astronomy Observatory, he University of Michigan Ann Arbor, Michigan 48104
        Received December 14, 1970
        New measurements of the microwave temperature of Mars are reported. The brightness temperatures measured during the planet’s close approach in 1967 were
        182±15°K (m.e.) at 1.85 cm, and 200± 11°K (m.e.) at 3.75 cm

        So you can stop claiming that lists of what YOU have never seen are really lists of what WE have never seen. Others have seen it … just not you.
        w.
        PS—IF, as you claim, we have NEVER seen any global actual data … then neither have Volokin and ReLlez seen any global actual data.
        And so if you are right about having no data … then why is the guess of a couple of modelers better than the ~50 years of estimates that we have from spectroscopic and brightness and other remote analyses?
        Could it be because their own personal results fit their model better?

      • “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.

  33. 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.)

    • I distinguish between data snooping on the one hand, and “p-hacking”, “data dredging” and “data fishing” on the other hand.
      Data dredging/fishing/p-hacking is looking at a large amount of data in search of something with a low p-value. A bad habit, to be sure.
      Data snooping is related, but different. In its most common form, data snooping is using information about the fit of data to a theory to determine whether to include the data in the analysis at all.
      See the treatment of Titan above as an example. Once they found out it didn’t fit their theory, they threw it out and didn’t use it in their optimized fit. That’s data snooping. They looked at the outcome before making a decision about inclusion. Note that it’s not a data dredge, they haven’t looked through vast reams of data, quite the opposite.
      Climate science is generally so blind to the problem of data-snooping that the ability to snoop tree-ring was touted as an advantage of tree-ring analysis. The proponents of treemometry said one reason their results were so reliable is that they could divide trees into “climate responders”, meaning trees whose tree-ring widths matched some temperature record of interest, and “climate non-responders”, meaning those trees that didn’t match the changes in temperature. That way, they said, they were able to only focus on the accurate treemometers, the “climate responders”, and use them to determine temperatures hundreds of years ago with good accuracy …


      Of course, if you go through a big block of data like tree-ring records, and you only pull out and use those that match a given temperature record, sure, you can “demonstrate” that tree-rings are an accurate indicator of temperature.
      But that is just alarmist-approved, industrial-strength data snooping.
      w.

  34. 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.

    • 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?

  35. 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.

  36. 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.

  37. 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.

    • Richard M September 2, 2015 at 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.

      Bizarrely (see below) this is not a couple of scientists confirming the work of Nikilov and Zeller.
      This is Nikolov and Zeller posting under fake names to make it appear as if there is independent support for the work of N&Z.
      Makes my head spin …
      w.

  38. 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.

    • Michael J. Dunn September 2, 2015 at 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.

      So you are busting my critique because of the “skeptical comments” in the thread? Really? You do understand that I didn’t write the comments?

      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.

      The equation I gave was a direct quote from the paper, you nasty little man.
      https://wattsupwiththat.files.wordpress.com/2015/09/volokin-figure-5.png
      The fact that you use it to attack me reveals both your ignorance of the subject matter and your vindictiveness.
      And yes, you unpleasant jerkwagon, I have known since I learned to use a slide rule fifty years ago in high school that addition of exponents is multiplication of the exponential items, duh. That’s how slide rules work.
      And just as you did, I also noted that their equation 5 did not agree with their equation 10a. Except unlike you, I’d read the paper so I knew it was their equation, not mine, that was at fault.
      So I was left with a quandary. Either I could directly quote the equation from the paper, or I could get into the error and wander off into the math, or I could just put the correct form in for their Equation 5, but with no explanation. None of them were very good options.
      Now, my general rule in writing my posts is the KISS principle, particularly regarding math. Many people don’t like math much, some dislike it a lot, so I have to make it interesting for my target audience, which is the educated layperson. And any excursion into things like questions of multiplication and addition of exponentials drives people off en masse. In addition, the post was already quite long, and people tend to go “tl;dr” pretty quickly in these days of the 30-second sound bite.
      To complicate the matter, it was in no way central to my argument. I didn’t even notice the problem until the post was more than half written.
      Then there was the fact that if I “fixed” Equation 5 without explanation, someone like you would be sure to come along and say “Willis, you always say quote my words exactly, but you didn’t quote Equation 5 exactly”. And that would be a fair complaint.
      Finally, I didn’t want to weaken my major objections by what might be taken as me just nit-picking the authors about petty items. I didn’t want people to think I was just looking for small mistakes to bust them for, because I wasn’t doing that—I had large mistakes I wanted people to focus on.
      So after some consideration, I chose to quote it exactly the way it was in the paper, rather than to get into the whole exponential question, or to “fix” Equation 5 without explanation. Now, you are certainly free to claim that I picked the wrong one of my three options … but that’s a different discussion.
      I bring all of this up to show you how much care and thought I put into each and every one of my posts. I don’t do things blindly. I’m playing a long game here. I have to be able to defend every word that I write, and that’s a good thing, that’s science at its finest. As a result I ponder each word choice, I double-check my results, and I give it my best shot.
      So while I’m no more immune to stupid mistakes than is the next man, let me suggest that if you think you’ve found that I’ve made a mistake, that you ask politely about it instead of making a total ass of yourself with unfounded allegations about the extent of my knowledge.
      If you’d like to actually discuss scientific matters rather than make uninformed, untrue, vicious personal attacks, then I’m your man. Just come back when you’ve decided to give up casting vile asparagus on my mathemability and mental horsepowder, and we can resume the conversation. An apology would be nice but isn’t essential. Just keep a civil tongue in your head, and we’ll do fine.
      Until then, let me politely request that you go spread your venom elsewhere.
      w.

      • 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.

      • 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.

      • Michael J. Dunn September 3, 2015 at 11:22 am

        Wow, what a thin skin. In order, because I don’t have much time:

        Michael, you accused me of being a sham, of claiming expertise that I do not have. I responded angrily to such an unwarranted and untrue accusation. Perhaps you just let other people casually insult you in such a manner.
        I don’t.
        I have little but my honor and my honesty and what hard-fought knowledge I’ve gained. I have no PhD. I have no science education. So yes, when you falsely and fatuously claim that “Willis knows less about what is going on than he propounds’, I will indeed slap your face and point out that you are acting like an unpleasant jerkwagon.
        Don’t like it? Then DON’T DO IT. Perhaps your friends put up with that kind of insult. I don’t.

        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.

        Dang, miss the point much? You said you didn’t like my critique for the most ludicrous reason imaginable—because of the readers comments. That’s dumb as a bag of ball bearings. In response I said:

        So you are busting my critique because of the “skeptical comments” in the thread? Really? You do understand that I didn’t write the comments?

        How about answering the issue rather than debating whether you “busted” or “disliked” or “disapproved’ of my critique? You slammed my critique because you didn’t like other people’s comments. I pointed that out. You still haven’t dealt 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.

        I don’t understand that comment 2).

        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.

