Guest Post by Willis Eschenbach
There are a number of lovely folks in this world who know how to use a shovel, but who have never sharpened a shovel. I’m not one of them. I like to keep my tools sharp and to understand their oddities. So I periodically think up and run new tests of some of the tools that I use.
Now, a while ago I invented a variant of Fourier analysis, that I called the “Slow Fourier Transform”. I found out later I wasn’t the first person to invent it—Tamino pointed out that it was first invented thirty years ago, and that it is actually called the “Date-Compensated Discrete Fourier Transform”, or DCDFT (Ferraz-Mello, S. 1981, Astron. J., 86, 619). Figure 1 below shows an example of the DCDFT method in use, a periodogram of the cycles in the sunspots:
Figure 1. Periodogram, annual sunspots. The horizontal axis shows length of possible cycles from one to 100 years, and the vertical axis shows the strength of those cycles.
Now, in Figure 1 we can see the familiar 11-year sunspot cycle in the data, along with somewhat weaker sunspot cycles of 10 and 12 years. It also APPEARS that we can see the claimed ~90-year “Gleissberg Cycle”.
However, a deeper examination of the sunspot data shows that the “Gleissberg Cycle” only exists in the first half of the data, and even there it only exists for a couple of cycles. Figure 2 shows a Complete Ensemble Empirical Mode Decomposition of the same sunspot data. The upper graph in Figure 2 shows the underlying empirical modes, and the lower graph shows their frequency:
Figure 2. CEEMD, annual average sunspot numbers. UPPER GRAPH: Panel 1 shows the raw sunspot data. Panels C1 through C7 show the seven empirical modes, in order of increasing period. The final panel shows the residual. If you add the bottom eight panels together, you get the raw data shown in the first panel. LOWER GRAPH: Periodograms of the empirical modes. These show the nature of the individual
The ~90-year purported “Gleissberg cycle” is shown in empirical mode C6. In the lower graph in Figure 2, we can see that after the 11-year cycles, C6 has the second-strongest cycle in the data … but in the upper graph, we can see that whatever signal exists, it is actually fairly short-lived, dying out after only a couple of cycles.
And that means that my periodogram shown in Figure 1 was misleading me—the peak at around 90 years was not actually significant. It only lasts a couple of cycles.
So I wanted to sharpen my periodogram tool so it would indicate which cycles are statistically significant. In the past I’ve tested my method by looking at periodograms of square waves, and of individual sine waves, combinations of sine waves and the like.
This time I thought “What I want to test next is something totally featureless, something like my imagination of the Cosmic Background Radiation. That would help me distinguish random noise from significant cycles.
Well, of course I don’t have the CBR to test my periodograms with, so here was my plan for generating some random noise.
I generated a series of sine waves at all periods from one year to thousands of years. They all had the same amplitude. Next, I randomized their phases, meaning that they all started at random points in their cycle. I figured, nothing could be more generic and bland than the sum of a bunch of sine waves of equal strength of all possible periods. Then I added them all together, and plotted the result.
Now, I’m not sure what I expected to find. Something like a hum, something kind of soothing. Or perhaps like on the ocean, when you have small wind-ripples on top of a chop on top of a swell with a bigger swell underneath that. Harmony of the spheres kind of thing is what I thought I’d get, complex but smooth like some mathematical BeeGee’s harmony… however, this was not the case at all. Figure 3 below shows a sample of one of the many different results I’ve generated by adding together thousands of sine waves of identical amplitude covering all the periods
Figure 3. Ten examples of what you get when you add together thousands of sine waves evenly blanketing an entire range of frequencies.
These results were surprising to me for several reasons. The first is their irregular, jagged, spiky nature. I’d figured that because these are the sum of smooth sine waves, the result would be at least smoothish as well … but not so at all.
The next surprise to me was the steepness of the trends. Look at Series 4 at the lower left of Figure 3. Note the size and speed of the rise in the signal. Or check out Series 3. There is a very steep drop in the middle of the record.
The next thing I hadn’t foreseen is the fractal, self-similar nature of the signal. Because it is composed of similar sine waves at all (or at least a wide range) of time scales, the variations at shorter time scales are very similar to variations at larger scales.
I was also not expecting the clear long-term cycles and trends shown in the various random realizations. Regarding the cycles, I had expected that the various sine waves would cancel each other out more than they did, particularly at longer periods.
And regarding the trends, I had thought that because none of the underlying sine waves contained a trend, then as a result the sum of them wouldn’t have much of a trend either. I was wrong on both counts. The signals contain both clear cycles and clear trends.
Another unexpected oddity, although it made sense after I thought about it, is that like a variety of natural climate datasets, these signals all have very high Hurst exponents. The Hurst exponent measures what has been described as the “long-term persistence” of a dataset. Since all of these signals are the sum of unchanging sine waves which assuredly have long-term persistence, it makes perfect sense that these signals also have a high Hurst exponent.
Upon contemplation, I also note that these series are totally deterministic, but with a very long repeat time. For example, the repeat time of all possible periods from 2 to 100 is 6.972038e+40 cycles.
The strangest part of all of this is that the signals look quite lifelike. By that, I mean that they look like a variety of climate-related records.Any one of them could be the El Nino Index, or the temperature of the stratosphere, or any of a number of other datasets.
So after I generated my random datasets composed solely of unvarying sine waves, I used my periodogram function to see what the apparent frequencies of the waves were. Here is a sample of a few of them:
Figure 4. Periodograms covering waves from one to 3200 cycles, in a dataset of length 12,800.
Now, at the left end of each of the graphs in Figure 4 we can see that the periodograms are accurate, showing all cycles as being the same small size. This is true up to about 100 cycles, or about 1/30 of the length of the dataset. But as we get further and further to the right, where we are looking at longer and longer cycles, we can see that we get larger and larger random peaks in the periodogram. These can be as large as forty or fifty percent of the total peak-to-peak range of the raw signal.
In order to gain a better understanding of what’s going on, I plotted all of the periodograms. Then I calculated the mean and the range of the errors, and developed an equation for how much we can expect in the way of random cycles. Figure 5 shows that result.
Figure 5. Periodograms of 100 datasets formed by adding together unvarying sine waves covering all periods up to the length of the dataset, in this case 12,800. Dotted line indicates the level below which we find 95% of the random data.
I also looked at the same situation at various dataset lengths, down to about 200 data points. Here, for example, is the situation regarding a random dataset of length 316, the same length as the annual sunspot record.
Figure 6. Periodograms of 100 datasets formed by adding together unvarying sine waves covering all periods up to the length of the dataset, in this case 316. Dotted line indicates the level below which we find 95% of the random data.
Now, this has allowed me to develop a simple empirical expression for the 95% confidence limit. As you can see, the error increases with increasing length of the period in question.
And this is the precise sharpening of the tool that I was looking for. Let me start by revisiting the first figure above, the periodogram of the sunspots, and I’ll use the same error measure of the amplitude of 95% of the random cycles:
Figure 7. As in Figure 1, but with the addition of the line showing the extent of 95% of the random errors as described above.
As you can see, this distinguishes the valid signal at 11 years from the two-cycle fluctuation at 88 years. If you compare this to Figure 6, you can see that a cycle at 88 years needs to be quite large in order to be statistically significant.
Now, I mentioned above that the random datasets generated by this method look very similar to natural datasets. As evidence of this, Series 7 in Figure 3 above is not a random dataset like the others. Series 7 is actually the detrended record of the historical variations in ∆14C, which I discussed in my previous post … compare that actual observational record to say Series 2. There’s not a lot of difference.
