# CEEMD and Sunspots

Guest Post by Willis Eschenbach

I’ve been investigating the use of the “complete ensemble empirical mode decomposition” (CEEMD) analysis method, which I discussed in a previous post entitled Noise-Assisted Data Analysis.

One of the big insights leading to modern signal analysis was the brilliant idea of Joseph Fourier. He realized that any given waveform can be expressed as a combination of sine and cosine waves. However, there are other ways besides Fourier’s method to decompose a signal, including periodicity analysis, principal component analysis, and CEEMD.

Let me give you an example of a CEEMD analysis. Here are the intrinsic modes for the annual average number of sunspots from 1700 to 2014. The top row is the sunspot data itself. For intercomparison with other signals, it is standardized to a mean of zero and a standard deviation of one.

Figure 1. CEEMD analysis of the mean annual sunspot numbers. Top panel shows the sunspot data, standardized to a mean of zero and a standard deviation of one. Panels marked C1 – C7 show the intrinsic modes of the signal. The bottom line shows the residual, meaning what remains after the removal of modes C1 – C7 from the signal. Note that all intrinsic modes are displayed at their true size, with all scales being the same.

This is a “complete decomposition” of the raw data signal, meaning that if we add the intrinsic modes C1-C7 together plus the residual, it will faithfully and exactly reconstruct the original signal.

One thing I like a lot about the CEEMD analysis is that I can actually see how the underlying intrinsic modes vary over time. I’ve said before that ascribing an inherent cyclical mechanism to natural observations is fraught with problems. Figure 1 is a good example of these problems. Look at intrinsic mode C4. It has a small signal at about 22 years … but not all of the time. For most of the first century of the record there is little signal at all. Then there’s an intermittent small ~ 22-year signal from about 1780 to 1850 ,,, which fades out and after a few year hiatus is replaced by a single ~ 25-year cycle, and that in turn is replaced with a ~ 22-year cycle out to the end of the data.

Or we can consider intrinsic mode C6, which varies in a similar irregular fashion. Mode C6 has a couple of strong cycles with a period of around 90 years at about 1800, and it then kind of tails off to nothingness. This makes it obvious why it has been so hard to discuss the existence or non-existence of the so-called “Gleissberg Cycle”, which Gleissberg claimed was ~ 80 – 100 years. When cycles come and go like that, it is hard to draw any firm conclusions. I mean, the ~ 80 – 100 year cycle is definitely there … but it’s only there when it is there, and the rest of the time, well, it’s simply not there.

Unfortunately, these kinds of appearing and disappearing cycles are far too common in natural datasets. There is a great temptation to think that they can be used for forecasting purposes … and they could if we ignore Murphy’s Law, which says that as soon as you start prophesying, the cycle will die out. For example, if we looked at the sunspot data in the year 1900, we’d think that there was a strong, statistically significant hundred-year cycle in the data … but after 1900 the cycle simply fades out to nothing.

Having seen the actual waveforms of the intrinsic modes in Figure 2, we can look at the periodograms of the various intrinsic modes to see what kind of signals exist in each of the intrinsic modes C1 to C7.

Figure 2. Periodograms of each of the intrinsic modes C1 through C7 of the annual mean sunspot number, 1700-2014. These show the strength of waves of the various periods in each on the intrinsic modes.

Figure 2 shows that most of the energy is in the ~11 year cycle, which is in intrinsic mode C3. Because the sunspot cycle varies between ten and thirteen years, the energy is not a sharp spike, but has energy across that range.

As discussed above, intrinsic mode C4 can be seen to have a very small bit of energy in the 22 year range, but as we saw in Figure 1, there’s nothing regular enough in the data to give a strong signal.

Again as discussed above, intrinsic mode C6 seems to have some energy in the 90-100 year range … but as Figure 1 shows, the ~100 year signal in C6, while strong, is mostly visible in the first half of the data. This greatly increases the odds that it is a spurious signal that could disappear in a longer record.

So that is an example of a CEEMD analysis of a signal. It gives us a picture of the intrinsic modes (Figure 1) and the periodograms of those same intrinsic modes (Figure 2). It shows the strength and the ebb and flow of the underlying cycles in the data.

Now, how else can this kind of analysis be useful? Well, it can show whether and how two distinct observational datasets might be related. As an example, here is the CEEMD analysis of both the Nino3.4 Index and the Southern Ocean Index (SOI). The Nino3.4 Index is a detrended sea surface temperature dataset for an area in the tropical central Pacific covering 5° North to 5° South and 120° West to 170° West. The SOI, on the other hand, is an index of the atmospheric pressure difference between Tahiti and Darwin, Australia. The two indexes seem to be measures of the El Nino/La Nina pumping action. The SOI and the Nino3.4 move in opposite directions, so the SOI is usually displayed inverted so that peaks in the SOI correspond with peaks in temperature. The next two figures show the CEEMD analysis of the two datasets:

Figures 3 and 4. Upper figure shows the intrinsic modes resulting from the CEEMD analysis of the Southern Ocean Index (SOI, red) and the Nino3.4 Index (black). These two datasets cover the same period as the sunspot data shown in Figure 1, 1870 – 2011.

Again, we see that there are various cycles which are strong in part of the record, but disappear or are greatly diminished in other parts of the record.

Note the close correspondence of the decomposition of the two signals, both in terms of the strength and shape of the intrinsic modes, and in their periodograms. It is clear that regardless of the fact that the Nino3.4 Index and the Southern Ocean Index are measuring different variables, they are both a measure of the same phenomenon.

And it is equally clear that there is no significant sunspot signal in either the SOI or the Nino3.4 data—the CEEMD analysis shows little commonality. Unlike the sunspot data, in the SOI and Nino3.4 data there is little strength at 11 years, and little strength at around 90 years. And again unlike the sunspots data, the majority of the energy is in the short-cycle (2-6 year) part of the spectrum.

Anyhow, that’s why I’ve grown fond of the CEEMD analysis … it shows when datasets have related cycles, and when they are unrelated.

Pushing towards full moon tonight, with Jupiter and Arcturus vying for the moon’s attention … what a world …

My best to everyone,

w.

My Usual Request: Misunderstandings bring communication to a halt, so if you disagree with me or anyone, please quote the exact words you disagree with so we can all understand your objections. I can defend my own words. I cannot defend someone else’s interpretation of some unidentified words of mine.

My Other Request: If you believe that e.g. I’m using the wrong method or the wrong dataset, please educate me and others by demonstrating the proper use of the right method or the right dataset. Simply claiming I’m doing something wrong doesn’t advance the discussion unless you can tell us how to do it right.

Yearly Sunspot Data: SILSO

SOI Data: Here

Nino3.4 Data: NOAA

Code: I’m using the “CEEMD” function in the R package “hht” for the analysis.

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April 20, 2016 11:21 pm

Very nice, Willis.
The 11-year ‘peak’ has two smaller peaks, one on each side of the main peak. These could be interpreted as modulation by a longer period [the ~100-year coming-and-going cycle].