        So you think you need “ESP” to read the damn underlying document before busting me? You believe you need ESP to tell you that if you don’t understand what I’ve done, or you think there’s an error, the polite thing is to ask?
        You stupidly assumed that an error in a document was mine, because you didn’t trouble yourself to do your homework. Rather than politely questioning the inconsistency, you attacked me, saying I didn’t know what I was talking about. That’s why I said you were “nasty”. You could have asked. Instead, you attacked.

        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…

        And yet you accuse me of not understanding what I’m writing about. OK, you are a big jolly man with a good sense of humor who is totally lacking in common courtesy, and who attacks people when he doesn’t understand what’s going on.
        Is that better?
        You don’t accuse a man of not knowing his stuff just because you don’t understand him. You ASK!
        As to your claim that:

        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.

        Don’t kid yourself. I didn’t even read the remainder of your comments, because I don’t discuss science with unpleasant jerkwagons who think it is fine to casually accuse me of not knowing what I’m doing.

        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.

        If my shirttail had actually been loose, you would be 100% correct, I’ve been shown to be wrong many times in the past. And while no man likes to be wrong, it’s an essential part of science. Heck, I’ve got two posts up, one is called “Wrong Again”, and the other is called “Wrong Again, Again” … so obviously yes, I do laugh at being found with my shirttail out.
        But in this case it was your own ass that was exposed to the breeze. You were the one who was wrong. You were so damn arrogant about how you are such a professional with scads of experience that you didn’t stop to either find out what was happening by reading the paper under discussion, or by simply asking me for an explanation of the discrepancy.
        Instead, you brought out your bogus accusation that I didn’t know what I was talking about … well, when you finally get your shirttail tucked in and you want to discuss the science, then like I said, I’m your man.
        But coming back here merely to justify your own stupidity, lack of politeness, and failure to do your homework? Is this what you describe as you being a “professional”? Because if so, I’m proud to be an amateur.
        Finally, if a man is a “professional” in science, I would think that he would actually read the scientific paper under discussion before starting to make personal accusations about other people’s supposed lack of understanding of the paper and the math therein.
        I can understand making scientific comments based on my exposition, but personal accusations? When you start accusing me of acting in bad faith, you damn well better have done your homework and you damn well better be sure of your facts.
        And you did neither.
        Sorry … like I said, you can take all of that elsewhere, I’m not interested in your pathetic justifications of your insults, nor am I impressed by your puffed-up self-importance. When you act like a jerkwagon, I’ll treat you like one, whether you are a beggar or a king.
        w.

    • Oh……….can……….I……….play……….too?
      ……….
      What……….does……….not……….matter?
      And……….why……….are……….you……….not……….quoting……….what……….you……….object……….to?
      Finally……….why……….are……….you……….writing……….with……….lots……….of……….periods?
      ……….w………..

      • 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!!

    • 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.

      • 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.”

      • 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).

  39. Willis, your thoughts and comments have always been informative and entertaining to me. Thank you!
    In your comment above regarding Mars’ global average temperature, you cite a paper by Michael Klein from 1971. I found the full text of that article here:
    http://deepblue.lib.umich.edu/bitstream/handle/2027.42/33679/0000191.pdf?sequence=1
    After a quick scan thought it I noticed that Klein provides 2 estimates of Mars global brightness temperature derived from two microwave-band measurements, i.e. 182 K and 200 K. Taking a simple average of these, produces (182 + 200)/2 = 191 K for Mars temperature. Also, on p. 212, M. Klein says:
    The two brightness temperatures measured in 1967 are in good agreement with previously published data, which indicate that the Martian brightness temperature at wavelengths between 1 and 21 cm is approximately 190 K (Hobbs, McCullough, and Waak, 1968). The weighted average of the 1.85- and 3.75-cm temperatures reported in this paper is 193 K ± 10 K.
    So, microwave measurements of Mars conducted in 1960s and 1970s revealed a mean surface temperature in the range 190 – 193 K. The authors of the paper discussed on this blog, arrived at 190.56 ± 0.7 K (see their Appendix B). Hence, their estimate of Mars global temperature seems to agree pretty well with these earlier calculations quoted by Klein… Volokin and ReLlez may have got it right after all … Your thoughts?

  40. Willis,
    What is the formula for planetary rotaion period and average temperature?
    It’s stated by you as obviously important …yet It’s not ever calculated or accounted for in earths planetary heat equation.
    Instead, an average insolation value is simply assumed as a split to cover 1/2 light and half dark. But, if rotational rate changes the average temperature, how does one correctly account for it?
    My first thought was it makes no difference…but you say it is a no brainer and needs to be considered.
    Thanks,
    Kirk

    • Willis,

      What is the formula for planetary rotaion period and average temperature?
      It’s stated by you as obviously important …yet It’s not ever calculated or accounted for in earths planetary heat equation.

      There is no general equation. This is because in the absence of an atmosphere, the night-time heat loss is dependent on how much heat is left unradiated at the end of the day. And this in turn is dependent on the specific heat of whatever the sunlight is warming, along with a variety of other factors.
      And this is in a situation with no atmosphere. With an atmosphere plus water vapor, the energy is constantly being redistributed by sensible and latent heat transfers. As a result, both the water vapor and the atmosphere act to reduce the day-night swings in temperature.
      Finally, every temperature difference causes a drop in average temperature. The problem is that there are several temperature differences at play—day/night, summer/winter, and pole/equator. As a result, it’s difficult to disentangle all of those to give us a total.
      However, it’s not important in the usual range of climate questions, as whatever it is it would be relatively constant. Since we are concerned mostly with changes in temperature, such a constant temperature depression would drop out of any relevant equation.
      All the best,
      w.

      • Thanks, tallbloke, good to hear from you. You say:

        The authors discuss the rotation question extensively in their previous paper:
        http://www.springerplus.com/content/3/1/723
        See the section starting above Eq24
        Takeaway summary: Rotation rates within the range found in the solar system make negligible difference to surface T.

        I took a look at their derivation, and I came away totally unconvinced. Here’s the statement that seems incorrect to me:

        The Law of Energy Conservation dictates that a change in rotational speed may only affect the magnitude of the diurnal temperature amplitude at the surface but not the diurnal mean, i.e. rotation solely acts to redistribute the total available energy between daytime and nighttime hemispheres through the planet’s thermal inertia.

