I’ve been looking at the Nikolov and Zeller paper again. Among other things, they claim to be able to calculate the surface temperature **Ts** of eight different planets and moons from knowing nothing more than the solar irradiation **So** and the surface pressure **Ps** for each heavenly body. Dr. Zeller refers to this as their MIRACLE equation. He says:

Why aren’t you all trying to disprove our MIRACLE equation rather than banging your heads against walls trying to prove or disprove who knows what and exclaiming you have problems with this or that? The question is how can we possibly have done it – there is no question that our equations work – if you haven’t verified that it works, why haven’t you? […] Why aren’t you thinking: “hmmmm, N&Z have given us an equation that lo-and-behold when we plug in the measured pressures and calculate Tgb as they suggest, gives us a calculated Ts that also matches measured values! You can’t disprove the equation? So maybe we are cooking the data books somehow, but how?

This is supposed to be evidence that their theory is correct, and people keep telling me ‘but they’ve got real evidence, they can make predictions of planetary temperatures, check it out”. Plus it’s hard to ignore an invitation like Dr. Zellers, so I checked it out.

*Figure 1. These are not the equations you are looking for.*

They first postulate something called the “Near-surface Atmospheric Thermal Enhancement” or “ATE” effect that makes the earth warmer than it would be without an atmosphere.

The “ATE effect” is measured by something called **Nte(Ps)**, which is defined and estimated in their paper as follows.

where **Nte(Ps)** is a measure of the “Near-surface Atmospheric Thermal Enhancement” effect.

**Nte(Ps)** is defined as the actual average surface air temperature of the planet **Ts** divided by the theoretical “graybody” temperature of the planet **Tgb** calculated from the total solar insolation **So **of the planet. **Nte(Ps)** is estimated using a fitted function of the surface pressure of the planet **Ps**.

Let me simplify things a bit. Symbolically, the right part of equation (7) can be written as

Nte(Ps)=e^(t1 *Ps^ t2 + t3 *Ps^ t4) (7Sym)

where “**e**” is the base of natural logs and **Ps** is the surface pressure on the planet or moon. There are four tunable parameters (t1 through t4) that are “fitted” or tuned to the data. In other words, those values are repeatedly adjusted and tuned until the desired fit is obtained. This fitting can be easily done in Excel using the “Solve…” menu item. As you’d expect with four parameters and only eight datapoints, the fit is quite good, and their estimate is quite close to the actual value of **Nte(Ps)**.

Amusingly, the result of equation (7) is then used in another fitted (tuned) equation, number (8). This is:

where **So** is total solar irradiation.

This is their piece de resistance, their MIRACLE equation, wherein they are saying the surface temperature of eight different planets and moons can be calculated from just two variables— **Pr**, the surface pressure, and **So**, the total Solar irradiation. This is what amazes the folks in the crowd so much that they write and tell me there is “evidence” that N&Z are right.

Obviously, there is another tuned parameter in equation (8), so we can rewrite this one symbolically as:

Ts= t5 * (Solar+ adjustment ) ^ 1/4 *Nte(Ps). (8Sym)

Let me pause a minute and point something out about equation (8). The total solar irradiation **Solar** ranges from over 9,000 W/m2 for Mercury down to 1.51 W/m2 for Triton. Look at equation 8. How will adding the adjustment = 0.0001325 to any of those values before taking the fourth root make the slightest bit of difference in the result? That’s just bizarre, that is. They say they put it in so that the formula will be accurate when there is no solar, so it will give the background radiation of 3 Kelvins. Who cares? Truly, it changes Ts by a maximum of a thousandth of a degree for Triton. So for the moment let me remove it, as it makes no practical difference and it’s just confusing things.

Back to the tale. Removing the adjustment and substituting equation 7 into equation 8 we get:

Ts= t5 *Solar^0.25 * e^(t1 *Ps^ t2 + t3 *Ps^ t4) (eqn 9)

This is amazing. These guys are seriously claiming that with only eight datapoints and no less than **five tunable parameters** , they can calculate the surface temperature of the eight planets knowing only their surface pressure and solar irradiation. And with that many knobs to turn, I am sure they can do that. I did it on my own spreadsheet using their figures. I get about the same values for t1 through t5. But that proves nothing at all.

I mean … I can only stand in awe at the sheer effrontery of that claim. They are using only eight datapoints and five tunable parameters with a specially-designed ad-hoc equation with no physical basis. And they don’t think that’s odd in the slightest.

I will return to this question of the number of parameters in a bit, because even though it’s gobsmacking what they’ve done there, it’s not the best part of the story. Here’s the sting in the tale. We can also substitute equation (7) into equation (8) in a slightly different way, using the middle term in equation 7. This yields:

Ts= t5 *Solar^0.25 *Ts / Tgb(eqn 10)

This means that if we start out by knowing the surface temperature **Ts** on the right side of the equation, we can then calculate **Ts** on the left side … shocking, I know, who would have guessed. Let’s check the rest of the math in equation (10) to see why that works out.

Upon inspection it can be seen that the first part of the right side of equation (10),

t5 *Solar^0.25

is an alternate form of the familiar Stefan-Boltzmann equation relating temperature and radiation. The S-B equation can be written as

T = (Solar / c1) ^ 0.25.

where T is temperature and c1 is a constant equal to the S-B constant times the emissivity. We can rewrite this as

T = 1/(c1^0.25) * Solar^0.25

Setting another constant c2 equal to 1 / (c1^0.25) gives me the Stefan-Boltzmann equation as:

T = c2 * Solar^0.25

But this is exactly the form of the first part of the right side of equation 10. More to the point, it is an approximation of the graybody temperature of the planet **Tgb**.

We can check this by observing that if emissivity is .9 then constant c1 is 5.103E-8, and c2 is therefore about 66. However, that value will be reduced by the rotation of the planet. Per the N&Z formula in their latest post, that gives a value of about 27.

Their fitted value is 25, not far from the actual value. So curiously, what it turns out they’ve done is to estimate the Stefan-Boltzmann constant by a bizarre curve fitting method. And they did a decent job of that. Actually, pretty impressive considering the number of steps and parameters involved.

But since t5 * **Solar**^0.25 is an estimation of the graybody temperature of the planet **Tgb**, that means that Equation 10 reduces from

Ts= t5 *Solar^0.25 *Ts/Tgb(eqn 10)

to

Ts=Tgb*Ts/Tgb.

and finally to

Ts=Ts

TA-DA!

**CONCLUSION**

Let me recap the underlying effect of what they have done. They are looking at eight planets and moons.

1. They have used an equation

e^(t1 *Ps^ t2 + t3 *Ps^ t4)

with **four free parameters** to yield an estimate of **Ts/Tgb** based on surface pressure. As one would expect given the fact that there are *half as many free parameters as there are data points*, and that they are given free choice to pick any form for their equation without limit, this presents no problem at all, and can be done with virtually any dataset.

2. They have used an equation

t5 *Solar^0.25

with **one free parameter** in order to put together an estimate of **Tgb** based on total planetary insolation. Since **Tgb** does depend inter alia on planetary insolation, again this presents no problem.

3. They have multiplied the two estimates together. Since the result is an estimate of **Tgb** times an estimate of **Ts**/**Tgb**, of course this has the effect of cancelling out **Tgb**.

4. They note that what remains is **Ts**, and they declare a MIRACLE.

Look, guys … predicting **Ts** when you start out with **Ts**? Not all that hard, and with five free parameters and a choice of any equation no matter how non-physically based, that is no MIRACLE of any kind, just another case of rampant curve fitting …

Finally, there is a famous story in science about this kind of pseudo-scientific use of parameters and equations, told by Freeman Dyson:

We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.

When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our newborn baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice.

“There are two ways of doing calculations in theoretical physics”, he said.“One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a selfconsistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.”

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?”

I thought for a moment about our cut-off procedures and said, “Four.”

He said, “I remember my friend Johnny von Neumann used to say,

with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students.

The Nikolov and Zeller equation contains five parameters and only eight data points. I rest my case that it is not a MIRACLE that they can make the elephant wiggle his trunk, but an expected and trivial result of their faulty procedures.

My regards to everyone,

w.

PS—There is, of course, a technical term for what they have done, as there are no new mistakes under the sun. It is called “overfitting”. As Wikipedia says, “Overfitting generally occurs when a model is excessively complex, such as having **too many parameters relative to the number of observations**.” **Five** parameters is far, far too many relative to **eight** observations, that is a guaranteed overfit.

PPS—One problem with N&Z’s MIRACLE equation is that they have not statistically tested it in any way.

One way to see if their fit is even remotely valid is to leave out some of the datapoints and fit it again. Of course with only eight datapoints to start with, this is problematic … but in any case if the fitted parameters come out radically different when you do that, this casts a lot of doubt on your fit. I encourage N&Z to do this and report back on their results. I’d do it, but they don’t believe me, so what’s the point?

Aother way to check their fit is to divide the dataset in half, do the fit on one half, and then check the results on the other half. This is because fitted equations like they are using are known to perform very poorly “out of sample”, that is to say on data not used to fit the parameters. Given only eight data points and four parameters for equation 7, of course this is again problematic, since if you divide the set in half you end up with** as many parameters as data points** … you’d think that might be a clue that the procedure is sketchy but what do I know, I was born yesterday. In any case I encourage N&Z to perform that test as well. My results from that test say that their fit is meaningless, but perhaps their test results will be different.

**[UPDATE]** One of the commenters below said:

Willis – go ahead – fit an elephant. Please!

Seriously N&Z are only demonstrating in algebra what has been observed in experiments, that heating a gas in a sealed container increases both pressure and temperature.

OK, here’s my shot at emulating the surface temperature using nothing but the data in the N&Z chart of planetary body properties:

*Figure 1. Willis’s emulation of the surface temperature of the planetary bodies.*

My equation contains one more variable and two less parameters than the N&Z equation. Remember their equation was:

Ts= 25.3966 *Solar^0.25 * e^(0.233001 *Pressure^ 0.0651203 + 0.0015393 *Pressure^ 0.385232)

My equation, on the other hand, is:

Ts= 0.8 *Tgb+ 6.9 *Density+ 0.2 *Gravity)

Note that I am absolutely not making any claim that temperature is determined by density and gravity. I am merely showing that fitting a few points with a few variables and a few parameters is not all that difficult. It also shows that one can get the answer without using surface pressure at all. Finally, it shows that neither my emulation nor N&Z’s emulation of the planetary temperatures are worth a bucket of warm spit …

**[UPDATE 2]** I figured that since I was doing miracles with the N&Z miracle equation, I shouldn’t stop there. I should see if I could beat them at their own game, and make a simpler miracle. Once again, their equation:

Ts= 25.3966 *Solar^0.25 * e^(0.233001 *Pressure^ 0.0651203 + 0.0015393 *Pressure^ 0.385232)

My simplified version of their equation looks like this:

Ts= 25.394 *Solar^0.25 * e^(0.092 *Pressure^ 0.17)

Curiously, my simplified version actually has a slightly lower RMS error than the N&Z version, so I did indeed beat them at their own game. My equation is not only simpler, it is more accurate. They’re free to use my simplified miracle equation, no royalties necessary. Here are the fits:

*Figure 2. A simpler version of the N&Z equation 8*

Again, I make no claim that this improves things. The mere fact that I can do it with two less tuned parameters (three instead of five) than N&Z used does not suddenly mean that it is not overfitted.

Both the simplified and the complex version of the N&Z equations are nothing but curve fitting. This is proven by the fact that we already have three simple and very different equations that hindcast the planetary temperatures. That’s the beauty of a fitted equation, if you are clever you can fit a lot using only a little … but THAT DOESN’T MEAN THAT PRESSURE DETERMINES TEMPERATURE.

For example, I can do the same thing without using pressure at all, but using density instead. Here’s that equation:

Ts= 25.491 *Solar^0.25 * e^(0.603 *Density^ 0.201)

And here’s the results:

*Figure 3. An emulation of the planetary temperatures, using density instead of pressure.*

Does this now mean that the planetary temperature is really controlled by density? Of course not, this whole thing is an exercise in curve fitting.

w.

Actually, there is a “miracle” here. Willis, you have the string: “too many parameters relative to the number of observations” with the HTML markup for bold displaying, rather than the bolding being applied. How you do dat in WordPress?

Nice summary BTW.

[Thanks, fixed. -w.][

Reply:Use these symbols: “& g t ;” if you want this to appear: >. (first take out the spaces between the symbols). Use “lt” for the “less than” symbol: < ~dbs, mod.]I truly wish I paid more attention in school. But from what I’m reading here, I can safely say my conclusion is: “That’s going to leave a mark.”

I agree. They actually fit their multi-parameter formula to only six planet bodies; two are said to have too little atmosphere. But one of those fitted is Europa. As they found in Wikipedia, it has a notional pressure of 10^-7 Pa. About a tenth of a milligram oxygen per sq m, estimated by spectrum. That is the whole “atmosphere”. And this, they claim, enables them to predict the “climate” to 3 figure accuracy using their miracle formula. Despite the fact that pressure has barely one significant figure accuracy, and the measure of “climate” little better.

Nice. And thanks for telling the whole Dyson/Fermi story. Had a chance to hear Dyson speak, oh, about 20 years ago. Good guy.

I do believe there is something useful to take from this exercise. I haven’t had time to cook up the math, but I am sure there is an important atmospheric effect. If you think about it, an atmosphere must cool hotspots on the surface of a planet and warm the cool spots. It will effectively prevent rapid re-radiation of incoming energy, and will lead to the accumulation of thermal energy in the surface. Sufficient atmosphere will delay the reradiation of energy back to space. When energy is retained until the next day, the surface will be warmer, and it will continue to get warmer until the surface is warm enough to reradiate over the entire day/night cycle an amount of energy equivalent to what it takes in during the day.

Here’s a question in the spirit of your post: How many characters are displayed as text adding up all pages available in WUWT?

You were very polite to N&Z.

Darn Willis, you moved to a new thread. Here’s something to help your problem with the calculus of equations 4 & 5 and your attempt to word it correctly to your Mathematica model program:

A spherical integration of the per-point average temperature field:

T.gb = ¼π ∫[0, 2π] ∫[0,1] T.i dμ dφ

or even clearer:

T.gb = ½ * ½π ∫[0, 2π] ∫[0,1] T.i dμ dφ

As for μ = cos(θ.i), this will only need to be evaluated at two locations, 0 & π/2; first is when the sun is directly above and the second at the 360° terminator that is 90° from the first. So the ultimate results of these two evaluations are cos(0)=1 & cos(π/2)=0.

T.gb = ½ * ½π * ∫[0,2π] ∫[0,1] root4( S.0 (1-α.0) μ / (εσ) ) dμ dφ

T.gb = ½ * ½π * root4(S.0(1-α.0)/(εσ)) ∫[0,2π] ∫[0,1] μ^(1/4) dμ dφ

First integrate ∫ [0,1] μ^(1/4) dμ:

= 4/5 * ( cos(0)^(5/4) – cos(π/2)^(5/4) )

= 4/5 * ( 1^(5/4) – 0^(5/4) )

= 4/5 * 1^(5/4)

= 4/5

Giving:

T.gb = 4/5 * ½ * ½π * root4(S.0(1-α.0)/(εσ)) ∫[0,2π] 1 dφ

T.gb = 4/5 * ½ * ½π * root4(S.0(1-α.0)/(εσ)) ∫[0,2π] dφ

Next integrate ∫[0,2π] 1 dφ

2π*1 – 0*1

2π

T.gb = 2π * 4/5 * ½ * ½π root4(S.0(1-α.0)/(εσ)) * 1

Simplifying:

T.gb = 8π/20π root4(S.0(1-α.0)/(εσ))

T.gb = 2/5 root4(S.0(1-α.0)/(εσ))

or

T.gb = 2/5 (S.0(1-α.0)/(εσ))^0.25

That is the final closed form equation given by Drs. Nikolov and Zeller.

Seems to me a planet with an atmosphere is actually a black body. By that I mean from the point where the atmopshere ends and becomes space where all radiation from the sun entering it is absorbed.

Clouds and rocks and ice are way inside the internals of a planet with an atmosphere so effectively there is no albedo effect preventing all solar radiation from entering and “heating” the planet’s atmosphere.

The ideal gas law holds good in my “it seems to me” opinion. As for so called “Green house” gases do they not simply help to spread the heat out more evenly/quickly with their radiative properties, such as an increase in CO2 in the Northern Hemisphere making the Arctic a bit warmer and the lower Northern lattitudes a bit cooler but the average mean remains the same?

Philip Finck says:

January 23, 2012 at 4:26 pm

Hey, I’m a reformed cowboy, and I’m working on reforming some more. Gotta say it’s a sight harder than it looks. However, at the urging of both my friends and my scientific opponents, I’ve been cutting back. In that spirit, I redacted some of my more memorable phrases before publication. And despite the loss to the colorful nature of my general reportage, I suspect that in this case they are right.

w.

I also have a miracle equation.

Take your age, and add 12… divide that number by 2, and subtract half your age…

Nicely done. The equations are subjected to steady heat to drive off the vapor, revealing a well-boiled bootstrap.

The right answer for the wrong reason is ALWAYS the wrong answer. (Used to teach cal. based Physics)

I suggest that to expect any reasonable statistical significance in a curve fit, you should have at least five times as many degrees of freedom (data points) as you have factors (parameters). You will always get a perfect fit when the degrees of freedom matches the number of factors. Years ago I heard a person proudly present a paper that did just that.

Sounds good to me. I will await the coming comments.

Willis of Ockham?

When I saw that MIRACLE quote in the other thread, I was (almost) sure it was a joke on somebody’s part. If it was actually from the real Zeller, then I think he just disqualified himself.

Wayne,

The problems with the integration occur before the steps you describe – it is the variable substitution mu = cos(theta) which is dubious. Simply try comparing

the integral of mu^0.25 on [0,1]

with the integral of cos(theta)^0.25 on [0, pi/2]

and see what you get.

@ Willis

> There is, of course, a technical term for what they have done,

> as there are no new mistakes under the sun. It is called “overfitting”.

I think you’re looking at this in the wrong way. You say ‘overfitting’, which suggests they are somehow dishonestly trying to ‘cook’ a formula to fit 8 examples.

I don’t think N&K (Ned&Karl) are dishonest. In fact, I think they are merely

learningthe relationships between pressure induced and radiative warming by trying to fit the set of parameters to a regression equation.“Learning is compression” in the sense that they want to find the

smallestset of parameters which fit the data. I.e Occam’s Razor: if two regressions, one with 5 parameters and another with 5000 parameters, both fit the data, which is better? Ans: keep it as simple as possible (but not too simple).You’re also missing the main point:

“Pressure by itself is not a source of energy! Instead, it enhances (amplifies) the energy supplied by an external source such as the Sun through density-dependent rates of molecular collision. This relative enhancement only manifests as an actual energy in the presence of external heating. “Look at my response to Tallbloke and GeoSmith …

http://wattsupwiththat.com/2012/01/22/unified-theory-of-climate-reply-to-comments/#comment-873665

… particular the derivation of the Ideal Gas Law.

http://en.wikipedia.org/wiki/Ideal_gas_law#Derivations

Note that the temperature T of a system in equilibrium can be computed from the just kinetic energy of the moving gas particles and their mutual collisions (density, implying pressure). We don’t need to know the radiative aspects of the system to compute the temperature! What part of the Ideal Gas Law do you not understand here?

So, having computed the temperature T we can then ask the question: where did the kinetic energy come from? Probably from solar heat energy absorbed by the surface.

But the point is we don’t need to know where the energy came from. Temperature T is soley dependent upon the internal kinetic energy of the gas and its density.

No change in pressure required. Yes, a pressure “gradient” necessarily exists on all planets with atmospheres, but that is accidental in the sense that even the gradient itself is not required to understand that at any point x,y,z the temperature is solely a function of kinetic energy and transfer of momentum by collisions.

N&K further make the claims that show no pressure change is needed

“In the case of an isobaric process, where pressure is constant and independent of temperature such as the one operating at the Earth surface, it is the physical force of atmospheric pressure that can only fully explain the observed near-surface thermal enhancement (NTE). “Isobaric?

Yes, if you choose a long-enough time scale:

“the near-surface atmospheric dynamics can safely be assumed to be governed (over non-geological time scales) by nearly isobaric processes on average, i.e. operating under constant pressure. This isobaric nature of tropospheric thermodynamics implies that the average atmospheric volume varies in a fixed proportion to changes in the mean surface air temperature following the Charles/Gay-Lussac Law, i.e. Ts/V = const. “Willis, please think about it some more before summarily rejecting it as nonsense.

“Figure 1. These are not the equations you are looking for.”

That’s hilarious!

And that is why I keep coming here.

Bravo!

This whole thing reminds me of a problem I have seen in other areas of science. Basically the scenario goes like this:

1) First make a really poor estimate of some physical quantity

2) Compare your estimate with reality, and you find there is a large difference!

3) Claim that the difference is not just the error in your calculations, but is actually due to a real hitherto unsuspected effect.

4) Announce you have found something new and important.

(and before anyone adds the obvious comment – yes, some parts of ‘standard’ AGW theory seems to suffer from that condition as well)

“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” — John von Neumann

Yawn. It is sad, Willis, that you have to go to such great lengths to point out the obvious.

So the gist is N&Z have demonstrated that a fifth degree polynomial will fit exactly and perfectly 6 points (or something like that)?

MIRACLE indeed. ROFL.

jimmi_the_dalek says: “When I saw that MIRACLE quote in the other thread, I was (almost) sure it was a joke on somebody’s part. If it was actually from the real Zeller, then I think he just disqualified himself.”