And this brings me to the reason for this post. I’ll start by quoting from my previous post linked just above, which discussed the results of a gentleman posting as “Javier”, who in turn used the results of Cliverd et al. If you have not read that post, please do so, as it is central to these findings. In that previous post I’d said:
Let me recapitulate the bidding. To get from the inverted 14C record shown in Figure 3 to the record used by Clilverd et al, they have
- thrown away three-quarters of the data,
- removed a purported linear trend of unknown origin from the remainder,
- subtracted a 7000-year cycle of unknown origin , and
- ASSERTED that the remainder represents solar variations with an underlying 2,300 year period …
The series shown as “Series 7” above is the result of the first two of those steps. As you can see, there is claimed to be a 7000-year signal that they say is “possibly caused by changes in the carbon system itself”. However, there is no reason to believe that this is anything other than a random variation, particularly since it does not appear in the three-quarters of the data that they’ve thrown away … but let’s set that aside for the moment and look at the result of subtracting the purported 7,000-year cycle from the ∆14C data. Here is the periodogram of that result:
Figure 8. Periodogram of the ∆14C data after removal of a linear trend of unknown origin and a 7,000 year cycle of unknown origin.
Note that this seems to indicate a cycle of about 960 years, and another at about 2200 years … but are they statistically significant?
In the comments to my post, Javier replied and said that I was wrong, that there indeed is a ~2400-year cycle in the ∆14C data. I pointed out to him that a CEEMD (Complete Ensemble Empirical Mode Decomposition) shows that in fact what exists is several cycles of about 2100 years in length, and then sort of a cycle of 2700 years length, and then another short cycle. This result is seen in the empirical mode C9 below:
Figure 9. CEEMD of the ∆14C data after removal of the linear trend and a 7,000 year cycle. Panel 1 shows the raw ∆14C data. Panels C1 through C9 show the nine empirical modes, in order of increasing period. The final panel shows the residual. If you add the bottom eleven panels together, you recover the raw data shown in the first panel.
In empirical mode C9 above you can see the situation I described, with short cycles at the start and end and a long cycle in the middle.
Mode C8 is also interesting, as it has a clear regular ~1000-year cycle at the beginning. Strangely, it tapers off over the period of record to, well, almost nothing. Again, I see this as evidence that this is simply a random fluctuation rather than a true underlying cycle.
In my discussion with Javier, I held that in neither case are we seeing any kind of true underlying cyclicity. And my thanks to Javier for his spirited defense, as it was this question that has led me to sharpen my periodogram tool.
And to complete the circle, Figure 10 below shows what my newly honed periodogram tool says about the ∆14C data:
Figure 10. As in Figure 8, periodogram of the ∆14C data after removal of a linear trend of unknown origin and a 7,000 year cycle of unknown origin, but this time with the addition of the line showing the limit of 95% of the cycles created by the addition of sine waves.
I note that neither the ~ 1,000-year nor the 2,400-year cycles exceed the range of 95% of the random data. It also bears out the CEEMD analysis, in that the ~1000 year period shows more complete cycles, and more regular cycles, than the 2400 year period. As a result, it is closer to significance than the ~2400 year cycle.
Conclusions? Well, my conclusion is that while it is possible that the ~ 88-year “Gleissberg cycle” in the sunspots, and the ~1,000-year cycle and the ~ 2400-year cycle in the ∆14C data may be real, solid, and persistent, I find no support for those claims in the data that we have at hand. The CEEMD analysis shows that none of these signals are either regular or sustained … and this conclusion is supported by my analysis of the random data. The fluctuations that we are seeing are not distinguishable from random fluctuations.
Anyhow, that’s what I got when I sharpened my shovel … comments, questions, and refutations welcome.
My best to everyone, and my thanks again to Javier,
w.
As Always: I, like most folks, can defend my own words and claims. However, nobody can defend themselves against a misunderstanding of their own words. So to prevent misunderstanding, please quote the exact words that you disagree with. That way we can all be clear regarding the exact nature of your objection.
In Addition: If you think I’m using the wrong method or the wrong dataset, please link to or explain the right method or the right dataset. Simply claiming that I am doing something the wrong way does not advance the discussion unless you can show us the right way.
More On CEEMD: Noise Assisted Data Analysis
Actually Willis, an interesting experiment would be to build not a random number, but use the orbital periods of the magnetic planets, and start generating sunspot records, and see if that’s what you get.
The problem is that there are literally hundreds and hundreds of periods involved in the sun, moon and planets. All of them travel in a complex motion, are tilted on their axes, have eccentricity in their orbits, and interact gravitationally with all of the others.
So just which “orbital period” are you suggesting we use … and how will you pick it in advance? Because if you just start looking at random, the Bonferroni correction will soon eat your results for lunch …
w.
Willis: You can silence the criticisms of your construction of sine waves by simply using the original sample and shuffling the data points to get random samples. By construction, this approach removes any periodicity in the series – but you will still “detect” periodicity using periodigrams. This approach has an added bonus of preserving any of the statistical artifacts that might be created by the underlying sampling distribution. For example, heavy tails can falsely show up as significant short-period cycles.
Great work! Look at Voit, “The Statistical Mechanics of Financial Markets” for even more of these types of tricks!
W said he used random phase, so I assume he used a random number fn to do that. If he just used the same fn to get the data he would have properly random data from a tested and verified algo. The danger with homespun methods is that you need to test them before relying on them, as Mickey Mann never ceases to demonstrate.
I don’t understand this comment. The “data” is just the sum of the sine waves with random phases. How could I “use the same fn to get the data”? What does that mean?
w.
Sorry if that was not clear. I meant in generating your random data. You used a random fn for the phase in simulating some random data. Why not just use the random fn to create random data. It seemed like this was a rather an odd way to create “random” data whilst using a random number generator.
It seems that you were expecting white noise and saw the stronger long periods as anomalous “false” cycles that people were often misreading as being real in this kind of data.
Your figure 5 shows your 95% which looks a lot like 1/x plotted backwards. ie it is “red noise”, not white.
This makes sense with the way you loaded the data by using equal period intervals, as I explained.
I’m sure you have created random walk / AR1 / red noise test data before, so I was saying it would be better to use the tested algo for random numbers and create it directly rather then the novel method where you apparently got an unexpected result.
Random number generators are usually far from truly random and their output is usually distributed uniformly. By utilizing that output only for the phase of the sinusoids, one takes the first step toward generating GAUSSIAN random data. The next step, alas not taken by Willis here, is to make the periods of the sinusoids incommensurable, thereby avoiding periodic repetitions. There’s a vast literature available on Gaussian time series.
Greg November 4, 2016 at 11:03 am
I used a uniform random number function to generate a value between -pi and +pi to randomize the phase.
However, my results are a million miles from being uniform random numbers … so why would I want to use that function to generate data?
w.
Why, well originally you said you wanted random numbers, so that would have been the obvious choice. Now it seems that you prefer a red-noise model, though you never explicitly stated that nor why you think it is the best null hypothesis for SSN.
Not saying that is necessarily wrong but if that is your intention you should say that is your model and why your chose it to decide what is significant for SSN.
If you want red noise you can just integrate the white noise from the random number generator. I suggested a cumulative integral but you seem to have missed it , which is why you are still asking why I think you could have used that fn to get the test data.
Instead of a thousand sine calculations and a thousand additions for each point it would require one sum!
Since you did not realise that you were making red-noise, you would not have realised this, otherwise I’m sure you would have gone straight for it.
You are making some very strident claims about what is/isn’t significant without saying why you have chosen a particular noise distribution model or without apparently realising which noise distribution you were using.
Now it may be true that these longer periods are not significant compared to random walk but so far you do not present any reason for assuming SSN is a random walk other than remarking the many “other” natural [ terrestrial ] data look a bit like that too.
