Riding A Mathemagical Solarcycle

Strange then that various commentators did actually predict the current solar quietness whilst the establishment was still predicting that cycle 24 would be another strong one.
http://personal.inet.fi/tiede/tilmari/sunspots.html
No doubt mention of Timo’s work will cause apoplexy in some quarters but he wasn’t the only one.

I am sure that there is a chaotic input into solar activity that would throw this. Also the sun does not have an inexhaustable supply of fuel. This is gradually changing with nuclear fusion reactions so this will alter output as time goes by.

Perhaps off topic, but do the global climate models also suffer from lack of out of sample testing?

The paper lays out the physics that were used to derive the parameters in the math. So you appear to be misrepresenting the paper. So then, please show us your math where you successfully reduced the physics of the entire planetary system to fewer than twenty or so. Oh, you can’t do that? So then why attempt to ridicule a paper that has twenty or so parameters that are linked to physical attributes of the planetary system? I’ve seen some poor arguments against papers before but your “arguments” against this paper – aren’t scientific.

RJ actually did do a forecast with a fraction of the data and he doesn’t claim his model is right (as it isn’t — it fails the simplest diagnostics). RJ does these models for fun. He’s not a political activist. It’s unfortunate that he got tangled in this whole PRP mess. I would have advised him to steer well-clear of publishing in PRP had I known he was doing so, as it has been obvious for many months that a blow-out like this was going to be inevitable. (Anthony: I don’t know how you didn’t see it coming. You must have had blinders on.)

Willis says “The way to test this kind of model is bozo-simple. Divide the data into the first half and the second half. Train your model using only the first half of the data. Then see how it performs on the second half, what’s called the “out of sample” data.
I bring up this study in part to point out that it’s like a Fred Flintstone version of a Fourier analysis, using no less than twenty tunable parameters, that has not been tested out-of-sample.
More importantly, I bring it up to show the appalling lack of peer review in the Copernicus Special Issue. ”
From the paper :
4 Forecasting
To test if the model has forecasting ability, we can redo the
correlation with data only up to the years 1950 and 1900 and
determine the forecast for the next 50 and 100 yr to see if the
model can predict the sunspot data we have already experi-
enced.
Figure 5 gives a forecast for the period 1950 to 2050 made
from the correlation of the model with data up to 1950.
“Figure 6. A comparison of monthly sunspot numbers from 1900 to
2000 (in blue) with the absolute value of the correlation model (in
red), derived using data only up to 1900 and the extended forecast
to 2000.”
Jeezus Willis you’re at it again. Read the frigging paper before shouting off on WUWT.
I’m not saying I find this very convincing but if you want to rip something apart at least read it first.
“In fact, the Salvador model shown in Figure 2 above is like a stone-age version of a Fourier analysis. But instead of simply decomposing the data into the simple underlying orthogonal sine waves, it decomposes the data into some incredibly complex function of cosines of the ratio of cosines and the like … which of course could be replaced by the equivalent and much simpler Fourier sine waves.”
Willis you are in danger of talking above you pay grade.
If you have a modulation of two cosines, it will appear as three peaks in a Fourier spectrum. Each with its own phase amplitude and frequency. You could then link some of the phase and amplitude terms so avoid needing extra parameters but it certainly would not be “much simpler”.
http://climategrog.wordpress.com/2013/09/08/amplitude-modulation-triplets/

Notwithstanding the above, I agree with Willis’ view that this is largely curve fitting. However, the out of data tests do suggest there may be something worth further study.
As I’ve pointed out to a couple of this team in personal communication (not this author) there is a danger of this kind of approach becoming numerology if you are ready to arbitrarily accept any combination harmonics sub-harmonics beats, resonances and amplitude modulations of any planetary periods.
I might buy the possibility of Ian Wilson’s VEJ idea but when I see
“– one-quarter Uranus orbital frequency equal to 21.005
–two modulating frequencies of 178.8 and 1253 (forming
a beat frequency of 208 yr).”
I start to to think , hang on. Without a concrete reason to suggest a link with U and then why the 4th harmonic but not 1st , 2nd or 3rd , the word numerology springs to mind.
You need to write out all the base frequencies all the possible permutations within in your scheme of combinations and you’d probably realise that you have enough numbers to start your number system. In that context the “planetary” constants are essentially random numbers.

lsvalgaard says: Both look like failures to me.
Clearly the fit is not as good. My point was the W was ripping into both the authors and the editors in no uncertain terms, for not doing something that was in fact in the paper.