Yes, “MIRACLE” does not engender confidence, does it? In fact, if I’d seen that first, I wouldn’t have read any further. And I suspect the statistical tests will be similarly discouraging, given the presence of exponentials in the “curve fit.”

Ts = (Ts/Tgb) * Tgb

crazy. Was this “peer reviewed”?

Very entertaining. And truly not all that complex of an analysis such that even a lowly chemist could follow along.

I suspect the AGW model maths follow along these lines also. The ole self fulfilling prophecy.

Willis:

I definitely am in agreement with what you say here. It is bizarre that they actually claim their fit as some sort of miracle!

The one comment I would make is I think that what your last part before the conclusion shows is simply that “t5” probably wasn’t a free parameter but was determined by them through their equation for T_sb. At least, that is what I assume that they did…although, who knows, maybe they tried to fit it! I wouldn’t put it past them.

If memory serves, when I reached essentially the same conclusion a couple of weeks ago, I found that even the “fitted” curve was not as good as it initially appeared if you put it on a log-log plot. I haven’t re-run the plot, but my recollection is that a couple of the bodies fall of the graph then.

Please don’t post the von neumann quote. I didn’t see it in the article until a bit later.

[Done. -w]Equation 8 is not (I think) a fitted equation. It’s their equation 2, using (for all planets) their modified earth albedo, and emissivity close to 1. So they only(!) have four parameters to find some functional form fitting their six points.

Determining the temperature of an atmosphere using the Ideal Gas Law as mentioned by John Day or using the Boltzman Constant with volume and pressure gives the approximate temperatures for Venus, the Earth, and Mars.

The only pressure relationship that would make any sense to me would be that due to the increased partial pressure of greenhouse or infrared absorbing gases in the atmosphere. It would seem reasonable that the planetary surfaces would tend to become warmer as the atmosphere became more dense due to increased net IR absorption overhead. The effect would likely be logarithmic, like increasing concentration, which also increases the net mass of greenhouse gas above.

This effect would probably be complicated by the special attractive properties of polar water molecules if they were present.

JamesD said @ January 23, 2012 at 5:31 pm

Yup! By Willis Eschenbach who seems to be suggesting the paper needs some revision 😉

One query that is related to Wilis analysis is that I suspect that most of the planetary temperatures have been determined spectroscopically. Which means that you will always end up with a SB distribution when fitting a curve, ie it is a circular argument. I aksed Nic about the temperature methods for the planets he used over at Spencer’s but he may have missed it.

jimmi_the_dalek says:

January 23, 2012 at 5:15 pm

“really poor estimate of some physical quantity”

Your are speaking of all of NASA’s data, right jimmi?

For those planets that have molten cores, the amount of heat flux at the planet’s surface due to its interior depends on the ratio of the planet’s surface area to its total volume. Would that have a significant effect on the surface temp for some of the smaller planets?

I’m amazed that most of you (including Willis) think that fitting a smooth (“natural”) curve with a few parameters is ‘overfitting’.

FYI, ‘overfitting’ happens when your regression produces an “unnatural” curves (i.e. full of ‘wiggles’).

Here’s a good example of overfitting:

http://www.gch.ulaval.ca/nnfit/english/man/nnfit2_man.html#surappr

Now look at the N&Z curve again and note how natural it appears. No wiggles. I.e. it matches the underlying physical process. This is a “good” regression, not overfitting.

😐

Something someone is sure of is wrong.

My applogies, I meant Ned not Nic in my earlier post.

“Your are speaking of all of NASA’s data, right jimmi?”

No, but I am thinking of some of their computer models….

Nick Stokes says:

January 23, 2012 at 5:38 pm

Interesting thought. I just looked to see. If so, they are using an emissivity of about 0.95, so that’s possible. What argues against it is that I doubt they realized that’s what they were doing. Also, to pull out all of the variables and constants (albedo, emissivity, S-V constant) into one single factor … what would be the reason to do that?

In any case, as you say … down to only(?) four parameters.

w.

Looking back at the original article, my favorite was the claim that higher temperatures would increase the pressure at sea-level. I’ve assigned my students the problem of computing the sea-level pressure from the mass of the earth’s atmosphere and the acceleration of gravity. Temperature has absolutely zero to do with it.

John Day says:

January 23, 2012 at 5:02 pm

You misapprehend the term “overfitting”. It is a mathematical error, not an accusation of dishonesty or deliberate deception. Generally the only people who do it are those who don’t realize they’re doing it.

Let me be very clear.

I don’t think N&Z are dishonest, that’s not my reading at all. I think they actually believe what they are claiming.I got conned one time by a guy named Bill, who was so good at it you could hardly stay angry at him. I told a friend of mine the problem with Bill was that he could weave together a pack of lies, half truths, invented facts, actual truths, and artful omissions so well, he could make anybody believe it.

My friend disagreed. He said that was not giving Bill his full due. He said the real problem was that Bill could tell a story so damn well, and with such feeling and majestic artistry, he ended up believing it himself …

w.

Terry says:

January 23, 2012 at 6:21 pm

Interesting, I hadn’t thought of that. So in addition to the circular argument I pointed out, where they use Ts to find Ts, we have one other.

w.

This looks a lot like reducton for the “The Jello Equation”

“We have been able to simulate these unique and complex Jell-O ® dynamics using spatial deformations [Barr, 1986] and other hairy mathematics. From previous research with rendering systems we have learned that a good dose of gratuitous partial differential equations is needed to meet the paper quota for impressive formulas.”

Source: Ray Tracing J ELL-O ® Brand Gelatin

http://www.cs.northwestern.edu/~ago820/cs395/Papers/Heckbert_1987.pdf

“John Day says:

January 23, 2012 at 5:02 pm

Temperature T is soley dependent upon the internal kinetic energy of the gas and its density.”

Is density even needed? Granted, temperature is a macroscopic property and not a microscopic property, but above a certain minimum density, is the following not true?

1/2mv2 = 3/2kT

See:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html

P.S. From the article: “Pr, the surface pressure,” I assume you meant Ps since that is what was used in the equations.

4 parameters + choice of functional form. After all they could have put exponentials, logs, or anything in their equation. This provides a lot of a additional curve fitting power and reduces the need for parameters. A school friend of mine had to fit a wind turbine velocity power equation which had 10 points. He did it with a single well chosen function and two parameters.

Its insufficient to just look at the parameters its also necessary to consider the complexity of the functional form because this is also a source of “information”.

@Willis

> You misapprehend the term “overfitting”. It is a mathematical error …

No Willis, you are misapprehending this term. Re-read my post above:

http://wattsupwiththat.com/2012/01/23/the-mystery-of-equation-8/#comment-873883

I think the term “overconfident” (i.e. “low entropy”) better describes an estimator which produces results which seem to be “too good” because there aren’t enough valid examples to sample. (Example, “label bias” in maximum-entropy classifiers)

That may be the case here, only 8 examples. But can you (or anybody) provide enough convincing counter-examples to disprove the N&Z claim?

@Werner Brozek

> Is density even needed?

Yes, because we need to compute the forces that the gas molecules exert on each other when then collide. (Force = rate of change of “motion” [

momentumin Latin]). If there are no collisions, then “no change of motion”=”no pressure”=”no temperature”.@Willis

Why haven’t you addressed my comments on the Ideal Gas Law, the

cruxof this N&Z theory?We do need some new theories however. We should just start with the actual observations first (of all bodies) and try to work what is really happening in all cases.

GHGs are not the end-all be-all answer. They do not work sufficiently in any case and certainly not in all cases. Much more is going on.

Energy is coming in, and is being released and is being stored up and emission is delayed and all the molecules in the whole system are participating in this over every single nano-second. Exotic issues like pressure and gravitational potential also have to be included because this affects how the energy comes about and how it flows in and out etc.

There may be a long-term balance between the solar energy coming in and its re-emission at some layer in some atmosphere, but there are time differences and different things are going on above and below that layer. Hansen says CO2 and GHGs run the whole system. Hardly.

I don’t have time to look into the equation(s) in question but I agree with John Day. I was trying to make the same point by saying that ideal gas law (or any other, more accurate equation of state for real gases) is just a relation between state variables (pressure, density, temperature). That’s all. You don’t need a thermodynamic system, well defined system boundaries, energy inputs/outputs over system boundaries and so on. It’s just about state variables at any point (x,y,z).

“But the point is we don’t need to know where the energy came from. Temperature T is soley dependent upon the internal kinetic energy of the gas and its density.”

Terry–“One query that is related to Wilis analysis is that I suspect that most of the planetary temperatures have been determined spectroscopically. Which means that you will always end up with a SB distribution when fitting a curve, ie it is a circular argument.”Actually, you look at the emission spectra for the planet in question, and select the _highest_ possible SB curve to identify the surface temperature (coming through windows in the atmospheric absorption). Thermal emission has a very characteristic curve, and barring Martian death rays, that upper limit represents the hottest thing emitting. Notchs in the spectra dropping below that surface temp value show where there’s absorption from GHG’s or clouds or whatever. The integral of the entire spectrum, on the other hand, should match the energy coming in (insolation), which provides something of a check point.

assman says:

January 23, 2012 at 7:31 pm

Indeed, which is why I pointed out that they have “five free parameters and a choice of any equation no matter how non-physically based”.

The form they use is quite curious. I’ve never seen it used before. It is the sum of two fractional powers of the same variable, Pr. Odd.

w.

w.;

Play devil’s advocate against yourself: if the N&Z hypothesis were correct, what form would you expect the equation(s) to take?

At:

http://wattsupwiththat.com/2012/01/19/perpetuum-mobile/#comment-873856

I would be interested in your response. GK

Antony

Are there 4-8 other planets/moons where Ts, So and Nte are known?

If yes, plug them into their magical equation 8 and see what you get. Just because you don’t understand the physical causes of the relationship which yields that equation does not mean the equation is valueless! If the data for the other planets/moons fit the equation, then they are on to something and CO2 is eliminated as a climate (temperature) forcing! QED. We can figure out the physics later. Einstein made predictions based on his equations and many of them were later verified. I, for one, would like to drive this stake in the heart of AGW and stop the hoax for good!

Bill

Great explanation – you sat down and plucked the keystone from their tower, now just a lovely pile of rubble…

But the larger mystery remains.

The gobsmacking absence of actual evidence of AGW…

The mind blowing arrogance that having a vague understanding of energy flows of the climate system allows climatologists to have CONFIDENCE in their statements that the system is heating “too fast” to be normal so they must blame mankind’s production of the trace gas Co2…

That’s the vast and murky mystery of “Can’t Equate”…

Willis – I think that you have got a bit of circluar reasoning going on there.

Let me explain how I see it.

(1) N&Z calculate Tgb (gray body temperature) as a function of Irradiance.

I trust that you are not objecting to that?

The temperature of solar bodies is primarliy due to solar irradiance?

The reason for that one free paramater, is because (from the viepoint of solar bodies) both irradiance and and grey body temperature are measured in arbitary units.

Otherwise Tgb would equal the fourth root of irradiance, measured in appropriate units.

OK do far – we can deduct one free dimension.

(If not it’s back to physics 101 for both you and me).

(2) Again you are being too hard in claiming that as Ts = Tgb * Nte

and Nte = Ts/ Tgb and so Ts = Tgb * Ts / Tgb or Ts = Ts

Very —– well very.

You did mention that the value of Nte was a value thatwas merely curve fitted?

In other words, the value of Nte is the value and THE ONLY VALUE available in the whole numbering system, where Nte doesequal Ts / Tgb.

It’s been engineered that way.

So it’s true that you have proved that Ts = Ts, but it’s not very relevant.

(I did that some days ago but realised that it is a complete red herring for the reason I have just pointed out.

The real meaning od Nte comes from equation 7 in the original N&Z paper, where they show that Nte is a function of atmospheric pressure.

I do agree that it is a rather awkward function and have spent some days working on that as well.

I surmise that its complexity is due to several small assumptions that are not completely correct.

I intend to take that up with the authors eventually, as it does not make any significant differnce to their theory, I’m content to leave it for the moment.

So back to square one.

By the way, you did ask for an escellator explanation of their theory.

I gave what I called and escellator explanation in an earlier post which you may have missed.

It was very brief – two lines and can perhaps be better described as a satellite explanation.

I have recently made a longer, clearer and more detailed explanation in a comment to Jeff Id’s Air Vent, which you may like to look up.

John Day says:

January 23, 2012 at 6:47 pm

John, first you claimed that my use of “overfitting” was somehow saying that N&Z were dishonest. I said that was not the case.There was an option in there for you to say “Sorry I accused you of calling N&Z dishonest when you hadn’t”.

You correctly note that I and most other folks think the use of 5 free parameters plus free choice of any kind of equation is overfitting.

One logical conclusion from noticing that is it might be prudent to try some fitting yourself, to see how easy it is to fit a few data points with a fistful of parameters.

It doesn’t take a whole lot of parameters. Four is plenty to do what they’ve done, particularly when given free choice of any fitting equation.

Finally, the idea that you can identify an overfit equation because it will be “full of ‘wiggles'” and that a smooth curve is “natural” is … umm … well, I’m reforming here, so I’ll just call it unsupported in the literature to the best of my knowledge, and set my incredulity aside.

w.

Thanks Willis. Well done.

LT is very happy to see some skepticism here.

Brian H says:

January 23, 2012 at 8:00 pm

1. I don’t really understand what the N&Z hypothesis is, so I can’t say anything about that.

2. I don’t expect there to be any MIRACLE equations of that form or any form at all.

w.

Brain H,

The form of the equation is this: Ts = (Ts/Tgb) * Tgb

John Day says:

January 23, 2012 at 7:46 pm

Because this thread is about equation 8. The clue is in the title.

Along those lines, I ask everyone kindly to

not debate the whole theory, gravity, the ideal gas law, or any other extraneous stuff on this thread. Please confine yourselves to the topic of the thread, the alleged “evidence” that their theory works. There is a “” thread open for your general discussions.commentsw.

Its really just sinking in for me that the prevailing model of planetary temperature doesn’t include atmospheric pressure!

How do GCMs do with Venus?

There swwms to be a lot of confusion about N&Z’s theory and how it fits in to the overall picture.

So I repeat her, the comment tht I made at the Air Vent.

The following is my understanding og their theory.

——————————————————————-

The so called greenhouse effect is an artifact of a failed experimental configuration, first perpertrated by John Tyndall over 100 years ago and repeated endlessly ever since.

Carbon dioxide, by its molecular weight and atomic structure, expands more rapidly under heat than does an average sample of air. This causes increased pressure in the sealed container holding the carbon dioxide sample, relative to the container holding just air. Increased pressure results in the temperature of the carbon dioxide to rise higher than the air in the other container. That is the so called greenhouse effect.

HOWEVER, when the pressure in the two vessels are allowed to equate, such as by providing a hole in the top for the excess gas to escape to the outside air, then the temperature in each vessel rises to a lower level than before and the temperature in both containers remains the same. Bye Bye, greehouse effect. This has also been demonstrated on a number of occasions, but with far less noise and propaganda than the false greehouse effect.

Now, when we turn to the real atmosphere, we see that gravity draws more air molecules towards the surface and leaves fewer higher up, where in any event, there is more room for them to expand as the diameter of the atmosphere keeps increasing, the further up you go from the surface, so pressure is lower for both reasons.

More molecules near the surface means higher pressure than further up. Higher pressure, as already demonstrated, means higher temperature near the surface and lower temperature further up. However, there is no net increase in temperature or energy for the whole atmosphere, only a redistribution.

Let me quote: “Adiabatic changes in temperature occur due to changes in pressure of a gas while not adding or subtracting any heat”.

“”””” John Day says:

January 23, 2012 at 1:40 pm

tallbloke says:

January 23, 2012 at 12:43 pm

George E. Smith; says:

January 23, 2012 at 12:05 pm

There will be no permanent increase in the Temperature following a pressure increase; unless that cooling is somehow prohibited…

Hi George; that was Ira’s argument, but it isn’t initial compression and consequent transient heating we are talking about here. It’s simply the way nature has compressible gases and gravity arranged in a pressure gradient as an ongoing condition which causes there to be lots more warmth near the surface when illuminated by a star. Simply put, there are lots more molecules per cc to hold kinetic energy (and therefore heat) near the surface than at high altitude. And the nearest star warms them up.

TB is correct. George is somehow hung up on the notion of ‘heat generated by compression’. “””””

Well John, If YOU think I am “hung up” on anything you are sadly mistaken; and it is obvious that you have never pumped up a car or bike tire with a hand pump.

The act of reducing the volume of a fixed mass of gas, requires applying a force proportional to an area, during a distance travelled by some “wall” reducing the volume. Some trivial calculus will show that the work done by a small change in volume dV, is simply PdV. That work is simply dissipated as “heat”, which will raise the Temperature of the gas above its orignial ambient Temperature. Unless you know of a container with zero thermal conductivity walls, that excess “heat” energy will leak out to the surroundings and the Temperature will re-establish equilibrium with the environment. The pressure will fall slightly during the cooling phase as required by the gas law, and the final equilibrium result will be a smaller volume at a higher pressure, at exactly the same Temperature as the environment; which presumably is thermally massive compared to our container of gas.

If the container of gas DOES NOT COOL DOWN as YOU seem to say it won’t, then your container becomes a perpetual supply of heating to the environment. Gee who knew you could warm your house just by pressurizing it.

The heating of a stellar mass of gas to form a star, is a consequence of the work done by the force of gravity, against the increasing gas pressure, that results from the eventual occurrence of collisions between the gas molecules once they are close enough to each other to have collisions. That heating and gravitational collapse, will continue unabated, until the Temperature, pressure, and molecular interraction time reaches the critical surface that defines the onset of thermonuclear hydrogen “burning”; hydrogen being the principal gas of the universe.

Then it will stop as thermo-nuclear energy takes over the heating to compensate for the radiation loss from the much cooler outer surface of the star. The core can’t rapidly cool, since the outer layers are opaque to the high energy photons, emitted at the “burning” site.

If anyone is “hung up” it is you who believe that a constant pressure can maintain a constant Temperature rise above the environment Temperature.

Any Temperature gradient in this unified theory of climate is a simple consequence of the non-equilibrium continual supply of external energy that is converted to heating at the bottom of the atmosphere, and subsequently must leak out through that atmosphere by a variety of thermal processes, some of which require a Temperature gradient (conduction for example).

I didn’t come down in the last shower, and you will have to do a lot better to try and get me “hung up.”

What I meant to say was:

There seems to be a lot of confusion about N&Z’s theory and how it fits into the overall picture.

So I repeat above, the comment that I made at the Air Vent.

The following is my understanding of their theory.

—————————————————————————-

I’m sure that there are typos as well in the main comment from the Air Vent.

I can do no more than apologise yet once again for my very poor typing and spelling.

@Willis

> There was an option to say “Sorry I accused you of

> calling N&Z dishonest when you hadn’t”.

Read my remarks carefully. I didn’t “accuse

youof calling N&Z dishonest”. You’re blowing my statements out of proportion. I said itsuggesteddishonesty.I’ll accept that you don’t really believe they’re ‘dishonest’. But look at your own words, which still

suggestyou believe this to be a form of “conning”

“Let me be very clear.

I don’t think N&Z are dishonest,that’s not my reading at all. I think they actually believe what they are claiming.I got…”_conned_one time by a guy named BillActually, the tone of your remarks and many of the others here suggest that N&K are a pair of complete idiots for claiming that a smooth curve (representing a natural law) could be modelled with a small number of parameters. (When the truth is that their regression formula elegantly represents what they have _learned_ about the relationship between kinetic warming and radiative warming)

I think you (and the others) owe N&Z an apology for insulting their intelligence with these remarks.

And I think you also owe us explanation of your views on the Ideal Gas Law issue, which is crucial for understanding the N&K theory (which I pointed out to you on 30 December http://wattsupwiththat.com/2011/12/29/unified-theory-of-climate/#comment-848028).

And don’t be so danged emotional. I still admire and respect your efforts in supporting getting the truth out on climate issues.

😐

I can do better than N & Z! I have developed an equation which tells me exactly what the aliens on the other planets are thinking right now! YOU CAN”T PROVE IT’S WRONG!!!

Bill Yarber says:

January 23, 2012 at 8:07 pm

First, Bill, I’m the author of the post, not Anthony. Are there other planetoids? I don’t know. But you have the cart before the horse.

It is up to them to actually establish their ideas in the manner you describe BEFORE they proclaim a MIRACLE. It’s not our job to do that.

w.

“”””” Look at my response to Tallbloke and GeoSmith …

http://wattsupwiththat.com/2012/01/22/unified-theory-of-climate-reply-to-comments/#comment-873665

… particular the derivation of the Ideal Gas Law.

http://en.wikipedia.org/wiki/Ideal_gas_law#Derivations

Note that the temperature T of a system in equilibrium can be computed from the just kinetic energy of the moving gas particles and their mutual collisions (density, implying pressure). We don’t need to know the radiative aspects of the system to compute the temperature! What part of the Ideal Gas Law do you not understand here? “””””

So what part of THIS SYTEM IS “NOT” IN EQUILIBRIUM is it that YOU do not understand. It is not even a closed system, since you yourself said it is being illuminated by a star which is constantly feeding energy into the system.

OOoops !! the ideal gas law applies ONLY to closed systems in thermal equilibrium. Gee!! that requires the whole system to be at a single uniform Temperature.

AusieDan says:

January 23, 2012 at 8:37 pm

Dan, they have not shown that Nte is a function of pressure. They have used a very carefully designed equation with four parameters to fit it to the Nte. This kind of fitting is meaningless, with four parameters you can fit an elephant.