There may be some mileage in this but so far you have failed to justify the basis for your significance test.
Best Greg.
“trick” is the meaningful word used here.
G
Who is it that you think you are tricking this time, George?
w.
So what. Baffle ’em, razzle-dazzle ’em, with snazzy pictures that answer the wrong questions if there even are related or meaningful questions.
I have no clue what you’re talking about. Let me ask you again to QUOTE WHAT YOU DISAGREE WITH, because at present you are just screaming at the wind, and that is less than useless.
w.
Yes, many natural processes like temperature time series are strongly auto-correlated due to the thermal inertia of the system. So to conclude that your analysis shows that the longer periods are not significant in SSN you need to show that the mechanism producing them has similar properties, or say that IF whatever produces sunspots is a random walk, the longer “periods” may be illusions.
Perhaps a simpler method would be do the FT on d/dt(SSN) and compare to white noise.
If you look at ddt , you will find that the peak solar activity is around 31 days. It does not look all that white either.
beg your pardon, there are big peaks around 13.5 days which is because of our one-eyed observation point of the predominant circa 27d equatorial rotation, though there is a peak at 30.25 days.
Odd indeed that this is reminiscent of the lunar periods. Maybe the same thing is causing both.
power spectrum of daily d/dt(SSN) for continuous daily record since 1849. Period in days.
This analysis leaves me with one over-riding question — how many people sharpen their shovels? I can honestly say that I have never sharpened a shovel, nor have I ever considered it something that needs to be done. I must not do enough shoveling.
This has raised many questions for me. Do all shovels need to be sharpened? What about snow shovels? I live in Florida now, but my snow shovels used to be plastic. If you have a painted shovel head, do I need to repaint it after I sharpen it.
How do you tell that your shovel needs to be sharpened? Do you measure the radius of the blade or do you worry more about the number of nicks? Do you use a grinding stone or a file?
And, of course, the obvious question — How much is your shovel blade wear affected by climate change?
I know what your thinking — this is the internet. If I wanted to find all of these answers, I could (except for the climate change question. I couldn’t find that one.)
https://www.sharpeningsupplies.com/Sharpening-a-Shovel-or-Spade-W90.aspx
You typically sharpen shovels when you want to use them as a weapon 😉
lorcanbonda November 4, 2016 at 10:13 am
Good questions all. As to how many people sharpen their shovels, I’d include those who earn a wage using a shovel … including myself in my younger years. Ten hours a day, pick and shovel, five days a week … I got a raise that year, to the princely rate of fifty cents an hour. But then I was fifteen, and overjoyed to have a job …
There’s shoveling, and there’s shoveling.
Shovels get dull like any other tool. But it depends on your usage. If you are using a “materials handling” shovel to pick loose sand up off of a concrete floor, the action will keep the flat edge of the shovel sharp by constantly whetting it against the concrete.
But if you do a lot of digging where there are roots in rocky soil, pretty soon you’ll find that your shovel won’t cut the roots …
These are a type of materials handling shovel, and if you are shoveling a concrete driveway, it will keep itself sharp … but snow shovels don’t generally need to be much sharper than an ice cream spoon unless you’re using it to chisel ice off the walkway.
If you need to sharpen it, it is likely being used in an environment where the paint will come off fairly rapidly and you’ll be where you started. However, the marine environment in Florida is death on tools, so you might want to paint it. However, a bit of rust won’t bother most shovels. You might consider just wiping the edge with an oily rag before putting it away if it is an issue.
Look at the edge. You’re not looking for a razor edge, typically more like a 45° bevel on each side. If there are bent-over sections of the edge, I flatten them out using a smooth-faced hammer against an anvil … or a hammer against a rock.
I just beat out any bent sections, grind or file the front and back edge nicks and all, and go back to shoveling. Nicks that are sharpened cut just fine.
Back in the day I always used a file. These days I use my Black and Decker battery-powered angle grinder …
My best to you,
w.
Regarding the upper graph set of Figure 2, the CEEMD of sunspots 1700-2015: I see noticeable correlation between adjacent components, generally occuring intermittently but enough to cause correlation throughout the period. So, I think the CEEMD resolved the sunspot record into an excessive number of components by failing to give consideration (or sufficient consideration) to C3 (the ~11-year cycle) being modulated by longer period ones.
I think a more accurate representation would be:
* Removing C2, and distributing its content to add to C1 and C3, as appropriate for frequency
* Removing C4, and distributing its content to C3, C5 and C6, as appropriate for frequency
* After that, consolidating C5 and C6, and possibly also shifting some of the lower frequency content of C6 to C7
This changes the number of components from 7 to 4, and I think such 4 components will stand out better as showing a longer period one as an identifiable cycle than the 7 ones shown. The four components would then be:
* Short term noise,
* The ~11-year cycle whose amplitude and frequency is (as already shown) not constant,
* A ~50-90 year cycle with similarly non-constant amplitude and frequency no more unsteady than shown in C4-C7 in the upper graph set of Figure 2, and standing out better than C4-C6 in that graph set, which would be the Gleissberg cycle, and
* a longer term variation of questionable statistical significance if the duration of 1700-2015 is considered but likely correlating well with the Dalton, Maunder and Sporer and Wolf minima and the minimum before the Oort Minimum, and the Oort minimum being a couple decades late but otherwise correlating well. That would be the Seuss cycle, with period averaging about 200 years.
One more thing: The Moeberg paleoclimate record shows a not-quite-constant bounciness with a period that is somewhat unsteady but mostly around 50-80 years.
It appears to me that Dalton minimum and the ~1910 minimum were minima of the Gleissberg cycle while the minimum of the Seuss cycle was between them. The upcoming solar minimum appears to me as being the Gleissberg and Seuss cycles bottoming out nearly simultaneously – it could reach a Maunder-like depth but for a much shorter amount of time than the Maunder Minimum. The Maunder Minimum appears to me as the bottom of a ~1,000 year cycle that is not sinusoidal, but distorted towards a sawtooth wave by taking less time to rise and more time to fall than a sinewave – which is also the case with the ~11-year cycle.
A test that I propose for my hypothesis: Adding the next 7 decades to the 1700-onward sunspot data, and looking for increased support of my proposed 4 components including the Gleissberg cycle.
There is quite a lot of overlay since the bandpass filters are never a clear cut-off at either end. Some intermediate frequencies will be split between bands. That could give the impression they are not significant, for example by attenuating a periodicity which sits near a border only half appears on each side. Like all tools it needs some appreciation of what it is doing and how to read it.
“The Moeberg paleoclimate record shows a not-quite-constant bounciness with a period that is somewhat unsteady but mostly around 50-80 years.”–Don Klipstein
Moe Berg’s records show a lifetime average of .243, though he batted .311 with Reading. He knew 12 languages and was once sent to assassinate a German nuclear scientist at a physics conference. After hearing the man speak, Berg slipped away without drawing his gun, realizing the man’s approach wouldn’t soon result in a nuclear bomb.
But you’re probably talking about Moberg. He can hit, but he can’t run.
http://sabr.org/bioproj/person/e1e65b3b
Donald L. Klipstein November 4, 2016 at 10:14 am
Donald, thanks for your comment, but you seem to misunderstand the “empirical” part of the CEEMD analysis. The bands were not chosen by you, me, or anyone else. They are determined empirically, based on the dataset itself. I’m sorry you don’t like what they say, but there it is, and you don’t get to rearrange it to fit your fancy.
Next, while it is fine to wave your hands at purported cycles like a “Suess Cycle”, and a “Gleissberg Cycle”, and a “Hale cycle”, and a “deVries Cycle”, and a “Hallstat cycle”, my point is that the evidence at hand does not support such constructs.