It’s an “open access” journal. This means it is a way of extracting “publication fees” from people who otherwise can’t survive a legitimate peer review. In any case, the journal is being pulled off the virtual “shelf” probably because it is too obviously fraudulent
http://www.pattern-recogn-phys.net/volumes_and_issues.html

Tallbloke, as you’re watching, can you enlighten us on the Uranus thing?

dikranmarsupial, fair point but the same is now true of PR with the tens of thousands of journals spewing out hundreds of papers each every year.
Even the previously “highly respected” titles now print garbage, so science is basically screwed.

Jan “Curve fitting is a very common error to make. It is easy to believe that you have found a good formula for predicting the future when you in reality have just performed curve fitting on historical data. ”
I can think of much more widely known example : the models use for AR4.
It’s the same problem except that they can’t eve back cast properly.

Dan/Greg, there are good journals, there are no so good journals, that was as true before the push for open access as it is now. Part of being a good researcher is knowing which journals to monitor for interesting papers and which journals are worth sending papers to. Science is actually in reasonably good shape, or at least it would be if the funding were a bit better, but we have had to put up with the financial downturn, just like everybody else, the money has to come from somewhere.
The real problem (IMHO) is researchers being assessed using metrics that favour quantity too strongly over quality. If there was no reward for publishing in a low quality predatory open access journal, there would be no low qualty predatory open access journals. The problem is that quality is much less easily assessed than quantity.

Willis — You write:

Each of the individual sin and cosine functions that make up the equation repeats in a regular periodic manner. How can their sum not be periodic?
If what you are saying is true, seems like it would make a theoretically perfect random number generator, one that never, ever repeats… and I doubt that.
Seems to me that the sum/product/difference whatever of a finite number of infinitely repeating cyclical functions has to be a repeating cyclical function, and that that is a recurring and big problem in random number generators

You are falsely conflating “periodic” with “quasiperiodic,” and conflating “nonperiodic” with “random.”
A sum/product/difference of periodic functions will only be periodic if all the periods are commensurate, i.e., have a least common multiple. If the periods are irrationally related rather than commensurate, then while the sum/product/difference will resemble a periodic function, it will never repeat exactly — hence the term “quasiperiodic.” A simple example is the sum cos(t) + cos(sqrt(2)*t): Because the two periods are related by an irrational number, sqrt(2), there is no value of T such that cos(t+T) + cos(sqrt(2)(t+T)) == cos(t) + cos(sqrt(2)*t) for all t; hence, the sum of two noncomensurate periodic functions is NOT periodic. While one can find T’s such that the average absolute error between f(t) and f(t+T) of a “quasiperiodic” function becomes smaller than some specified value “epsilon,” it can never be exactly zero; in the given example, these “quasiperiods” are related to the “continued fraction expansion” of sqrt(2).
Admittedly, any finite-precision approximation to a quasiperiodic function will be periodic, because any set of finite-precision numbers necessarily has a finite least common multiple — but that false “periodicity” is a property of the finite precision approximation, not the underlying quasiperiodic function — which itself can never repeat exactly, but only approximately in an “average absolute error smaller than some specified epsilon” sense.

If the sunspot numbers are due to the interaction of a variety of constant, cyclical processes, then curve fitting may indeed serve as an excellent predictor of future behavior, especially over the near term. In addition, the longer your calibration period is, the more likely your near term predictions are to be accurate (in the absence of chaotic processes). However, if chaotic processes are also involved then Willis is right. So in my opinion this curve fitting exercise is more a test of chaos vs the interaction of repeating cyclic phenomena.

impact factor is not that easy to game as it can be computed so that it discounts self-citations and citations from papers in the same journal. Google scholar also helps you judge the citations a paper has recieved because it will list for you all the papers that have cited it, and you can judge the quality from the reputations of the authors of the citing papers.
It is unlikely that predatory journals will try and game impact factors etc. There is no incentive for them to increase the quality of the journal, while performance is measured by quantity over quality there will always be a ready supply of authors wanting their papers published in the journal, no matter what its reputation.

I agree with you Willis – this is an astonishingly gimcrackery approach. I would add that the fit is not even very good (note the poor fits around 1780-1790, 1840, 1870, 1895, 1960). Perhaps it looks good because of the colours used. As you say, Fourier transform model with high frequencies removed would almost certainly do better.
I also agree with you statement “this model is not chaotic in the slightest. It is totally deterministic, and will assuredly repeat in exactly the same way after some unknown period of time.” For one thing, it is not sensitively dependent on initial conditions (unless he incorrectly thinks that the model parameters are initial conditions) because future states are completely determined by the equation, not by previous states.

agfosterjr you are missing the point, the patterns are “obvious” to the human observer *even though they don’t exist*. That is the problem.