April 21, 2016 1:06 am

Back when we were discussing the influence of planets, I showed that an amplitude modulation of the sunspot cycle by a ~100 yr cycle could generate the side peaks:
http://www.leif.org/research/AGU%20Fall%202011%20SH34B-08.pdf

george e. smith
April 21, 2016 8:05 am

Willis, what Dr. S is saying makes sense to me. If you have an 11 year “carrier” period, that is amplitude modulated by a longer period modulation, you should get upper and lower sideband frequencies on each side of the carrier as he suggests (well what he said suggests that to me.)
The presence of ‘noise’ in the signals (lucky us), well fluctuations could make it not nice and symmetrical as a spectrum, but his idea is a plausible explanation.
In any case, what you are doing, seems to be an interesting tool. I’m sure the mathematicians would likely want to know something about the boundaries of validity of such machinations; but if they have misgivings, then let them tell us about it.
G

george e. smith
April 21, 2016 8:23 am

Upper and lower sideband information is a standard part of amplitude modulation of a fixed frequency carrier.
Transmission of the accurate signal requires a transmission path bandwidth that incudes the upper and lower sidebands. It’s been a long time , but I believe each sideband is phase shifted from the carrier, and I think the two sidebands are either 90 degrees apart or 180.
in principle ALL of the modulation information content is contained in the sidebands; the carrier contains NO information (other than the frequency).
So it is common to suppress the carrier, to save transmitter power, and just transmit the sidebands (still need the same spectral width). In fact the two sidebands are supposed to be identical, at Fc + FM and Fc – FM, so you only need one of the sidebands, which immediately halves the spectrum width. That of course gives you suppressed carrier single sideband transmission, which is a very efficient AM modulation system.
Well, in reception, you need to know the carrier, both in frequency and phase, so the carrier power is just depressed, rather than eliminated, so the receiver can find a signal to lock onto to replace the carrier.
So what Dr. S suggests makes all the sense in the world. The fluctuations (noise) in the information, may make your spectrum look not perfectly symmetrical about the carrier (11 year) period, but it probably really is .
Single sideband radio on your short wave receiver sounds like somebody running a buzzsaw over the top of your message, which sounds like garbage. But restoration of the carrier to get a phase reference, shuts down the buzz saw.
So what you might be thinking is a … frequency … modulation about the 11 year nominal period, is actually just an AM modulation of a fixed carrier frequency, of 11 year period.
G

george e. smith
April 21, 2016 8:25 am

Hoo put dat +/- FM instead of Fm. Maybe the editor did some assuming and made an ASS out of itself.
g

Peter Sable
April 24, 2016 6:08 pm

what does CEEEMD look like with an amplitude modulated signal?
it should look somewhat like this in the frequency domain, meaning the frequency should be shifted by w1-w2.
https://en.wikipedia.org/wiki/File:AM_spectrum.svg

Peter Sable
April 25, 2016 2:23 pm

well, I made some synthetic data and ran a CEEMD analysis on it.

So did I. CEEMD won’t show a 100 year modulation, it only shows the basic waveform. That’s because multiplication in the time domain is convolution in the frequency domain.
Here’s an example of CEEMD on a modulated waveform. As you can see, it only decomposes it to the basic cycle, the modulation cycle doesn’t show up anywhere.?dl=0

April 21, 2016 5:15 am

100 year cycle may be simply due to change in the predominance of one or the other hemisphere.
http://www.vukcevic.co.uk/MaunderN-S-excess.gif

April 21, 2016 5:17 am

As we get energy etc from both hemispheres at the same time, any asymmetry doesn’t matter.

April 21, 2016 12:16 am

I take a view that 11 year sunspot cycles are human numerical construct and are not the true representation of the physical reality of the solar activity.
Sunspots are associated with rise and fall of the solar toroidal magnetic field, and normally appear in pairs. Direction of the magnetic field vector B in the northern hemisphere coincides with the direction of solar rotation (positive orientation, B>0) during even-numbered cycles, it is the opposite for the southern hemisphere.
Relationship between direction of rotation and the magnetic field vector orientation is reversed during the odd-numbered cycles (for the northern hemisphere B<0).
Thus, both hemispheres individually display approximately 22 (and not 11) years quasi-periodic cycles and may need to be analysed individually with sign of the magnetic field vector orientation taken into account.
In addition poloidal (polar) magnetic field also has approximately 22 years quasi-periodic cycles, but out of the phase with the toroidal magnetic field cycles.

April 21, 2016 12:20 am

I take a view that 11 year sunspot cycles are human numerical construct and are not the true representation of the physical reality of the solar activity
Unfortunately, Mother Nature does not share your view.

April 21, 2016 12:36 am

Quite opposite, mother nature doesn’t take your view, it responds to the reality as it is. Numerous analysis at this blog have repeatedly shown there is no significant 11 year cycles presence in the climate events, but the 22 year quasi-periodic (Hale) cycles are in abundance
http://www.vukcevic.talktalk.net/5Spectra.gif

April 21, 2016 12:39 am

Except there is no 22-year cycle in solar activity.

April 21, 2016 12:51 am

“Except there is no 22-year cycle in solar activity.”
Not in one you and your colleagues been selling, but I don’t buy anyone’s product without taking a look at it.
“Except there is no 22-year cycle in solar activity.”
Could not be more wrong.
Undeniable facts are:
– sun has approximately 22 year polar magnetic field quasi-periodic oscillations
– solar North and South hemisphere’s have individual (often slightly out of phase and different in the magnitude) have approximately 22 year toroidal magnetic field quasi-periodic oscillations.
How are you going to get out of that one ?
(digging a hole?)

April 21, 2016 12:55 am

None of these are measures of solar activity.
Your ‘Hale Cycle’ is artificially created by inverting the sign of every other cycle and is not indicative of solar activity [there is no negative activity]. You have been told this so often that it should not be necessary to beat that dead horse anymore.

April 21, 2016 12:57 am

Dr. Svalgaard
“Except there is no 22-year cycle in solar activity.”
from Dr. Svalgaard’s website
http://www.leif.org/research/Solar-Polar-Fields-1966-now.png

April 21, 2016 1:00 am

The sign of the polar fields are not solar activity.
You are again trying to pollute WUWT.

Steve Crook
April 21, 2016 12:58 am

Thanks for taking the time to do the replies, many would not have the patience or interest. Informative *and* entertaining…

kim
April 21, 2016 12:59 am

The shape of the peak of the solar cosmic rays is a 22 year cycle.
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April 21, 2016 1:01 am

But is not solar activity and the modulation does not take place in the sun, but 100 AU away.

Greg
April 21, 2016 1:07 am

Defining “activity” as an unsigned quantity and then denying that there is a 22y periodicity is like failing to recognise that velocity is a vector quantity and only analysing speed as the “activity” of an object.
But as always those who have spent their lives in an educational context regard anyone else’s statements as “pollution” and are incapable of addressing difficult questions from the back of the class.