        First, the Law of Energy Conservation doesn’t apply to temperature, because temperature isn’t conserved. Energy is conserved, but temperature is NOT conserved. So they are incorrect in that part of their claim.
        Next, suppose the moon were rotating very rapidly. The day/night temperature differences would be small. However, because it rotates slowly, only once every 28 days, the night side has time to cool way down and the day side has time to heat way up. As a result, the lunar diurnal temperature swing is quite large, about 270°C or thereabouts. You can see this in the graph in the head post.
        Now, Dr. Brown points out the following lovely derivation:

        Now let’s assume that the temperature is not uniform. To make life simple, we will model a non-uniform temperature as a sphere with a uniform “hot side” at temperature T + dT and a “cold side” at uniform temperature T – dT. Half of the sphere will be hot, half cold. The spatial mean temperature, note well, is still T. Then:
        P’ = (4 pi R^2) epsilon sigma ( 0.5*(T + dT)^4 + 0.5(T – dT)^4)
        is the power radiated away now. We only care how this scales, so we: a) Do a binomial expansion of P’ to second order (the first order terms in dT cancel); and b) form the ratio P’/P to get:
        P’/P = 1 + 6 (dT/T)^2
        This lets us make one observation and perform an estimate. The observation is that P’ is strictly larger than P — a non-uniform distribution of temperature on the sphere radiates energy away strictly faster than it is radiated away by a uniform sphere of the same radius with the same mean temperature. This is perfectly understandable — the fourth power of the hot side goes up much faster than the fourth power of the cold side goes down, never even mind that the cold side temperature is bounded from below at T_c = 0.

        But since energy radiated by the lunar sphere is a constant equal to the amount of radiation it is receiving, what this means is a non-uniform distribution of temperature on the lunar surface reduces the mean lunar temperature. The mean temperature has to drop in order to keep the radiated power constant.
        And that is why the moon is so cold. Straight Stefan-Boltzmann calculations combined with a lunar albedo of 0.13 and an emissivity of 0.98 give us an (incorrect) calculated lunar temperature of
        Input W/m2 = 340 W/m2 (same as earth) * 0.87 (coalbedo) = 296 W/m2
        Temperature = (296 W/m2/ (.97*5.67E-8))^(1/4) = 271K = -2°C
        However, the moon is much, much colder than that. Its temperature (per the Volokin paper) is 197.25K ≈ -75°C. This is because of the large diurnal swings, which lower the mean temperature.
        From the diagram of the moon’s temperature in the head post, we can see that the lunar temperature swing is about ± 135°C. Using Dr. Brown’s formula above with 296 W/m2 of absorbed solar energy gives us a calculated lunar temperature of 190K … which compares very well with the figure from the paper of 197K, given that I’m working off of just one set of lunar temperature measurements and not lunar averages.
        So I’m sorry, but I don’t believe Volokin and ReLlez’s other paper is any more credible than this one. They are wrong when they say that

        … a change in rotational speed may only affect the magnitude of the diurnal temperature amplitude at the surface but not the diurnal mean …

        for a simple reason. As Dr. Brown shows, ANY change in diurnal temperature amplitude affects the mean temperature, and the moon is a prime example.
        My best to you, and yes, despite the fact that you’ve banned me from commenting on your blog, I do read your blog regularly. Curiously, after all this time I’ve realized that I’m kinda glad to be banned there, because it frees up the time I’d spend in mostly fruitless protest if I could comment there, and I can put that energy into writing posts like this one.
        Life works out strangely, and my wish is that it work out well for you.
        w.

      • Oh, yeah, I forgot to add the math. I use a function which I derived from Dr. Brown’s formula in my comment above. The function uses the variables of expected temperature given the incoming power p1 (W/m2), the temperature swing dT (°C), and the emissivity epsilon, to calculate the resulting surface temperature (K).

        newt=function(p1,dt,epsilon=1,sigma=5.67e-8) {
          ((p1 + 18 * dt^4 * epsilon * sigma -
              6 * sqrt(dt^4 * epsilon * p1 * sigma + 9 * dt^8 * epsilon^2 * sigma^2))/(
                epsilon * sigma))^(1/4)
        }

        Sigma is the Stefan-Boltzmann constant, 5.67E-8.
        For the moon, this function gives us:

        newt(p1=296,dt=135,epsilon=.98)
        [1] 191.1

        w.

  41. Willis: Dimensional analysis is usually extremely useful, but not the way it was carried out in your top equation. In W/m2, the m2 comes from the product of two distances measured on orthogonal axes – area. When Joules refers to kinetic energy and has units of kg-m2/s2, the meters are measured in the direction of motion – along one axis.
    However, radiation isn’t a form of kinetic energy and its direction of motion – if it can be equated to kinetic energy – is actually perpendicular to the area. If we attach directional labels to the distances (m_x, m_y and m_z), we get W/(m_x*m_y) for flux and kg-m_z^2/s^2 for kinetic energy.

    • Thanks for the comment, Frank. Actually, the top equation (as I thought was clear from my explanation but may not have been) is not mine. It is taken directly from the paper in question.
      In any case, I was unaware that there were different base SI length units for different directions (m_x, m_y, and m_z in your terminology). Do you have a citation for that?
      w.

      • WIllis: I should have referred to the top equation in this post, not “your top equation”. Sorry.
        In the Wikipedia article on dimensional analysis, there is a discussion of the Huntley extension to directed dimensions, but I certainly hadn’t read this article before writing my comment.
        https://en.wikipedia.org/wiki/Dimensional_analysis#Huntley.27s_extension:_directed_dimensions
        SI base units are very useful, but there are plenty of other units that are useful in a less formal version of dimensional analysis often called the “factor label method”. A simple example: For two similar triangles with sides 2, 3, and 4 meters, and 7, x, and y meters:
        2 m short side/7 m short side = 3 m medium side/x m medium side = 4 m long side/y m long side
        If one uses units of meters for all lengths, all ratios will be dimensionless, but students often don’t get the right ratios. In chemistry:
        y mL * z g/mL / x g/mole = y*z/x moles g/mL = density g/mole = MW
        For the reaction 2A —> B, we might have:
        [y mL_A * z g_A /mL_A / x g_A/mole_A ] * moles_B/2 moles_A * w g_B/mole_B = y*z*w/2*x g_B
        So when I looked at the dubious top equation, I recognized that the meters involved in measuring area and the meters^2 in kinetic energy involve different directions. Years of creating my own labels caused me to create m_x, m_y and m_z. In elementary mechanics, we decompose a force F into F_x and F_y. Then we get more sophisticated and use vector quantities, dot products and cross products to liberate ourselves from any particular coordinate system. work = F dot s. However, every vector quantity has a direction and units associated with it, like the displacement (s) in F dot s
        Some radiative physics. Given a radiative imbalance of y W/m2 and a heat capacity of z J/m3/K:
        y W/m2 / z J/m3-K = y/z K-m/s
        We get units of K/s (a warming rate) multiplied by meters. m2 is area and m3 is volume, so obviously the remaining meters must be perpendicular to the surface area – for example the depth (d) of the ocean mixed layer being heated by the radiative imbalance.
        y W/m2 / [z J/m3-K * d m] = y/z*d K/s
        In aeronautics, a dimensionless coefficient of drag c_d is used to calculate the force of drag F_d produced by a wing of area A, moving at a velocity v through a fluid of density p:
        c_d = 2*F_d / p*v^2*A
        You might say that the meters used to measure area and the meters used to measure velocity involve different directions and you would be correct. If you make a wing longer and skinnier, but keep the area constant, the coefficient of drag changes. Since the force of drag and the velocity are measured in the same direction, meters in the direction of motion cancel, but not meters perpendicular to the direction of motion.