Good presentation. Personally, I think the best test of predictivity is future out of sample data, but splitting the sample should at least be tried.
About this: BONUS MISTAKE: In the abstract, not buried in the paper but in the abstract, the author makes the following astounding claim:
The model is a slowly changing chaotic system with patterns that are never repeated in exactly the same way.
Say what? His model is not chaotic in the slightest. It is totally deterministic, and will assuredly repeat in exactly the same way after some unknown period of time.
A chaotic system is deterministic (unless it is a stochastic chaotic system, but no such claim is made here), but their model is perfectly periodic. Lots of chaotic systems can appear periodic over a few to many cycles, an example being the near periodicity of Earth’s revolution about the sun; another is the near periodicity of the heartbeat.

marsupial says: “Actually, it does, Google scholar will tell you how many times a paper has been cited; ”
citation counting is measure of conformity, not quality.
Met Office cites japanese paper that is complete bunk and eliminates data that does not agree before “finding” that the data “validates” Hadley “bias corrections”.
All this means is that Hadley find a geographically subjective paper, that says their adjustments are good, is a convenient citation that supports their speculative correction methods.
In engineering this would be recognised as a positive feedback, which causes is inherently unstable but is inevitably bounded by a negative feedback. The result is a system that latches to an extreme.
The current AGW paradigm is such a latched in extreme.
Quality is not a key factor in such a process.

Fitting a “Fourier Series” is easy if there is a “fundamental”, which there doesn’t seem to be for planetary orbits. (Well, you can always choose a low-enough harmonic. The Earth’s orbit is the 8766th harmonic of a period of 1 hour!). You can also exactly fit a time series, GUARANTEED, to an artificially chosen (your choice) of harmonics by a Discrete Fourier Transform (the FFT). Or choose your own basic functions in a wavelet-like approach. Gram-Schmidt them if you like. Choosing your parameters based on physical data also sounds very advisable. Whatever you like.
Now, having fit your elephant, test it. Wait 50 years for the new data! Not wishing to wait, you can simply go back, discarding say 50 years of data, and recalculate the parameters to the then-available data. Calculate forward to today. Does it fit the data you threw out? It better. And it better not BE diverging more and more as you approach the present.
About 45 years ago in a physics experiment I tried curve fitting. I tried graph paper from every bin in the campus store. Some results were quite lovely. My Professor (Herbert Mahr – bless his heart) was kind enough to commend my industry and my artistic effort and then remark that “this doesn’t mean anything.” Curiously, the exact same four words Willis said above.

Greg A paper that has been cited many times is much less likely to be fundamentally flawed than a paper that has recieved few citations. The reason for this is that it has been scrutinised by more eyes and has been tested by its use as the basis for other work. The chance of a flaw going undetected decreases the more the work is used, but never dissapears entirely. Of course you can find examples where the metric doesn’t give a reliable indication, but that will be true of any metric, and is not a good reason for ignoring a metric that is amongst the best that scientists have found useful so far.
Now if you think that scientists are conformists, I have to say my experience is different, there is nothing we like more than to show something is incorrect (falsification is an important concept in science) or to demonstrate some result that our research field will find surprising (that is what makes high impact papers). It is often said that getting academics to coordinate is like herding cats – there is more than enough truth in that for the analogy to work rather well.

“So this exercise by Salvador is valid as a predictive tool to see what his predictions are for the next two cycles and therefore is falsifiable per Popper’s requirement.”
true, but there is little reason to think that his model will work well, given that it has performed badly in the out of sample testing that has already been performed. Also since two cycles is a rather small amount of data compared to that used in the existing out of sample testing, it will not be that easy to draw a solid statistical conclusion either way.

Willis Eschenbach says:
January 22, 2014 at 3:43 am
“Thanks, Kasuha. Each of the individual sin and cosine functions that make up the equation repeats in a regular periodic manner. How can their sum not be periodic?
If what you are saying is true, seems like it would make a theoretically perfect random number generator, one that never, ever repeats… and I doubt that.
Seems to me that the sum/product/difference whatever of a finite number of infinitely repeating cyclical functions has to be a repeating cyclical function, and that that is a recurring and big problem in random number generators … but I’ve been wrong before …”
__________________________________________________________________
There’s no point in opinions or beliefs if we can check it:
http://www.wolframalpha.com/input/?i=periodicity+of+y+%3D+sin%28%28x+%2B+sin%28x%29%29%2F%281+%2B+sin%28x%29%29%29
Note that sin and cos functions are interchangeable if we have parameters in them which affect phase. Which is this case.
But it’s also not true that it would make perfect random number generator. It would be actually a very bad random number generator.