My best to you,
w.
The 1700-2015 data alone does not support the Seuss cycle to an extent of statistical significance, and I think the reason is that 1700-2015 covers less than two periods of it.
– which also shows the Seuss cycle. I also note here that the Figure 10 periodogram has a spike at a period close to the second harmonic (~500 years) of the ~1,000 year cycle that shows up well there. Other spikes show up as possibly the 3rd, 4th and 5th harmonics. However, existence of these harmonics at slightly-off-frequency (slower for 2nd, 3rd and 4th harmonics) is suspicious, but possibly explainable if they are stronger when they are running slower and weaker when running faster. Notably also, the ~11-year cycle has its amplitude unsteadiness and its period unsteadiness correlating with each other (slower when weakening).
Meanwhile, I think the Figure 9 CEEMD graph set supports existence of the Seuss cycle (C6), and the Gleissberg cycle (C5, although something of that frequency briefly shows up in C4). The amplitude of these cycles is unsteady – like that of the ~11-year cycle. The frequency of these is non-constant, but the ~11-year cycle also does that a little. The ~1,000 year cycle shows well, but in C8 before the MWP and in C7 during and after. C7 may have most of existence being lower harmonics (especially the second harmonic) of the ~1,000-year cycle – which is non-sinusoidal by having a faster rise and slower fall than a sinewave (like the ~11-year cycle) according to
I suspect CEEMD could be improved upon by comparison of phasing of one cycle with the one of the next lower frequency or two for detection of harmonics to assign to the lower frequency cycles that generated them. And notably, I think the ~11-year cycle has its amplitude being very unsteady – so I think longer period solar cycles can do the same and still exist. As I said before, I think CEEMD resolves more components than actually exist by failing to detect relationships between one resolved component and another. (When I said that previously, I mentioned a component being modulated by a longer period one – which I still think is true – although now I want to add harmonic relationships to this.)
As for the deVries cycle: That is another name for the Seuss cycle. As for the Hallstadt cycle: I did not claim it exists.
As for the Hale cycle: I did not claim before now in this thread that it exists, although I believe it may have some physical effects on/over some regions of Earth. The Hale cycle is the sun’s global magnetic field reversing polarity once per full cycle of the ~11-year cycle so a full cycle of the sun’s global magnetic field polarity is ~22 years, and a ~22-year cycle of physical effects on Earth would be from interaction of the sun’s periodically reversing magnetic field with Earth’s (comparatively) more-constant magnetic field.
Sharpening shovels probably isn’t all that important. Unless you have an axe to grind.
If you think sharpening shovels is not important, it’s clear you haven’t done enough shoveling …
w.
Willis: These results were surprising to me for several reasons. The first is their irregular, jagged, spiky nature. I’d figured that because these are the sum of smooth sine waves, the result would be at least smoothish as well … but not so at all.
You may be familiar with the Weierstrass Function (http://mathworld.wolfram.com/WeierstrassFunction.html) that is continuous everywhere and differentiable nowhere. Historically, this was an important moment in mathematical understanding because it showed that continuity in no way implies differentiability, not even in a weak sense.
I hear patterns when the rain drops into the barrel — regardless of whether or not. At the Cedar River Watershed Education Center (east of Seattle) drums have been placed under a dozen drip points, so “the patterns” are fast and fantastic. Doing a DCDFT here would not be appreciated.
~~~~~~~~~~~~~~~
At 83 comments and counting, I hope you don’t mind if I comment on:
“There are a number of lovely folks in this world who know how to use a shovel, but who have never sharpened a shovel.
We use USFS** sharpened shovels/scrapers as volunteers — building and fixing trails in the Cascades. [**Not a garden-store type shovel.] And, yes, we keep them sharp.
John, a sharp shovel is a wonderful tool …
w.
Russian SpetsNaz offensive shovel:
http://www.incredible-adventures.com/graphics/russian_throw_shovel.jpg
I wonder what you would show if you only used “new” sunspot count. Historically each time a spot rotated into view, it was counted as a “new” sunspot. I guess it would be difficult in the old days to know if the spot was “new” or was just long lasting.
And I do have to sharpen shovels because our soil is sand, stones and volcanic ash.
So the Maunder Minimum and Dalton Minimum are either long lived urban legends or one-off events.
Willis,
Very nice work and presentation. I am wondering if you have seen https://www.youtube.com/watch?v=l-E5y9piHNU – “All Climate Change is Natural” – Professor Carl-Otto Weiss. Given your interest and analysis, I think you might find his work interesting and complementary to your own. – Barbara
Thanks for the link, Barbara, I’ll take a look.
w.
I wonder if the smarter dinosaurs concluded this about major impactors during the late Cretaceous.
Thanks, Willis, very interesting and perception-changing. Regarding the conversation about ∆14C: All analyses are based on time. I would like to see an analysis based on sunspot cycle (SSC) instead of time. By this, I mean that the peak say of cycle 1 would be 1, of cycle 2 would be 2, etc, the ‘middle’ of the trough between cycles 1 and 2 would be 1.5, etc. Of course there would be some arbitrary decisions and approximations to make, but the end result would be (I think) to make much clearer the relationship (or non-relationship) between ∆14C and SSC. The same base used for other values – temperature for example – would also give a clearer picture of the relationship (or non-relationship) to SSC. In particular, a Fourier analysis of SSC on this base would show a much stronger cycle at frequency 1 than the time-based Fourier analysis shows at frequency ~11 (and that’s the point). I suspect that analysing various measures using this base might also throw up some unexpected ‘cycles’ which might turn out to be interesting/useful.
[Yes I could do it myself not just ask you to do it, but I have less skill, less tools, less data, and being in the middle of moving house, less time. The value that you would add would be very high.]
@Javier
perhaps you can help me
where did the 2400 yr cycle came from?
last I checked it was clear which of the longer solar cycles [longer than the 11-22 yr sc]
were relevant…
http://www.nonlin-processes-geophys.net/17/585/2010/npg-17-585-2010.html
i.e. do you agree that the DO cycle of 1470 years is not relevant?
HenryP,
I don’t understand your question.
I don’t believe the evidence supports that the D-O cycle is of solar origin. But of course the D-O cycle is relevant. It is the most drastic, abundant, abrupt climate change in the geological record.
A little-appreciated relation in trigonometry is the sum/difference relation:
sin x +/- sin y = 2*sin(1/2*(x +/- y)) * cos(1/2(x -/+ y))
(as well as I can render it in plain text)
Implication: adding 2 sine waves of different periods produces a complex wave of a higher frequency (x + y) modulated by a second wave of a lower frequency (x – y).
So, for example, a wave of 10 years added to a wave of 11 years frequency will produce an apparent wave of 1 year frequency modulated by another wave of 21 years frequency.
When you create canonical ‘white noise’ as you have, you will get a result that includes a multitude of waves of 1 year frequency (the interval between successive wave components in your construction) modulated at frequencies from 2N – 1 years (assuming you started at A years and finished at N years) down to 2A +1 years.
The relative phases will determine whether the addition is constructive or destructive.
Reminds me of the search for meaning in brain waves, a notoriously random thing. Evoked signals, which are often below the amplitude of random brainwave strength, can be calculated through the process of mathematically subtracting peaks and troughs of the electrical potentials picked up on the surface of the head (after scratching it up a bit, buttering it with jelly, then squishing an electrode cup into the jelly). Over time you get a straightish line from which evoked (have the subject listen to something, like a series of white noise or frequency centered pings) signals rise out of, all done in real time.
The 2402 year cycle is known as the Charvatova cycle (Ivanka Charvatova).