      • Frank, thanks kindly for the link to the “Huntley extension”. As is often the case with Wikipedia, I came away both educated and confused, but your examples clarified the concept nicely.
        I’m curious what difference this would make to their analysis … but probably not curious enough to actually do it, because the whole “pick a formula, fit a curve, discover a new thermodynamic property” nonsense is so distasteful to me. Yes, curve fitting has its uses … but planetary average temperatures isn’t one of them.
        Most useful, and most appreciated,
        w.

  42. I made it this far this time, “The formula that is at the root of all of this, a simple dual-exponential, is extremely unlikely to be adequate to the task.” Not bad, if I do say so my self. My better angel must have been with me.
    Just so I don’t have to read any more, could someone tell me if WIllis confused the dimensions in dimensional analysis with the dimensions in a fractal sense or with the derivatives in a Taylor series expansion? I’d be forever indebted if someone could just sum it up for me. Thanks.
    Oh, by the way Willis…. some months ago I mentioned the Lewis Number. It would do you a lot of good to figure out the physical significance of Le = 1.

    • Dino, since you are a man who boasts of not finishing my posts, and then asks others to do your reading for you, I’m amazed that you are under the mistaken impression that I pay the slightest attention to your opinion …
      w.

      • Oh, I wasn’t asking you. I assume you read your own posts and you are sometimes at the limits of your understanding and most times past it. It makes no sense to ask you to explain your posts.
        Don’t get too stuck on the Le = 1 thing. It a graduate level question. Let me bring it down…… So have you figured out the relation between the taylor series expansion, auto-correlation and dimensionality?

      • Dinostratus September 4, 2015 at 10:03 am Edit

        Oh, I wasn’t asking you.

        Oh, I didn’t say you were asking me, nor did I think you were. It’s obvious from your comment that you were asking others. Reading comprehension is your friend.

        I assume you read your own posts and you are sometimes at the limits of your understanding and most times past it. It makes no sense to ask you to explain your posts.

        And yet I have a peer-reveiwed piece in Nature Magazine (albeit small) and peer-reviewed studies in other scientific journals as well. They obviously think my scientific understanding is perfectly adequate. Call me crazy, but I’ll take their opinion of my abilities and scientific understanding over that of an anonymous internet popup … particularly one like yourself, who seems to specialize in unpleasant personal attacks.

        Don’t get too stuck on the Le = 1 thing. It a graduate level question. Let me bring it down…… So have you figured out the relation between the taylor series expansion, auto-correlation and dimensionality?

        Get “stuck on the Le=1 thing”??? You still don’t seem to get it. I pay absolutely no mind to whatever you might babble about science. It might be wrong, it might be right … but I couldn’t care less.
        I make no attempt to ever follow your “scientific” suggestions, Dino. Since you obviously dislike me intensely for unknown reasons, it would be extremely foolish of me to pay the slightest attention to your “scientific” claims and suggestions. Whatever they are, I’m sure they are designed to cause me grief.
        Sorry, amigo, but you’ve succeeded in canceling your own vote with me. That’s not easy to do, usually I will pay at least some attention to the non-ad-hominem parts of a comment, because there might be some scientific cheese at the end of the maze.
        But with you, it’s always just an unpleasant dead end.
        Sadly,
        w.

      • You’re getting angry. Good, I can feel your anger. I am defenseless. Take a math book. Strike me down with all of your hatred and your journey towards the dark side will be complete!

      • Dinostratus September 5, 2015 at 3:21 pm

        You’re getting angry. Good, I can feel your anger. I am defenseless. Take a math book. Strike me down with all of your hatred and your journey towards the dark side will be complete!

        Angry? Actually, you make me laugh. Dino, if I were to get angry with you, you’d know it. But I only get angry about important things, and on my planet, that doesn’t include you.
        We now return you to your fantasy that you are Darth Vader, the all-important Dark Lord … fitting, I suppose.
        w.

      • No, that’s a quote of the Emperor. Darth Vader was the dude in all black who had an asthma problem.

      • Dinostratus September 6, 2015 at 5:30 pm

        No, that’s a quote of the Emperor. Darth Vader was the dude in all black who had an asthma problem.

        I do well in Trivial Pursuits except when it comes to movies. I don’t go often. And in any case, all those extra-terrestrials start to look alike after while. Well, except for the guy with the red horns, whatever his name was, and the big fat dude, Jabba. I saw the movie with Jabba. I didn’t see the one with the red-horn guy.
        In any case, let me rephrase my statement to correct previous error:

        We now return you to your fantasy that you are the Emperor, the all-important boss of everything … fitting, I suppose.

        Regards,
        w.

      • Maybe that’s your problem. Maybe it’s the simple details that you can’t easily assimilate and keep. That is, your mind wanders before all the puzzle pieces are all in place. You then post your mental wanderings as if it is some sort of personal triumph and profound truth. It’s not. It’s a mark of laziness and disrespect for the reader. You make very little progress and in a circuitous manner.
        That’s it! It’s your disrespect for the reader that gets on my nerves. Your posts mock those who’ve forced themselves to sit down and learn all the pedantry and formalism of the Buckingham-Pi theorem, asymptotic expansions, etc. etc. It wasn’t fun WIllis. It was hard. Hour after hour of sitting and forcing every distraction out of the mind trying to under stand why MLT is so GD important.
        Perhaps you should be taking some sort of medication. Something for your ADHD and save us the insult,

  43. It seems intuitively correct to me to say that solar irradiance and atmospheric pressure alone will determine long term average surface temperature. After all, what else could determine it? The proviso here, though, is that the “average surface temperature” has to be averaged not only in time but also in space; and by that I mean the temperature needs to be averaged throughout the entire depth of the atmosphere. This will correct for lapse rates, phase changes, and atmospheric opacity (i.e. greenhouse effect). Once all that is taken into consideration, the composition of the atmosphere should no longer matter.
    Of course, you could say that this approach solves the problem only by deeming it not a problem. However, I think the difficulty lies not with my method, but with our inaccurate notion of “surface.” The atmosphere of a planet simply has to be considered an extension of its surface; or rather, the surface of a planet is a region which includes its atmosphere.
    I should also think that this relationship, while straightforward, may well be too chaotic to be fit by any curve.