So no, they have shown no such thing as Nte being a function of pressure. Nor is there any reason to think it should be a simple function of pressure, given the number of other factors involved in the climate.

w.

John Day says

I think you’re looking at this in the wrong way. You say ‘overfitting’, which suggests they are somehow dishonestly trying to ‘cook’ a formula to fit 8 examples.

——-

No it does not say they are dishonest at all.

It does say they are very, very naive in the area of data analysis. Overfitting is a mistake any science or engineering or social science or economics graduate is taught to avoid.

Something is seriously wrong with the basic education of these 2 PhD’s.

As I read this work, I started to smile, then to grin, then to say out loud: “Aha!” This is fun stuff. I wish understood it all as well as you do, Willis. Keep it up.

— John Andrews; in Knoxville.

@Willis

What is your opinion of Roy Spencer’s use of 5 fitting parameters (the same as N&Z) to predict the surface temperature of just ONE planet, namely the Earth?

my source:

http://www.skepticalscience.com/just-put-the-model-down-roy.html

follow up question:

Is the underlying physics of Spencer’s model questionable as well?

I look forward to your response.

The demonstration that the equations are a tautology is not as convincing as I first thought. If you start from equation (8) and rearrange it to a more sensible form you just get

Tbg = 25.3966 S^0.25

which as you say if just the Stefan-Boltzmann equation for a grey body, with the emissivity absorbed into the constant. So this is hardly surprising.

Then from equation 7 you get

Ts = Tgb * exp(t1 * Ps ^ t2 + t3 * Ps ^ t4)

I do not see that rearranging it to give Ts=Ts actually shows anything – you have inserted the tautology, not them.

On the other hand, that fitted expression is very dubious . Note that the insolation is all in Tbg. The rest of the expression is fitted to pressures. However though it is said that there are 8 planets used, three of them are essentially the same – Mercury, the Moon and Europa all have P=0, so

are not independent data values, and Titan has P almost zero. So I do not think the fit says anything except that you can fit 5 points with 4 parameters.

George E Smith says

Note that the temperature T of a system in equilibrium can be computed from the just kinetic energy of the moving gas particles and their mutual collisions (density, implying pressure). We don’t need to know the radiative aspects of the system to compute the temperature! What part of the Ideal Gas Law do you not understand here? “””””

——-

Somewhat ironically George claims that temperature can be calculated from —mutual—- collisions of gas molecules. This is not true.

The ideal gas theory considers molecules to be too small to collide with each other and ignores that factor as being

Seems George needs to spend some time actually studying the ideal as law

Willis, you are losing your marbles mate. Why don’t you stop the grandstanding and speak to N&Z, they will either put you right or accept that they are wrong. What you are doing with these threads is obsessive and completely wrong. If they are wrong then thats two theories that are wrong, the other is surface heating by back radiation. Have you read the paper by Oleg Sorokhtin from 2005? Excellent and supportive of N&Z

LazyTeenager :

January 23, 2012 at 9:53 pm

Please read a bit on how thermodynamical equations dovetail beautifully to statistical mechanics equations where the scatterings do play a role and temperature appears connected by the statistics to the average kinetic energy of the molecules which scatter against each other. True for the ideal gas law too.

Willis – go ahead – fit an elephant. Please!

Seriously N&Z are only demonstrating in algebra what has been observed in experiments, that heating a gas in a sealed container increases both pressure and temperature.

A gas that expands by a larger amount than air, will rise to a higher temperature.

When each vessel is allowed to vent to the atmosphere, so pressure is not increased, then they will both rise to the same level, which will be lower than either when fully contained.

No Greenhouse effect involved, only the effect of pressure in the presence of incoming heat.

So if four parameters are required, then please go ahead and use four.

It’s not ours to pick and choose.

I believe thatN&Z used data from all the available solar bodies. As far as I am aware the other planets have significant internal heat sources of their own, while data is hard to get for the smaller outer moons.

Surprisingly, it seems difficult enough to get good data for our own moon.

Gregory Andreev says:

January 23, 2012 at 9:50 pm

Spencer’s model is a simplified version of the current paradigm. I am neither a skeptic nor an AGW supporter. I am a heretic. Both Spencer and the GCMs are trying to measure a constant that they call “climate sensitivity”. I think that the climate sensitivity is a function of temperature, and as such a global average conceals a host of mechanisms which are crucial to the climate.

See my post “

” for a discussion of how climate sensitivity varies daily in the tropics.It’s Not About FeedbackSo … I have little use for the current climate models, simplified or not, from either side of the aisle. Much more interesting models are those of

andOu, which I discuss in “Bejan“.The Thermostat HypothesisBest regards,

w.

George E. Smith; says:

“So what part of THIS SYTEM IS “NOT” IN EQUILIBRIUM is it that YOU do not understand. It is not even a closed system, since you yourself said it is being illuminated by a star which is constantly feeding energy into the system.

OOoops !! the ideal gas law applies ONLY to closed systems in thermal equilibrium. Gee!! that requires the whole system to be at a single uniform Temperature.”

This is not correct. Ideal gas law applies to any point (x,y,z) of gas when ideal gas approximation can be used with reasonable accuracy (real gas that behaves sufficiently like an ideal gas). When not, there are more detailed equations of state gor real gases. Equilibrium or not is irrelevant.

Nothing is to be gained by Willis or Ned attempting to denigrate each other. Ned has some good ideas but I disagree with his conclusions, as obviously does Willis.

My summarised thoughts are that there are two broad situations in a simple model of the Earth. a) the 30% of the Earth with no clouds and b) the 70% with clouds.

a) If a packet of air containing IR absorbing gases is considered, it will exchange heat with its surroundings by evaporation/condensation, convection, conduction and radiation. The closer to the earth’s surface, the smaller the significance of radiative transfer, yet at high altitudes, radiation is the dominant mechanism. The IPCC view is that only radiative heat transfer takes place and clouds are effectively ignored.

b) For the 70% of the Earth’s surface covered by clouds, radiation from the Earth’s surface is irrelevant. Heat is transferred primarily by evaporation/condensation and convection. Cloud temperature is mainly set by the lapse rate. Heat is absorbed from the sun and lost to space mainly by radiation, from the tops of clouds. IR absorbing gases have little impact on heat transfer.

My view is that overall the impact of IR absorbing gases is far less than that claimed by IPCC but not zero as claimed by Ned.

Looking forward to any constructive criticism.

martin mason says:

January 23, 2012 at 10:17 pm

Martin, that’s what I’ve been waiting for, for them to show that I’m wrong. That’s why I put my work up here in public, for people to try to find things wrong with it and poke holes in it. N&Z are welcome to point out any errors above.

I raised some questions on the other thread, and the folks there (including Ned Nikolov) showed me where I was wrong. I admitted it, and thanked them for fighting my ignorance.

To date, most folks agree that five parameters and eight data points is a non-starter. If you are defending their five-parameter fit, I refer you to “Johnny” von Neumann. If N&Z want to defend it, I am most interested to hear their reasons.

All the best,

w.

Again, please, folks, take the general debate to the other thread! This thread is about equation 8. Not lapse rates, not your pet theory, none of that. Please take it elsewhere.

w.

How many parameters does it take to draw an elephant.

http://mahalanobis.twoday.net/stories/264091/

More than 4.

LazyTeenager says:

“The ideal gas theory considers molecules to be too small to collide with each other and ignores that factor as being…[?]”“An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly eleastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other.”Source: http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/idegas.html

Willis,

As a matter of interest, I have fitted a much simpler equation to the estimate the temperature for each of the eight solar bodies in question:

Calculated Ts = Tgb * (1 + (Parameter * Surface Pressure / 101,325)

The value of parameter is 0.033, which I used solely to get a reasonable fit to the data.

The figure of 101,325 is my understanding of the standard pressure on earth at 20 degrees C.

So this could be reduced to just one parameter, 3.257E-07 or thereabouts, (not to take up too much space with spurious accuracy).

Now my little one parameter model does not fit nearly as well and the N&Z version, yet the correlation with the actual measured values of Ts is 0.9806404.

That means that 0.962 of the actual are “explained” by the equation (correlation squared).

Not very good, I hear you cry!

Yes I would have to agree, but in my defence I would claim that mine is only a little equation.

What’s more, if my understanding of these matters is correct, I would claim in its defence that the NUL hypothesis has a Pr < 0.01, with a two tailed test, for eight data items.

So it still seems possible to me that the N&Z theory deserves serious study.

Tennis – anyone?

jimmi_the_dalek says: “How many parameters does it take to draw an elephant….” and

“The demonstration that the equations are a tautology is not as convincing as I first thought.”

Great comments throughout, jimmi.. I fear you’re right about the source of the tautology. I’d been wondering what the result of substituting equation 7 into equation 8 would be if 8 were a fit of data derived from 7. This thread and the previous ones have shown me how easy it is to toss off statements that seem logical, but upon closer examination are error-laden.

You are crazier than an outhouse owl, Willis, and I do admire your analytical skills. Distilling things down to their fundamentals is almost a lost art in the “global climate” arena. “Sic ’em”, Bulldog!

Willis: “To date, most folks agree that five parameters and eight data points is a non-starter.”

Where are you getting your data. Just here? Your own thread? If not, do you mind to show us?

AusieDan says:

January 23, 2012 at 11:41 pm

As a matter of interest, I have fitted a much simpler equation to the estimate the temperature for each of the eight solar bodies in question:

Calculated Ts = Tgb * (1 + (Parameter * Surface Pressure / 101,325)

That’s terrible. For Venus, Tgb is 181.6 and pressure is 6.2e+6. Put those in your formula and you get 5,622 kelvin for the surface temperature.

w.

good post.

Thanks.

Willis said:

>>Again, please, folks, take the general debate to the other thread!

Do you mean your other thread ? You only allowed discussion of your pet theory ! Neither yours nor Ned’s reflect the real world.

AusieDan says:

January 23, 2012 at 10:44 pm

See my update to the head post, wherein I make the elephant wave his trunk …

w.

wayne says:

January 24, 2012 at 12:52 am

I get all my data from an international data supplier, everything is cheaper from China … however, if you want to defend using five parameters on eight data points, go right ahead. I can hardly wait to hear your definition of overfitting.

w.

Dr Burns says:

January 24, 2012 at 1:17 am

No, I meant the other thread I

to when I first asked, sorry for not linking it again.linkedw.

Leaving aside the curve fitting part of the discussion:

I thought equation 8 was derived from equation 7 “allows us to derive a simple yet robust formula” as stated by N+Z, not “another fitted (tuned) equation” as stated by Willis.

So substituting anything from 7 into 8 will always end in X = X results, it’s substituting a formula into itself.

Willis Eschenbach says:January 23, 2012 at 9:00 pm

John Day says:

January 23, 2012 at 7:46 pm

@Willis

Why haven’t you addressed my comments on the Ideal Gas Law, the crux of this N&Z theory?

Because this thread is about equation 8. The clue is in the title.

Along those lines, I ask everyone kindly to not debate the whole theory, gravity, the ideal gas law, or any other extraneous stuff on this thread. Please confine yourselves to the topic of the thread, the alleged “evidence” that their theory works. There is a “comments” thread open for your general discussions.

w.

Willis, the supporting material you so daintily call “other extraneous stuff” is in fact the evidence that their theory works. “So by ruling out of court” things like the similarity of their

non linearregression, to the clausius curve, you cut N&Z off from the facts supporting their theory.As Jimmi points out above:

“I do not see that rearranging it to give Ts=Ts actually shows anything – you have inserted the tautology, not them.” In other words, you’re being arsey for the sake of it.

Regarding the number of data points, it is trivially true that research work into solar system dynamics is made more difficult by the fact that there aren’t enough planets with good measurements in place to satisfy arsey stats fiddlers with a predisposition to dispose of a promising theory. That’s just how it is.

Now, regarding the alleged number of free parameters:

Eq. 7: Ts/Tgb = NTE(P)

Eq. 8 simply solves for Ts, i.e. Ts = Tgb*NTE(P)

Also, the constant 29.3966 in Eq. 8 is not a ‘tuned parameter’, but a result of combining 4 constants from the gray-body temperature in Eq. 2, i.e.

(2/5)*[(1 – 0.12)/(ϵ*σ)]^0.25 = 29.3966

In addition, you already knew that the purpose of the small constant Cs in Eq. 2 is, to make Eq. 2 predict a temperature of 2.725K (instead 0K) when So = 0 (no radiation present).

In short Willis, you are a serial shark jumper leading a charmed life.

My initial thought, applied to the original paper’s comments, was that they have re-invented lapse rate heating.

I still stand by this.

Willis, with your recent output I’m worried that you might be a warmist troll?

I did the curve-fitting in Excel, using the Solver minimizing a sum-of-squared-error function. The interesting thing is that (with my least-squares error function), other tuning parameters appear, leading to a lower LS error. Maybe LS is not the best criterion, I haven’t checked.

I then proceeded to leave out one planet at a time and redoing the fit. It turned out that there are many local minima, so it matters how you initialize the tuning parameters. I decided to always start from Nikolov’s values. The tuning parameters varied by about 10%-20%.

Especially when leaving out the outlier Venus, the parameters T3 and T4 are completely different. T4 doubles, T3 is reduced to near zero.

Based on this, I would say that Willis is right about fitting the elephant.

Atmospheric compression creates heat due to that compression, by increasing the KE of that gas through the work done on it.. Jupiter, with its atmosphere of hydrogen and helium, radiates more heat than it receives. since there are no GHG’s in the Jovian atmosphere there must be another mechanism to create that extra heat and that must be gravity.

Gravity starts suns so why not also provide extra heat to a simple shallow atmosphere a few tens of Km deep.

They are using only eight datapoints and five tunable parameters with a specially-designed ad-hoc equation withno physical basis.Presumably why the elevator speech is still “in the post” 🙂

W. I am surprised that you are surprised when you found the Boltzmann constant could be derived from eq 7.

So curiously, what it turns out they’ve done is to estimate the Stefan-Boltzmann constant by a bizarre curve fitting method. And they did a decent job of that. Actually, pretty impressive considering the number of steps and parameters involved.As they are working with gray body temperatures which follow the Boltzmann concept, it should not be a surprise.

It is a bit like being surprised that ohms law I = V/R is related to P = V^2/R etc etc and that substitutions can be made…

When dealing with natural laws, many relationships can be found between parameters of laws which bolster the acceptance of laws.

A proposed law that can not fit with all other known laws would have extreme difficulty in being accepted.

The concept of splitting your dataset in two to test your theory is fine when your dataset is large, but with 8 data points it is unrealistic.

They only have 8 data points.

tallbloke says:

January 24, 2012 at 1:33 am

Thanks, tallbloke. Here on this thread I’m focused on what they did in equations 7 and 8. There are many aspects to their work. I oppose the idea that it can all be settled in one thread. At present there are four threads. The original one. The answer by Ira Glickstein. The response to comments. And this thread. This thread is about equations 7 and 8. You have plenty of room to discuss the “evidence that their theory works” and the “similarity of their non linear regression” and the “clausius curve” on any one of those three threads. I have asked, and will continue to ask, that you stick to the topic here.

“Inserted the tautology”? I have shown that the underlying structure of equation 8 is Tgb * Ts / Tgb. I have not “inserted” anything.

You are correct. That’s how it is. However, the universe having given you very few data points doesn’t mean that you are justified in drawing conclusions from that tiny sample as though you had sufficient data.

Equation 7 contains parameters t1 thru t4, four parameters.

I discussed this above and acknowledged the possibility that it was not a parameter … including the fact that still leaves four parameters and eight data points. The oddity that confused me is that to get 29.3966 from your formula there you need to have an emissivity of 0.955, which seems strange. But no matter, four parameters is plenty to be too many.

That’s some excellent detective work, considering that in the head post I said:

But yes, you are correct.

Dang … that actually sounds about right in some strange way. Me and the sharks have been friends, well, not friends exactly but we have had a kind of wary mutual underwater respect for decades now. I’d sign up to be a shark jumper, sounds like fun.

As regards my charmed life, Napoleon is rumored to have said that he didn’t care if his generals were good, as long as they were lucky. And my aikido teacher said the best aikido is, when the fight is starting on third street, you’re walking down seventh street. I can only wish that everyone have that kind of good fortune.

My best to you,

w.

Jimmy_the_Dalek says:

……

Wayne,

The problems with the integration occur before the steps you describe – it is the variable substitution mu = cos(theta) which is dubious. Simply try comparing

the integral of mu^0.25 on [0,1]

with the integral of cos(theta)^0.25 on [0, pi/2]

and see what you get.

….

You are quite right that the 2 integal above give different results. But you have overlooked a small detail, that results in an incorrect conclusion in this context . The correct comparision would be

to compare

the integral of mu^0.25 on [0,1]

to

the integral of sin(theta)*cos(theta)^0.25 on [0, pi/2]

and if you do that you get the same result in both cases.

Why ? Well it goes like this. Think of theta and phi as the latitude and longitude of the Earth ( and assume Earth to be a sphere rather than a an ellipsoid ) you can then identify the position of every point on the surface with those two numbers.( elementary geography ok ?).

Now you may or may not know it but the vertical distance between two positions that have the same longitude, and f.x. a 1 degree diffrence in latitude is the same regardless of which longitude you are on , but when you have two points with the same latitude and a 1 degree difference in longitude the horisontal distances are different for different latitudes, on the equator the length of the 1 degree latitude arc is aproximately the same as length of a 1 degree longitude arc, but when yo go from there towards either one of the poles th horisontal degrees get smaller and end in a zero on the pole while length of the longitude degree is still the same as on the equator. And to calculate the length of 1 degree difference paralell with the equator at latitude theta you have to use sin(theta).

And the exact same thing happens when you use integation to calculate an area on the surface of the Earth and with positions determined by spherical coordinates, the sinus of the latitude sneaks uninvited into the equation as a scaling factor of for the paralells.

So there is nothing dubious about the mu = cos(theta) substituion , and its effect can be seen from the following

the derivative of mu w.r to theta is d(mu)/d(theta) = -sin(theta)

and from that we get d(theta)=(-1/sin(theta))d(mu)

insert mu for cos(theta),and the left hand in the equ. above for d(theta) into

the integral of [sin(theta)*cos(theta)^0.25 d(theta)] on [0, pi/2] as well

as adjust the interval limit to reflect the new variable mu to [cos(0),Cos(pi/2)]

the result becomes

The integal of sin(theta)*(mu^0.25)*(-1/sin(theta))d(mu) on [1,0]

the sin(theta) factor now cancels out and we are left with

The integral of (-1)*(mu^0.25) on [1,0]

switch the upper an lower integation limits to [0,1]

and change the sign on the integrand to reflect that switch

our final result now has become:

the integral of mu^0.25 on [0,1]

Q.E.D.

P:S. Jimmy , take a quick peek at the wikipedia entry for Spherical Coordinates if I have not managed to convince you that there is nothing sinister about tha<t substtution.

tallbloke says:

January 24, 2012 at 1:33 am

Upon further contemplation, I realized that this statement couldn’t be true, since the albedos are different for each planet. As a result, if it is a constant for all planets it is a tuned parameter.

w.

“that still leaves four parameters and eight data points”It’s only six data points. If you look at the table in their original post, they didn’t try to fit the Moon or Mercury.

I get the feeling that there are a number who can see Willis’ limitations who are no longer coming here to post. There has been a lot of shouting recently and what I did in that environment was to opt out and go back to study, carefully, the original material.

I studied N&Z carefully only because the shouting drove me to do so… but presently I felt I had discovered a goldmine, a game-changer. The remarks of many others indicates that I am not the only person to have had that “aha!” experience. But from then on, much of my energies have been diverted into consolidating this, so that one can answer doubts just once, not tire oneself out with repeating oneself again and again to more and more individuals. So you won’t see me much. And it’s not just N&Z talking about pressure-induced atmospheric temperature, there is a tradition even older than that of Arrhenius and Callendar, that has recently produced a whole spate of work, practical experiments and data fitting theoretical maths and physics. Graeff, following Loschmidt. Now not just Jellbring and Gilbert but also Sorokhtin. And a growing number of climate skeptics, many of whom have diverted currently to Tallbloke’s threads.

The pressure figures of Huffman for Venus fit very precisely, they will not go away. These figures, Willis, are in addition to the single planetary fits used by N/Z. Then there are the experimental figures of Graeff that fit his theoretical calculations. Then there are those of Miskolczi, where data fit theory so precisely that it could not be accidental, again M overturns the ghg stuff. And I now start to wonder if the much-criticised Gerlich & Tscheuschner were on to something similar, and if they too will be vindicated.

It’s not easy coping with a whole paradigm shift. I am still reeling myself. There are still bits of the new paradigm I do not understand. And bits of the maths I still have to come to terms with – where N&Z might still be wrong. However, I prefer to stay with the work where the data clearly has excellent fit to the theory, than where there is more emotion and less data. Right now I’m working on developing a protected wiki environment that will be able to answer each major doubt issue for all comers. To me, this will help the science.

All the best Willis, I still think your earlier work on tropical thunderstorms and Darwin was superb.

Willis Eschenbach says:January 24, 2012 at 3:21 am

tallbloke says:

January 24, 2012 at 1:33 am

Also, the constant 29.3966 in Eq. 8 is not a ‘tuned parameter’, but a result of combining 4 constants from the gray-body temperature in Eq. 2, i.e.

(2/5)*[(1 – 0.12)/(ϵ*σ)]^0.25 = 29.3966

Upon further contemplation, I realized that this statement couldn’t be true, since the albedos are different for each planet. As a result, if it is a constant for all planets it is a tuned parameter.