April 21, 2016 1:10 am

Solar activity is not a vector.

kim
April 21, 2016 1:07 am

I love this action at a distance. We knew this wasn’t going to be easy.
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April 21, 2016 1:07 am

lsvalgaard April 21, 2016 at 1:00 am
“The sign of the polar fields are not solar activity.”
but you take great deal of pride in using the polar fields to correctly predict intensity of the next sunspot (solar activity) ‘cycle’ and rightly so.

April 21, 2016 1:09 am

So?
That still does not mean that there is a 22-year cycle in solar activity.

Greg
April 21, 2016 1:10 am

Defining “activity” as an unsigned quantity and then refusing to accept that there is a 22y periodicity is like failing to recognise that velocity is a vector quantity and only analysing speed as the “activity” of an object.
But as always those who have spent their lives in an educational context regard anyone else’s statements as “pollution” and are incapable of addressing difficult questions from the back of the class.

Greg
April 21, 2016 1:15 am

But is not solar activity and the modulation does not take place in the sun, but 100 AU away.

Then it would seem that the chosen definition of “activity” is probably not one that is particularly useful. Clearly there are effects of physical changes in the sun that has far reaching impacts that are not properly characterised by simply counting spots on the surface, which are simply one manifestation of the underlying causes.

April 21, 2016 1:20 am

A useful definition of solar activity is one that involves the energy the sun puts out, and the effect of that on the Earth. Examples are Total Solar Irradiance, Ultraviolet Radiation, Magnetic Storms, and Cosmic Ray Modulation. There are tiny second order effects in some of these, not caused by Sun, but they are not significant for this discussion.

kim
April 21, 2016 1:23 am

I’m still promoting the idea of two of one type of solar cosmic ray peak shapes and one of the other in each phase of the approximately 66 year oceanic cycle. It’s a wonderfully mechanistic clock, and Leif admits at least a lower order effect.
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April 21, 2016 1:27 am

And not caused by a difference in solar activity [and in the energy the sun puts out].
The tiny cosmic ray 2nd-order effect [of the order of 1%] is related to how cosmic rays diffuse in the outer heliosphere, which in turn depends on the sign of the polar fields. But is a very small effect.

kim
April 21, 2016 1:28 am

Cycles in second order effects can add, perhaps even multiply.
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April 21, 2016 1:32 am

If they are tiny, they don’t matter, even if added.

kim
April 21, 2016 1:48 am

You don’t know all the lower order mechanisms, you can’t be sure of their magnitudes, and you can only speculate about how they interact.
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April 21, 2016 2:10 am

We can only talk about what we know. I do not ascribe unknown effects to unknown causes.

Greg
April 21, 2016 1:55 am

A useful definition of solar activity is one that involves the energy the sun puts out, and the effect of that on the Earth.

I would have thought that primary aim is understand the physical processes in the sun and extending out into the solar system.
Defining “activity” as TSI is one useful measure, it does not refute the existence of others that may affect the earth or give insight into functioning of the sun. There clearly are c. 22y periods in the sun , whether you chose to call that “activity” does refute their existence.
If you wish to ASSUME that the only way the sun can affect the earth is via TSI that is your affair but not a valid reason to call Vuk’s observations as “pollution”.
I don’t take his suggestions at face value any more than I do yours, but I do find them interesting, not pollution. That is just another attempt to shut down discussion and open investigation.

April 21, 2016 2:16 am

You are not paying attention [perhaps willfully]. We are interested in the energy that we receive. It comes in various forms: TSI, Ultraviolet, Solar Wind, etc Energy is positive and additive, and none of these sources have a 22-year cycle. And none of these things involve filtering in any form. The energy we receive over a rotation [or a year] is simply the sum of what we receive on each day of the time interval. If the intervals have equal length, the mean is equivalent to the sum, just easier to deal with conceptually.

kim
April 21, 2016 2:00 am

Yes, he is limiting. If the sun acts on the climate to cause some of the variations, it does not do it through simple TSI.
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kim
April 21, 2016 2:27 am

Both the UV variability and the cosmic ray mechanisms have end points through the clouds which have huge dynamic range. They may both be working, and it is difficult to imagine that they either or both together might not have greater effect than simple TSI.
Thermostatic, multiplicative, and self-limited. Who could ask for anything more?
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April 21, 2016 2:33 am

Both UV and cosmic rays are synced to the solar cycle as is TSI. And none show a significant 22-year cycle. The magnetic field in a given hemisphere has a 22-year cycle, but the field in the other hemisphere has the opposite 22-year cycle, so as we get stuff from both hemispheres, the two cycles cancel out, and the overall effect is just the unsigned solar activity 11-year cycle. So, for people that still don’t get it: there is no 22-year cycle in solar activity.

kim
April 21, 2016 2:44 am

Earth’s albedo doesn’t necessarily cancel, and probably doesn’t.
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April 21, 2016 2:47 am

So what? There is no demonstrated 22-year cycle in the albedo. If you know of one, show me, if not…

kim
April 21, 2016 3:01 am

Heh, I suspect that the record for albedo is not even as long as Willis’s ocean metrical record, and certainly shorter than the sunspot record.
Hey, I’m not even arguing for the 22 year cycle. I’m just speculating how, despite your steady TSI, the sun may effect climate.
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April 21, 2016 3:05 am

Speculation is a poor substitute for observations. Even if you fervently believe that the Sun MUST influence the climate big time, the evidence simply is not there.

kim
April 21, 2016 3:11 am

It’ll be awhile before we find a 66 year cycle in albedo, if there is one. In the meantime, we could look at what’s hiding under all that marvelous haze, lots of salty water.
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kim
April 21, 2016 3:13 am

Leif, I do very much appreciate your insistence on evidence. It is very grounding.
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Toneb
April 21, 2016 3:27 am

Leif, I do very much appreciate your insistence on evidence. It is very grounding.
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Yep, something that is glaringly absent in most threads on here.

April 21, 2016 3:36 am

Ignoring magnetic polarity of incoming energy and at the same time ignoring the Earth’s magnetic field effect it is a wrong way to go about it.
NASA: Solar coronal mass ejections CMEs in the even-numbered solar cycles tend to hit Earth with a leading edge that is magnetized north. Such CMEs open a breach and load the magnetosphere with plasma starting a geomagnetic storm (there is the source of the 22 year cycle in the climate indices ).
It is this ‘conflict’ of the solar and the Earth’s magnetic field polarities that is totally left out of the any climate effect considerations. Until such time this is recognized it may not be possible to quantify solar effect on the climate change.
Introducing various ‘fudge’ factors in the temperature models is not substitute to going back to the basics.