  44. Willis
    In your response (Willis Eschenbach September 2, 2015 at 10:24 pm) to Kirkc (September 2, 2015 at 5:22 pm), You play down the importance of planetary rotation (not because it does not impact upon temperature, but because what ever it is, it is a constant and thereby not important “in the usual range of climate questions”)
    On the contrary, whilst planetary rotation will not impact upon whether tomorrows climate/weather will be the same as todays, the impact of planetary rotation is directly relevant as to whether there is any GHE on planet Earth, and if so, its magnitude.
    First, one has to know the “no atmosphere temperature” of a planet. This will, as you state be influenced by, a plethora of factors, amongst these being geothermal from the core, the latent heat capacity of the surface, and how the surface responds to incoming solar (which cannot penetrate a rock to any great extent but can penetrate oceans by up to say 100 metres, albeit that most incoming solar is absorbed within about 70 cm to 3 metres), and of course, it will be influenced by planetary rotation. Put simply, has the planet got enough time at night to dissipate the ‘excess’ energy that was built up during the day? Thus if say CO2 impedes photons from the surface on there way out to space, is there enough time during the 12 hours of night for the daytime ‘excess’ energy to be dissipated? Compare Earth with Venus where there is about 243 Earth days for the night to dissipate the energy built up during the Venusian day.
    In your article, you state:. “As near as I can determine there is one parameter used in the calculation of Tna, the hypothetical and UNKOWABLE “no atmosphere temperature”” (my emphasis), So we are not off to a good start. The first variable, you state cannot be assessed.
    Second, one needs to know what temperature the planet would have with an atmosphere of known density and volume, irrespective of its precise composition (ie., whether it has or does not have radiative gases, and irrespective of their precise concentrations). Since you consider the no atmosphere temperature is unascertainable, I would hazard a guess that you consider the temperature of the planet with an atmosphere (irrespective of its composition) is also unknowable. So this too causes a problem.
    Third one would need to know the actual temperature of the planet with its actual atmosphere and to know the precise composition of this atmosphere. Even for planet Earth, we do not know what its actual temperature is, and this is why the temperature is never presented and instead one sees data based upon anomalies of a small number of station measurements unevenly spatially distributed, and ARGO does not even measure the warmest oceans/seas, possibly because these tend to be of modest depth (circ 1000m or less).. I recall reading a post sometime back made by someone who linked about 6 or so different NASA papers putting the temperature of this planet between about 9 degC and 18 degC!
    We have no idea, within a few degrees what the temperature of this planet is so we do not know whether the temperature is something other than it theoretically ought to be.
    Given the lack of knowledge of these 3 variables, it is impossible to assess whether there is any GHE effect (at least that caused by gases other than water vapour), still less to put a figure on it.
    On a water world, such as planet Earth, where water exists in all 3 forms, the natural water cycle will always have a significant impact upon the temperature of the planet (due to heat transport and latent energy in phase changes), but that is not the GHE as is being talked about by the warmists.
    Incidentally, there is a lot we do not understand since even on the moon, the coldest temperatures recorded are about 35 degK (Southern hemisphere) and 26 degK (southern Hemisphere). These are in the shadow of craters that have not seen the light of day (ie., have received no solar) for eons, and yet they are not the 3 degK which we are told is the background temperature of space. Why not, if they have been radiating into and have been receiving this ‘cold’ radiation for billions of years and if the moon is itself is cold (ie., whilst it still possesses a very small liquid core, the thermal capacity of the rock, surrounding the core, is such that the core does not heat the surface)? It will be interesting to get some update on Pluto following the recent fly pass.

  45. Further to my comment above,. “and 26 degK (southern Hemisphere)” should have been the Northern Hemisphere.
    My main disquiet with this paper is the over extrapolation of sketchy data. We do not know the temperatures of these bodies with sufficient certainty to make the comparisons. Heck, we do not even know the temperature of planet Earth, and all sorts of assumptions are being made as to the temperature of the other bodies in the solar system.
    Mars, the Moon and Triton have so little in the way of atmosphere, I question whether they can be realistically be comparable to rocky bodies/planets with an atmosphere.
    As others have noted Titan will always be problematic because of the methane cycle, but taking that difficulty into consideration and the inevitable wide errors that there are with accurately accessing temperature and atmospheric composition, Titan did not lie that far off the plot in the papers fig4. I would be concerned if it was lying at say around 3.2 Ts/Tna or 1,2 Ts/Tna, but it is not. Fig4 ought to contain error bounds, the plotted line ought to have been a thick band not a thin line, and had it been a thick band (reflecting realistic error margins) I suspect that Titan would lie within the band.

  46. Willis, I have some problems with the Fig. Moon’s suface temperature.
    The SB Avg Earth no Atmosphere surface temperature is not -18 °C but it should be the same as Avg Lunar Temperature – 2.5 °C. The local temperature at the moon surface depends on the thickness of the surface layer because it is influenced by the heat capacity and the thermal conductivity of the surface. So, you should add an information how the temperatures are measured on the moon. I think it is radiation thermometry.

    • Without borehole data, we have no real knowledge about how much geothermal heating there is, I recall seeing that the temperature at about 1 metre depth is about 238K, but whether that is a function of conduction of warming caused by solar irradiance impacting the surface, or geothermal heat from the core, I do not know.
      But my understanding based upon what I have read on Nasa papers is that whilst they consider that the moon has a small liquid core variably cited at about 800 degC to 1700degK, it is so small and so far from the surface that effectively little heat reaches the surface. I do not know what that assumption is based on since I do not know to what depth we have drilled the moon, and over what depth we have real measured temperature data. Since the minimum temperature observed on the moon is circa 30K (in the shadow of craters that have not seen solar irradiance for billions of years), I presume that geothermal of at least that must be making its way to the surface. However, this is all conjecture since without proper bore hole data.
      I would not expect the Erath’s no atmosphere temperature to be -2.5 degC due to differences in albedo, rotation, latent heat capacity of the surface (especially that of the oceans which also do not absorb 100% of the solar at the surface but rather a not insignificant quantity at depth) etc.
      I would suggest that there are too many differences between the Moon and the Earth to make that comparison.

      • “Without borehole data, we have no real knowledge about how much geothermal heating there is, I recall seeing that the temperature at about 1 metre depth is about 238K.”
        Richard, thanks for your hint. I found a paper from M.G. Langseth 1973 et al.: Revised lunar heat flow values. They present some data of the bore hole experiment. The temperature at a deph of 90 cm is -22 °C and is nearly time independent. At 49 cm the temperature oscillates between -23°C and -25 °C. The mission was Apollo 15 with the coordinates 26N, 4E of the landing point. For these coordinates and an albedo of 0,12, I expect a SB average surface temperature of +5 °C.
        “I would not expect the Erath’s no atmosphere temperature to be -2.5 degC due to differences in albedo, rotation, latent heat capacity of the surface (especially that of the oceans which also do not absorb 100% of the solar at the surface but rather a not insignificant quantity at depth) etc.”
        You can find this value in many textbooks, for instance W. Roedel, Physik in unserer Umwelt: Die Atmosphäre, Springer, 3. Auflage. No atmosphere means that there are no oceans. Heat capacity and rotation play a minor role in calculating the average, as long as the heat capacity is independent of temperature.