It’s the albedo for rocky planets without an atmosphere. Assumed to be the same for all the bodies tested. So, Moon: measured albedo 0.12 Earth with no atmosphere, about the same, etc. So, not tuned; measured from the Moon, and applied elsewhere.

Read Nikolov and Zellers work and their contributions to the threads on my website for details would be my advice to anyone who wants to address what they actually say. You’re not banned from reading my website Willis, just from trying to gishgallop their (or anyone elses) theory into the dust.

Willis,

Consider the following.

E=Mc^2

Therefore, c=sqrt(E/M)

therefore E=M * (sort(E/M))^2

therefore E=E

You can do it with any equation, and this is all you have done.

On the other hand, the fitting is definitely overdone, especially as 3 of the planets have P=0.

Also, your original objection has merit IMO – as they have omitted all properties of the atmosphere from their formulae, they have done the equivalent of postulating a totally transparent atmosphere with no chemical or optical properties – that cannot be right.

And whoever suggested that it is worth tracking down where that planetary data came from is correct – some of it must be spectroscopic in origin so the possibility of inadvertent circular argument is there.

Willis sez:Eq. 7: Ts/Tgb = NTE(P)

Equation 7 contains parameters t1 thru t4, four parameters.

It doesn’t have to contain them because the parameters operating together in the form specified by N&Z are equivalent to (NTE)P and Ts/Tgb.

That’s why there’s two equals signs in there. One of them.between Ts/Tgb and NTE(P) and another one of those funny little parrallel line thingies (=) btween NTE(P) and the four parameters.

Sheesh.

Willis, I’m withholding detailed comment on the correctness of your ingenious analysis of equation (8), as it has distracted everybody from the

equation (2) ‘elephant’which is already glaring at them from within the original N & Z paper.If equation (2)

iscorrect, as I believe it is, and you do not yet understand it, then your above analysis (even if it is correct) is of secondary significance, compared to the paradigm shift which their equation (2) implies for GHE theory.I have not seen a coherent criticism (by anyone!) of equation (2). Their new integration model is used to produce their fundamentally different “mean planetary gray body temperature” (Tgb) evaluation, which certainly features in (but eventually disappears from) your analysis.

Since Ned and Karl published Figure 1 in their “Reply to Comments” paper, I have found no error in the conception of that integration model or the resulting equation (2). So, show me where their equation (2) is incorrect (or where the simple geometry of its integration limits is in error) and I’ll reconsider whether your above analysis is worth analyzing in detail. The fact that your analysis effectively removes Tgb from the theory, as though it were irrelevant, is deeply troubling.

Could everybody have got the mean gray body temperature of an “airless, rotating, sun-lit sphere” so wrong in the past? I believe they could have, and await identification of any error in Ned & Karl’s equation (2) or in their brilliant new Tgb model.

Jorgekafkazar defines the ideal gas theory

——–

I am happy with your definition by I will respond with a derivation here: http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/

To summarize: the derivation is all about individual molecules, their kinetic energies and how that determines the impulse on the walls of the container, and hence the pressure. There is no need to consider collisions between molecules at all. It is not relevant.

You do need to consider molecular size at higher gas densities. Hence the old fashioned van der waals equation of state.

Willis

I think that the point you raise in this thread is valid.

However, that does not mean that N&Z are wrong but rather that the equation in question (and the ancillary fitting) does not necessarily carry the significance to which N&Z would have attribute to it.

When English is not the first language of an author, it is necessary to give wide latitude to the language being used. I appreciate that this can often be difficult since precision in language is often of utmost importance. It is unfortunate that they used the expression ‘miracle’. Clearly the choice of that expression to a native English speaker is wrong but this should not in itself be used as a vehicle of harsh criticism or judgment when dealing with someone whose first language is not English

“Why aren’t you all trying to disprove our MIRACLE equation”

That’s easy enough, really, there are no miracle equations.

Willis, your rebuttal almost makes me weep with joy. Well done! I hadn’t gotten around to N&Z as I’ve been distracted by Jelbring (see post coming soon that should finish that discussion once and for all) but I too was bothered by an empirical fit with no derivation or sound theoretical or physical basis (handwaving doesn’t count, especially not when the handwaving is based on sketchy ideas like “gravitational heating” in a steady-state planet.

Your quote of the Fermi-Dyson story reminds me of the good old days when I used to go to a lot of physics workshops where people presented the results of computations in condensed matter or nuclear physics based on diagrammatic perturbation theory. I don’t know if you are familiar with these fields, but they frequently involve trying to approximate a non-convergent or weakly convergent series with a few terms (usually terms selected because they come from the subset of all the

possibleterms that actuallycouldbe summed over, e.g. in some cases “ladder diagrams”, ignoring all the ones that they couldn’t or wouldn’t compute). I got so cynical while listening to talk after talk of this sort that I formulated the following:The Fundamental Axiom of Diagrammatic Perturbation TheoryAll the diagrammatic terms thatIdid not include inthiscomputationdo not significantly contribute.I heard this axiom stated, in so many words, time after time after time, never with the slightest actual justification. Indeed, any justification offered was always

a posteriori— they had a target result, or perhaps a few target results, that they wanted to explain. They had a computer code that would allow them to vary the degree of a non-convergent and/or incalculable series out to some order in a computable subset of all of the terms. They would then — intentionally or not — run the code a few dozen times with different numbers of included terms and — Surprise! Wow, look at that, if we include the first four regular terms and sum over all of the ladders, we get within 10% of the right numbers!Of course, if one kept the first

fiveorsixterms, and summed over ladders and all of the other permutations of diagram types to systematically higher order — the kind of thing one would like to be able to do before claiming that a perturbative series result is actually valid — the answer would getworse. And the particular set of diagrams kept varied from computation to computation, presentation to presentation. Clearly another case of fitting the elephant, junk science skillfully hidden, although hey, theorists gotta eat.I also spent my share of time trying to fit nonlinear functions that

didhave something of a theoretical basis in order to extract critical exponents, and that’s a damn difficult game. Nonlinear function fits with multiple, weakly covariant terms, often havemanylocal optima, and one can sometimes get two or three distinct solutions all of which get worse if you perturb the solution parameters a bit locally (they are all gradient search optima) and which may be very nearly equivalently as good. This is well-known as therough landscapeproblem — many optimization functions (and function fits are always optimization problems, although in e.g. linear regression there is frequently a unique best solution because of a smooth landscape) have parametric optimization surfaces that look like mountainous terrain — in N dimensions.In that regard, their solution has a very suspicious aspect to it. It is the exponential of a sum of powers of the pressure. I have no idea how to enter equations into this interface yet (if you do know, or if Anthony knows — perhaps it would be a good idea to post a toplevel “Howto” document describing how, along with how to include figures and so on — can one embed figures in straight html?) so I’ll have to go with latex-style ascii equations, but:

N_TE = exp(t1*P^t2 + t3*P^t4) = exp(t1*P^t2) * exp(t3*P^t4)

Now, there is one other thing that Fermi was famous for — dimensional analysis and “Fermi estimates”. N_TE is a dimensionless number (ratio of two temperatures). The exponential function has a power series expansion (and hence

mustbe dimensionless in physics. Its argumentmustbe dimensionless in physics. This means that:t1*P^t2

mustbe dimensionless! Well if it is, t1mustbe somereference pressure, taken to thesame poweras the term it multiplies:t1 = 1/P_1^t2 -> P_1^0.065 = 1/0.233 = 4.29

or:

P_1 = 5.407 x 10^9 = 5.4 x 10^4

atmospheres(where I’m ignoring the difference between atmospheres and bar — really this is bar). Wow, the temperature on the surface of mercury depends on a pressure of 54 thousand

atmospheres! I wonder where that number comes from?For the uninitiated, the pressure in the ocean goes up by roughly one atmosphere for every ten meters of depth. 5.4 x 10^4 atm is thus the pressure at 5.4 x 10^5 meters, or 540

kilometersof depth inwater!Alas, the Earth’s oceans are only a few tens of kilometers deep at their deepest points. That sort of pressure doesn’t exist onanyof the planets in the list being fit. — the pressure on the surface of Venus is a mere 93 or so bar. You might find it — pretty far down — on one of the gas giants — or somewhere down inside the Sun.This scale is, of course, absurd. There is no way that the temperature on tiny, nearly airless planets could

meaningfullydepend on a pressure of 54 kbar. So we have the first term:exp(t1*P^t2) = exp((P/P_1)^t2) = exp( (P/54000)^0.065 )

where P 1/0.00154 = P_3^0.385

or

P_3 = 2.019 x 10^7 = 202 bar

Hmm, once again, I’m having a difficult time seeing where 200 bar could be a relevant pressure in

anydescription of planetary climatology. It is over twice the size of the pressure at thebase of the atmosphere on Venus, and yet is supposed to apply to a list of planetary bodiesonly two of which have atmospheres as high as 1 bar. Even Mars has almost negligible air pressure at the surface at 6 to 10millibar.Let’s write out N_TE properly then, shall we, in manifestly dimensionless form:

N_TE = exp( (P/54000)^0.065 ) * exp( (P/202)^0.385 )

Willis already dealt with the leading term in the T_s expansion — it is self-fullfiling prophecy. Let’s see what N_TE is for Earth:

N_TE(Earth) \approx exp(0.49) * exp(0.13) = 1.54 * 1.14 = 1.75

A nice number, order unity. What about the other planets? Well, for Venus this is clearly going to be a much larger number (but still not huge). For Mars it will be a much smaller number. The whole point of the big exponents is that it causes N_TE \approx 1 as soon as P << 1 bar. In fact, for small P — where even P = 1 bar is "small" in this game — we can power-series expand the exponential and observe that

this is a linear fit to all of the planets but Earth and Venus, plus a quadratic and probably a cubic term that reach from Mars to Venus. The power series in P (again dimensionless) is certainly nolessmeaningless, and I’d predict that an ordinary 4th or 5th order power series expansion in P would work as well as this strange product of exponentials of powers of ratios of P and two utterly non-physical reference potentials.I defy anyone to find any

physicsthat would lead to the particular reference pressures 202 bar and 54 Kbar in the atmospheric science of Mercury, the Moon, Europa, Triton, Titan, or Mars. I double-dog-dare anyone to look for the mysterious meaning of 54 Kbar pressures in predicting the climatology of the Earth or Venus. Go on, show me how 1 g of gravity and atmospheric pressure that ranges from 1 bar to 0 can, for an ideal gas, make 54 Kbar an important, nay, critical pressure.I’ll tell you exactly what this fit is. It is a double fit. One piece is negligible for very low pressures, where the other fits all the nearly airless planets on the list. That term, however, becomes comparable to the other right around “Earth” (1 bar) and fits

only the range part between Mars and Venus!There isn’t the slightest bit of physics in either one.rgb

Arrg. The interface (or my mouse) ate a half paragraph out of my previous reply. Somewhere between where I compute the first term and the second it should have said something like “Now let’s do the same thing for the second term, and evaluate its reference pressure.” plus a half line of algebra that seems to have disappeared but follows exactly the same solution approach as the first term.

Sorry,

rgb

Anna v says

Please read a bit on how thermodynamical equations dovetail beautifully to statistical mechanics equations where the scatterings

——-

Thanks Anna. The ideal gas definition there matched mine pretty well, but I dont want to get hung up on definitions when it is clear what the derivation of the ideal gas law from first principles requires as it’s basic assumptions.

And I also misspoke about a “linear” fit for the small planets. I meant a fit with only one term such as N_TE = 1 + (P/P_0)^\alpha… for some entirely meaningless P_0 and \alpha. One

mightmanage it with a linear fit indeed, or linear with a weak quadratic correction, though. I don’t care. Numerology isn’t physics, especially when the nonlinear curve fits turn out to depend on utterly nonphysical parameters.rgb

John Marshall says

Gravity starts suns so why not also provide extra heat to a simple shallow atmosphere a few tens of Km deep.

———

The difference is that the initial heating of the sun or earth by gravity is only important during the sun or earth’s accretion phase.

That phase is largely over, though it is believed that gradual sinking of heavier material may be contributing a small amount to the internal energy budget of the sun, earth and Jupiter etc.

Nowadays the energy budget determining the surface temperature is determined largely by solar insolation.

Willis, you created the tautology yourself as others have pointed out. Should make you wonder about the rest of your analysis.

On the other issue I just happened to read a bridge column last night where the only way to defeat the contract was leading away from an ace. Normally considered a stupid play but in this case the bidding made it pretty clear that something unusual was needed.

Yes, using multiple parameters to fit an equation is normally wrong, but that does not make it wrong all the time. You are making the same mistake a poor bridge player would make in assuming certain general concepts are always true.

You need to understand what they have done more closely. I pointed out in another thread that you need to consider figures 5 and 6 and note what the curve fitting produces. All and all I think you are over-reacting in this case. I can understand it somewhat given the silly comments by N&Z attacking non-PHDs. It doesn’t help your case here which is pretty much waving your arms.

Look, it’s pretty clear that there are major problems in N&Z’s hypothesis. But, attacking what may turn out to be a reasonable correlation based on an “In general” set of logic leaves a bad taste in my mouth and is not up to your normal standards.

jimmi_the_dalek says:January 24, 2012 at 3:42 am

On the other hand, the fitting is definitely overdone, especially as 3 of the planets have P=0.

Also, your original objection has merit IMO – as they have omitted all properties of the atmosphere from their formulae, they have done the equivalent of postulating a totally transparent atmosphere with no chemical or optical properties – that cannot be right.

Hi Jimmi,

One of the surprising things N&Z have discovered is that the particular composition doesn’t matter. The planets still fit the curve omitting the properties. Pressure clearly dominates the setting of surface temperature (along with insolation). However it is worth noting that even moons in the outer solar system have precipitable gases like methane, and these have radiative characteristics. So the question of transparent atmosphere’s with all the attendant radiative balance issues (incorrectly) raised in the Jelbring thread doesn’t arise.

Your elephant fitting skills are really impressive except that you kinda miss the point.

The N&Z claim is:

Ts/Tgs = f(Pn)

Now if you take values of Ts/Tgs and Pn and put them to the graph, you get a set of points which is interpolate-able by a smooth function. Yes, the function they used is rather arbitrary and four parameters is a lot but someone smarter may figure out a way how to use even less parameters to just fit these points. Just looking at the graph also shows that there are actually multiple subsets of our eight examples which are pretty likely to generate very similar fits: take one of (Moon, Mercury, Europa), one of (Triton, Mars), one of (Earth, Titan) and Venus and you’ll get pretty similar fit with each such combination.

That does neither prove nor disprove whether there is any physical reality behind that fit. My personal opinion is, what plays important role in real surface temperature compared to gray body temperature is thermal capacity of the atmosphere and wind speeds and directions – but if these two appear to be correlated to atmospheric pressure in a favorable way, it is possible this arbitrary fit is real.

Substituting (7) to (8) is nothing more than evaluation of how realistic the fit is, as you basically take the fit and get back to source data from it. The only thing you prove by reducing it to Ts = Ts is that you omitted all of the fit’s imperfections on the way.

So the sun still matters

1. Ts=Ts.

Of course it does. You’ve just proven by your own hand that their equations are properly balanced. If you could resolve them to Ts=1.5Ts theat would a be a problem.

2. E=IR and P=I^2*R. Using the precise same method that you have, I can resolve these to show that E=E, I=I, R=R and P=P. If I couldn’t, there would be a problem. That I can shows that the equations are properly balanced just as you’ve done by resolving Ts=Ts.

3. If SB Law did NOT show up as being integral to their equations, then there would be a problem. A major portion of their premise regards the proper application of SB Law, and they’ve produced equations that do precisely that, properly apply SB Law. That you can discover SB Law within their equations is no surprise. If you couldn’t, THAT would be a surprise.

4. I failed to understand your vitriol and agressiveness toward N&Z from day one. It hasn’t been objective, and your failed mathematical analysis in this thread is a prime example. Plenty of people have noticed it, and Lucy Skywalker’s admonishment upthread ought to give you pause. That said, perhaps the reason for your antagonism is contained in this thread where you once again draw attention to your own “thermostat hypothesis”. I’d ask you this Willis:

Is your cherished “thermostat hypothesis” so prescious to you that you would tear down the work of others to protect your own?

I have raised the issue of free parameters many times before in the AGW debate.

How many GCMs are there, 55 or so?

I have said on a number of occasions send me 1000 or so random spins of a roulette wheel and I will send you a model that will show you can win money when applied to the data you have sent me. Hell, send me 55 lots of data and I will send you models that will win you money against all of them.

Of course a lot of these models are going to be different, not majorly different mind you. They will all use the same parameters some will be fixed but some will be free, like bet size, frequency of bet etc. The value of the parameters will however be slightly different between the models again not majorly.

My models will be very similar to the GCMs except that there will be less free parameters and the difference between the value of the free parameters will also be very likely less than in the GCMs. For aerosols for instance there can be a factor of 4 in the value of the parameter between models!

Of course someone will say a lot of these models are different and at the absolute best, only one could be right. Well that is exactly what is said about the GCMs. So the models are averaged and their output, we are now assured, is very close to reality having averaged out any gross errors.

Well I just do the same to my roulette models and get an output that I could now claim is close to reality and that reality is that you can win money consistently playing roulette.

So what is the difference between the the two sets of models?

Well we know for certain that you can not consistently win money playing roulette, we are confident in the Laws of Probability. We know, though my math is sound in my models, that I have obtained the result by use of the free parameters and my assigning particular values to them. In short they are bollocks!

Of course we know for sure that climate modelers make use of many free parameters in their models, aerosols, black carbon, clouds, land use etc etc. However, because climate science is still in its infancy (and that is why there are so many free parameters!) I cannot declare them an absolute bust as I can with my roulette models.

Using the models to establish some sort of Law or theory of climate science is so arse about that I might as well use my roulette models to create a new theory of probability!

However, whilst they might provide talking points and allow you to draw up some interesting possible scenarios why would anyone imbue them with great credibility, notwithstanding that the math might stand up, when so many free parameters are in play?

Like the Nikolov and Zeller paper, the math may appear ok but with so many free parameters, how much trust can you have in the outcome?

Not a great deal in my opinion.

Like the climate models the paper makes some interesting talking points is it anywhere near proof of anything?

Well like the GCMs clearly not.

Alan

You don’t need to look at the math to see that the authors might be pushing their luck with equation (8). You just need to look at the graph and the number of points and the fact that several have no atmosphere anyway. I don’t think there is enough data or evidence to say they are right.

I don’t think there is enough to say they are wrong, either. They could be right, but there is insufficient evidence, so claiming it as a result is premature. Personally, I don’t care, because I don’t plan to live on any of these other planets or moons. However, I am very concerned about the earth and I truly believe that the AGW crowd have got it badly wrong. I can see some merit in the ATE effect and I find it disappointing that we are not debating the important stuff.

Willis is right. Obviously.

AM> So what is the difference between the the two sets of models?

Part of it is: if you take the GCMs code, and the correct initial conditions, they will predict tomorrow’s weather, or next week’s weather, for you.

@George E. Smith

> Well John, If YOU think I am “hung up” on anything

> you are sadly mistaken; and it is obvious that you

> have never pumped up a car or bike tire with a hand

> pump.

> The act of reducing the volume of a fixed mass of gas,

> requires applying a force …

Yes, I think I understand the ‘heat of compression’. What I meant was that your ‘hang up’ seems to be that you think ‘heat of compression’ is what N&Z is all about.

> If the container of gas DOES NOT COOL DOWN as YOU

> seem to say it won’t …

No, I didn’t say that. If you remove the source of heat (i.e. sun) the system will cool down. And yes, if you restore the source of heat, the system will get hotter. But it doesn’t matter. Read on.

What you (and the others) are not grasping is that the specific details about any

radiative heating/cooling mechanismis not needed to understand how pressure establishes temperature via the Ideal Gas Law. I again invite you to read the derivation of gas law, which shows how, at the atomic temperature can be calculated at the molecular level using only Newtonian mechanics and the equi-partition theorem. Do we agree that this derivation is correct?http://en.wikipedia.org/wiki/Ideal_gas_law#Derivations

Note that there is no reference to radiation energy here. Surprisingly, no mention of collisions either, but implicitly necessary because dp/dt would be zero otherwise. If momentum doesn’t change then there can be no forces, which establish pressure, which cause the molecules to repel each other and try to expand the occupying space.

Yes, the sun (and other sources of energy) are supplying the energy needed to “motivate” these molecules. But do you see that, at this level,

we don’t care about the sources of energywhen applying the idea gas law. We just accept the system, as is, with the “particles already in motion”. (Mostly by transferring heat from surface, but I digress, we don’t carehowthis happens, only that it sets the molecules in motions with a Boltzmann distributions of speeds.)And from that we derive pressure (and volume by integrating the divergence) from temperature, or vice versa.

Yes, we can assume regard the Earth as an “isolated system in equilibrium”, and its atmosphere as being sufficiently ‘ideal’ (TBD) and by using the concept of ‘local equilibrium or by picking a long-enough epoch of time or space such that the average pressure suffices to describe the dynamics of the system. (How else could we discuss the ‘temperature of a system’ that is not in equilibrium).

Yes, the sun is pouring in energy all time. But the Earth radiates it back into space (at a different wavelength of course) such that EnergyIn = EnergyOut. (Otherwise we would have ‘runaway heating’ which we both agree doesn’t exist. right?) So, we have equilibrium (more or less) in that sense.

But that’s not complete N&Z theory (which will be further elaborated in Part II). But it seems to be a reasonable starting point for the theory.

Note that I’m not claiming the entire theory is correct. I don’t know all of the details either. But I think this theoretical foundation is sound enough to let these guys explain it with out a lot of jeering and insults (about their curve-fitting etc). Let’s take a respectful wait-and-see attitude. OK?