April 21, 2016 3:39 am

NASA: Solar coronal mass ejections CMEs in the even-numbered solar cycles tend to hit Earth with a leading edge that is magnetized north. Such CMEs open a breach and load the magnetosphere with plasma starting a geomagnetic storm
No, this is not correct. NASA or no NASA. You have been told this several times before, but you don’t learn.

kim
April 21, 2016 3:41 am

Vuk, same clock can work with that mechanism, two of one kind and one of the other in each phase of an approximately 66 year cycle. And why shouldn’t it be manifested in albedo?
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April 21, 2016 4:46 am

“And why shouldn’t it be manifested in albedo?”
Hi kim
I’m not the ‘albedo man’, may be someone else referred to it.

ferdberple
April 21, 2016 5:52 am

a “cycle” means the object returns to its initial state at the beginning of the cycle.
some of the sun’s parameters return to the initial state after 11 years, but the magnetic field orientation returns after 22 years.
thus while solar intensity might be said to have an 11 year cycle, the solar magnetic field maybe said to have a 22 year cycle.
what I’m seeing in the discussion is a lot of hair splitting to avoid addressing a really very obvious point.

April 21, 2016 5:58 am

You are right: the very obvious real point is that the energy [in its various forms] that the sun puts out and that we receive has an 11-year cycle, not a 22-year cycle. The energy [called solar activity] scales with the square of the magnetic field and hence does not depend on sign of the field, and in any event, the two hemispheres have opposite polarities and that is tru in every cycle, thus, again, does not give rise to any 22-year cycle.

Mark T
April 21, 2016 7:03 am

“A useful definition of solar activity is one that involves the energy the sun puts out, and the effect of that on the Earth.”
Useful, yes, but that is also one that doubles the frequency of any underlying signal, i.e., the frequency of the magnitude (typically squared, which is either power or energy) is twice the fundamental frequency of the signal itself. Signal processing engineers exploit this regularly: cyclostationarity of phase-shift keyed communication signals provides frequency, phase, and rate information.

April 21, 2016 7:08 am

No, it does not. We get the maximum energy every ~11 years.

george e. smith
April 21, 2016 8:43 am

Since earth detected charged particles whether of solar origin or ‘cosmic’ origin are going to be deflected by magnetic fields in the vicinity of the solar system, mostly the solar polar field, then the arrival of such charged particles on earth is likely to be bipolar since the deflection direction of charged particles, depends on the polarity of the solar magnetic field.
So yes cosmic rays should show a 22 year periodicity.
I interpret Leif’s position as being that ” solar activity ” relates to other measures of solar physical processes, such as may manifest as TSI variations; and isn’t including just switching of solar magnetic field polarity.
Evidently Vuk, chooses to consider polar reversal of solar magnetism to constitute “solar activity “.
Lucky for me, I’m too ignorant of solar Physics, to have my own independent view.
That’s why I come here to learn from WUWT.
G

April 21, 2016 9:14 am

So yes cosmic rays should show a 22 year periodicity
They show a strong 11-year period with a tiny 2nd order modulation with a 22-year period on top of the basic fundamental 11-year cycle..

Crispin in Waterloo
April 21, 2016 9:34 am

It is obvious from the above that there is one school of thought that only TSI matters with respect to earthly climate which I view as a gross over-simplification. There is another that observes the polarity of the sun N-S aligns, or not, with the magnetic field of the Earth and I think there is general agreement about that.
As an observer of ‘events’ (data) I see there is some common sense in the idea that magnetic fields and their interplay affect the Earth’s climate. Leif says there isn’t, or more correctly, asks for evidence, and rejects a priori anything originating from Vuk. Yeah, well, no, fine. Lack of evidence, or acceptable evidence, is not evidence of ‘lack’. I still see the magnetic field of the sun as an important influence on things magnetic in the solar system. Svensmark’s hypothesis depends on solar magnetosphere variation, right?
So I accept that there is some periodic magnetic influence and magnets ‘in agreement’ or ‘disagreement’ definitely affect the magnetosphere around the Earth.
The Earth’s north pole is bifurcating. I observe that the polar vortexes (weather) are tending to form repeatedly centered over the north pole that is inside Canada (=data) and avoiding the one over the edge of Siberia. Is it true that polar vortexes form and sit over a magnetic north pole? Isn’t that where the incoming particles concentrate to form a ring of aurora activity?
If the aurora are indeed caused by energetic particles directed by the magnetic field (which seems to be agreed)
and the position of the pole moves around, and the solar magnetic field is sometimes with or against the pole of the Earth, then it is very reasonable to look for modulation of the effect exerted by our weak North pole. There is one school of thought that says the Earth’s magnetic field is enhanced by solar phenomena. I am saying ‘phenomena’ so as to avoid the easy slap-downs and dismissal one finds on a subject replete with so many appeals to authority. One of the great freedoms we have is to be allowed to think.
Too much about this topic is ossified. To pretend that electrical and magnetic influences are not dominant at certain scales is pointless. There remain many possibilities for additional understanding, including the Dark Matter that surrounds us, and the even Darker Matter that surrounds that.
Leif, I find the claim that there is no 22 year solar cycle indefensible. We have been measuring it for 90 years. I find the claim that the polarity of solar magnetic field has no detectable or meaningful influence on the Earth’s climate equally indefensible. First, it contradicts common sense and second, there is no proof of no influence.
Pinch effect, purely electrical in origin, at scale http://www.bibliotecapleyades.net/imagenes_universo/electricuniverse24_03.jpg

April 21, 2016 9:47 am

and the position of the pole moves around
Except that it doesn’t.

Bob Boder
April 21, 2016 9:49 am

Crispin;
Why would Leif, who doesn’t believe the is an affect caused by the 22 yr cycle, admit that there is one with out evidence? Right or wrong he is on the side of the Null Hypothesis he doesn’t have to prove anything to make his argument. The burden is on Vukevic or anyone else to prove otherwise, they have made arguments which have all been refuted at least to a certain extant by Wilis and Leif over time. This doesn’t make them wrong but it certainly establishes that they don’t know that they are right nor can they prove it to anyone else.

kim
April 21, 2016 11:03 am

===========================

Pamela Gray
April 21, 2016 6:18 pm

Kim, that sounds waayyy to much like a carnival barker selling snake oil. Honestly. Think before you post.

kim
April 22, 2016 12:21 am

You don’t like my clock? Think how long it’s been ticking.
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April 22, 2016 12:23 am

Drive-by one-liners don’t cut it. If you have some intelligent to say, say it.

kim
April 22, 2016 1:33 am

See George E. Smith below with his 66 year period modulating signal giving the 9 and 13 year sideband frequencies. Think how long the Pacific Ocean has had to equilibrate with the tiny forceings of my clock.
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April 22, 2016 1:41 am

When I looked at that some years ago, I found a modulating period of 122 years:
http://www.leif.org/research/AGU%20Fall%202011%20SH34B-08.pdf
so my clock runs slower than yours. Perhaps the actual period is 104 years, which matches what you can simply see by eye
http://www.sidc.be/images/wolfaml.png
No sign here of 66 year cycle.

April 22, 2016 7:55 am

What’s remarkable to me is that the underlying differential equations producing a change in frequency of rather random events are so stable that the 11 year cycle is so stable . It’s coherence length is more cycles than have yet been observed . One area of analysis I know next to nothing about is “quasi-periodic” phenomena where the underlying dqs have a stochastic component so the period drifts and a Fourier type analysis doesn’t really capture the reality . In all cases it’s the reality that’s real ; our decompositions are just attempts to reduce the dimensionality down to something which fits in our heads .