    • Addendum
      ” I found a paper from M.G. Langseth 1973 et al.: Revised lunar heat flow values. They present some data of the bore hole experiment. The temperature at a deph of 90 cm is -22 °C and is nearly time independent. At 49 cm the temperature oscillates between -23°C and -25 °C. The mission was Apollo 15 with the coordinates 26N, 4E of the landing point. For these coordinates and an albedo of 0,12 I expect a SB average surface temperature of +5 °C.”
      I wondered about the large difference between my transient EBM-calculation (+5°C) and the measurements at a depth of 49 cm (-24°C +/-1°C). The cause is that I used for the effective heat capacity 2.8*e7 W/(m2*K), which is characteristic of the “wet” earth. For the “dry” moon the effective heat capacity should be smaller. With 1*e6 W/(m2*K) I found -25 °C for the landing point which is in better agreement with the experiments
      The free publication of Volokin et al 2014 “On the average temperature of airless spherical bodies and the magnitude of Earth’s atmospheric thermal effect” was very helpful for my investigations. A planet without an atmosphere seems to be very different from a planet with an atmosphere. This is not true. The heat transport from a planet to space is always a sum of radiative heat transport and material heat transport (convection, diffusion). An airless planet has a sharp border, the surface, while the transition from material heat transport to radiative heat transport in the atmosphere is gradual.

  47. What is missing from this discussion is consideration of the effects of convection. We now know that real greenhouses warm by limiting convection. Yet 50 years ago schools taught that real greenhouses warmed due to blocking outgoing IR.
    This same fallacy is now being repeated by scientists that we taught this nonsense in school. We are told that CO2 warms via the “Greenhouse Effect”, by blocking outgoing IR radiation.
    The warming of the surface is due to convection. This leads to a lapse rate dictated by gravity at 9.8C/km in dry air. Otherwise the atmosphere would be isothermal. The phase change of atmospheric gasses (water) moderates the 9.8C/km to about 6.5C/km.
    This lapse rate warms the lower region of convection above that dictated by an isothermal atmosphere, while cooling the upper region. The center of mass of the convecting region is about 5km in height, giving a surface warming of 5km x 6.5C/km = 33C as compared to an isothermal atmosphere.

    • ferdberple
      What’s missing is water/water vapor. A greenhouse w/o water/water vapor is an oven. It’s the water that makes all of the difference. LWIR/SWIR, convection are side shows compared to the water.

    • ferd,.
      I’ve been saying that for ages but to no avail here.
      Keep trying though 🙂
      The fact is that the surface is warmer than S-B simply because descending warming air in high pressure cells constituting half the atmosphere inhibit convection beneath the descending column so that the surface below is then able to rise above S-B.
      Just as in a real greenhouse and nothing to do with GHGs.

  48. It was suggested earlier in this thread that dimensional analysis ought to be a part of high school physics.
    Here in the UK, back in the 1980’s, it was.
    I still have my copy of Nelkon and Parker, Physics for A level.
    And in a book of approx. 950 pages, dimensional analysis is first applied to a problem relating to a pendulum on page 33.
    i.e. it was introduced and applied to problems at the very beginning of this course.
    Dimensional analysis was useful for confirming that an answer was within the bounds of plausibility.
    It was always comforting to have completed a test with 20 minutes to spare, in which case you could run back through your answers and perform a quick check on the correspondence of the dimensions of the question and your proposed answer.
    Of course, the magnitude could still be way out of the ball park.
    The downside of having been thoroughly familiarized with D.A. is that for the rest of your life you will be repeatedly irked by the jaw-dropping errors made by sci/tech journalists.
    The most common of these being references to kilowatts/hour, megawatts/year or similar, as though these were representative of the total energy output of something.
    To be honest, I would not encourage a young person to learn physics. Certainly not if they are then expected to live a life subjected to the moronic schemes and delusional thinking of scientifically illiterate government agencies and journalists.
    Dumbing down is probably a blessing for most people.
    We now need a generation of dumb people who can function happily in the new age of state sponsored mass hysteria.

  49. There is a pdf available the link is below. When you look at the properties of the pdf you find that the author is a K Zeller. The authors of the paper are Den Volokin and Lark ReLlez. Note that the second author’s name is Kral Zeller backwards. Can any one determine who Volokin, ReLlez and Zeller really are. One has only a gmail address (Volokin) and the other has a street address in Salt Lake City with no email address ReLlez. This is pretty strange. I have no idea what it means. There is a Karl Zeller who is a meteorologist at the USDA Forest Service. But it’s late and I’m not going to do any more sleuthing tonight.
    I placed the link down here because it was so unwieldy. It points to a files directory at tallbloke.files.wordpress.com.
    [NOTE: Link converted to an actual link. -w.]

  50. People invariably misunderstand the word ‘fundamental’ in dimensional analysis.
    It merely means forming the unitized base of a particular system of measurement.
    It does not mean ‘fundamental’ in the sense of having especial physical profundity.
    Thus, it is perfectly possible, and indeed very convenient in considering the theory of electro-magnetism, to have the quantity of electricity and the quantity of magnestism, measured in ‘Maxwells’ and ‘Webers,’ as fundamental units.

  51. Sorry. More correction needed to avoid gibberish.
    Quantity of electricity is measured in ‘coulombs’
    Quantity of magnestism is measured in ‘maxwells.’
    The dimension of ‘action’ is then immediately ‘coulomb maxwells’.
    And there are Heaviside’s units, which avoid the pesky 4*pi which turns up everywhere.

  52. Sadly, Willis has completely missed the point of the paper that he so roundly criticises.
    The paper shows why the Greenhouse Effect, whether it is 33K or some other figure is mass induced and not GHG induced.
    The most basic, critical point is that the mass of gases above a solid surface acquires energy by conduction and convection from that surface and in doing so creates atmospheric opacity to outgoing IR.
    The opacity that matters is the opacity caused by the presence of that mass and the more densely the mass is compressed the more energy it will acquire from whatever insolation reaching the surface is available.
    Compressed gases create opacity (resistance) to outgoing IR without needing to have ANY radiative capability.
    That is why the degree of surface heating above S-B is proportionate to surface pressure which is itself purely a consequence of mass and gravity.
    The AGW theory treats the atmosphere as being transparent to outgoing IR unless there is radiative capability. Willis seems to agree with that.
    That is the fundamental error.
    Energy permanently engaged in maintaining constant up and down convection within an atmosphere is energy originally drawn from outgoing IR and to the extent that such energy was removed from the radiative exchange with space that removal represents the atmosphere’s opacity to outgoing IR.
    It is that opacity to ouitward IR that provides the upward pressure gradient force that opposes the downward force of gravity to keep an atmosphere in hydrostatic balance.
    It is not relevant that energy driving movement upwards matches energy driving movement downwards because it is the total of the two blocks of energy that matters and not the fact that they work in opposing directions. As long as there is constant movement whether it be up or down then energy is required and it is taken from kinetic energy at the surface which then needs to be warmer than S-B to fuel the constant movement tied up in convective overturning.
    No GHGs necessary.
    For so long as there is both radiative balance with space AND energy in convective ascent equals energy in convective descent then the atmosphere will be retained in hydrostatic balance for as long as insolation continues.
    Any permanent imbalance in either the radiative or convective (adiabatic) exchanges will cause the atmosphere to be lost.
    The simple presence of an atmosphere forever suspended of the surface is proof that radiative exchanges neutralise convective imbalances and convective changes neutralise radiative imbalances.
    Surface temperatures above S-B are a product of ONLY mass, gravity and insolation.
    Every weather or climate phenomenon is simply the stabilising process in action..