Stay tuned and grab some popcorn George, this is going to be fun.

[Ned and Karl. Have I got your N&Z foundation “approximately correct”?]

OK, so clearly writing so long a reply (and actually doing the work in it) made it too difficult for people to see or read down to, so let me simplify. N&Z’s “miracle equation, written in dimensionless form, is:

\[N_{TE} = exp( (P/54000)^0.065 ) * exp( (P/202)^0.385 )\]

(sorry for the two forms, by Andrew said WordPress might grok inline latex and I’m testing as these are both actual latexisms and might render the equations correctly — if it works).

[COMMENT: Robert, I fixed the first one. To enter latex into wordpress, start with “$ latex” with no space between the two, and finish with “$”. One oddity is that you need braces around numbers containing a decimal point. –willis]

In this expression, there are two reference pressures, given

in bars. The first is 54 Kbar, the pressure one might find at the bottom of a column of water roughly 8% of the radius of the Earth in height. The second is 202 bar — not quite so bad, but more than twice the pressure found on the surface of Venus, the planet on the list with the heighest surface pressure.Neither of these dimensioned numbers — which

absolutely have to be the result of a reasonable derivationif N&Z’s “fit” is to be meaningful — has any possibility of being relevant in any way to climatology. They are bullshit. Willis was too kind — the reason this part of N&Z’s result is wrong isn’tjustbecause it is a four parameter fit of an absolutely arbitrary functional form — it is that when one makes the arguments of the exponential dimensionlessas they must bethe characteristic pressures that emerge are absurd.N&Z’s fit is the

oppositeof good physics. They didn’t even do the elementary dimensionless analysis that would have revealed that their fit contains numbers that could not possibly have the slightest bearing on the temperature of the nearly airless planets. What this function does is fit the airless planets (with a non-physical but monotonic function in P, the one with the 54000 in it). This function ranges from 1 to 2 over the range of pressures given (presuming one can meaningfully speak of a mean “pressure” on the surface of the moon or mercury). The second function is 1.02 for Mars (at a pressure of 0.01 bar, which is really on the high side). It is basically 1 (to three significant digits or more) for all of the moons and smaller planets.This explains how N&Z get a good fit to eight data points with only four parameters. All the “airless” planets have almost no atmosphere and their surface temperature compared to some arbitrary parametric baseline is a very weak function of the pressure — so weak that increasing the pressure by six orders of magnitude on the low end of things makes only a 10% or so change in $N_{TE}$. The mechanism that keeps Mars, Earth and Venus warm, OTOH, appears to be

totally different!The second term fits only these three planets — really only the last two, as 1.02 for Mars is a 2% shift and ignorable. So lessee, can I fit a two point monotonic difference function with a two parameter exponential that is basically “one” at the baseline/origin (Mars) and all pressures below! I believe I can! I bet I can do a really, really good job, too, with at most 2% total error to split three ways!There is one very important lesson to be learned from N&Z. I mean aside from “check your dimensions and answers to make sure they are physically reasonable before publishing them”. There

doappear to be two very distinct physical mechanisms at work here, comparing nearly airless planets to ones with actual atmospheric pressures large enough to keep your blood from boiling. Could they have discovered — gasp — thegreenhouse effect?Naaaaahhh, not on this website, not with all the people who are still in a state of abject denial that the greenhouse effect exists at all

in spite of the top-of-atmosphere IR spectrum measurements of it in operation.I’ve said it before, and I’ll say it again. Being “skeptical” about the

existenceof the Greenhouse Effect is really pretty stupid. We have one very important thing that Arrhennius didn’t have — satellites with IR spectrometers. I don’tcarewhat mechanisms create the thermal profile of the atmosphere compared to the surface. Thefactthat the mean temperature of the Earth is established as balance between incoming radiation and outgoing radiation, thefactthat emission in the CO_2 band is in approximate thermal equilibrium with the top of the troposphere (that is, “cold”) means that the emission from the surface in the water window has to be higher than it would have been with no atmosphere at all, to keep flux balanced. That means that the surface temperature must be higher. Done. End of story. The GHE is “real” — you read it right off of the IR data.I’m not asserting that it is the

onlything going on. I remain open minded about the effects of convective mixing and so on, although I adamantly reject the argumentsso farthat attempt to assert that “gravity” causes some actual warming. I’m open minded about additional sources of free energy. I’mveryopen minded about modulation of the GHE and its (probable lack of) sensitivity to CO_2 concentration — the same satellite data suggests that the only way increased CO_2 could increase surface temperatures is by literally lifting the tropopause, and we’re talking about changes ofhundredths of a percentin volume concentration, with a higher molecular mass, in a three-D atmosphere with an enormous base volume and mass, nearly all of it concentrated well below the tropopause. Then there are all of the negative feedbacks.It is important to differentiate between CAGW, AGW, and GW from all other mechanisms. CAGW is (IMO) very, very unlikely. The large climate feedbacks proposed to lead to disaster are increasingly contradicted by the thermal record. AGW is not unlikely at all —

someresponse to increased CO_2 is a very reasonable hypothesis, although it could be far smaller than simple arguments might suggest, especially if overall feedbacks arenegative, as the overall stability of the climate suggests. Finally, the GW from all other sources is a very interesting question. I don’t really mean “warming” compared to an imaginary baseline “no atmosphere” temperature, I mean that the actual atmosphere with all of its nonlinearities, driven convection, contact with a heat-storing ocean withitsnonlinearities and driven convection, and dependence on solar state has large temperature fluctuations clearly visible in its past thermal history, fluctuations that are poorly understoodnoisethat is at least of the same order of magnitude as any possiblesignalof AGW. This confoundsanyattempt to make overreaching conclusions based on observations of the thermal record only.Here’s a very nice way to put it. If the thermal trace of the last 1000 years, and the solar data for the last 1000 years, were given to someone, would that person be able to infer the CO_2 concentration from the data? What about the last 10,000 years? What about the last 1,000,000 years?

I’d have to say that the answer is

categorically no. The temperature goes up. The temperature goes down. The greenhouse effect is clearly visible in that it never goesall the way downto where it would be without it, but there are fluctuations that are within a factor of 3 or 4 of equalling thetotal temperature shiftassociated with GH warming in the “standard” view. CO_2 (when one addsitin my means of proxies) does seem to fluctuate with temperature but as afollowerof secular changes, not as a leader (through understandable mechanisms, actually).That’s why I think that looking for atmospheric and solar mechanisms that can produce \Delta T fluctuations

on the order of1-5 K is really rather worthwhile. We know that they are there — a glance at T(t) over any time scale longer than two centuries reveals them, pretty much no matter where you are in the thermal record. N&Z are focussing on trying to explain “the big \Delta T” — the one associated with the real GHE — without it. A far more reasonable thing to do is to understand why and how the atmosphere and Sun and ocean can dynamically interact to flip the Earth into a multitude of locally stable states with temperatures that can differ by (smaller but still large) \Delta Ts quite independent of CO_2.Absolutewarming due to CO_2 could be signal, sure, orit could be noise!Specifically, it could be negligible compared to natural processes that make the temperature go up or down by a lot more than changes in CO_2 concentration, and negative feedbacks in the larger oscillations could evencancelmost of any secular increase.rgb

William M. Connolley says:

January 24, 2012 at 7:08 am

“AM> So what is the difference between the the two sets of models?

Part of it is: if you take the GCMs code, and the correct initial conditions, they will predict tomorrow’s weather, or next week’s weather, for you”

So I could run GISS model E initialised with todays conditions and get next weeks weather could I William?

You sure about that?

Anyway very nice of you to take time off, from your job of buggering up Wikipedia, to take part in the debate.

Alan

William M. Connolley says:January 24, 2012 at 7:08 am

Willis is right. Obviously.

Here’s a nice example of the kind of supporter Willis (and WUWT) is going to be left with.

if you take the GCMs code, and the correct initial conditions, they will predict tomorrow’s weather, or next week’s weather, for you.Lol.

And of course, next years, and the year 2100.

“Pass the Koolade Bill.”

I’m glad to see discussion of the statistical aspects of this problem. However, I have to point out that thus far this discussion has been somewhat stunted in its content.

While it is true that one needs “datapoints” to build and test a model, it is more precise and revealing to call them “observed events.” The observed events are a subset of a complete set of statistically independent events or “statistical population” belonging to a study.

The “predictions” of a model are extrapolations from conditions defined on the model’s independent variables to the outcomes of the events in the population. Thus, the predictions bear a one-to-one relationship to the elements of the population. The model is tested by comparison of the predicted to the observed outcomes in a subset of the observed events that is reserved for testing.

By climatological tradition, the methodology of a climatological study fails to identify the statistical population and the model fails to make predictions with the consequence that the model cannot be tested. It follows that the methodology is not a scientific one from the lack of testability of the model. To join climatology to the sciences, we need to turn this situation around.

Nick Stokes says:

January 24, 2012 at 3:23 am

Story just gets better.

w.

Willis Eschenbach says:

January 24, 2012 at 9:09 am

Nick Stokes says:

January 24, 2012 at 3:23 am

“that still leaves four parameters and eight data points”

It’s only six data points. If you look at the table in their original post, they didn’t try to fit the Moon or Mercury.

Story just gets better.

w.

And note from my argument (and a bit of actual arithmetic, sigh), one of the two forms fit is “one” for all but two points. So really what they have done is joined two fits — an exponential that is 1 for mars and pressures below but a two-parameter fit of Earth and Venus that is as “miraculously” good as you like — I think I could make it 100% accurate with algebra and a hand calculator, but that’s just me, trying to fit an arbitrary two parameter monotonic function that can be made to cut off arbitrarily sharply for pressures below a cutoff with two data points, or I could let a routine split the 2% maximum error up among Mars, Venus and Earth.

The three moons — all with very similar insolation and atmospheric pressures — and Mars are then fit with the two remaining parameters (the ones where 54 Kbar is the characteristic pressure). And look at the exponent! 0.065! It can transform even a tiny number into a big one! Talk about sensitivity…

rgb

Lucy: Your comment is the only one I feel comfortable with at this time. The push-pull of people absolutely convinced of their correctness has become noise. There are many who already treat this matter as settled. It reminds me that perhaps I am getting too old and too far behind the 8 ball to play with emerging science. I look forward to your slow thoughtful analysis and your calm spirit. GK

Lucy Skywalker says:

January 24, 2012 at 3:38 am

You “get the feeling”, do you? Sadly, from the rest of your post, your science has come down to just that, following your feelings.

Lucy, thank you for commenting. I don’t know what you are reading, but Jelbring is easily shown to violate conservation of energy. Believe my

or not, Jelbrings claim that gravity magically separates hot and cold air into two piles is a joke.analysisA process that separates air into hot and cold with no energy input? That’s magical thinking, “something for nothing” thinking, “I feel it’s true” thinking, not scientific thinking. That’s a “Maxwell’s Demon” claim. And all of your “feelings” can’t turn it into something real. Let me be perfectly clear here. Anyone who believes Jelbring after reading my analysis and Robert Brown’s analysis and the comments of the other scientists here is a scientific newbie. A naif. A babe in the scientific woods. Someone who failed their logic class. A Pollyanna. Someone whose heart over-rules their head. Truly, we’re not talking rocket science, disproving the Jelbring hypothesis is

routinely given as an exercise to first year physics students…So … you can go on all you want about how many scientists believe Jelbring and how many skeptics are “diverting to tallbloke’s threads”. I’m sure there are hundreds of gullible folks doing just that, it doesn’t surprise me one bit. As H. L. Mencken said, “No one in this world has ever lost money by underestimating the intelligence of the great masses of the plain people.”.

I’m just saying … don’t sell your physics textbooks quite yet, because as much as you and the others might want Jelbring and N&Z and the others to be right, wanting them to be right is not sufficient.

w.

I lean to tallbloke’s understanding over willis’. There is way too much smug nitpickery in willis’ ‘analysis’ and not enough straight-talk. The kicker for me is his complaint that both sides of an equation actually equal one another — his ‘Ts = Ts’. eGads, he knows better than to pull that one out of the junk pile — after all, that’s why they call these things equations.

My suggestion is to read the threads over at tallbloke’s to get wider and less prejudiced view of N&Z.

Note to Willis: I grew up that that ‘Bill’ you mention (or his clone with the same name) — we pulled off some wild scams and conns together, what great fun it was. 🙂

Robert Brown said @ January 24, 2012 at 4:34 am

It’s a shame that this

neededto be said. But well said anyway.I have commenced reading Lilith. You are a talented man, Robert.

@Robert Brown: I think you put latex in like so: $\latex n^2$. If that worked, it is dollar signs around latex, with a backslash latex adjacent to the opening dollar sign. If it didn’t work…

@Robert Brown: Oops, there should be no backslash on the latex, according to WordPress docs: .

tallbloke says:

January 24, 2012 at 3:39 am

My point exactly. It’s actually has nothing to do with the various planetary bodies:

It’s not the even albedo from the moon. Here are the albedos from the paper, along with the corresponding t5 parameter if we used that albedo …

These albedos range from a low end of 0.11 for the moon’s albedo to 0.75 for Triton’s albedo. The corresponding value for your parameter t1 ranges from 24.5 down to 18.6. And as a result, your value for t5 of 25.3966 is, as I said, a tuned parameter and not the “result of combining 4 constants” as you claim.

However, their use of one albedo for all bodies should make you stop and think hard about their claim, tallbloke … because it brings up a critical question—

why would calculating Venus’s temperature with the moon’s albedo come out correct?Answer me that riddle, and you’ll be well on your way to understanding the problems with tuned parameters.Thanks for the invitation, but as I said before, I wouldn’t increase your page view count by one. You don’t do science there, tallbloke, you have joined RealClimate and Tamino in banning people for their scientific opinions. I don’t visit those sites either, why on earth would I want to visit any place that censors scientific opinion?

And given N&Z’s ludicrous claims about their MAGICAL equation … why would I want to continue down their path, whether on your blog or not? Look at the update to the head post, tallbloke, where I show that I too can spin straw into gold with a simple equation … the difference is, they actually believe and passionately defend their equation, they think it means something … whereas I know that both mine and theirs are just trivial curve fitting.

So why would I want to inquire further into N&Z’s theories? Someone who doesn’t even understand the bozo-simple concept of “overfitting” is not someone whose other work I want to waste time on.

w.

Uh-huh. And how many GCMs will you need to “sample” before you find one that’s right about tomorrow or next week? And what are the odds the same one will be right for the next “prediction”?

(I note the ambiguity in your grammar. Did you mean “the GCM’s code” or “the GCMs’ code”. The latter is the plural possessive, which you seem to be referencing with “they”. Since their authors claim they are just “projecting” the effects of tweaks of various parameters and make no effort to match initial conditions, the chances of any one being right about next week’s weather for the right reasons is vanishingly small.)

N&Z, I believe, are quite explicit in disclaiming any intention or ability to “predict” weather or climate, but are establishing, they say, that the baseline temperature of a planet is the result of the mass of its atmosphere (the sole actual determinant of pressure). Since that doesn’t vary over less than geological time, it is not, as they state, responsible for short-term swings. By the same token, GHGs are not responsible for the prevailing “baseline” climate.

tallbloke says:

January 24, 2012 at 3:47 am

So let me see if I’m following this. Your claim is that there is not a single tuned parameter in equation 7?

w.

@Robert Brown: Thanks for your contribution here. The discussion is enormously better for it. I just started participating in these discussions with the recent posting by Bob Tisdale, which had some serious statistical misunderstandings in it, so appreciate reading good reasoning that also teaches me something.

As an illustration, one of the several problems of F&R 2011 (the topic of Bob’s article) is assuming in their model that independent variables would affect the dependent variable after exactly an N month lag. I suspect that non-multiple-of-month cycles would be obscured with monthly averages, but more importantly they didn’t consider that input X might affect the dependent variable for several months. So I found an R package that does Distribute Lag models (which seems to fit the question) and tried modeling with that.

With DLNM’s I was able to get roughly the same adjusted R-squared as F&R’s model, even though I did not include a time trend. Woot for me! Except… the results were not physically plausible. The curves all fit nicely, but the meaning of the results didn’t make sense, so all I’d done was a bit of a parlor trick.

OzWizard says:

January 24, 2012 at 3:48 am

I discussed the derivation of equation 2 over on the comments thread. It is (as far as I can tell) a reasonable estimate of one way to calculate “graybody” temperature, corresponding to a certain set of assumptions about how that imaginary planet would be different from its current state.

However, I see nothing in it to cause a “paradigm shift”. There’s nothing in there that invalidates anything about the theory of the greenhouse effect. It’s just a different definition of a “graybody temperature”, it doesn’t affect a dang thing about the theory.

w.

richard verney says:

January 24, 2012 at 4:02 am

What it means is that 1) the authors are clueless about mathematical models, about fitted parameters, and about overfitting, and 2) so are all of their friends who read and discussed their ideas before they were published here.

Does this mean that they are wrong? Of course not. It just means that they are clueless about math and models, and they hang out with similarly clueless people. Sure, they could still be right … but it doesn’t improve the odds.

While your heart does you good in that paragraph, it doesn’t say a lot for your brain. Are you claiming that Zeller didn’t know what a MIRACLE is? I doubt that greatly. But set the exact wording aside, Richard, and consider his claim. Clearly, he thinks that the result of a fitted equation with four or five parameters is hugely, world-shakingly significant.

Spare me …

w.

Taking pressure to the powers of 0.0651203 and 0.385232. That’s… interesting.

This constant usage of the words “MIRACLE” and “MAGIC” as well as “PERPETUAL” are not helpful. They are an attempt, to lead people to a dismissal of facts presented, without due consideration. They are disrespectful and can be easily dropped. Let’s try reasoned arguments using reasoned words. I don’t care who first started using them. GK

Kip Hansen says:

January 24, 2012 at 9:30 am

So you judge your science, not on what you think of it, not on what someone else says about it, but on

whether you like the styleof the people that are commenting on it. Not their science, but their style. You think you can tell good science from science with mathematical errors in it based on whether the person explaining the error indulges in “smug nitpickery”.OK, so you don’t consider the underlying issues yourself, instead you judge science on the optics of the presenter of the idea. Good to know that for when you next comment.

w.

PS—I pointed out that what they have done in the right side of the equation is to approximate the equation Tgb * Ts / Tgb so that people could understand what they have done. It looks like some random equation with a raft of fitted parameters and a couple variables. But at the heart it is only Tgb * Ts / Tgb.

My complaint is not that they have done that. That’s not a problem. The problem is that they have used 5 fitted parameters and (as Robert Brown points out) a very cleverly designed algorithm to do that, which means that they have not done anything worth paying attention to. With that many parameters it is easy to hokey up an estimate of Ts. But if that estimate is meaningless as theirs is, you’ve done nothing more than show that Ts = Ts.

Robert Brown says:

January 24, 2012 at 9:17 am

Interesting analysis, Robert. I tried to untangle what their use of two functions of the same variable might be doing, but I couldn’t see it.

Folks, Robert has pointed out an important thing. By using two functions of the pressure, what they have done is to provide what is essentially two equations spliced together, one of which covers the Earth and Venus, and the other of which covers the rest of the planets. Quite clever of them, actually, but of course at the end of the day it is as meaningless as my fitting of an equation using Tgb, pressure, and gravity to the temperature data.

w.

Lucy Skywalker says:

January 24, 2012 at 3:38 am

“I get the feeling that there are a number who can see Willis’ limitations who are no longer coming here to post.”

Yes, their goose has been well and truly cooked by Willis’s article, their fox has been shot. Anyone with a basic knowledge of science, or in this case,just basic mathematics, is aware that when the number of ‘fudge factors’ exceeds the number of unknowns then any ridiculous proposition can be formalised. It isn’t really a ‘Miracle’. Well done Willis – that’s what I call a game-changer.

Lucy, have you ever thought that you and Tallbloke do harm to the sceptic cause by promoting nonsense?

Apart from that you made a good post Lucy, I see that you write well – maybe you should seek a career down that path. Have you ever tried fiction or fairy stories?

Oh – just looked at your website! Good luck.

Robert Brown says:January 24, 2012 at 9:17 am

And note from my argument (and a bit of actual arithmetic, sigh), one of the two forms fit is “one” for all but two points. So really what they have done is joined two fits — an exponential that is 1 for mars and pressures below but a two-parameter fit of Earth and Venus that is as “miraculously” good as you like — I think I could make it 100% accurate with algebra and a hand calculator, but that’s just me, trying to fit an arbitrary two parameter monotonic function that can be made to cut off arbitrarily sharply for pressures below a cutoff with two data points, or I could let a routine split the 2% maximum error up among Mars, Venus and Earth.

The three moons — all with very similar insolation and atmospheric pressures — and Mars are then fit with the two remaining parameters (the ones where 54 Kbar is the characteristic pressure). And look at the exponent! 0.065! It can transform even a tiny number into a big one! Talk about sensitivity…

Agreed, the obvious reason for the pressure dependence of Earth and Venus is the pressure dependence of their atmospheric absorption/emission due to pressure broadening of the absorber/emitter spectral lines, far from falsifying the Greenhouse theory this result is what would be expected. The GHE is amplified by pressure (no surprise to anyone who understands the physics)!

Willis Eschenbach writes:

neither my emulation nor N&Z’s emulation of the planetary temperatures are worth a bucket of warm spit…I agree with you regarding the quality and value of your input.

kdk33 said @ January 24, 2012 at 10:02 am

What utter tosh! Water at the bottom of the ocean is denser than water at the surface at the same temperature. From the Wikibloodypedia:

Alan Millar says:

January 24, 2012 at 7:53 am

William M. Connolley says:January 24, 2012 at 7:08 am

“AM> So what is the difference between the the two sets of models?