April 22, 2016 8:24 am

I am not a fan of cycles and such, but we have learned something about the cycle that may be important:
The generation of new flux from the polar flux is an orderly process than can be nicely understood in terms of the differential equations [we can integrate them forwards in time], so the rise to the next cycle is orderly [that is why we can predict the new cycle from the polar fields], but the subsequent reversal and rebuild of the the new polar fields is a random process: of the 3000 active regions generated during a solar cycle, the flux from only about 5 makes it to the poles, so we have ‘small number statistics’. The 5 could by chance be 4 or 6 or maybe 3 and 7. This is good, because it prevents a run-away: there is always a good chance that the next cycle would be small if by chance fewer regions reached the poles.

kim
April 22, 2016 1:41 am

And you’ve fallen silent over the albedo record. You should know we haven’t the observations to say anything definitive. When we do it may well be revelatory, given the power of clouds to change the effect of a steady TSI.
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April 22, 2016 1:43 am

I only talk about what we have data for. No need to talk about suppositions. That I ‘fall silent’ does not mean that I agree, but rather that I don’t think it worthwhile to talk about it.

kim
April 22, 2016 1:46 am

Meh, the 66 year cycle is the PDO. You are focussed on the sun and TSI. I’m simply proposing a mechanism by which the ocean may integrate other manifestations of the sun’s output.
========

April 22, 2016 1:48 am

But there are no other ‘manifestations’ of the solar output. All follow the sunspot number.
So you may simply have shown that PDO is not related to solar output, since the periods don’t match.

kim
April 22, 2016 1:51 am

You ‘fell silent’ after challenging me to find a cycle in the albedo record, and after I responded that we haven’t the record to do so. No further curiosity about what might be the implications if albedo didn’t cancel as the sun’s forces do.
It’s a clue. You are entitled to ignore it.
=====================

April 22, 2016 1:53 am

As I said: silence means it is not worth discussing.

kim
April 22, 2016 2:01 am

Heh, these ‘other manifestations’ vary a great deal more than TSI, as you have well taught me, and they vary enough to explain climate variation. Albedo, possibly manifesting these variations, is likely capable of not canceling in its effect, as the sun’s TSI cancels.
=========================

April 22, 2016 2:06 am

No, they don’t [their energy is way down compared to TSI]. And in any event, they vary just like the sunspot number. Time to ‘fall silent’ on meaningless discussion, don’t you think?

kim
April 22, 2016 2:12 am

I think there may be another clue. What is the ‘energy’ of a cloud? The earth’s response with albedo doesn’t require great inputs of energy to vary magnificently.
=================

April 22, 2016 2:18 am

But it takes a lot of energy to vary the cloudiness [to evaporate all that water].

kim
April 22, 2016 2:15 am

I’ll repeat my earlier point; what if albedo doesn’t cancel? Frankly, why expect it to cancel?
===================

kim
April 22, 2016 2:29 am

Simply, though the sun does the same thing all the time, the earth does not.
======================

April 22, 2016 2:34 am

It would, if the sun were the major driver, so you have just conceded that it is not. That seems to be a good way to wrap this particular digression.

kim
April 22, 2016 2:33 am

There’s your problem, Leif; it is not just the energy input that varies cloudiness.
=============

April 22, 2016 2:45 am

Yes, it is, as the water has to evaporate. The cosmic ray thing is already observationally dead and would never be efficient anyway, and in any event varies just like the sunspot number. So again, I have no problem. People who believe fervently that the PDO is solar driven have a problem with the differing periods.

kim
April 22, 2016 2:54 am

Well I’m simply not going to believe you if you try to tell me that cloudiness varies only with energy input.
Look, the two major theories of how the sun may effect climate are the UV/ozone/barometric one and the cosmic ray one. They both mediate through albedo, and may both be working.
I’ve proposed a mechanism, in which I have little faith, but you’ve not lessened my faith with your insufficient meteorology.
==================

April 22, 2016 2:57 am

They both mediate through albedo, and may both be working.
If they do, they should still vary with the sunspot number which has no strong 66-yr cycle, so you have a problem with your faith. Of course, real faith is the ability to believe in miracles contrary to all evidence.

kim
April 22, 2016 3:04 am

Ah, a logic trap from oversimplification. Of course the sun does not do the same thing all of the time; that was simply a concession to your sun’s forcings cancelling. But there is no need for the earth’s response to cancel, in fact, it is more likely that it will not cancel.
=============

April 22, 2016 3:08 am

But the sun does do the same thing all the time, except varying the amplitude of the activity. AFAWK, if the solar dynamo ever stopped, it could not start again as there would be no seed field for the next cycle.

kim
April 22, 2016 3:11 am

In response to your 2:57, I’ll simply ask for the albedo record to support your speculation that albedo ‘should still vary with the sunspot number’. There is no necessity for your ‘should’.
I’ve shown you a mechanism for a 66 year cycle. I’ve little faith in it, but you’ve just handwaved it away with simplistic meteorology. Heh, and with speculation about albedo.
====================

April 22, 2016 3:14 am

support your speculation that albedo ‘should still vary with the sunspot number
No, that would only be the case if the clouds varied with the sunspot number, which they don’t. Who brought up the albedo? Not I.

kim
April 22, 2016 3:17 am

The perfect transmitter varies the amplitude and the imperfect receiver garbles the signal in myriad ways. It is absurd to expect the earth’s fidelity.
=======================

April 22, 2016 3:22 am

Thus absurd to claim that climate variations vary as solar activity. Or that there is a solar signal in climate. and if there is not, all is just faith-based, which is not science as I do it. But, to each his own. You faith may be strong enough to give you a warm feeling, like peeing in your pants does. Does not work for me.

kim
April 22, 2016 3:26 am

You presume a great deal more understanding of clouds and albedo than we presently have. Have I tempted you into speculation in order to refute my speculation?
============

April 22, 2016 3:32 am

No, I don’t speculate without explicitly saying so, and I didn’t bring up the clouds, precisely because they are poorly modeled. But having lived a long time in a hot, humid climate, I have a good personal approach to clouds, how they form and develop. Not science, but good enough for my purpose.
If someone claims that clouds are driven by solar activity, he should bring forth good evidence, and I don’t see any that are convincing [to me]. Your bar for credulity may be a lot lower than mine, at your peril.

kim
April 22, 2016 3:32 am

Your missing the point; the tune may still be understandable, though not all the notes have perfect fidelity.
My suggestion does not require albedo to follow the sunspot record with the fidelity you require for your faith.
=====================

April 22, 2016 3:34 am

So, you are backpedaling on this. Fair enough, as I thought your point was a stretch to begin with.

kim
April 22, 2016 3:39 am

Leif, you are bluffing about our record of albedo and clouds, and you are simply wrong about cloudiness so precisely correlated to energy input.
======================