She found that there was disorder in the SSB orbit of the sun. The sun carves
out a three leaf clover shape every ~59.5779 years (tri-synodic). This tre-foil
configuration gets disordered in ~2402 year cycles.
Also:
The sun returns to the same position on the ecliptic every ~2649.63 years.
This is a 360 degree rotation of the sun’s outwardly directed acceleration.
The earth is caught up between a large moon and an accelerating sun.
So . . we get a large tug from the sun every ~2649.63 years.
Our axial precession cycle is a simple beat created by these two cycles.
2649.63 x 2402.616 / ( 2649.63 – 2402.616 ) = 25772 years
Please visit Weathercycles.wordpress
” Fibonacci and climate “
Conclusions? Well, my conclusion is that while it is possible that the ~ 88-year “Gleissberg cycle” in the sunspots, and the ~1,000-year cycle and the ~ 2400-year cycle in the ∆14C data may be real, solid, and persistent, I find no support for those claims in the data that we have at hand
Willis says which I for once tend to agree with him.
I believe you are referring to this: http://www.informath.org/Contest1000.htm
Amusing anecdote about this challenge. and a warning about methods:
I tried to solve this challenge and one of the things I did was look for a weakness in how the challenger generated his artificial data. One of the things I did was attempt to recreate the challenger’s methods for creating the artificial data.
I used the standard off the shelf Octave red/pink noise generators that involve generating Gaussian noise, performing a DFT (via FFT), shaping the noise with a settable beta, and then doing the inverse DFT back to the time domain. I did this to see if there was some pattern I could discern in this that is somehow different than naturally generated signals.
I turns out with this method, the phase versus frequency graph looks completely different than a natural signal. In nature, the phase looks contiguous and forms a spiral when you graph imaginary versus real from the DFT. WIth the above method, imaginary versus real looks pretty random.
I got all excited that I’d solved the challenge because it was 3am and I’d forgotten I was working with my artificial data, not the challenger’s. Doh! I checked and the challenger’s data had the nice spiral of imaginary versus real.
It turns out if I generate the random sequences in the time domain using the standard AR equation I get the nice spiral shape, just like nature. I suspect that’s what the challenge author did.
So IMHO the DFT/iDFT method for producing noise, and possibly Willis’ method, will have subtle differences in phase relationships of the signal. I don’t know how meaningful that is to Willis’ Monte Carlo method described above, but I already suggested the literature uses the AR method to generate the proper spectrum for confidence levels, so this anecdote is another reason to use the AR method – it acts more like a real world auto-correlation and not a math model that emulates it in some fashion.
best regards,
Peter
Willis,
your calculations are convincing ….and if someone is in doubt, its up to him to
follow your calculations, fill in own values to prove that the periodicity values of 88,
208, 1000 and 2400 yrs cycles are NOT ARTIFACT of periodicity analysis deficiencies
…..it is clear that those periodogram analyses themselves produce those LONG-YEAR
– periodicities by their inherent defects…… I would rather appreciate a final word from
Mc Kittrick or another high calibre statistician as second opinion… this question is too
important to leave it open….. in the meantime, I will give all points to Willis, to have it
brought up….
…… B the way, the always quoted 14C-values are INPUT measured on Earth within
the troposphere and are NOT measured OUTPUT VARIATIONS of the Sun….. all those
people, who dedicate themselves to the 14C- input on the planet, declare this Earth INPUT
as being a solar OUTPUT and hide Earth orbital variations are REAL cause of 14C-variations……
….. Willis, you should look into a further matter: Cycles with growing amplitudes and periodicities,
There is one which grows by 6.95 years all along the Holocene. Literature, take Part 1 of the Holocene
cycle analysis at http://www.knowledgeminer.eu/climate-papers.html, the Climate Pattern
Recognition Analysis, Part 1 …… Take Alley, R:B: 2000 GISP2 as data series…..
…..
The growing cycle could be resolved, knowing the exact growth of 6.95 years and its
commencement date. Regards JS
For those of you who have taken delight in rubbishing my methods, and who have advised me to use white noise, and told me that I’m doing it wrong, wrong, wrong, let me point out that someone actually followed my request, which was:
Peter Sable, to his credit, suggested the “redfit” algorithm.
He pointed me to a Fortran program … and while I can still get by in Fortran, I went to see what I could find in R. I found a package called “dplyR”, which inplements the “redfit” algorithm in R. It returns the 99%, 95%, and 90% confidence intervals. Here are those results:
Please note that THESE ARE THE SAME AS MY RESULTS. Both sets of results show that the ~1000 year cycle is right at the 95% CI level, and also that the 2400-year cycle is far from significance …
From there we can go to the sunspot data … here is that result:
Again, this gives exactly the same result as my analysis—the 11-year cycle is significant, the so-called “Gleissberg Cycle” is not.
So I hold by my claims that the “Gleissberg” solar cycle, as well as the 100-year and the 2400-year cycles in the ∆14C data, are entirely unremarkable and are not distinguishable from random fluctuations.
And for all of you good folks who have told me over and over in this thread things like that I’m just an uneducated fool who is doing it wrong and I should have used equal frequency intervals …
Sorry … but this time, you are the ones who are wrong.
w.
Willis:
You will cause me to switch from Octave (Matlab) to R finally…
What did you get for tau* (the characteristic time scale of the AR1 process) for the 14C data?
I’m surprised it’s as big as I think it shows from the frequency domain.
best regards,
Peter
* it’s funny, I’ve seen the parameter for AR1 called alpha, beta, and tau in the literature. I bet there are more…
BTW this reminds me that AR1 modeling only works on stationary data. Did you detrend the data before running the analysis?
Yes.
w.
You are approaching Saint Svalgaard status.
Steven Mosher November 5, 2016 at 1:53 am
And you are approaching incoherency. I can’t even tell whether your comment is aimed at me or at Peter, and I can’t tell whether your comment is a compliment or an attack.
You really should cut back on the drunkblogging, Steven, it’s not doing your rep any good.
w.
Oh sorry, I’ve often called Lief a Saint for putting up with idiots. Since like 2007..
Any way.
You of course had a choice to take it as a compliment. Odd that you didn’t. oh well. water duck back
As for mind altering substances. nope. never touch the stuff.
[your really should learn to spell Leif’s name correctly -mod]
its a running joke since 2007 that I will mis spell his name.
but since you are a mod if it means that much to you ( he didnt care) you always have the option
of editing it. In fact It would take you less than time than being pendantic.
Steven Mosher November 5, 2016 at 5:25 pm
Steven, as I said, it was totally unclear. In my words, “I can’t tell whether your comment is a compliment or an attack” So I didn’t take it as a compliment because I was unable to take it or not take it as anything.
My bad, won’t happen again.
w.
What is the time period covered by the graph using sunspot data? 315 years? Having only one minimum of the Seuss/deVries cycle, whose minima may be more discernable than its maxima? And I think the Gleissberg cycle is unsteady but it exists. As I said before, I propose this graph being redone after another period of the Gleissberg cycle – I expect that to show it coming closer to being countable as statistically significant.
Given that we haven’t seen the “Gleissberg cycle” since about 1850, that is to say about 160 years, I fear that whatever it may be it doesn’t qualify as a “cycle” …
w.
You say “…neither case are we seeing any kind of true underlying cyclicity.” When referring to the 1,000 year DeVries cycle or the 2100-2700 year Bray (Hallstatt cycle). Later you amend this with “…while it is possible that the 88-year “Gleissberg cycle” in the sunspots, and the ~1,000 year cycle and the ~ 2400-year cycle in the ∆14C data may be real, solid, and persistent, I find no support for those claims in the data that we have at hand.”