Part of it is: if you take the GCMs code, and the correct initial conditions, they will predict tomorrow’s weather, or next week’s weather, for you”

So I could run GISS model E initialised with todays conditions and get next weeks weather could I William?

No! But you

can“Forecast the…er…Facts”. Naturally, being a Great Sophist*, William doesn’t say whether the “Facts” will turn out to beempirically corrector not. And why bother, when prediction success is not his goal to begin with?*Note to William, there aren’t any…

It seems so painfully familiar it got me wondering if either Nikolov or Zeller ever wrote a textbook for fluid mechanics?

Nitpickery, whether (considered) smug or not, is what is called “The Scientific Method”. You present your idea, all the methods and data you used to verify that idea, to the public, and they then try and “pick” it apart (try it themselves, see if it works). This is known as “falsification”, if it succeeds, your idea is partially or completely wrong and you go back to the drawing board. Pride often causes people to not acknowledge that it is time to start over. Pride is the enemy of science, too much pride and we would still be using stone tools (if that).

The actual main reason Galileo was put on trial for “heresy” was because of his style. He constantly insulted his detractors, and so they wanted to hurt him. This is also shown by recent scholarship that shows that the church itself was actually on Galileo’s side. The entire scientific method was invented to get around the problems of people choosing style over substance. Before the method was used, it was

allstyle, you decided what the natural world was like based on who had a better styled argument on which Old Dead Greek Guy was right and which was wrong. I, for one, would rather have “nitpickery”, whether smug or not, with substance, instead of lack of or incorrect substance no matter the style. If you prefer style over substance, you will be taken in by con artists a lot, you can even take yourself in this way. You will note that in the end, everyone has come to believe Galileo despite the fact that he had terrible style (his nitpickery was very smug).Just as an aside, what Napoleon then followed his preferred generals statement with was “Good generals make their own luck”. Setting things up so that you are more likely to get a lucky break (walking down seventh street when you suspect you might get into a fight on third street), being able to spot that break, knowing what to do to take advantage of it (perhaps already having set things up so that you can do so), and doing so fast before it gets away, are what he is talking about. The set of people who have had luck presented to them is greater than the set of people who have taken advantage of it (and possibly arraigned things so that it could happen) and been called “lucky”.

malagaview says:

January 24, 2012 at 12:02 pm

So your contention is that the N&Z emulation of planetary temperatures is in fact worth a bucket of warm spit?

I do love people who come by with only venom. No numbers. No ideas. No logic. No insights.

And more than anything, no attempt to falsify, contradict, or even clarify or expand on a single thing I or anyone else has said.

Just venom, pure and simple. What a life, go around and dribble your toxic thoughts on a variety of websites, don’t contribute a thing, just make a nasty comment and move on.

Oh, well. Here, we do science, malagaview. Try it, you might like it.

w.

Regarding the difference between the parameters in climate models and the parameters in a simple empirical model:

There is a big difference. A simple empirical model is designed to fit one particular piece of data and as such the empirical form is designed to do this. Climate models are designed totally differently: They are designed to emulate the atmosphere mechanistically. Their parameters are of an entirely different sort.

While von Neumann statement about free parameters is true for properly-chosen free parameters, it is also true that I could give you a function with 1 million free parameters that nonetheless could still not fit some very simple data.

And, the proof is in the pudding: Despite the fact that you have close to 20 climate models out there, none of them have been able to successfully fit the historical global temperature record without anthropogenic forcings. Even if you believe in a mass conspiracy theory that has prevented any groups from trying to do this or reporting a successful result of doing this, you have models in the public domain that any “AGW skeptic” could use to disprove my statement.

Now, there is one point worth noting: Since the forcing due to anthropogenic aerosols is a big unknown, it is true that models that include anthropogenic forcings that have different climate sensitivities can do equally well in reproducing the global temperature record by having different aerosol forcings. This is the reason why, in practice, the historical global temperature record does not constrain the value of the climate sensitivity that well.

So, despite the fact that the climate models tell us that the global temperature record can’t be reproduced without anthropogenic forcings, this record does not do that much to constrain what the climate sensitivity of the models has to be in order to get a good fit. Climate sensitivity is better constrained by other empirical data and most significantly by a combination of all empirical data available. Such data includes paleoclimate data (especially the Last Glacial Maximum)), data from major volcanic eruptions like Mt Pinatubo, and data on the present-day seasonal cycle.

[SNIP: Dr. Nikolov: I’d like to believe that you would have second thoughts about this. Could I ask you to, uhhh, rephrase this? -REP]

Joel Shore says:

January 24, 2012 at 1:31 pm

Yes, and that’s an exhaustive exploration of the climate model space … NOT. What we have is a number of models built on the same principle by people who believe the same things and that sometimes share chunks of code. The idea that your theory is right because your models can’t replicate the past is typical of the circular reasoning of AGW supporters.

This is PARTICULARLY TRUE OF TUNED MODELS, as you well know, Joel. You are seriously proposing this procedure:

1. You take a model which has been carefully tuned to replicate the past using inputs a, b, c, d, and e.

2. You pull out input “e” and note that the model does poorly without that input.

3. You conclude that “e” is a valid and necessary part of the system that the model is trying to represent.

So no, Joel, I’m not at all surprised that when you take half the forcing out of a tuned model, it doesn’t do well, and neither should you be.

That’s the problem with tuned models, just as in the tuned model in equation 8. Here’s a great example.

In my model above, I used gravity, density, and Tgb. Now, if I pull out Tgb and leave the rest unchanged,

a) will the fit get better or worse?

b) will the difference in the fit mean anything at all?

You see the problem in your claim, I’m sure.

w.

I admire your patience Willis. Good work.

I suspected something was very wrong when they claimed that the mean temperature of a planet is not affected by the uniformness of the temperature. That is simply not consitent with the non-linearity of the Stefan-Boltzmann law.

Willis: Strange then that neither you nor any other skeptics have ever taken me up on my challenge to “retune” the models and show how you can fit the historical global temperature record without the anthropogenic forcings! At some point, the people who claim this is possible have to demonstrate it, no?

That is why I went through the trouble of demonstrating a specific case with N&Z whereby I did change the data (by artificially lowering the surface temperature data for the 3 celestial bodies that had a significant radiative greenhouse effect back down to the conventially-calculated blackbody emission temperature) and then I retuned their model and showed how it still fit this changed data! If you did the same thing with a climate model, you might have a convincing case. In the absence of doing so, not so much!

This should help….

http://www.cs.northwestern.edu/~ago820/cs395/Papers/Heckbert_1987.pdf

> 1. You take a model which has been carefully tuned to replicate the past using inputs a, b, c, d, and e.

No, that isn’t how GCMs are built. It is funny, that as soon as you stray away from the stuff you know about, you go hopelessly wrong.

Legatus said @ January 24, 2012 at 1:06 pm

[several things I must agree with]

but…

We believe Galileo where he was correct. Unfortunately, Galileo was a man of

greatstyle and relished being the life and soul of the party in an era without television. He promoted, in his subsequently banned book “Dialogue Concerning the Two Chief World Systems”, the idea that tides were caused by the rotation of the Earth contra Galilean Relativity, and insulted the Pope in the same book. It’s worth noting that Galileo wrote inside his own copy of the book that he knew his tides argument was utter balderdash (paraphrasing here).Immediately before this, Galileo was also embroiled in a vicious dispute with the Jesuit astronomer Fr de Grassi. de Grassi had demonstrated that comets occupied space between the Earth and sun; Galileo insisted they were an atmospheric phenomenon. Galileo had engineered his own downfall by alienating his friends such as the Jesuits and the Pope, and playing into the hands of his enemies The Pigeon League. [/nitpick]

“By using two functions of the pressure, what they have done is to provide what is essentially two equations spliced together, one of which covers the Earth and Venus, and the other of which covers the rest of the planets.”

This makes me less impressed with their curve-fitting abilities. It’s the trivial way to get to what they want:

1. create a curve that maps one subset and is 0 elsewhere

2. create a curve that maps the other subset and is 0 elsewhere

3. Add the two curves. We have a curve that maps everything!

Of course, they’ve used the exponential version of this recipe:

1. create an exponential curve that maps one subset and is 1 elsewhere

2. create an exponential curve that maps the other subset and is 1 elsewhere

3. Multiply the exponentials. We have a curve that maps everything!

Terry Oldberg had some good points about the statistics involved. When fitting curves, It is necessary that one use up any and all available datapoints, so that nobody can take your curve and map it to an observed event that you’ve missed.

I can’t wait until scientists manage to measure the irradiation, surface temperature and surface pressure of another planet. Then we’ll be able to see how equation 8 stacks up. Personally, I’m not confident that it will stand strong.

Joel Shore,

How well do the models do when the aerosol OR solar forcing is taken out??

Oh yeah, they are tuned to have all those forcings!! Snicker.

Joel Shore says:

January 24, 2012 at 2:14 pm

I’ll do it in a hot second, Joel. Of course, you’ll provide the model, the supercomputer, the graduate assistants, the programmers, and the funding, no?

Joel, that’s just a red herring. If you take a tuned model and pull out one or more of the inputs, it will do worse than with all the inputs.

You know that. I know that.

Your statement is the equivalent of “If I pull the anthropogenic inputs out of the climate models, then they can no longer hindcast the planetary temperature, and that shows that humans cause warming”.

Now, this is the important part. That is

exactly the sameas saying “If I pull the Gravity inputs out of Willis’ model, it can no longer predict the planetary temperatures, and that shows that Gravity causes warming”.In neither case does it mean anything.

It means nothing that my model can successfully and exactly hindcast the planetary temperatures. It is tuned to do that.

It means nothing that the climate models can successfully and kinda closely hindcast the planetary temperature. They are tuned to do that.

It means nothing that my model cannot hindcast the planetary temperatures without the Gravity term. It doesn’t mean that Gravity causes planetary temperatures.

It means nothing that climate models cannot hindcast the planetary temperatures without the Anthropogenic term. It doesn’t mean that us anthroposubgeniuses cause planetary temperatures.

So let me request that stop bringing this bogus “test” up as though it proves something. It means nothing. You can’t have it both ways, Joel. You can’t bust H&N for a fitted model and then say fitted climate models are probative.

For those who claim that the models are not tuned, see

for the results of the tuning. Here’s the odd part. All the models give very different results for climate sensitivity. At one end, some say the climate is very, very sensitive to forcing, up to six degrees for a doubling.KiehlOthers say much less, down in the 1.5 – 2 degree per doubling range.

Yet all of them, each and every one, does reasonably well at hindcasting the global temperature. They all disagree greatly about the future, they are terrible at hindcasting precipitation, but lo and behold, they can all hindcast planetary temperature as accurately as H&N can.

Strange, that. What are the odds that by chance they would be so widely different on a basic parameter like climate sensitivity, and they would disagree so widely about what the future holds … and yet they would all be able to hindcast the historical record so well?

Joel, if you think that can happen based on physical principles without tuning, I’m not sure what to say except, read Kiehl. There is a good discussion of the implications of Kiehl’s paper (2007)

.herew.

Joel Shore: “Strange then that neither you nor any other skeptics have ever taken me up on my challenge to “retune” the models and show how you can fit the historical global temperature record without the anthropogenic forcings!”

You have a climate model that can fit the historical data for more than a few hundred years? Got a charted sample of that somewhere?

WIllis, it does not surprise me that a “cowboy” like you was one of the first to spot

bullshitwhen you saw it. Great work on this Topic thread, I no longer give any scientific credence to the work of N&Z. THANKS!– Ira

John Marshall says: “…Jupiter, with its atmosphere of hydrogen and helium, radiates more heat than it receives. since there are no GHG’s in the Jovian atmosphere there must be another mechanism to create that extra heat and that must be gravity.”

No, there’s plenty of methane in Jupiter’s atmosphere, so wrong on that count. The extra heat may be from Uranium or other radioactive elements in the core, so your last “must” is wrong, too. Some say there may be some fusion, too, but we lack evidence of that.

Uh, Willis:

Perhaps the BEST empirical evidence for the NZ ideas is presented by Huffman, concerning his treatise on the origin of the temps on Venus. Whose treatise you evidently have completely discarded, IIRC, by stating that it “gives you a headache!” Oh, yah, W., that’s a very scientific reason to ignore him, indeed! (Could the “headache” be caused by the Confirmation Bias Syndrome?)

You (as well as all the other self-proclaimed “experts” here, BTW, including, especially, the expert-sounding Brown, Joel, et. al.) seem to carefully ignore Huffman’s proofs. But in all fairness and honesty, maybe it’s time that you tried to discredit his empirical data for Venus, also? If you do that, then I think you will have also proved NZ wrong, and I will admit I’m also wrong. But not before, I’m thinking…

And beyond all this physics, which I admit is over my head, we have no evidence AT ALL that increases in GHGs have ever caused increases in temperature. The present era is a very good example. Where’s the beef?

Ira:

“WIllis, it does not surprise me that a “cowboy” like you was one of the first to spot bullshit when you saw it. Great work on this Topic thread, I no longer give any scientific credence to the work of N&Z. THANKS!

– Ira”

REAL scientific conversation in action, Ira. LOL. It could easily be in the Climategate emails!

Konrad Hartmann ran a nice little physical experiment at Tallbloke’s showing the relationship between pressure and temperature in the presence of a radiative source. This should help the understanding of the tire pumpers, like George Smith.

Regarding the curve fitting issue, Wilis seems to be of the opinion that some number of parameters, X, automatically becomes an overfit. I agree with John Day. It depends on what is being modeled and how convoluted the thing that one is fitting to is. In the case of an almost random walk looking data set, like historical temperature, pushing the number of parameters to force the fit is a problem. I don’t see that N&Z are doing that. They are not fitting an elephant. Still, there is a problem with the number of parameters. It could be that their model is wrong and that their results are only due to overfit. But it could also be true that their model is right, in which case the number of parameters do not make it wrong, as Willis seems to think.

From my perspective, N&Zs main point is that higher pressure means more gas density which in turn means more captured radiative energy which then means higher temperature. I can’t see how Willis’ quibbling about curve fitting helps with proving or disproving that idea. Konrad Hartmann’s experiment, however, is a real contribution.

LazyTeenager says: “To summarize: the derivation is all about individual molecules, their kinetic energies and how that determines the impulse on the walls of the container, and hence the pressure. There is no need to consider collisions between molecules at all. It is not relevant.”

Nice try, Lazy. How you do squirm! If it is not relevant, then why did you bring them into the discussion? January 23, 2012 at 9:53 pm:

“The ideal gas theory considers molecules to be too small to collide with each other and ignores that factor as being…” –Lazy Teenager.

William M. Connolley says: “…if you take the GCMs code, and the correct initial conditions, they will predict tomorrow’s weather, or next week’s weather, for you.”

Beyond that, they’re worthless.

Surprising that someone would “over fit” to that extent and not recognize doing it. However, I caught the “non-mathematician scientists” at work doing that sort of thing routinely. So, maybe not so surprising.

Doesn’t mean they’re conclusions are wrong. Simply means their approach gives, at best, extremely weak confirmation of cause and effect. Basically worthless as it stands.

Willis says:

“Thanks, tallbloke. Here on this thread I’m focused on what they did in equations 7 and 8. There are many aspects to their work. I oppose the idea that it can all be settled in one thread.”(1) It’s your thread, Willis; (2) covering all of N&Z in a single thread is proven bogus by what we’ve seen here. Even restricting discussion to two lousy equations has resulted in chaos. We even drew in Der Übertroll, to no particular gain. (3) It’s your thread.

Naive question: Isn’t this pretty close to the ‘elevator speech’ that Willis was asking for a few posts back? Sounds pretty common-sensical. One might ask

howthe gas captures radiative energy. In Willis’s challenge, the gas was transparent to IR. So it gets energized byconductionfrom the IR-absorbing surface. No GHGs necessary. And gravity makes it denser. All you need is an external source of radiation./Mr Lynn

Good response… That was my first reaction also, and was wondering if I was “out to lunch”. I still may be, but it’s nice to have company. GK

“”””” Edim says:

January 23, 2012 at 11:13 pm

George E. Smith; says:

“So what part of THIS SYTEM IS “NOT” IN EQUILIBRIUM is it that YOU do not understand. It is not even a closed system, since you yourself said it is being illuminated by a star which is constantly feeding energy into the system.

OOoops !! the ideal gas law applies ONLY to closed systems in thermal equilibrium. Gee!! that requires the whole system to be at a single uniform Temperature.”

This is not correct. Ideal gas law applies to any point (x,y,z) of gas when ideal gas approximation can be used with reasonable accuracy (real gas that behaves sufficiently like an ideal gas). When not, there are more detailed equations of state gor real gases. Equilibrium or not is irrelevant. “””””

Well Edim, now we have a real conundrum: “””””

This is not correct. Ideal gas law applies to any point (x,y,z) of gas when ideal gas approximation can be used with reasonable accuracy “””””

How about that: I went to your point (x,y,z) to look for the ideal gas, and I found nothing at all there. Now it is possible that something might at some time have been near there; but Werner Heisenberg tells me it doesn’t stay there any length of time, and I have no idea where the hell it went. Whatever it was, that maybe at one time was at x,y,z, it sure as hell wasn’t a gas, let alone an ideal gas; maybe an atom or molecule came by sometime; but NO, you cannot have a gas at x,y,z .

Whether the gas is real or ideal is somewhat inconsequential Yes we know that real gases consist of a very large number of molecules, or else they don’t have a definable Temperature, and without a definable Temperature, any equation of state, whether ideal or Van der Waals, or other is useless.

If the N&Z miracle equation can foretell the Temperature of the atmosphere on any planet, evidently without any consideration of what energy surces (if any) are present, then clearly I need to look for some alternative work from what I do now.

Now if you have five variables and eight observed data points, then I suppose you can write a formula that recovers those eight data points quite well, well with eight variables you should get all eight with complete accuracy. I have absolutely no qualms about such an equation.

One can even do it in words: eg “Bad boys rape our young girls, but violet gives willingly.”

Hows that for a miracle equation ? Every Radio Shack hobbyist knows that equation derives all the colors of the standard resistor color code; a “cool” way to remember a finite number of simple facts. Unfortunately, it gives a completely wrong set of answers for the colors of the rainbow. Dang ! I thought I was on to something there.

Dr Roy Spencer’s “third order polynomial” which he warns us is for entertainment only crashes and burns outside of the sphere of influence for which Roy designed it. That’s why he told us it was just for fun.

N&Z miracle is for fun only, it replicates the finite set of numbers that were used to create it.

scf (Jan. 24, 2012 at 3:45 pm):

Thanks for taking the time to respond and for the kind words! Your response make me wonder whether my message got across to you as I had intended. Though independent statistical events and datapoints are related, they are different concepts. Though IPCC assessment report 4 references datapoints, it does not reference the complete set of independent statistical events, the so-called “statistical population” of the IPCC’s study yet observed events from this population (if any) provide the sole basis for testing this study’s model.

“”””” LazyTeenager says:Note that the temperature T of a system in equilibrium can be computed from the just kinetic energy of the moving gas particles and their mutual collisions (density, implying pressure). We don’t need to know the radiative aspects of the system to compute the temperature! What part of the Ideal Gas Law do you not understand here? “””””

January 23, 2012 at 9:53 pm

George E Smith says

Note that the temperature T of a system in equilibrium can be computed from the just kinetic energy of the moving gas particles and their mutual collisions (density, implying pressure). We don’t need to know the radiative aspects of the system to compute the temperature! What part of the Ideal Gas Law do you not understand here? “””””

——-

Somewhat ironically George claims that temperature can be calculated from —mutual—- collisions of gas molecules. This is not true.

The ideal gas theory considers molecules to be too small to collide with each other and ignores that factor as being

Seems George needs to spend some time actually studying the ideal as law “””””

Now Lazy; in my book, there is no lower form of animal life, than someone, who doesn’t even have the guts or confidence in their own position, to actually put their name to such unmitigated balderdash, as you have alleged here; to whit.

“”””” George E Smith says

——-

Somewhat ironically George claims that temperature can be calculated from —mutual—- collisions of gas molecules. This is not true. “””””

So now you truly lazy bladderwort, Why don’t you just go and find exactly WHERE it was that ” I SAID THAT” Just try and find where I said anything even vaguely resembling that.

For a start, my command of the English language, is sufficiently adequate, that I would never write anything quite that garbled.

So do us all a favor, and go back and find WHO IT WAS WHO ACTUALLY DID SAY THAT

Then why don’t you come back and give me an apology.

Do not put words into my mouth. I choose my words carefully; words have meaning; different words have different meaning; I choose to not use different words.

So if you are going to quote me; do so IN MY WORDS They mean exactly what I intended them to mean.

And do it quickly before I decide to post what I REALLY think of people like you.

William M. Connolley says:

January 24, 2012 at 2:44 pm

Ooooh, William doesn’t think that climate models are tuned, excuuuuse me! If this was Wikipedia, he’d just erase my statements …

William, you are an unpleasant man who has made a life out of

to your views from the Wikipedia pages on climate science. You did it in such a slimy way that Wikipedia finally threw you out on your keester.erasing any oppositionLet me be clear. I do not like seeing you on my threads. You are a wrecker and a destroyer, not a builder or a teacher. Dissension and disagreement follow you like a bad smell.

I advise everyone, this man is a danger. Google his name, he is quite infamous. He is quite happy to do just about any underhanded thing to advance AGW alarmism. There has rarely been a clearer case of Noble Cause Corruption, as throughout his whole skeevy list of actions that finally cost him his title at Wikipedia, while ruthlessly squelching opposition views, he has always seen himself as being the white knight crusader for saving the planet, and devil take the hindmost.