April 22, 2016 3:44 am

Go to the tropics and watch the sky every afternoon and see the clouds build as the result of the intense heating during the day. That tells you the real story. Here is an albedo record:
http://www.leif.org/research/albedo.png
No solar cycle here.

kim
April 22, 2016 3:50 am

As I said before, there is no necessity for your ‘should’ above. You are speculating what ‘should’ be.
===============

April 22, 2016 3:57 am

necessity is not necessary, sufficiency is sufficient.
Here is from a well-known paper about clouds:
http://www.leif.org/research/clouds.png

kim
April 22, 2016 3:57 am

As if thermostatic tropical cumulonimbus tell the whole story of albedo.
Your graph is unconvincing. It supports my thesis that albedo need not follow energy input reliably.
=================

April 22, 2016 4:01 am

it excludes GCRs as being important. Now TSI has been decreasing, so no wonder the albedo also has. So much for ‘support’ of your claim.

kim
April 22, 2016 4:02 am

And your excerpt supports my speculation that more than one mechanism acts to effect the solar action upon albedo.
=======================

April 22, 2016 4:08 am

Well, so you concede that we have cut your two mechanisms down to one: UV. This is real progress on your part. congratulations. Insight is always good, especially if hard won.
Now, UV also follows the sunspot cycle very reliably, so you are back at your problem with the disparity between periods. My point is that your evidence [if there were any] is crumbling and you are back to faith [which often can sustain people in difficulty].

kim
April 22, 2016 4:17 am

No, your excerpt does not cut the mechanism to one.
And you’ve not shown that albedo must follow the energy input.
=======================

April 22, 2016 4:20 am

it disposes of the GCR effect. You only mentioned one other possibility, hence from two down to one.
Perhaps you should have mention the several other ones you have in mind and their supporting evidence, before make absolute statements.

April 22, 2016 4:26 am

From my excerpt: “the most promising mechanism [for increase in clouds] seems to be a rise in evaporation rates following the rise in sea-surface temperature”.
I’ll go with that obvious explanation.

kim
April 22, 2016 4:30 am

You should reread your excerpt before declaiming so definitively about what it eliminates and does not eliminate. Hint, the clue is toward the end of it.
And you are bluffing about albedo and energy input.
=============

April 22, 2016 4:33 am

I don’t take hints. Say what you have to say or shut up.
I am telling what others say about clouds and energy input. How can that be bluffing?

kim
April 22, 2016 4:41 am

And relative humidity appears to be dropping with increasing SSTs. So much for the ‘obvious’ explanation.
==========

April 22, 2016 4:54 am

That would only be in extreme cases if the temperature increase would be very high, and is only a cop out phrase. All scientists have one like that.
And humidity has actually been increasing:
so much for your objection based on desparate conjecture
It seems you don’t really know much about these things.

kim
April 22, 2016 4:43 am

=================

kim
April 22, 2016 5:01 am

Are you confusing specific humidity and relative humidity? I hope not.
===========================

April 22, 2016 5:39 am

In the humid air above the tropical oceans the difference hardly matters.

kim
April 22, 2016 5:04 am

Hint: For cloudiness the relevant metric is relative humidity.
===============

kim
April 22, 2016 5:56 am

We are talking about the albedo of the whole earth, not just where the difference doesn’t matter. Your graph of rising specific humidity does not refute my suggestion of dropping relative humidity.
Regardless, you are trying to force albedo into a Procrustean Bed, and clouds are wild and wooly beasts.
===================

April 22, 2016 6:01 am

“The specific humidity is an extremely useful quantity in meteorology. For example, the rate of evaporation of water from any surface is directly proportional to the specific humidity difference between the surface and the adjoining air.”
The specific humidity is the important quantity as it determines how much water there is in the air. When that air rises to the point where it becomes saturated clouds form.
And I don’t need to refute ‘suggestions’. If you think you have something, show the evidence. The fact is that cloudiness has increased over the last 50-100 years in sync with the increasing sea-temperature.

kim
April 22, 2016 6:30 am

Hail Brittanica(that’s a private joke for you).
You have a lot of faith in the cloud record.
Can you find a graph of relative humidity to support your point?
==========================

April 22, 2016 6:33 am

Can you? you are the one making the dubious claim.
Perhaps it is time for a little tutorial:
http://www.leif.org/research/How-Clouds-Form.png

kim
April 22, 2016 6:43 am

Your own excerpt speaks of relative humidity as if it is the important metric, not specific humidity. You are handwaving.
==============

April 22, 2016 6:46 am

When the cloud forms, relative humidity is 100%, so in that sense it is important, but whether a cloud can form at all depends on the specific humidity: the has to be water to begin width. All this is Met101.

kim
April 22, 2016 7:00 am

I was surprised a few years ago to learn that clear air can have a relative humidity greater than 100%. You need nucleating agents, too, like cosmic rays, or the plentiful output of microscopic sea critters.
So why does your excerpt talk in terms of relative humidity when you consider specific humidity more important in cloud formation?
=========================

April 22, 2016 7:07 am

In general over the tropical oceans where most of the clouds form, air with high specific humidity rises [and already containing salt aerosols] and thus cools. When the air has risen to such a height that it has cooled to the point where the relative humidity reaches 100% a cloud forms. Over a desert, on the other hand, the specific humidity is so low that the rising air never reaches a point where the relative humidity becomes 100% and no cloud forms. So, in that sense, the relative humidity is important, but only secondarily: the water has to be there to begin with.

kim
April 22, 2016 7:25 am

At the point of cloud formation, relative humidity is the most important. You are telling me that yourself.
==============

April 22, 2016 7:36 am

Yes, the relative humidity at height where the clouds form is always 100%. If this is not reached, no cloud. The determining factor in reaching 100% is the water content [the specific humidity] to begin with, and that has increased over the past many decades due to rising sea-water temperature. So, clouds have also increased. A good proxy for cloudiness is the number of hours of sunshine in, say, a year. This is easy to measure and has been measured since at least the 1880s. Here are some typical stations:
http://www.leif.org/research/Sunshine-Factor.pgn
In years with large volcanic eruptions the sunshine is decreased without that being due to clouds. You can see that in the record, e.g. for Krakatoa in 1882 and Pinatubo in 1991. But apart from those rare events, sunshine hours have generally been falling, so cloudiness has generally increased, in sync with rising temperatures, as expected.

April 22, 2016 7:39 am
April 22, 2016 7:40 am
kim
April 22, 2016 7:42 am

Hmmm, your graph above does not show a steady rise of albedo with rising SSTs.
I think your problem is that you expect albedo to be in lockstep with the solar signal in order to show a solar effect. I don’t think it is that simple.
======================

April 22, 2016 7:47 am

It shows cloudiness [inverse sunshine] increasing with increasing temperatures, as is natural and expected. How that translates into albedo is perhaps complicated, but also irrelevant as the cloud record does not match the solar cycles, and I don’t think the albedo-producing process also can produce a solar signal, if the clouds don’t have it. But, I guess if you are desperate enough, you might posit such a ridiculous idea.

kim
April 22, 2016 8:02 am

I was speaking of your 3:44 AM graph of albedo.
Yes, albedo is complicated. That a signal is not apparent there does not mean absence of signal. Perhaps I should end with that speculation.
As usual, I’ve learned from you.
=====================

April 22, 2016 8:06 am

It show generally decreasing albedo as deduced by measuring earthshine [sunlight reflected off the Earth to light up the Moon] and so has an additional link of inference [and uncertainty].
That a signal is not apparent there does not mean absence of signal.
If there were a signal, it would not be absent.

beng135
April 22, 2016 8:42 am

Jeesh. I hope Dr S’s students aren’t this obtuse.