Just looking at 14C data, in isolation, while looking for paleotemperatures is problematic. 14C paleotemperatures depend on an accurate model of the total atmospheric carbon mass. It varies a lot over time. Using this technique is virtually impossible before 11000BP due to the Younger Dryas cooling and warming, the previous ice period, etc. These were periods of huge changes in the total atmospheric carbon mass. Since 11000BP there are some serious changes in a few well documented colder periods, like the 8.2kyr event, but it is relatively stable. Therefore, the earlier data was removed (correctly IMO) regarding your comment “thrown away three-quarters of the data.”
14C temperature estimates are somewhat circular, since what you are measuring (temperature) is affecting the total carbon you use in your calculation. 14C temperatures should not be used alone for this reason, which is what your Fourier analysis shows I believe. 14C is commonly combined with 10Be because while they each have data issues, the problems are in complementary areas. They correlate well (R2=0.8) and analyzed together they each offset weaknesses in the other.
See Roth and Joos, Clim. Past, 2013. For an analysis of 14C error see their Appendix A, the radiocarbon errors are high. Their Figure 1 is very instructive as well:
http://meetingorganizer.copernicus.org/3ICESM/3ICESM-405.pdf
Once we add in the worldwide glacier, paleontological and ice raft data we can conclusively find the Eddy cycle (~1,000 year) and Hallstatt (2100-2700) cycle. See Bond, et al. 1997 (Science); Debret, et al., 2007 (Clim. Past). The ice core and glacial records, plus the ice raft data are the most conclusive evidence for most people.
So, your conclusion that 14C temperature records, by themselves, have problems is true; the cycles you speak of are based on much more than 14C data. Even if you ignored the 14C data, the cycles would still be there. All paleo-temperature proxies fall apart statistically in isolation; which is a shame. But, this should not stop us from using them. They are all we have.
found this also in my notes
http://iie.fing.edu.uy/simsee/biblioteca/CICLO_SOLAR_PeristykhDamon03-Gleissbergin14C.pdf
and it seems to confirm what you and Javier are saying.
I determined the Gleissberg presently at 86.5 years but this may have to do with the current planet configuration – I also can confirm that there is correlation of the Gleissberg with the position of Saturn and Uranus.
The position of the smaller planets apparently also affect the length of the shorter term solar cycles.
In theory, I think if you put a program to it, you could look at the position of all the planets of the solar system, and as suggested, also look at the position of the sun itself, and you should be able to predict solar activity.
it works just like a clock.
Amazing.
Andy May November 5, 2016 at 5:37 am
Despite your claim that we have to stop our analysis at 11000 BP, the link you refer me to (Roth and Joos) goes back to 21,000 BC … so it appears you’ve bought into the cherry picking. I’m sorry, Andy, but your own citation shows that the claim is meaningless.
Not only that, but your own citation shows that the increase in the errors doesn’t even START until 13000 years ago, so AT A MINIMUM Javier and his predecessors have thrown away two thousand years of very valid data that your own citation says are as good as the more recent data.
So yes, Andy … you are cherry picking at a rate of knots.
You say that we have to “add in” a bunch of other data. Here we’ve been discussing the work of Javier and Clilverd, neither of which say we have to “add in” anything. They claim that the ∆14C data is enough ON ITS OWN to establish the existence of the cycles. I say no.
In any case, I went to check out “Bond et al, 1997”, with the “et al.” sadly not including James Bond, but instead even more sadly including that noted scientist and harridan, Heidi Cullen … hardly inspires confidence. The link is here. It turns out to say NOTHING about 1000-year and 2400-year cycles as you have claimed. Instead, he identifies a 1470-year cycle which appears NOWHERE in the ∆14C data. So your claim that we can just somehow “add in” a 1470-year cycle to the ∆14C records is a joke. Bond et al. themselves say:
Sez it all …
So I fear your claim about having to “add in” Bond is … well … unwise. It does not support your claim, it diametrically opposes it.
ALL paleotemperature proxies fall apart in isolation? Andy, are you sure we’re talking about the same thing? And if what you say is true and all paleo proxies fall apart, how likely is it that their sum will be any better?
And I am NOT saying the cycles don’t exist. What I said was simple—there is not enough evidence at hand in the ∆14C data to support the existence of such cycles.
I’m sorry, Andy, but you are a long, long ways from establishing your claim. However, I do appreciate the fact that you seem to agree that the ∆14C data does not support the existence of the claimed cycles.
w.
Whew! I’ll let my comment speak for itself, but I will address some of your comments that I think are in error or misinterpretations of what I said. First, it is my opinion (and the opinion of many others) that prior to the end of the Younger Dryas, using 14C data for a paleotemperature estimate is not likely to be accurate. 14C paleo-temperature determination is a work in progress and not very advanced IMO. I don’t think that we know how much carbon was in the atmosphere during Younger Dryas cooling with any precisions. Just my opinion.
I can assure you that Javier does not think 14C data alone is enough to establish the Hallstatt (Bray) cycle and he never said that in any of his posts as far as I can recall. You’ve put those words in his mouth. I can’t speak for Clilverd on the subject, but I think he was using the Hallstatt cycle to show his 14C methodology worked, not the other way round.
Your statement that there is not enough evidence in the 14C data to support the long term solar cycles is true, I doubt anyone would argue the point with you. But, I posted my comment because I didn’t want any of your readers to turn that around and say there isn’t a Hallstatt or Eddy cycle. They do exist and that is well established and it has been for over 40 years. Dr. Nicola Scafetta has a very nice new paper in Earth Science Reviews on the topic. Link: http://ac.els-cdn.com/S0012825216301453/1-s2.0-S0012825216301453-main.pdf?_tid=fb1280ca-a39d-11e6-96ef-00000aacb362&acdnat=1478381139_bc8e306a0a39538609a5b70be9ad2cae
See his Figure 10, both the Eddy Cycle and the Hallstatt cycle meet the 95% confidence level according to his analysis. As for Bond’s 1997 paper, on page 1 (magazine page 1257) he identifies a 2800 year cycle that I take as the Hallstatt cycle. If you want mathematical precision, you are in the wrong field. Geology, paleontology and paleo-climate studies all involve using very uncertain indicators. We, hopefully, get more precise with time; but its a struggle.
Andy May November 5, 2016 at 2:53 pm
Andy, thanks for your reply. First, when someone says that his opinion is backed by “many others” but he does not specify who they might be, I fear my suspicion index goes up rather than down.
Second, YOUR OWN CITATION used the ∆14C data back 22,000 years so I guess he’s not one of the “many others” you are relying on.
Third, the uncertainty in the ∆14C data from YOUR OWN CITATION does not even begin to increase until 13,000 years BP, so as I pointed out before, Javier and Clilverd are cherry-picking a minimum of two millennia of data.
Fourth, neither you nor the others have shown the effect of your cherry-picking. If you want to use less than a full dataset, you can’t just wave your hands and say “I don’t like the old stuff”. You have to show the effect of your deletion of data and fully justify it, and justify the exact choice of your cutoff-date based on objective criteria … in short, you need to justify it with something more than “my opinion” backed by unknown “others”.
Fifth, if there is that much uncertainty in the ∆14C records, why can we use it as far back as 50,000 years with good accuracy?
Sixth, the ∆14C data comes with the error estimate of the original authors. While it increases with increasing age, the same is true of e.g. the paleo records you are using to claim the existence of the Hallstatt cycle.