William, you are so far in the wrong that it is doubtful that you could ever get back in the right. You are a dishonest, untrustworthy, and nasty person that has burnt all possible bridges. You can get back, but you’ll need to build the bridges.

Now, I have no desire to ban you from here, that’s not my style. I would greatly prefer it if you talked about nothing but the science. It would be nice if you put a curb on your tongue and a muzzle on your insinuations, but if you want to be a jerk I wont stop you. I just wanted to let you know how I feel about your presence. It makes me want to put Vaporub on my upper lip.

w.

… aw, man, now I’ve gone and blown my shot at reforming, I’ve fallen back down to the bottom of the twelve steps. Nothin’ else to do but stand up and start climbing all over again …

Ira Glickstein, PhD says:

January 24, 2012 at 6:01 pm

Thanks, Ira. Practical experience is greatly under-rated in the sciences. Being out in the real world as a commercial fisherman and a mechanic and a diver and a builder and the like give a man a pretty good BS detector.

I’d never heard of N&Z until they were posted here. I didn’t read their post until I read yours. My comment on their kind of gravito-thermal theories was:

The other thing to my advantage is that I worked as a bureaucrat for some years. I’ve both written and read dozens and dozens of project proposals and grant reports and replies to overseas donors and the like. Bureaucrats love the kind of bafflegab that N&Z are putting out above, the type that seems to say something but says nothing at all. So for example, sorting through dozens of applications which I could fund, partially fund, or not fund has definitely helped my ability to see through empty rhetoric.

That’s why I pushed people to give an elevator speech, to show that they’re not just all hat and no cattle, that they do understand the theory that they are defending.

All the best, keep up the good fight,

w.

Willis says: “…now I’ve gone and blown my shot at reforming…”

Der Übertroll strikes again!

Willis, you are too kind in your rebuke of Joel Shore. C’mon Joel, which models are out there for skeptics to tune, test, and evaluate first hand? Willis and Tilo really say all that needs to be said about the models. Nostradamus predictions brilliantly hindcast as well..

..

and John Marshall says: “… since there are no GHG’s in the Jovian atmosphere there must be another mechanism to create that extra heat and that must be gravity.”

Well that solves it then! Good grief, Must avoid using “must” on all but laws and first principals lest the word itself becomes your argument.

Seems even more apropos now, so I will repost what I said ten days ago on “A matter of some gravity” thread. Willis kind of echoed the second one. I think eventually someone will also realize what I did about Jelbring’s greenhouse effect definition being actually his own invention.

“Jim D says:

January 14, 2012 at 8:11 pm

Elevator speech on Jelbring:

The atmosphere is warmer as you go down in it because of the adiabatic lapse rate (g/cp) therefore greenhouse gases have nothing to do with the adiabatic lapse rate (true). The adiabatic lapse rate causes the greenhouse effect (false).

Elevator speech on Nikolov and Zeller:

You can fit a four-parameter curve to surface temperature over blackbody temperature ratio of seven solar system atmospheres just as a function of mass (not albedo or composition or clouds!). Therefore these other things don’t matter. It doesn’t matter that you can’t derive this curve except by a mathematical fit to the data. Who needs to explain why it fits?”

Actually, it was just a wee time-out, some misdirection. His friends/pawns continued in his brief absence, and he’s now back on the Editorial Board, making up for lost time.

jorgekafkazar says:

January 24, 2012 at 10:05 pm (Edit)

Surrender, puny humans! No one can resist Der Übertroll!

Very funny, jorge,

w.

WE, you do sound threatened. But thanks for showing up your real side, you’d managed to hide it for quite a while. As for your link; neither you nor Watts understands wiki’s NPOV policy. This may help a bit.

> you are so far in the wrong

Oh dear. Because, as I clearly stated further up, I agree with you on N+Z. Does that mean you’re wrong, too?

“Note that I am absolutely not making any claim that temperature is determined by density and gravity. I am merely showing that fitting a few points with a few variables and a few parameters is not all that difficult. It also shows that one can get the answer without using surface pressure at all.”

1) What does Willis think the definition of the density of a compressible gas would look like without using pressure in the equation?

2) Can Willis or anyone else produce an equation which which will lie along a smooth curve which gives fit to the planetary surface temperatures using the radiative properties of gases rather than surface pressure which is as good as N&Z’s, or Willis’ density solution?

I really think Willis comments need moderation. You can be funny (which Willis often is) or even a bit smug because you know something on this particular niche field, but you should never be demeaning. People make mistakes because they dont know something but not because they are stupid. What is happening here is that they are chased away to places where science does not run high. Take the Conolley comment. Even though he erased many of my contributions he’s not beyond repair as noboddy is. I was actually happyly surprised he popped up here. If he participates here within the rules he should be welcome. He might find out there are other ways to argument then to suppress opinion. I dont think he got an opportunity to learn that here today.

PS: I agree with your scientific opinion on this issue and greatly value your contributions. Just the style sucks big time lately. I guess Lucy was trying to say something similar but was not clear enough. ;-).

I have added an additional update, showing that I can beat their emulation of the planetary temperatures (lower RMS error) using only three parameters instead of five … take a look. I’ve done it with density instead of pressure as well.

w.

One of the mysteries of this paper is where the observed T_s values (which they claim to predict) came from. For most, no information on sources is given at all. Europa? Triton? What did they use and how did they get a global figure?

One of the hallmarks of WUWT has been a policy of eschewing

ad hominemattacks on other commenters. From Anthony’s Policy page:/Mr Lynn

So many errors everywhere, best to just have a guess and then argue with everyone over their guess. Then call it science at work.

Would it not be better if Nikolov, Zeller and Eschenbach and all the other great minds and interested parties here work together to Iron out the kinks and come up with something solid?

As an innocent bystander (lol) the condescending tone and the “I’m right and you’re wrong” attitudes are becoming old and worn out and sooooo boring!!

Ha! I did a quick search and found an article on Contracting (IRYW) disease, some folks may need to be tested.

Beware Contracting “I’m Right, You’re Wrong” Disease?

http://artpetty.com/2010/03/03/

Willis Eschenbach says:

Your usual can-do “do-it-myself” attitude seems to have disappeared here. However, I’ll note that you have already essentially shown the claim you are making here to be wrong. As I recall, you basically showed that for all of its complexity, the GISS Model E global temperature result hindcast / prediction closely follows the radiative forcings. Hence, if you don’t include the fact that radiative forcings have gone up due to the anthropogenic component over the half century, you aren’t going to be able to do a good job reproducing the global temperature record.

The parameters that you speak of are not parameters that are tuned to reproduce the global temperature record. They are parameters that, to the extent they are adjusted, are adjusted to reproduce things like correct cloud fraction or correct sea ice fraction. (It is also worth noting that the climateprediction.net experiment has done lots of runs where they have allowed such parameters to take on a whole spectrum of values.)

I have already addressed this in my previous comment:

So, yes, you are correct that the fact that the models can hindcast does not turn out to constrain the climate sensitivity that much, because there is too much uncertainty in the anthropogenic aerosol forcing and so different estimates of that and different climate sensitivities can pretty much offset each other.

However, there is no evidence that one can reproduce the temperature rise over the last ~40 years without including a steadily increasing radiative forcing and the only known such forcing is the forcing due to added greenhouse gases.

> I really think Willis comments need moderation.

Agreed.

Willis, among your many eccentric talents, you are pretty good at heaping out verbal scorn and abuse. In the case of Stoat, the blast he got from you was well deserved. I’ll have to give you an ‘Attaboy!’ for that one.

But in the case of N&Z, your words have directly and indirectly brought down a ton of scorn and derision on their work which is completely undeserved. You owe them a big apology.

Their thesis is not at all about curve-fitting data to 8 points. You’ve got it backwards. In those 8 planetoids they noticed a remarkable correlation between pressure and temperature. Using those 8 planets as a ‘training set’ they were able to come up with an empirical power law which gave a ‘good fit’ between pressure and temperature.

But that was just a preliminary step in their research. Such empirical power laws don’t explain why they work. Zipf’s Law predicts word frequencies, city sizes, personal incomes etc but even Zipf couldn’t come up with a good reason why it worked so well. All he could say, waving his hands, was it due to some ‘principle of least effort’.

N&Z have done better than Zipf. They have started a new theory, based in classical physics, which explains _why_ you only need to know pressure to determine temperature.

Does the pressure somehow ‘create’ the temperature? Of course not. It’s plain-old-physics that’s been around for a century: the Ideal Gas Law.

Think of it as a ‘dual solution’ in the abstract problem space. The theory doesn’t add any new laws or change any of the old laws of physics. It just ‘inverts’ the way we look at them such that radiation it put in the background and pressure is brought out as the ‘explanatory mechanism’.

So the Sun is still pouring out radiated energy, and the planets still absorb that energy as heat. Mostly the surface, but GHG’s are still absorbing too (as much as they always have). What’s different is that part of the physics is all subsumed as an assumption in the Ideal Gas Law.

As for curve fitting, you (and others) are totally mistaken in the idea that you can claim the sin of ‘overfitting’ by merely counting the numbers of parameters in the model.

In the first place, the 8 planets in question are merely the ‘training set’ used to train the model. Obviously the ‘test set’ comprises all of the other planets in the Universe, which I don’t have a number for, but I don’t think 5 or 6 parameters would be considered ‘overkill’ for that job.

In the second place ‘overfitting’ is not always bad. When you use trig functions on your computer you are invoking polynomial models because there are no ‘closed form’ solutions for these functions. So the models are carefully crafted to fit the expected values of the function over as many ‘useful’ ranges as possible. ‘Overfitting’ (implying perfect match) would be welcome here.

Overfitting can be bad when you train models using subsets of the data you want to model but not always. Most of the time you can get a good fit on the training set. Depending on the model used, the results on the test set can diverge greatly from the expected values. Polynomial fits (without regularization) are notorious for this. Also, outliers in the training set can throw the models off. But not always, support vector machines are surprisingly robust in this respect. You can ‘overfit’ the SVM’s training data all you want, and test sets still fit good too. (But they don’t explain anything about the features used. Bummer.)

So we need to stay tuned to the N&Z Show, Part II. Keep our scornful thoughts down to a minimum and learn some new ideas about old planetary physics.

Ned and Karl, keep up the good work! And keep those papers coming!

😐

I might be an idiot (please do point out if so) but to me it occurs that the atmospheric pressure has a lot to do with how heavy the celestial body is and how fast it rotates on its own axis?

venus has a thick atmosphere because it hardly rotates (243 earth days for 1 venus rotation)

mars has no atmosphere and it rotates like earth but has 1/10th the mass.

the physical explanation is the atmospheric molecules stick around due to gravitation , but might be spun off if spinning too fast. lol.

as we cannot change mass and rotation speed of earth (unless we build too many wimmills which will make earth lose its kinetic energy) earth atmosphere will remain at , say, 1 bar.

So, for every CO2 molecule that goes up in the air one has to drop down (or we would be violating an important rule here)

scf (Jan. 24, 2012 at 3:45 pm):

Further to my remarks of Jan. 24, 2012 at 9:21 PM, as the IPCC’s models are not testable, the IPCC’s inquiry into anthropogenic global warming cannot have had a scientific methodology but the IPCC has represented it as having had a scientific methodology. This is a really colossal error in the construction of the IPCC’s inquiry but few bloggers or climatologists exhibit an awareness of this error. If we could get people thinking in terms of statistical populations and samples rather than the nebulous term “datapoints,” we could turn this situation around!

What the h*** is the point of this post???

So you prove that Ps = Ps and that makes it wrong?

This post is worthy of RC, orwelian doublespeak at its best.

So you got better results by using eq. Ts = 0.8 * Tgb + 6.9 * Density + 0.2 * Gravity

Ok, now show us how you can just insert the expressions for the variables and get the result Ts = Ts. If you cant, your nothing but a POS with a personal agenda.

LucVC: “Take the Conolley comment. Even though he erased many of my contributions he’s not beyond repair as noboddy is.”

William Connolley is a political crusader Luc. Truth and science have no meaning for him except as potential vehicles for advancing a political agenda. Where he can use science for that purpose he will do so. Where the science goes against him he will suppress it. Nothing he does here will ever change that. In this Willis post he saw an opportunity to cheer lead something that he felt was good for his agenda, and that is really all that his comment consisted of. Willis was right to distance himself from Connolley’s intentions, even if he did it a little more emphatically than necessary.

Willis Eschenbach says:January 25, 2012 at 2:09 am

I have added an additional update, showing that I can beat their emulation of the planetary temperatures (lower RMS error) using only three parameters instead of five … take a look. I’ve done it with density instead of pressure as well.

Harry Dale Huffman beat you to it. Anyway, show us your working so we can see how you derived density without using pressure. Two sides of the same coin.

DRE says:

January 23, 2012 at 4:50 pm

“The right answer for the wrong reason is ALWAYS the wrong answer. (Used to teach cal. based Physics)”

This entire exercise reminds me of the oposite of the above which I experienced, ie getting the wrong answer for the right reason. In dynamic physics sophomore year where the problem involved James Bond shooting a bullet and calculation of the terminal effects, I got an answer of .006 jules or whatever. The professor took time to note that though he gave me almost full credit for the wrong answer since my error was simply in rounding, he should have given me no credit for my stupidity in not realizing the answer was supposed to be.007.

Willis Eschenbach says:January 25, 2012 at 2:09 am

Very nice, Willis. However, you did not create an elephant as requested. 😉

What you did is confirm the relationship may be even stronger than N&Z have found. I don’t think that was your intent. It still may be junk but it would take investigations of the values you used to determine that as a fact.

Did you read the Sorokhtin paper?

http://translate.google.com/translate?sl=ru&tl=en&js=n&prev=_t&hl=en&ie=UTF-8&layout=2&eotf=1&u=http%3A%2F%2Ffiz.1september.ru%2Farticlef.php%3FID%3D200501111

It’s a little beyond my abilities but it appears he uses real physical values in comparing Earth and Venus (which are probably the only two planets worth comparing).

@Willis

> I can beat their emulation … using only three parameters instead of five …

There are at least a zillion planets (maybe more) in the Universe. Does your 3-parameter model work better for those too? Do you understand why your parameters work as well as they do in terms of real-world physics?

If not, then you are just “gaming the system”.

When are you going discuss the science behind N&Z, instead of playing with models (something we “skeptics” normally scorn)?

@Willis

> Please confine yourselves to the topic of the thread …

Oops sorry, I forgot that is against the rules you have arbitrarily set up for this

~~game~~post.😐

Willis says …. “they claim to be able to calculate the surface temperature Ts of eight different planets and moons from knowing nothing more than the solar irradiation So and the surface pressure Ps for each heavenly body. Dr. Zeller refers to this as their MIRACLE equation…” …..”My simplified version of their equation looks like this: Ts = 25.394 * Solar^0.25 * e^(0.092 * Pressure ^ 0.17)” = A SIMPLER MIRACLE

You folks just don’t get it do you, you’re not seeing the forest for the trees: Willis’ rendition of our MIRACLE is also a MIRACLE!!!!!!! What is the Miracle you don’t see? We calculate the average global equilibrium surface temperature on any planet/moon using only Solar input and surface pressure! Why is this a miracle? Because it implys that the AGW theory is bogus. Why does it do that? Since the average global surface temperature of any planet/moon IS the basic bottomline determinator of that planet/moon’s climate and our Eq 8 accurately calculates this temperature without using greenhouse gas information.

Dr. Nikolov & I have been working on this for over 2 years, our first attempts looked like Willis’ simpler miracle, and we’ve played with density also, but we are trying to get it exact, currently Eq 8. You CAN NOT fit an elephant with an exponential equation, you can with a polynominal. The argument about the number of constants in our equation 8 would be valid it it were a polynominal – it’s not.

We are handing WUWT ‘THE NAIL’ to the AGW coffin and you guys have forgotten about the coffin and are fixated on the details of the nail! Is it galvinized? Why isn’t it a wooden spike? They need 2 more nails. Wonder what kind of hammer they plan to use?

AusieDan: “Carbon dioxide, by its molecular weight and atomic structure, expands more rapidly under heat than does an average sample of air. This causes increased pressure in the sealed container holding the carbon dioxide sample, relative to the container holding just air. Increased pressure results in the temperature of the carbon dioxide to rise higher than the air in the other container. That is the so called greenhouse effect.

HOWEVER, when the pressure in the two vessels are allowed to equate, such as by providing a hole in the top for the excess gas to escape to the outside air, then the temperature in each vessel rises to a lower level than before and the temperature in both containers remains the same. Bye Bye, greehouse effect. This has also been demonstrated on a number of occasions, but with far less noise and propaganda than the false greehouse effect.”

Dan, I had read this earlier and had meant to get back to it. This is new information for me, and I’d like to know a little more about it. So basically, we have been arguing about climate sensitivity from the perspective of about 1C of warming per CO2 doubling, plus some undefined feedback. The 1C of warming for 2 X CO2 has been regarded as a given, due to the lab experiments with enclosed CO2. Now, if I understand your argument correctly, you are saying that the 1C is also false, and that the extra CO2 in the atmosphere will simply cause atmospheric expansion, not temperature increase. Do you have a link where I can learn more about the work you are refering to?

Dr. Zeller: “You folks just don’t get it do you, you’re not seeing the forest for the trees: ”

LOL. I’m very sympathetic with your frustration here. My thought is that people are picking on your method, “galvanized nails or wooden spikes”, because the underlying physics isn’t clear to them. Hopefully your part 2 explanation will help with that. Also, remember that skeptics to AGW really are skeptics that will try to pick apart everything, even in cases where it is true and to their liking. Think of it as process rather than final conclusion. I think your ideas are basically sound, so please don’t be despirited because you have run into a dustup. In most cases in the past when scientists have produced new ideas the rest of the scientific community didn’t simply throw up their hands, acknowledge the brilliance, and embrace the change. Much more often there was a fight with the people who’s ideas were being displaced and with those that had come to accept those ideas. So buckle your chin strap and explain, explain, explain – then I think you will prevail.

I agree with Karl!

The major point that Willis

totallymissed (but follows from his own regression analysis) is that the planetary surface temperature CAN be explained in a straightforward fashion over a broad range of atmospheric conditions using ONLY pressure and solar irradiance . No other model can currently do that! This is the main point of our theory! The grand implications of the strong relationship shown in Fig. 5 (the NTE – Pressure curve) is that the so-called GH effect (we call it ATE) is a pressure phenomenon that is completelyunrelatedto radiative transfer! Hence, the GH effect in its physical nature is NOT a reduction of the surface IR cooling to space as currently assumed, but is a Pressure-induced Thermal Enhancement (PTE) … It is that simple!kzeller says: “

We are handing WUWT ‘THE NAIL’ to the AGW coffin and you guys have forgotten about the coffin and are fixated on the details of the nail! Is it galvinized? Why isn’t it a wooden spike?”Great analogy, Dr. Zeller. A wooden spike to kill the AGW vampire that wants to suck the blood out of the US.

Our official response to Willis’ ‘analysis’ of Eq. 8 will be coming very shortly….

We through we should not engage in correcting high-school math errors such as those made by Willis above, but it looks like we have to it at least once to set the record straight, so we do not have to degrade this discussion anymore in the future … Stay tuned!

KZ> “Why is this a miracle? Because it implys that the AGW theory is bogus”

Ah, you mean that only supernatural intervention could render the well-established greenhouse effect physics wrong. At last, something we can agree on.

John Day says: “@Willis > ‘Please confine yourselves to the topic of the thread …’

Oops sorry, I forgot that is against the rules you have arbitrarily set up for this game post.”

Since the objective was to focus on the two equations in question without going off on a million tangents, I think the rules are less than arbitrary. As a result of them, we only have to wade through half a million rants, maunderings, troll castings, nit-pickings, and irrelevancies.

kzeller says:January 25, 2012 at 9:51 am

We are handing WUWT ‘THE NAIL’ to the AGW coffin and you guys have forgotten about the coffin and are fixated on the details of the nail! Is it galvinized? Why isn’t it a wooden spike? They need 2 more nails. Wonder what kind of hammer they plan to use?

Dr. Zeller, you guys need to consider that you’re presenting your ideas to a bunch of skeptics. You should use that fact to hone your own views. Yes, a lot of comments will be useless but that does not mean there isn’t good information available. And, if you can’t argue your points here what do you think will happen when you present them to AGW believers?

Personally, I think you are wrong when you believe you can replace the GHE with gravity. And, as I’ve said before, I think the relationship you found in the planets might be very important. That’s where you should try and improve your paper. You need to highlight the physical factors that lead to the miracle equation in more detail.

Don’t get discouraged.

William M. Connolley:

There is no ‘well established’ GHE physics! The whole notion about the GHE being a radiative phenomenon is based on a confusion that down-welling IR radiation warms the surface on a global scale. This confusion in turn comes from the fact that radiative transfer is being solved in climate models

decoupledfrom convection. Once these two heat transport mechanisms are robustly coupled (i.e. solvedsimultaneouslyas a part of the same system of equations) as it happens in the real atmosphere, the convective cooling completely offsets the warming effect of ‘back’ radiation. This can be easily demonstrated mathematically.What needs be realized here is that the long-wave ratiadive transfer in the atmosphere is only a RESULT (a BYPRODUCT if you will) of temperature, NOT a cause for it! Temperature, on the other hand, is a function of solar heating and pressure!

The situation with the current GH theory is one of confusion between cause and effect. It resembles quite the paradigm we had in medieval times prior to Copernicus, when it was believed that the Earth was at the center of the Universe based on the superficial observation that Heavens revolve around Earth. Similarly, the fact that we measure a significant LW radiation coming down from the atmosphere, it does not mean that that flux is actually responsible for the atmospheric thermal effect!