April 22, 2016 8:44 am

There are people of all sorts…
Some can help it, and some cannot.

kim
April 22, 2016 3:52 pm

It’s all useful. He gets to mount majestic heights of purple prose to declaim against groundless speculation, and I get to groundlessly speculate with a master.
====================

Slacko
April 22, 2016 7:09 pm

lsvalgaard April 21, 2016 at 1:20 am
“A useful definition of solar activity is one that involves the energy the sun puts out, and the effect of that on the Earth. Examples are Total Solar Irradiance, Ultraviolet Radiation, Magnetic Storms, and Cosmic Ray Modulation.”
You’re contradicting yourself Leif. You already said that Cosmic Ray Modulation takes place at a distance of 100 AU. (lsvalgaard April 21, 2016 at 1:01 am)

April 22, 2016 7:49 pm

But controlled by the Sun, and intercepted by the Earth.

kim
April 23, 2016 7:54 am

Tick-Tock-Tick/Tock-Tick-Tock,
It’s been going on forever, that grandfather’s clock;
Tiny forcing, that the oceans can’t mock,
We can’t see it yet, and that’s a lock.
====================

Espen
April 21, 2016 12:18 am

Interesting! Do we have sun spot proxies that could be analyzed to see if the ~90 year cycle persists in a much longer perspective?

george e. smith
April 21, 2016 10:15 am

“””””….. lsvalgaard
April 21, 2016 at 9:14 am
So yes cosmic rays should show a 22 year periodicity
They show a strong 11-year period with a tiny 2nd order modulation with a 22-year period on top of the basic fundamental 11-year cycle.. …..”””””
Yes I certainly didn’t mean the fundamental frequency of the CR variation was 22 years, just that a small 22 year affect should be there.
I think of cosmic rays as being from ” way out there” rather than charged particles from the sun. And those ‘real’ CRs would be much higher energies than solar charged particles, so their deflection by magnetic fields in the region of the solar system, would be small.
And if as Leif says, mere solar polarity reversals, do not constitute “activity” in the sense of energy output manifestations, then they would put a 22 year signature on solar ‘activity’ as Leif defines it.
That works for me.
G

george e. smith
April 21, 2016 10:16 am

That’s they would NOT put a 22 year signature.
g

April 21, 2016 10:29 am

mere solar polarity reversals, do not constitute “activity” in the sense of energy output manifestations
In a given cycle we receive output from negative fields in the north and from positive fields in the south. In the next cycle we receive output from the positive fields in the north and from negative fields in the south. In all cycles we receive output from both positive and from negative fields, thus no 22-year cycle.

April 21, 2016 12:19 am

brilliant as usual
thank you
i took a look at monthly mean sunspot counts 1818-2015 and found that i could describe the irregular cycles as the sum of two independent processes – one cyclical and the other a random Hurst process.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2767274

AJB
April 21, 2016 8:36 am

Still only one and a load of hands in the air then. I guess that’s progress of sorts 🙂

kim
April 21, 2016 12:33 am

It would be fun to see the ocean analysis extended to the length of the sunspot one. Sure, not possible.
A technique with possibilities, thanks.
====================

AJB
April 21, 2016 12:54 am

“Anyhow, that’s why I’ve grown fond of the CEEMD analysis … it shows when datasets have related cycles, and when they are unrelated.”
Good article Willis but I don’t like that “unrelated” word; far too black and white for my taste. If you said “might not be related” or “not obviously related” I’d be happy. Nothing wrong with Fourier’s idea that any waveform can be expressed as a combination of sine and cosine waves, except that it neglects to mention how many. Or rather, it fails to express the level of complexity we might be (and probably are) wading into. We have no idea of the number, amplitude or time base of any of them except for dominant ones in any one dataset which may be modulated to oblivion in another. Fading in and out is the least of it. All these methods are fine for simple, straightforward signal analysis but nature and the universe at large is a lot more complex than that. Call it the n-body where n tends to infinity problem, or the numerologists’ low hanging fruit has already been picked and we’ve wondered into statistical la la land conundrum 🙂

george e. smith
April 21, 2016 9:15 am

Well Fourier analysis deals with continuous signals, and our data gathering almost always is only gathering sampled data, and for that sampled data to have any meaningful information content, then the sampling regimen has to conform to the Nyquist sampling theorem, otherwise you do not have valid data to even analyze.
And implicit in the concept of sampled data systems, is that the ” signal ” MUST be band limited, otherwise you cannot sample it with any finite number of samples.
So the fact that the sampled data is inherently band limited, then any Fourier decomposition of such a signal is not going to produce any frequency components outside the band limit.
Ergo only a certain number of modes will have other than zero content, in Willis’s analysis.
G
PS Fourier analysis, in the form of decomposition into sin and cosine terms, will have only harmonically related frequencies if the signal is strictly cyclical; as in:
F(t) = F(t-tau) where tau is the period of the cyclic repetition. For non (strictly) cyclic signals then a continuous spectrum of frequencies can occur. It will still have to be band limited, to be sampled.
But the same sort of decomposition can be done with other functions besides sin and cos.
You can do similar decompositions in terms of things like Bessel Functions, Legendre Polynomials, Tchebychev Polynomials, and so on.
Any orthogonal set of functions, can be used to do Fourier like decompositions. The choice is often dictated by co-ordinate systems, or other conditions.
Orthogonality means that the integral of the product of two of such functions over the full range of the independent variable, is either zero or non zero depending on the two functions. i.e. Integral (Fn(x)).(Fm(x) is zero if n and m are not equal, and is non zero if n=m.
So if you have a sum of such terms sigma Fi(x) over all values of I, you can multiply the real function by Fn(x), and also all of the Fi(x) terms and integrate over the full range, you get zero for all the n not = m terms, and only a non zero value for the I=n term, which you used to multiply the whole signal by. This simple process (time consuming) enables you to determine what every one of the individual components is.
Gaussian functions are quite common in laser propagation mode analyses. Bessel functions show up in optics when diffraction by circular boundaries (lens edges) occur, but rectangular apertures revert to simpler sin and cosine functions, instead of Bessel functions.
This old horse used to run a pretty good race, when push came to shove.
G

April 21, 2016 9:47 am

Yes, in the spirit of skepticism, one ought to avoid absolutes (okay, ought is an absolute!), but only when appropriate. Why not avoid weasel words altogether, and say something like “show now relation to the nth intrinsic mode”?