Seventh, I’m not at all clear about the very basis of your entire objection. I am completely in mystery as to why you are referring to inaccuracies in “using 14C data for a paleotemperature estimate”. You might be right about that, but I’m not doing anything like that. I’m just trying to find short-term (~ 2400 year) cycles in the 14C data, not use the 14C data to estimate the temperature in the year 35245 BC. Why is the early data not valid for a simple cyclical analysis? Yes, there are large secular changes, but IF the Hallstatt cycle is real we should still see it on top of those secular changes.
And I can assure you that he does NOT accept that the “evidence” for it in the ∆14 data is nothing but a far-from-statistically-significant blip … nor have you accepted that, from all appearances. You say that the “14C data alone” doesn’t establish the Bray cycle, as though the 14C data were actually significant. It can’t do it either alone or in concert with others, not unless they happen to have the same bizarre combination of ~2000 year cycles interspersed with the odd 2800-year cycle …
But even AFTER:
1. throwing away 3/4 of the data, and
2. arbitrarily subtracting out a 11,000 year perfectly straight linear trend of unknown origin, and
3. arbitrarily removing a 7000 year cycle of unknown origin which is NOT even the proper size (biggest cycle in that chunk of data is 6,600 years)
the claimed cycle is STILL not statistically significant. It’s not that “14C data alone” is not enough … it’s that we have no evidence that the blip in the 14C data is more than just a random fluctuation.
Finally, Javier says that if we best-fit a 2300 year perfectly regular sine cycle to the ∆14C data, we can use it to forecast the future evolution of the sun, and through that, we can forecast the future evolution of the temperature … so he clearly thinks the cycle in the 14C data is both real and significant, or he wouldn’t fit his cycle to it.
So you and Javier say the Hallstatt cycle is real in part BECAUSE of the ∆14C data, and he says his ∆14C method is valid BECAUSE of the Hallstatt cycle? I’m not touching that one.
Javier and others have been strenuously stating and restating THAT EXACT POINT. To all appearances they think the blip in the Fourier analysis is statistically significant. It is not, it is far from it.
The so-called “Gleissberg cycle” has been “well established” for much longer than that, and I haven’t found any evidence for that either. Am I the only one who has looked critically at Gleissberg’s original work? Go take a look, his statistics are hilarious. I discuss the issues here and here.
Is there a significant “Hallstatt cycle” in the 14C data? NO, it is far from significant. Does this mean the cycle doesn’t exist? NO. It may well exist.
Dr. Scafetta? Dr. May, I fear you have been misled. Dr. Scafetta is a well-meaning fellow, but his “science” is laughable. Not only that, but he has repeatedly refused requests from a variety of people for his data and his computer code that underlies his claims. That repeated refusal alone excludes him from the ranks of scientists.
Setting that aside, he says in the opening of his abstract:
If you look at Figure 9, empirical mode C9 shows the so-called “Hallstatt cycle” in the 14C data. If we look at peak-to-peak times it has three short cycles averaging 2065 years, interrupted by one cycle of 2665 years. And if you look at trough times it’s even worse—2015 years, then 1880 years, and finally 2810 years. The data is all over the place. His claim is simply not true.
And the 10Be records are even worse, because the Greenland records disagree totally with the Antarctic records. See here and here for further discussion of the problems with 10Be data.
And according to the “redfit” algorithm, while the Eddy (1000-year) cycle barely touches 95% confidence, the 2400-year cycle is less than half the size it would need to be in order to be significant. But enough about redfit confidence (which agrees with my own analysis), let’s talk Scafetta confidence.
First, Scafetta specializes in creating complex equations with lots of tunable parameters, sometimes more than the celestial bodies he is investigating, and claiming that such a result is statistically significant. See here for further details.
Next, the paper is paywalled, and no way I’m paying good money to read his multiple-tunable-parameter nonsense. Unlike Scafetta, I’m a follower of the man that Enrico Fermi called “Johnny” Von Neumann.
Next, we KNOW the 2400 year cycle in the ∆14C data is not statistically significant … so I’ll let you think about how significant comparing some carefully hand-picked regular astronomical cycle to an insignificant fluctuation might be …
Comparing some astronomical cycle to a meaningless wiggle in the ∆14C data and calling it significant? Sorry, that dog won’t hunt.
Finally, did Scafetta find something somewhere in the universe with a period near to some period in natural climate data? Sure, that’s his specialty. And given the number of total possible cycles out there in the solar system, with a sun, seven planets, the moon, and the earth each with independent orbits, eccentricities, tilts, precessions, I’m only surprised that it took Scafetta this long to find such a cycle. Seriously, Andy, citing Scafetta loses you lots of points with serious statisticians everywhere … not to mention losing points with Enrico Fermi.
Sure, you can “take” a 2800-year cycle as being the “Hallstatt cycle” … but there is no support for that claim in the 14C data. I also note that that is way outside Scafetta’s already-broad “2100 to 2500-year cycle”. So call it what you want, it is NOT what Javier or Clilvert or Scafetta or I are talking about. You’ve fallen into the old trap about “How many legs does a cow have if you count a tail as a leg?”
Sorry, I’m not buying that that claim stretches far enough to turn a 2400-year cycle into a 2800-year cycle. While the indicators are “uncertain” as you say, they are far from being that uncertain.
Andy, you keep saying that the 2400-year “Hallstatt cycle” is real and has been known about and everyone agrees … but when I asked for evidence, you send me a vague claim about a 2800-year cycle. My experience in the world of solar claims is that I’ve found almost none of them that hold up to serious statistical investigation, including the best-known of them all, the so-called “Gleissberg Cycle”. As a result, you telling me that something is true “in your opinion and in the opinion of many others”, and claiming that a 2800-year cycle in Bray is the same phenomenon as a ~ 2100-year cycle in the ∆14C data, carries no weight with me. That’s just an appeal to some un-named and unknown authority.
So … let me make you (and anyone else) the offer about the Hallstatt cycle that I’ve made so many times about 11-year solar influences. Find the study that you think most clearly establishes the existence of a 2400-year cycle, or as Scafetta describes it, a “2100 to 2500-year cycle”. Send me two links, one to the study and one to the data they used, and we can see if the authors did their homework correctly. Bearing in mind that something like half of all peer-reviewed scientific studies don’t make the long-term grade, these days I suspect everything … and I also suspect that far too many scientists just take things like the so-called “Gleissberg cycle” on trust.
So I’d like to see just what it was that convinced you that the 2400-year cycle is real. I don’t want one link, nor do I want a tableful of links. Give me two links, one to the study that you believe is the best possible evidence for the Hallstatt cycle, and the other to the data used in the study, and we can see just how it holds up under a serious evaluation.
Finally, be clear. I’m not saying the Hallstatt cycle (or the Gleissberg cycle) don’t exist. You can’t prove a negative. I’m simply saying, I haven’t seen the evidence, and unlike far too many scientists these days, I don’t believe something until I see the evidence. It used to be that scientists took “nullius in verba” seriously … and I still do.
And since the ∆14C data contains NOTHING at around 2400 years, just intermittent ~ 2000-year cycles with a long gap in between, the ∆14C data does nothing to support the existence of the cycle.
Thanks for your comments,
w.
PS—How many legs does a cow have if you call a tail a leg?
Four … because calling a tail a leg doesn’t make it a leg, any more than calling a 2800-year cycle “Hallstatt” makes it a 2400-year cycle
Is solar activity will continue to decline?
http://images.tinypic.pl/i/00837/r9x6hkzrone4.gif
@ren
I don’t know if I showed you
but if you carefully look at this graph
http://www.leif.org/research/Solar-Polar-Fields-1966-now.png
you can draw quadratics[hyperbole and parabola] starting from 1971 and ending in 2014 for the solar polar field strengths that would represent the average field strengths. It is doubtful that solar activity will fall further as this is exactly half the Gleissberg.