As we have shown in our Reply Part 1 through analysis of Moon temperature data here:

http://wattsupwiththat.com/2012/01/22/unified-theory-of-climate-reply-to-comments/

the actual magnitude of the atmospheric GH effect is about 133K. It requires many thousands of Watts of

additionalradiation (about 14,800 W m-2 to be exact) to raise the temperature of Earth from the gray-body value of about 155K to the present temperature of 287.6K. The observed average downward LW flux is only about 343 W m-2. So, even from the standpoint of this piece of evidence, it is clear that the GH effect CANNOT be possibly caused ‘back radiation’. Our interplanetary analysis explains the GH effectcompletelythrough pressure … What can be more clear than that?Mr Lynn says:

January 25, 2012 at 5:18 am

LucVC says:

January 25, 2012 at 1:59 am

One of the hallmarks of WUWT has been a policy of eschewing ad hominem attacks on other commenters. From Anthony’s Policy page:

Yeah, you’re likely right, Mr. Lynn, and I’m working on it. However, I don’t take well to being insulted by such a charming, intelligent, witty fellow as Mr. Connolley. He and I have a bit of history.

w.

Tilo Reber:

God…Now, THAT’S funny!!!!! Thanks for giving me my daily belly-laugh!

Richard M says:

No…He isn’t. He is presenting it to people who call themselves “skeptics”. There is clearly a huge difference as illustrated by the fact that many people here are still taking Nikolov & Zeller’s work seriously.

John Day says:

Yes…Willis and my point exactly. The difference is that he is telling you outright that he is gaming the system whereas Nikolov and Zeller are not.

The science has already been discussed…and shredded! The “theory” does not even obey the 1st Law of Thermodynamics…I.e., it violates conservation of energy!

The authors claim that convection makes the radiative greenhouse effect has been demonstrated to be due to an extreme error in how they added convection.

The fact that average temperatures on various planets are lower than the conventionally-calculated blackbody temperature has been explained as a well-understood consequence of Holder’s Inequality applied to non-uniform temperature distributions.

What more do you want?

djorgekafkazar says: Great analogy, Dr. Zeller. A wooden spike to kill the AGW vampire that wants to suck the blood out of the US.

Congratulations dj… , you’ve read the blog words, found & tasted some candy, now read the original post and part 1 for the hidden dishes making up our Sublime Smorgasbord. 🙂

John Day says:

January 23, 2012 at 9:25 pm

@Willis

> >There was an option to say “Sorry I accused you of

> >calling N&Z dishonest when you hadn’t”.

>Read my remarks carefully. I didn’t “accuse you of calling N&Z dishonest”. You’re blowing my >statements out of proportion. I said it suggested dishonesty.

I went back and reread your original comment wherein you make the “dishonesty” statement.

I guess it depends on what your definition of “is” is.

@jorgekafkazar

> Since the objective was to focus on the two equations in question

> without going off on a million tangents, I think the rules are less

> than arbitrary. As a result of them, we only have to wade through

> half a million rants, maunderings, troll castings, nit-pickings,

> and irrelevancies.

With respect, I disagree with that approach. All it does is encourage the meanderings and useless “dancing around the fire”.

The addition of planetary physics to the discussion would have, IMHO, a focusing effect to gauge and filter out the chaff and gaming.

One other piece of advice, to all: “Don’t feed the trolls!”

😐

> He and I have a bit of history.

Do we? I’d forgotten you I’m afraid. And you’ve forgotten me enough to get my title wrong, but then people often do. Or perhaps you’re just being impolite again; it can be hard to tell lack of politeness from lack of competence sometimes.

NN> we should not engage in correcting high-school math errors such as those made by Willis above

Interesting! I haven’t spotted any maths errors by WE, though I didn’t look that closely. I shall watch out for your interesting analysis. I do hope you’ll provide the promised errors in maths, rather than interpretation.

NN> The major point that Willis totally missed (but follows from his own regression analysis) is that the planetary surface temperature CAN be explained…

Err no. That is the point WE is desperately trying to make (indeed has made, quite convincingly) but you haven’t yet understood: that it is all to *easy* to explain the temperatures, using curve-fitting. Explaining it with physics is much harder, you should try it sometime.

Richard M

Where have we claimed that we replace the greenhouse effect with gravity?

What we state is that the GH effect, when measured as a dimensionless number (Ts/Tgb), i.e. the relative thermal enhancement, is completely explainable by pressure. Is pressure a gravity? No! Pressure is a FORCE resulting from the atmospheric mass per unit area AND gravity! What is the kinetic energy of a gas that determines its temperature? It is a product of Pressure and Gas Volume (PV), i.e. FORCE x Distance = Joules. In other words, you cannot have kinetic energy and temperature of a gas without a FORCE. On a planetary scale the force of pressure is INDEPENDENT of solar heating, atmospheric volume, or temperature, because we have on average an

isobaricthermodynamic process at the surface. So, changing the mass of the atmosphere will change the FORCE generated by gravity at the surface, therefore, changing the temperature. Our non-dimensional NTE factor (the relative thermal enhancement) is a manifestation of that physical characteristic of pressure called FORCE … How is that for a physical explanation? We elaborate more on this in our Reply Part 2 …The key to grasping our theory is understanding the actual physical

meaningof different parameters such as pressure, irradiance, temperature, and energy and the best way to do that is to properly deciphering the units …Joel Shore says:

The science has already been discussed…and shredded! The “theory” does not even obey the 1st Law of Thermodynamics…I.e., it violates conservation of energy!Nice try, Joel. The Gas Law does not violate the 1st Law of Thermo, sorry! What violates that law BIG TIME is the idea that changing the concentration of minor gases in the FREE atmosphere can increase the kinetic energy of the troposphere and cause surface warming, or the assertion that some ‘heat-absorbing’ gases which amount to less than 0.5% of atmospheric mass can raise Earth’s surface temperature by 133K above that of an equivalent gray body! That’s more than a violation of the 1st Law, it’s a SUPERSTITION. Do you know how much of addition radiation is needed to actually raise the temperature of the Moon by 133K?? 14,800 W m-2 …

Please, tell your friends at Kodak that you are failing the assigned task here, and they should stop wasting money on you … 🙂

> One other piece of advice, to all: “Don’t feed the trolls!”

But we can ask the Moderators to step in and snip/ban the trolls, when it becomes clear that they are trying to disrupt, not contribute to, the discussion.

😐

Ned Nikolov says:January 25, 2012 at 11:30 am

the actual magnitude of the atmospheric GH effect is about 133K. It requires many thousands of Watts of additional radiation (about 14,800 W m-2 to be exact) to raise the temperature of Earth from the gray-body value of about 155K to the present temperature of 287.6K.

A reasonable value for surface heat capacity would bring the temperature of Earth to about 250K and the GHE could do the rest.

The observed average downward LW flux is only about 343 W m-2. So, even from the standpoint of this piece of evidence, it is clear that the GH effect CANNOT be possibly caused ‘back radiation’. Our interplanetary analysis explains the GH effect completely through pressure … What can be more clear than that?We know what the cause of the large discrepancy that you calculate, it is your assumption of zero heat capacity, include that then we can talk

NN> properly deciphering the units …

Good point. So given that Nte is dimensionless, and Ps is in N/m2: in “Nte(Ps) = e^(t1 * Ps ^ t2 + t3 * Ps ^ t4)”, what units are t1 and t3 in?

William M. Connolley says:

See my reply to Richard M above for a physical explanation …

You seem to have limited knowledge about how science works. Do you know that all major theories that gave birth to so called ‘first principles’ have began with fitting empirical data to curves and inferring responses and functions? Do you have a science degree in a non-soft science area?

Willis,

Degrees of freedom vs parameters. End of story. Not to be Shakesperian, but this seems to be much ado about nothing, or perhaps a tempest in a tea pot. Not that you are, of course, not right.

William M. Connolley says:

January 25, 2012 at 12:39 am

Threatened by you, Billy? By YOU??? Oh, stop, please stop, is this your new plan? This is truly beyond evil, I see through your nefarious plot—you intend to kill me by making me laugh myself to death. It’s diabolical, I beg you, please have mercy, don’t threaten me again, my stomach can’t take the laughter and my cheeks are aching from grinning at your antics …

As for “showing my real side”, yes, my real side does indeed think that you are a unpleasant and undesirable person. You are willing to do anything to promote your POV, and it sure isn’t an NPOV. Your claim that we don’t really understand why you were forced out of Wikipedia is pretty funny, though. You were thrown out, but it had nothing to do with your POV and everything to do with you being a POS. You see, Billy, I was one of the nobodies who actually believed Jimmy Wales when he began wikipedia. And I was one of the nobodies who tried to do what Jimmy said, contribute. And I was one of the nobodies who got resounding erased, and re-erased, and re-erased, by the King Of Wikipedia climate censorship. That would be you … it didn’t matter if I posted facts, didn’t matter if God himself said it, if you disagreed with it, it was gone.

So I see you quite clearly and accurately, Billy, and what I see turns my stomach. And yes, that is my real opinion, my “real side” if you will.

Gosh, Billy, did you really think when I said that I was referring to your meaningless opinion on this issue? Your reading comprehension is worse than I thought … no, belay that, actually, given your history at Wiki, your reading comprehension has always been uniformly horrible, so I guess it’s no worse than ever.

And now you announce your intention to school me on computers, clearly another part of your devilish “make him laugh until he croaks” plan. I could point out that I wrote my first computer program when you were in nappies, Billy, but that wouldn’t be true. I wrote my first computer program before you were born.

But please, don’t spare us your hilariously obvious insights about computers, continue with your brilliant comic exposure of your fantasies, prejudices, and personal shortcomings. This is great entertainment, and to date the laughter hasn’t killed me, so do your worst, keep it up, leave’m dying in the aisles.

w.

PS—Some people have said that I’m too crude or too hard on poor William. Quite the opposite. The problem is not that I am too outraged at what Mr. Connolley has done.

The problem is that the rest of you are not outraged enough.The man has ruthlessly censored real, valid scientific opinion for years, and you want to play patty-cake and go all California on him, ask him about his feelings and invite him to share? Not me. He doesn’t deserve to hang out with decent people, I am never happy to see him show up, he is a force for damage and dissension who leaves trouble in his wake, and I think it is important that people know who he is and what he has done.Is he beyond the pale, beyond redemption? I have no idea. But for him to show up and immediately start, not by adding to the scientific discussion but by attacking me personally, should give you a clue. You can pat his head if you want, I’m kinda attached to having all my fingers, he is unrepentant and he bites. I’ll wait until he shows some sign of at least noticing the trail of damage he has done to free scientific thought before I change my opinion.

Willis Eschenbach,

We are in total agreement on this:

“The problem is not that I am too outraged at what Mr. Connolley has done.

The problem is that the rest of you are not outraged enough.”

@Joel Shore

> The authors claim that convection makes the radiative greenhouse effect

> has been demonstrated to be due to an extreme error in

howthey added> convection.

Assuming, for the sake of argument, that this ‘extreme error’ is real, that doesn’t rule out that there might be a

correctway of adding convection to make this idea“work” (or not). I suppose N&Z will further address this issue in Part II.

But these convective claims do make sense to me in this qualitative way (waving my hands): the surface of the Earth absorbs most of the heat energy coming from the Sun. The atmosphere much less, especially the bulk of it O2 and N2 being transparent to heat radiation. But the GHG’s, though present in much smaller percentages, do behave like the surface in that they are capable of absorbing radiated heat too.

Here’s the difference: when the GHG’s heat up they can rise up and release this heat much closer to the TOA. (Too bad, Surface, you’re Grounded!) Furthermore, H2O can change states, up in the clouds, and release even more heat (of condensation) up high.

I know this is nothing new, but it sounds like GHG’s comprise a kind of ‘heat engine’ which involves both heating and cooling to me. The trick is to nail down the physics here in a quantitative way, which seems to be a very controversial topic. Beyond my pay grade. I hope N&Z (et alia) will give us further analysis of this and possibly eliminate some the controversy with their new ideas.

@me

> … when the GHG’s heat up they can rise up and release this heat much closer to the TOA…

Forgot to mention that O2 and N2 are also involved, of course, by being warmed by conductive transfer of heat from the surface to the air in direct contact with the ground. So they are also part of this ‘heat engine’.

Nick Stokes says:

January 25, 2012 at 4:09 am

Indeed, that has been asked before and not answered as far as I know. Nor do I know at what level one measures “surface pressure” on a planet with no ocean.

w.

Regarding Connolley, Willis says: “You were thrown out, but it had nothing to do with your POV and everything to do with you being a

POS.”Seconded, doubled and squared. Connolley is a despicable insect who is unable to get traction with his climate alarmism, so he misuses his insider position to censor opposing points of view, no matter how polite and scientifically factual. Connolley is simply dishonest.

The difference between Wikipedia propaganda and WUWT – the internet’s “Best Science” site – is that Connolley is allowed to post his comments here. If equivalent comments were posted on Wikipedia, censor Connolley would arbitrarily delete them if he was not in personal agreement.

That makes William Connolley a despicable human being. Unfortunately for Connolley, he is unable to censor comments here like he does on Wikipedia – a blog that is losing credibility precisely because of Connolley’s dishonest censorship of different points of view.

Ned Nikolov says:January 25, 2012 at 11:54 am

Where have we claimed that we replace the greenhouse effect with gravity?

Sorry I didn’t specify all the factors. I have mentioned them all in other comments this past few weeks. It was probably due to commenting recently on the Jelbring paper.

However, the problem is and will always be … without changing the effective radiation height nothing can warm the planet above the surface temperature and not violate thermodynamic laws. All of the planets that have atmospheres have radiating gases so there is no problem here.

I believe what you may have found is the GHE ltself is limited by equation 8. That puts just as big a nail in the AGW coffin as anyone needs. It means further additions of GHGs will have no impact. If you can demonstrate the physics that leads to this limit then you truly will have made a huge contribution.

John Day says:

Yes…That can be ruled out. It is ruled out by the fact that when the scientific community has added convection correctly, they do not get the result that N&Z get. Besides which, it is easy enough to correct what N&Z did in adding convection to the toy model of the radiative greenhouse effect and one indeed sees that their claim of the radiative greenhouse effect disappearing is no longer true.

NN> See my reply to Richard M above for a physical explanation …

That doesn’t answer my question. I asked, what units are some of the constants in your equation in? Surely you can answer that simple question?

In your version, it is the “0.233001”. Is it dimensionless (I can’t see how it can be) or if it has dimension, what are the dimensions?

WE>

You’ve gone a bit dull I’m afraid. But I need to make a slight correction: NPOV should have been WP:RS (http://en.wikipedia.org/wiki/Wikipedia:RS). Yes, I know neither you nor any of yours care about wiki’s policies, but those of us who edit have to.

WE> I was one of the nobodies who tried to do what Jimmy said, contribute…

Really? Not under your own name, then. Did you do it secretly?

Ned Nikolov says:

The Gas Law is not what we are talking about violating Thermodynamics. What violates the 1st Law is your misapplication of it to claim that the Earth can emit 390 W/m^2 from its surface but only 240 W/m^2 as viewed from space, and that the discrepancy can be explained anything other than the fact that some of the surface emissions are absorbed by the atmosphere!

(1) Perhaps you didn’t notice but there is an object in the center of our solar system called “the sun”. It emits radiation to the Earth…and the Earth also emits radiation back out into space. Hence, the Earth is not an isolated system and you can’t apply conservation of energy as if it is.

(2) Nobody but you seems to believe that “heat absorbing” gases raise the Earth’s temperature by 133 K. They raise it by 33 K. The other 100 K is accounted for by the fact that different temperature distributions with different average temperatures can yield the same average emission of 240 W/m^2.

No…It is called “science”.

Really…And, you calculated that how exactly, given that a blackbody at 288 K is only emitting 390 W/m^2?

I am not at Kodak anymore. Speaking of failing…I must admit that I expect MUCH higher standards of science and scientific integrity from our public servants than I have seen displayed here!

Ned Nikolov said @ January 25, 2012 at 11:30 am

Sorry, wrong! It’s in T R Oke’s

Boundary Layer Climatesand a host of other places. It’s part of theReceived View. That is, it’s what is taught at universities. Do you not understand what “well established” means? Get a grip! If you want to overthrow a paradigm theory, you don’t start by refusing to acknowledge that it is the established paradigm theory. I said earlier that you need to show that you understand what it is that you are claiming to overthrow. Ignorance doesn’t cut it.Pseudo-scientists do so love to compare themselves to Copernicus and Galileo don’t they? It is

nota “superficial observation that Heavens revolve around Earth”. There’s nothing “superficial” about it. I observe it most nights. Yes, I know because I accept the Received View in astronomy that Earth revolves around the sun, but it’s manifestly not what Iobserve.It’s worth bearing in mind why Copernicus model* was only slowly accepted by astronomers. It predicted a variation in diameter of 8:1 for Mars and 6:1 for Venus. There is no observable change for Venus and only a ratio of 2:1 when making naked eye observations. This is why Galileo was abjured not to take the model literally, but it was OK to use it mathematically. It wasn’t until that discrepancy was resolved that the Copernican model of the planets orbiting the sun (in perfect circles with even more epicycles than Ptolemy used) was accepted.

“The whole notion about the GHE being a radiative phenomenon is based” on observed emission spectra, not confusion. It may well be “wrong”, but you sure as hell are not making your case for anyone with a grounding in basic physics and philosophy (logic).

* Footnote: I wonder how many “sceptics” are now going to stop believing the Copernican model of the solar system just because it’s a model. Maybe they will just deny that it’s a model…

Richard M:

Please, consider the following important point (, which we have not discussed in the papers released to the public) – There is NO effective radiation height in reality. The concept of an

emission heightcome from theincorrect applicationof the SB law when estimating the mean temperature of a sphere (see our Reply part 1). That simple equation produces about 255K (-18C) for Earth. This temperature is then erroneouslyidentifiedwith the actual measured temperature at about 5 km in mid troposphere, and a conclusion is drawn that this is where most of the IR radiation had to be emanating from. The reality is that IR radiation is coming out from all heights in the atmosphere simultaneously including the surface. It’s acontinuumof IR fluxes in different wavelengths reaching space from various depths of the atmosphere. That continuum of emitted IR radiation with depth is what enables the remote sensing of vertical temperature and moisture profiles (as well as other atmospheric parameters) from satellites.The ’emission temperature’ of a sphere computed from the simple inversion of the SB law is not really compatible in a physical sense with any palatable real temperatures measured in the atmosphere or at the surface … Hence, the emission height is another fiction of the GH theory with no physical equivalence!

“Nick Stokes says:

January 25, 2012 at 4:09 am

One of the mysteries of this paper is where the observed T_s values (which they claim to predict) came from. For most, no information on sources is given at all. Europa? Triton? What did they use and how did they get a global figure?

Indeed, that has been asked before and not answered as far as I know. Nor do I know at what level one measures “surface pressure” on a planet with no ocean”

As I pointed out if either T or P is specroscopically determined then the other will have a SB distribution.

Dr. Nikolov

You know much more about fysics then i do.

Stilli have this question.

Maybe the word back-radiation is misleading but its meaning does not have to be so.. Maybe we should recall it into “blocking radiation” or something. There is in fact no production of down-welling flux of 343 W m-2.. There is a delay of outgoing radiance.

It’s like my banket in a cold night. It doesn’t warm me but it isolates my body.

With no blanket i schould lose a lot of bodywarmth. So in fact my blanket warms me a lot. What of course is in fact not true.

tallbloke says:

January 25, 2012 at 8:23 am

Thanks, Tallbloke. I guess my point still isn’t clear to you, and it’s not in how I derived density.

What N&Z have done is

just curve fitting. You can do it as you have done, with solar and pressure. You can do it as I have done, with Tgb and Gravity and Density. You can do it with solar and pressure using a much simpler equation than you used. You can do it with solar and density and a simple equation.My point is, it is a painfully easy curve to fit. You can fit it in a host of ways. But that doesn’t mean anything, TB. With four parameters you can fit an elephant. I’m a good mathematician and it’s a simple elephant, so I did it with three, but it’s STILL JUST FITTING AN ELEPHANT!

Using five parameters and a free choice of any equation when there are only eight data points is a

laughable newbie mistake, tallbloke. It’s not a MIRACLE. It’s not a blinding insight. It is a trivial equation fit, and I’ve just demonstrated that by fitting it in a variety of ways.But forget about my demonstrations.

Go ask the statistician of your choice. Ask them if fitting eight data points, given a free choice of any equation under the sun and five free parameters, is a valid and meaningful procedure.They will tell you what I am telling you. It is risible. The fact that N&Z included it in their argument shows that they also are clueless about models and parameters. It should be a sign to anyone considering their theory.

I can’t state this strongly enough, tallbloke. Five parameters, eight data points and a free choice of equations is a no-brainer fit and it means nothing. Zip. Zero. It has no probative value. Ask a real scientist, TB, you’re embarrassing yourself claiming this procedure is valid.

w.

Richard M says:

January 25, 2012 at 8:56 am

No, no, no, and no. Let me say it a different way, as clearly I still have not gotten the point across to you.

I have not “confirmed the relationship may be even stronger”. I’ve just fit the same points with a different curve. So far, N&Z fit it one way, and I’ve fit it three other ways using different variables and different equations and different numbers of parameters.

All that means is that the problem is trivially simple, because there are five tunable parameters and eight data points and I’m given free choice of any equation, no matter how non-physical it might be.

So none of the fits mean anything, Richard.

w.