Willis
This is an incredibly patronising post and filled with sneer. One could accuse you of “Kettle calling Pot black” here.
BTW the author does do your suggested “Bozo test”.
Furthermore, he qualifies what he meant by ‘chaotic’ at the end of the paper (he wasn’t referring to the model as such rather the process).
I passed on the opportunity.
Yet saw fit to pull him on it.
On the paper…
It ain’t sophisticated stuff but then neither is applying a discrete Fourier transform – but then he now has a parameterised function that (for testing) is a whole lot neater than trying to expand a signal in the frequency domain with extra terms beyond the sample window; and before you say it, there are a myriad of ways to deal with this but none of them as simple as they seem and none of them right only “best-for-case”. I don’t know enough about solar cycles to know if this all has any value but overall I found it interesting and showed exactly what he wanted to show.

Matthew R Marler says:
January 22, 2014 at 11:02 am
Lots of chaotic systems can appear periodic over a few to many cycles, an example being the near periodicity of Earth’s revolution about the sun
Yeah I think, but I could be wrong, Willis was talking about the model, so we may all be talking cross-purposes here. But if he is assuming that chaotic systems are not periodic as you suggest then he is wrong and you’re right. The signal can be non-stationary (that is periodicity is not constant and can change randomly throughout the chronology). Of course there is a matter of scale. That point was made at the end of the paper.

There is mention here of Fourier Analysis (FA) that is not specific enough. Most likely FA should not even apply here. FA is familiar in its two most basic forms as the Fourier Series (FS) [ for example, … 2 Cos(f) + 7 Sin(2f) +…] which applies to periodic functions (integer harmonics), and the Fourier Transform (FT -integral transforms) that apply to non-periodic functions. The famous Fast Fourier Transform (FFT) efficiently computes the Discrete Fourier Transform (DFT), and being a computation on discrete data, can APPROXIMATE either the FS or the FT when they can’t be solved analytically (the usual case). [ Incidentally, although composed of the sum of two periodic components, Cos[f] + Cos[sqrt(2)f], for example, is not periodic.] As another reference example, the highly regarded Akasofu linear trend + sinusoidal is neither a FS nor a FT, partly periodic, partly not, but is delightfully easy to envision as just an equation. In this post, we also have, most basically, just an equation.
It is not clear that Fourier Analysis should be applied to sunspot data (it seems otherwise), which is at best quasi-periodic. Indeed the equations Willis posts are phase-modulation or frequency-modulation equations and almost certainly can (in theory) be solved in terms of discrete frequencies (something like, but a lot more tedious than the usual Bessel-function sideband amplitudes). An FFT could be then applied to verifying these “sideband” calculations, if they were done, but it is far from certain any additional insight would result.
Before working on this however, one might want to consider what physics (if any) would suggest a modulation result. And, the projections of the model into the test gaps would need to be a lot better – like approaching the quality of the full fit.

Willis,
Look up the term superficial again please.

RJ’s calculations have been available (in .xls format) for more than 3 months.

Thank you Willis; thank you Anthony; thank you “Pattern Recognition” scientists. Duking it out with your different definitions — trying to find a common ground or the specific failure — different hypotheses, statistics, math, this is what it is about. Continuing the scientific method. I hope the very hard, hurtful, feelings can heal. It is difficult enough to slug it out over scientific principles and methods, but when one holds a horribly falsified academic process called peer review sacred, the science can be lost.

Steven Mosher says:
January 22, 2014 at 5:25 pm
FrankK.
Last I checked its gone up since 1988. See how easy it is when u dont quantify things
——————————————————————————————-
?? Nonsense. He predicted it would keep rising beyond 2000 to 2030
http://wattsupwiththat.com/2012/06/15/james-hansens-climate-forecast-of-1988-a-whopping-150-wrong/
It hasn’t so far from 1998 to 2013. See how easy if you ignore the obvious!

More good news,
Morner was a thesis advisor to Jelbring,
http://www.pog.nu/03education/education.htm
How many publication rules does that break? Mashey is having a field day.

