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.
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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 mechanism is 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 energy when 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 care how this 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 derivation if 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’t just because it is a four parameter fit of an absolutely arbitrary functional form — it is that when one makes the arguments of the exponential dimensionless as they must be the characteristic pressures that emerge are absurd.
N&Z’s fit is the opposite of 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 do appear 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 — the greenhouse 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 existence of the Greenhouse Effect is really pretty stupid. We have one very important thing that Arrhennius didn’t have — satellites with IR spectrometers. I don’t care what mechanisms create the thermal profile of the atmosphere compared to the surface. The fact that the mean temperature of the Earth is established as balance between incoming radiation and outgoing radiation, the fact that 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 only thing going on. I remain open minded about the effects of convective mixing and so on, although I adamantly reject the arguments so far that attempt to assert that “gravity” causes some actual warming. I’m open minded about additional sources of free energy. I’m very open 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 of hundredths of a percent in 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 — some response to increased CO_2 is a very reasonable hypothesis, although it could be far smaller than simple arguments might suggest, especially if overall feedbacks are negative, 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 with its nonlinearities and driven convection, and dependence on solar state has large temperature fluctuations clearly visible in its past thermal history, fluctuations that are poorly understood noise that is at least of the same order of magnitude as any possible signal of AGW. This confounds any attempt 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 goes all the way down to where it would be without it, but there are fluctuations that are within a factor of 3 or 4 of equalling the total temperature shift associated with GH warming in the “standard” view. CO_2 (when one adds it in my means of proxies) does seem to fluctuate with temperature but as a follower of 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 of 1-5 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.
Absolute warming due to CO_2 could be signal, sure, or it 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 even cancel most 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 analysis or not, Jelbrings claim that gravity magically separates hot and cold air into two piles is a joke.
A 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 @ur momisugly January 24, 2012 at 4:34 am
It’s a shame that this needed to 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:
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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 style of 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.