1971 and 2014 were dead end stops. Indeed, one could argue that the periods around 1971 and 2014 were in fact mini solar cycles, if you look at the solar polar field strengths.
Keeping with Gleissberg, the next 43.5 years [counted from 2014] will be a mirror image of what we see,
i.e. cycle 25 will be more or less equal to cycle 17.
[8 Schwabe cycle = 1 Gleissberg]
the periods around 1971 and 2014
sorry, to clarify
should have been
the periods = a few years, just before 1971 and 2014
Certainly falls in the next two years, because we have a minimum.
Temperatures in northern areas dipped below freezing for the first time this winter in Poitou, Nancy, Dijon and Nevers on Friday. Meanwhile, those living in the southeast will not be spared. Little more than a week after Marseille basked in 25C sunshine, residents will wake up to temperatures of 5C on Monday.
While forecasters have rejected claims that this winter will be one of the coldest on record, the good news for winter sports fans looking to book holidays is that between 30cm and 60cm of snow is expected in the Alps at altitudes about 200m, as temperatures dip 8C below the norm for early November.
http://www.connexionfrance.com/weather-cold-winter-snap-rain-alert-orange-meteo-france-18595-view-article.html
Willis, this is a very interesting article, on which I have a few points/questions.
1. Could you explain what “empirical mode C6” is in layman’s terms? Or ven in mathematician’s terms?
2. Re the Gleissberg “cycle”, my understanding is that it is not a proper cycle of sinusoid type, but rather a limit on the span of many (say 5-10) solar cycles. It says that after a lot of short cycles in a row, as happened from 1920 to 1996 (on average), they cannot persist. And indeed it seems to be true that they are not persisting: Cycle 23 was over 12 years long, and Cycle 24 is shaping up to be long too (though I realize that is subject to dispute). If this occurs then it is not true to say that it “only operated” in the first half of the period. If Cycles 24, 25, and 26 turn out to be all less than 11 years, then your assertion would be correct.
3. It’s a weird way that you created your “random” data. With 11600 cycles of integer periods, the “average” cycle length is 5800 years, so their sum is bound to be dominated by the longer periods. Suppose that cycles of periods 6000 and 6001 years had very similar phases, then their reinforcement would affect a large period of time. Whereas for the 10 and 11 year periods, they would get out of phase quite quickly. So, I am not the least bit surprised by the graphs you show.
4. Your “random” data bears no resemblance to any credible physical process. So I don’t see that it makes sense to compare observational data to it.
Regards,
Rich.
See – owe to Rich November 5, 2016 at 8:54 am
Thanks, Rich, questions are good.
There are a number of ways to break a complex wave down into simpler waves. The best known is Fourier analysis. CEEMD is similar, but it uses the form and nature of the data itself to empirically select the frequency bands involved. These selected bands are called “empirical modes”, and are arranged in generally increasing period length.
Empirical mode C6 happens to be the one that contains the ~88-year so-called “Gleissberg Cycle”. As the CEEMD analysis shows, this “cycle” only appears for a cycle and a half in the early part of the record, and then disappears.
Rich, I fear that you haven’t thought this one through to the end. It reminds me of the sign in my home-town roller skating rink which said “Please do not skate faster than the average of the other skaters.”
In ANY varying system with an average value, the value CANNOT stay permanently below the average … but this doesn’t imply any “limit” or “cycle”.
For example, take a pair of dice. The average value of a million throws is 7.5. Now according to your theory, after “a lot of small throws in a row”, they cannot persist … and that is true. Sooner or later we’ll throw something larger than average.
But that does NOT mean that dice have a “Gleissberg Cycle” of some kind.
Some will be above average, some will be below average …
It may be a weird way to go about things, but that’s how I learn. I don’t sit around and theorize a lot. I theorize, then I just try things to see how they come out. In this case I thought “I know that all complex cycles are just built up of sine waves, and I’m using the periodogram to investigate those waves … what would I get if the sine waves covered all the periods and had identical amplitudes?” Then I went and wrote the program to try it.
As to your lack of surprise at the results, everyone but me seems to be wise after the fact, as if being surprised were some kind of scientific character flaw. One big surprise was that I actually could convert that raw data into a method for estimating uncertainty that agrees with the known “redfit” method … was that a surprise to you, or did you foresee that as well?
Since number 7 in Figure 3 is not actually random data, but is observational, I’d have to disagree.
Regards,
w.
PS—Rich, after writing for the web for years, I’ve generally stopped saying things like “Your “random” data bears no resemblance to any credible physical process.” unless I had 100% certainty on the subject and had ruled out every other explanation.
That statement is far too all-inclusive to have much chance of being true. The “covers everything” nature makes it easy to falsify. For example, I could build an electronic circuit which would be the exact analogue of my “random” data generating method above, it’s just the addition of AC currents … and an electronic circuit is definitely a “credible physical process”, so this falsifies your statement.
As an example of this at work, in the paragraph above I originally wrote “That statement is far too all-inclusive to be true.” However, I changed it to “That statement is far too all-inclusive to have much chance of being true.” The second form is far superior to the first, and what’s more, the second is likely true and the first is likely not, because the second is easily falsified.
Willis, thanks for your detailed replies. I’ll use the same numbering in a rejoinder here.
1. Thanks for the explanation of mode C6. I’d need to read the paper to understand how it works, but at least I now understand what it is qualitatively.
2. You are using a random walk with dice as an analogy to what I said about Gleissberg “cycles” – fair enough. But in random walks it is known that the deviation from 0 (i.e. the mean) of the walk reaches with high probability a distance proportional to the square root of the number of steps (=throws of the dice, or number of solar cycles). My assertion is rather that there is an invisible barrier which stops the deviations exceeding some threshold, where the square root would be bound to breach it sooner or later. Since 88 years is 7 mean solar cycles, and if I allow 1.5 years of individual deviation, then that barrier on total deviations would be about 10 years. Now, I don’t have any data to hand to demonstrate this, so I certainly cannot prove my “assertion”, and I now see that Gleissberg Cycles seem to mean different things to different researchers, but anyway that is where I am at. Thank you for rekindling my interest in this topic – sometime I’d like to find better support for the assertion.
3. Yes, I like the way you learn, and I previously typed a compliment to that, but then deleted it as I worried it would sound patronizing!
4., including your postscript. So, given your electrical circuit example, was I sloppy to write “any credible physical process” instead of “any credible natural physical process”? My point remains that it doesn’t seem valid to use confidence intervals from the “Eschenbach process” to say whether an observed spike in a spectral analysis is significant or not.
Thanks,
Rich.
Rich, your response is much appreciated. My only objection was to this one:
Since my analysis gives an identical answer regarding the ∆14C data as does the known “redfit” method, I’d say that that is a clear example in favor of my method …
I also note that the general idea must be right, because the uncertainty bounds in both the “redfit” method and my method graph as straight lines (on a non-log scale), or as identical curves on a log scale.
Having said that, I’ll use the “redfit” method in future, because it is based on known algorithms, it is part of an “R” computer language package, and it is tested and used in the field (it was developed for use in dendrochronology). That will avoid at least some further questions.
Finally, I’ve mentioned before that I tend to play a deep game, and that I often have other hopes in mind for my writing. One of my hopes in describing this novel method was that I would get pointed to established methods for establishing confidence levels … and boy did I ever! My great thanks to Peter Sable for the link to a description of “redfit”. From there I was able (after much looking) to track down the FORTRAN code, which I figured I’d have to translate to R.
I just didn’t expect that I’d be lucky enough to find an R package that was a straight port to R of the FORTRAN program I was pointed to, or that my confidence results would be that good a match to this known method.
Best regards,
w.