    • Stephen Wilde September 5, 2015 at 8:25 am

      Sadly, Willis has completely missed the point of the paper that he so roundly criticises.
      The paper shows why the Greenhouse Effect, whether it is 33K or some other figure is mass induced and not GHG induced.
      The most basic, critical point is that the mass of gases above a solid surface acquires energy by conduction and convection from that surface and in doing so creates atmospheric opacity to outgoing IR.

      Say what? The atmosphere doesn’t magically become opaque to outgoing IR because it has acquired “energy by conduction and convection”. That’s hand-waving pseudo-scientific nonsense. To the extent that the atmosphere is “opaque” to IR, it is because of the presence of greenhouse gases.
      You get to create your own opinions, Stephen, but you don’t get to create your own facts …
      w.

  53. “Here we use a simple, physically
    based model to demonstrate that, at atmospheric pressures
    lower than 0.1 bar, transparency to thermal radiation allows
    short-wave heating to dominate, creating a stratosphere. At
    higher pressures, atmospheres become opaque to thermal
    radiation, causing temperatures to increase with depth and
    convection to ensue. A common dependence of infrared
    opacity on pressure, arising from the shared physics of
    molecular absorption, sets the 0.1 bar tropopause”
    http://faculty.washington.edu/dcatling/Robinson2014_0.1bar_Tropopause.pdf
    Note the words ” opaque to thermal radiation” which is IR and the paper makes it clear that it is the mass and not composition of the atmosphere that is opaque to IR.
    Furthermore, the more mass there is (greater pressure) the greater the opacity to IR regardless of atmospheric composition.

    • Thanks, Stephen. That paper does NOT say what you said, which was:

      … the mass of gases above a solid surface acquires energy by conduction and convection from that surface and in doing so creates atmospheric opacity to outgoing IR.

      Instead it says that IF, note the IF, there are “greenhouse” gases in the atmosphere, the opacity of the atmosphere increases with density … which we all knew, or at least most of us knew. The novel and interesting part of that paper is relating the change in density to the location of the tropopause.
      But nowhere does it say that the atmosphere becomes more opaque to IR because it “acquires energy”, whether by conduction or any other means.
      w.

      • Please quote the words in the paper that you are referring to since I saw no indication that the observed phenomenon was dependent on radiative capability within the atmosphere.

      • They say:
        “pressure-broadening or collision-induced absorption applies
        generally to thick atmospheres,”
        Collision induced absorption is conduction (which then provokes convection).
        Conduction occurs even without GHGs.

      • Stephen Wilde September 6, 2015 at 10:12 am Edit

        Please quote the words in the paper that you are referring to since I saw no indication that the observed phenomenon was dependent on radiative capability within the atmosphere.

        Glad to. You could start with:

        The greenhouse effect necessary to maintain temperature T0 at p0 is related to τ0.

        Or this one:

        Thus, the Earth-like case in the Kasting et al. model absorbs an additional 24 W/m2 of solar flux than the actual Earth’s 240 W/m2 and so needs less greenhouse effect than our model to generate the same surface temperature.

        In fact the paper talks about radiative transfer throughout, viz:

        Below middle stratospheres, radiative transfer is dominated by pressure-broadening and collision-induced absorption, which have κ ∝ p, and, thus, n = 2 from integration

        If they are talking about the greenhouse effect and radiative transfer, they are talking about greenhouse gases and radiative capacity in the atmosphere.
        w.

      • Thus conduction and convection dominate until pressure falls to 0.1 bar whereupon a radiatively induced stratosphere becomes possible. Furthermore, the dominance of conduction and convection increases with pressure and that pressure (involving atmospheric mass) creates opacity to IR from the surface.

      • Stephen Wilde September 6, 2015 at 10:25 am

        They say:

        “pressure-broadening or collision-induced absorption applies
        generally to thick atmospheres,”

        Collision induced absorption is conduction (which then provokes convection).

        In a word … no. Collision induced absorption is NOT conduction. It is an entirely different process, by which molecules which normally don’t absorb IR can absorb it. This occurs because collisions can induce a dipole moment, making the molecule able to absorb IR.
        It has nothing to do with conduction or convection as you claim. Here’s a good description of the process:

        MOST of the absorption which occurs in the atmosphere in the infra-red region is due to the minor constituents such as water-vapour, carbon dioxide and ozone. The major constituents oxygen and nitrogen possess no dipole moment so that their vibrational and rotational energy states cannot be excited directly by absorption of radiation. However, dipole moments are induced during collision processes; transitions due to these can be seen in very long absorbing paths such as are present in the atmosphere. SOURCE

        I know a drowning man will grasp at a straw, but you don’t even have a straw, you’re making your claims up out of the whole cloth.
        w.

        • “In all of these bodies, the tropopause separates
          a stratosphere with a temperature profile that is controlled
          by the absorption of short-wave solar radiation, from a region
          below characterized by convection, weather and clouds”
          Collision induced absorption can also occur with non radiative molecules that acquired energy by conduction from the ground. It is not exclusive to energy acquired by radiative absorption.
          The above extract refers to convection dominating in the troposphere and convection is driven by conduction at the surface.
          So, we have a region dominated by conduction and convection which shows an increase in IR opacity with increasing pressure.
          Why are GHGs required for that ?

  54. Stephen Wilde says (5 September 2015 at 8.25am): Compressed gases create opacity (resistance) to outgoing IR without needing to have ANY radiative capability.
    Stephen,
    I profoundly wish that your assertion were true. But can you point me to any, ANY, physics textbook that supports such a revolutionary hypothesis?
    David

  55. Willis,
    I repeat:
    “Here we use a simple, physically
    based model to demonstrate that, at atmospheric pressures
    lower than 0.1 bar, transparency to thermal radiation allows
    short-wave heating to dominate, creating a stratosphere. At
    higher pressures, atmospheres become opaque to thermal
    radiation, causing temperatures to increase with depth and
    convection to ensue. A common dependence of infrared
    opacity on pressure, arising from the shared physics of
    molecular absorption, sets the 0.1 bar tropopause”
    http://faculty.washington.edu/dcatling/Robinson2014_0.1bar_Tropopause.pdf
    Note the words ” opaque to thermal radiation” which is IR and the paper makes it clear that it is the mass and not composition of the atmosphere that is opaque to IR.
    Furthermore, the more mass there is (greater pressure) the greater the opacity to IR regardless of atmospheric composition.

    • Stephen,
      I agree 100% with Willis that you have misinterpreted the Robinson and Catling paper.
      They are referring to the fact that a lower (more dense) layer of the atmosphere (which certainly DOES contain GHGs) will, as a consequence, be more opaque to LW radiation (i.e it will be more absorptive) than a higher layer.