Until last week, the “official” consensus understanding of the longest of the Milankovich cycles, eccentricity, was that both its 100,000 year period and the 400,000 year modulation of its amplitude, were a direct consequence of interaction of earth’s orbit with those of s.a.t.u.r.n and j.u.p.i.t.e.r .
But, post PRP-gate, can we now still say this? Can we even mention the names of other planets in the s.o.l.a.r s.y.s.t.e.m at all? Are there any such things?
It looks like the PRP scandal has put the scientific community firmly on course to return to the pre-Copernican geocentric view of the universe. Who reviewed Galileo and Copernicus? A few like-minded Jesuits? All this heliocentrism will have to be rejected. Nothing affects the earth’s orbit because the earth does not orbit, instead a 2d disc sun rotates in a glassy sphere around a static 2D Narnia-diskworld earth.
It will of course be a delight for the research community with its powerful computational resources to return to the task of getting epicycles to work correctly after an anomalous and inadequately peer reviewed interval of several centuries.
Great to see science striding confidently in the right direction!

In talking about using the Fourier Transform on the sunspot data and/or the model, this is hardly the “blunt instrument” Roger suggests (Jan 23, 12:14 am). But neither did Willis give any details (Jan 22, 6:34 pm). I assume we are talking about using the FFT of a time series.
First, above at 7:32 pm Jan 22, I mentioned that any “beat frequency” should not be in the spectrum. This is true, but I need to refine that comment. The reason relates to the use of the absolute value, which you would never do before taking a spectrum. In the math model, the underlying signals are clearly bipolar as being derived from cosines. But then they take an absolute value. I believe I have also seen suggestions (if not assertions) that every other cycle of actual sunspot data is (in some sense) flipped, and is accordingly sometimes “un-rectified” for proper interpretation. Thus while the cycles “bumps” have an 11 year periodicity, the fundamental period would be 22 years. The 11 year cycle is built into the math model, although as an artifact of the (non-linear) absolute value. By eye, if there are harmonics of the 22 year period in the actual data, they seem to be odd harmonics (i.e., a third harmonic of period 7.3333 years).
It could well be that the “sign” of the alternating cycles is irrelevant to any astronomical consequences or implications for Earth’s climate. Does Nature “self-rectify” and disregard the sign? Quite possibly. But the absolute value has severe consequences for using Fourier Analysis.
Seeing an 11 year cycle and lower frequencies due to any amplitude variations (even beat-like effects) is consistent with using absolute value. Without this, we should expect a 22 year period largely devoid of lower frequency components.
This and many other issues with Fourier Analysis are familiar to electrical engineers from the early days of building power supplies to “envelope” extraction of speech and music.

lsvalgaard said, January 23, 2014 at 10:08 am
“Bernie Hutchins says:
January 23, 2014 at 10:00 am
The reason relates to the use of the absolute value, which you would never do before taking a spectrum. ?
The sunspot number is strictly positive and there is no physical justification for introducing a sign that changes at sunspot minimum.”
Thanks Dr. Svalgaard. I kind of had the feeling you would be the one who would know. Agreed that the counting numbers are strictly positive. But I could suppose it might be like ocean tides: two a day for one rotation, and if you have a picnic on the beach, you are chased by the water twice a day in much the same (absolute!) way, despite a once-daily rotation.
You put a (?) after my sentence about never using absolute value before taking an FFT. My reason for stressing that is simply that it would of course give you an FFT of a different signal. For example, instead of a single sinusoidal you would get DC plus all even harmonics, of the sinewave which is now gone completely. Taking absolute value (technically the magnitude of a complex result) AFTER the FFT is common, rather than displaying real and imaginary parts (or keeping a separate phase display).
I am not by any stretch knowledgeable of, or a fan of, sunspot “counts”. (Is this particular spot one or two – and do we count this tiny one as much as this huge one? Etc.) Very noisy data at best? But I think that what I said (the cautions) about using the FFT, are correct.
Again thanks for the reply.

Leif –
Thanks – got it.
I was at a talk on AGW where one individual said that the skeptics were using silly notions – even counting sunspots – good for a laugh it seemed. The way he said it, he might have said tea-leaves or chicken entrails. For more than 50 years, I have known about sunspots, short-wave reception, the ionosphere, etc. This individual was a professor of electrical engineering specializing in upper atmospheric physics, space plasma physics, and radar. Nature is just subtle. People are perplexing!
Thanks for all your good work.
Bernie

cd: Yeah I think, but I could be wrong, Willis was talking about the model, so we may all be talking cross-purposes here.
The authors said “The model is a slowly changing chaotic system with patterns that are never repeated in exactly the same way,” and Willis correctly pointed out that the model is perfectly periodic. But then he contrasted “deterministic” with “chaotic”.