      • A lower denser part of the atmosphere will be more absorptive than a higher less dense level because it receives more conducted and convected energy from the surface even with no GHGs at all.
        If Robinson and Catling did not say that then they should have done.
        ANY absorption increases opacity. Nearly all absorption is by conduction and convection and that which is caused by GHGs via radiation only alters convection to a negligible degree compared to naturally induced solar and oceanic variability.

  56. Willis said:
    “The atmosphere doesn’t magically become opaque to outgoing IR because it has acquired “energy by conduction and convection”. That’s hand-waving pseudo-scientific nonsense”
    Is it seriously proposed that kinetic energy at the surface absorbed via conduction by atmospheric mass can nonetheless simultaneously be radiated out to space ?
    When the atmosphere first rose off the ground then (assuming current mass, gravity and insolation) the Earth’s temperature viewed from space would have appeared to be 222K but only during the progress of the first convective overturning cycle.
    During that first cycle kinetic energy at the surface was diverted to convective overturning via conduction and was therefore not capable of being radiated to space at the same time.
    Once the first convective overturning cycle completed then the Earth’s temperature as viewed from space returned to 255K as per S-B because the kinetic energy being taken up was then simultaneously being returned to the surface.
    Forever afterwards that same 33K of kinetic energy has been locked into the convective overturning cycle and will remain there for so long as the atmosphere remains suspended off the surface against the constant force of gravity.
    Even an 8 year old should be able to grasp such simple concepts.

    • Stephen Wilde September 6, 2015 at 4:08 am

      Willis said:
      “The atmosphere doesn’t magically become opaque to outgoing IR because it has acquired “energy by conduction and convection”. That’s hand-waving pseudo-scientific nonsense”
      Is it seriously proposed that kinetic energy at the surface absorbed via conduction by atmospheric mass can nonetheless simultaneously be radiated out to space ?

      I haven’t a clue either what that has to do with the statement of mine you quoted, or what it actually means.
      You double down on your bad bet when you say:

      When the atmosphere first rose off the ground then (assuming current mass, gravity and insolation) the Earth’s temperature viewed from space would have appeared to be 222K but only during the progress of the first convective overturning cycle.

      Er … um … well … ah … I hate to ask, but were you watching this mythical creation of the atmosphere “[rising] off the ground” some billions of years ago with a globally averaging thermometer in your pocket to determine that the Earth’s surface temperature was 222K, and not 220K (but only during the “first convective overturning cycle”)?
      w.

      • If the surface temperature enhancement is 33K and it is attributable to atmospheric mass conducting and convecting then during a first convective cycle that much energy would have been deducted from radiation to space until the convective loop closed. Hence 222K and not 220K.
        We all know that there was no actual bodily rising off from an original surface but that is a useful image for understanding the principle (unless you just don’t want to).
        It is possible to apply simple logic without having to have been present.

  57. All forms of absorption increase opacity.
    Why should radiative absorption increase opacity but not conductive / convective absorption ?
    The paper refers to the phenomenon described as applying to a wide range of planets with atmospheres of widely differing compositions with no mention of any effect from different GHG levels.
    The paper refers to pressure as the determining factor yet pressure is derived from mass plus gravity. How could radiative capability have any effect ?

    • Stephen, I have often been curious about the percentage of different sources (conduction/convection vs. radiation) of energy in disparate atmospheres, and how this changes as the percentage of GHG changes.
      In general it makes sense to me that in a non GHG atmosphere some or perhaps most if not all of the 33 degree increase would be made up for by additional conduction from the surface until the flow between the atmosphere and the surface equalized. So, in such a non GHG world, as the surface heated the residence time of energy in the planets system would increase proportionate to the amount of atmosphere; the larger the atmosphere, the greater the increase in energy in the system. In a zero atmosphere world the energy would simply radiate away.
      Add ANY atmosphere and as the residence time of insolation energy increases, the energy content must rise above a world where the energy simply radiates away. Increase the atmosphere, and you increase the residence time and energy accumulation even further. Add in just a few GHG molecules and they will most likely radiate (some away to space, and some towards the surface) conducting atmospheric energy and NOT surface radiating energy. This is net atmospheric cooling, accelerating the loss of energy from the atmosphere. As you increase the amount of GHG molecules the chances of some GHG molecules intercepting radiation from the surface to the molecules increases. This energy, directed inward would not induce cooling. As GHG molecules increase the ratio between how many receive conducted atmospheric energy (cooling) vs. surface radiate energy (not cooling) would also change.

      • David A,
        You seem to have got the point about the significance of conduction and convection within the mass of an atmosphere creating IR opacity by resisting the transmission of IR through the atmosphere to space.
        AGW theory (and Willis) think that opacity to IR arises only from the intervention of radiative capability within the atmosphere which is manifestly wrong. Does
        The Robinson and Catling paper shows that for pressures greater than 0.1 bar there seems to be a universal rule related to the common absorption properties (via conduction and convection) of all types of gaseous matter that IR opacity due to conduction and convection takes control.
        Once one attributes IR opacity to non radiative gaseous materials via conduction and convection then it becomes clear that any opacity caused by radiative capability counts for nothing relative to the opacity caused by the presence of gaseous matter in an atmosphere that is substantially non-radiative.
        You then go on to have a stab at the effect of radiative opacity within an atmosphere the opacity of which is primarily due to conduction and convection but I’m not sure that I follow your exact reasoning.
        My view is that such radiative opacity, within an atmosphere dominated by opacity from conduction and convection, simply interferes with the lapse rate slopes above and below the point of hydrostatic balance and within columns of ascending and descending air.
        The sign of the interference is reversed above and below the point of hydrostatic balance and within ascending columns as compared to descending columns so that the thermal effect nets out to zero as I explained here:
        http://hockeyschtick.blogspot.co.uk/2015/07/erasing-agw-how-convection-responds-to.html
        The key to it all is that conduction and convection above an irradiated surface causes IR opacity in the atmosphere above without any recourse to radiative capability and as per Robinson and Catling that form of opacity dominates in atmospheres with a pressure of more that 0.1 bar.
        The concept of IR opacity arising from conduction and convection and, moreover, being dominant, has completely passed over the heads of warmists and lukewarmers alike. Many sceptics are aware of the issue but thus far have not been able to articulate it clearly.

  58. The observed surface temperature enhancement is the net result after all confounding factors (including friction and any radiative imbalances) have been dealt with internally by convection to produce hydrostatic equilibrium.
    You could look at the ‘raising of the atmosphere’ event as a slow molecule by molecule process or you could envisage the atmosphere as simply being left over material from the initial aglommeration of planetary mass.
    Either way it makes no difference to the general principle that less energy left for space than otherwise would have done due to its retention within the process of convective overturning.
    Note that convective overturning involves constant movement in both ascending and descending columns. Those two pools of energy cannot just be magicked from nowhere.

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