April 21, 2016 9:49 am

I thought I had put a “” close tag in there after “ought”. I bet my fingers did not agree.

April 21, 2016 9:52 am

Funny how you can’t explain an html error on an html edit box…. 🙂

Greg
April 21, 2016 12:56 am

Interesting stuff.
In fact the 9 and 13 year peaks in the ENSO C3 and C4 bands are found in both Pacific and Atlantic oceans. The 9y is very likely lunar, I have not found a cause for the circa 13y periodicity
https://climategrog.wordpress.com/2013/03/01/61/

Greg
April 21, 2016 1:31 am

That is the same periodicity that is found in Atlantic cyclone energy.
I think these bumps are what is commonly assumed to be solar signal by those who close one eye when it goes into anti-phase.

Greg
April 21, 2016 1:44 am

The ACE thing was discussed on C.Etc.
https://judithcurry.com/2016/01/11/ace-in-the-hole/
There is clear evidence from around the globe that look at lot like lunar driven variations. Probably variations is ocean currents in and out of the stable tropical regions.
Two of those peaks in SST and ACE lie very close to El Chicon and Mt Pinatubo and at that point are roughly in sync with the solar cycle. There is huge scope here for false attribution by the many naive attempts at multivariate regression that have been published.
More importantly I don’t think I have seen a single such regression which includes a lunar variable.

Greg
April 21, 2016 2:18 am

Here are the regions where there is a clear 9y cycle. The previous plot only showed those where there was also the 13y periodicity.
There is also a 9.3y period in the Indian ocean. I can’t recall why is was not included in the above.

george e. smith
April 21, 2016 10:32 am

If you convert the 9, 11, and 13 year periods to frequency, you get: 0.111111, 0.090909, 0.07692308, which gives frequency differences of 0.0202 and 0.014, or roughly 0.018 each or five times slower than the 11 year carrier period , suggesting a 66 year amplitude modulation of the 11 year carrier period, producing the 9 and 13 year thereabouts upper and lower sidebands (frequency).
An 11 year period carrier frequency, amplitude modulated by a 66 year period modulating signal should give you about 9 and 13 year sideband periods.
G

kim
April 21, 2016 1:42 pm

Hello, PDO.
========

charplum
April 21, 2016 10:41 am

I could not help but notice that in your chart the spectrum is filled with numerous short period cycles. I have found the same in a cyclic analysis of the NINO 3.4 region.
In this case as you will see in the charts I use the monthly data until 2014; thereafter, I use the daily data. I did this because I wanted more definition to the more recent data.
My first step is to perform an Optimal Fourier Transform (Dr. Evans). I thin use this output is input in a Marquardt process. Initially I arbitrarily selected to fit the data with 90 cycles. That means when going through the Marquardt process I have 270 initial guesses plus one added guess for an offset value.
In most cases when I do this the Marquardt process improves the quality of the fit.
The results of this analysis is given in the link. The overall fit to the NINO region 3.4 data is over 0.94, I think the figures included in the link speak for themselves as to their fidelity to the measured data. In the link you will find a data table that furnishes the details on the 90 cycles that fit the data. In the table you will also see that the Marquardt process improved the quality and you will also see the Sum of the Squares (SSE) errors for the original OFT and also for the process the data went though. I also include a separate correlation coefficient for the data overall and also for data after the date indicated. I did this because I thought some of the older data had more noise.
https://onedrive.live.com/redir?resid=A14244340288E543!13127&authkey=!AFikPGdFAeg_vxY&ithint=folder%2c
To substantiate the cycles used I swept single frequencies through the data to see where humps or peaks show up with higher correlation coefficients that may indicate that those items are in play. For the longer period cycles these appear as humps and not peaks. Here is what I found.
https://onedrive.live.com/redir?resid=A14244340288E543!13128&authkey=!ALO7UHHbAWDJVLM&ithint=folder%2c
I hope you take the time to look at this. I think it will be worth your time.

Jimmy Haigh
April 21, 2016 1:05 am

When we record sunspots we only see half of the sun at any one time. Would we not need to record the data from the entire sun in order to get more meaningful data? Not so easy for historical data I know…

April 21, 2016 1:11 am

Luckily, the sun rotates so we do get to see the backside.

Greg
April 21, 2016 1:23 am

This rotation will of the disc of observation will introduce a periodicity of c. 27d ( equatorial region ) which means that “monthly” averaging is not the best way to decimate the data. Averaging will only correctly remove gaussian distribute ‘noise’ not periodic cycles, those will produce aliasing.
Equally annual averages are not good practice.
Where daily data are available they should be low-pass filtered at twice the resampling period BEFORE being resampled.
This DP101 but so many still seem to think that taking the mean is some kind of magic wand solution that fits all situations. Apparently Nyquist’s theorems only apply to electroncs.

April 21, 2016 1:31 am

That is why we often analyze the data in terms of 27-day rotational means. In practice, there is very little difference with the monthly means. And the annual average is a good measure of what we have received from the visible disk in the course of the year, regardless of the rotation. This is Solar-physics 101.

Greg
April 21, 2016 1:36 am

It is true that is you want an earth centric measure the observed disc is a useful measurement.
Taking 27 day means does not address the need for anti-alias filtering. A mean is NOT a filter. It will only address random noise.

April 21, 2016 2:22 am

But we do not want to apply any filters. We want to know the accumulated effects. That is what is meant by ‘activity’.

Greg
April 21, 2016 3:19 am

Thanks. I think that is problem. What is meant by “activity”. Are we defining activity as “that which affects the earth’s climate”? Or is it supposed to be some objective property of the solar processes for which we can search for an earthly trace.
In the former case a mean would be suitable way to calculate the integral over a certain period. But this also has the implicit ASSUMPTION that it is TSI which is the determining factor on climate. This is the most obvious one to look at but is not definitive.
Does “activity” simply mean earth facing TSI?
I’d always understood the meaning of solar activity to be measurements of what is happening on and in the sun, as a means to model and understand the sun itself.

April 21, 2016 3:28 am

Are we defining activity as “that which affects the earth’s climate”
Still not paying attention.
Not climate [actually I think it does not], but all the other aspects of solar activity: geomagnetic activity, aurorae, spacecraft drag, creation of radionuclides [e.g. C14],, These things tell us a lot about the sun and its activity. And calculating averages [‘integrating’] works for those things as well.

April 21, 2016 4:48 am

lsvalgaard: Like many here, I appreciate your insistence on evidence, and your knowledge. However, you lack etiquette skills in dealing with people whom you feel are beneath you, intellectually. It is not polite, nor civil to treat people in this way, and it somewhat negates your points. Calling someone’s post ‘pollution’ is not nice, nor is saying ‘still not paying attention’ – especially when Greg was trying to establish a definition. Both Vuc and Greg’s points are interesting and worthwhile reading. I always appreciate Vuc’s ‘out there’ view.
I’ve no wish to get personal myself, but for all your immense solar knowledge, and your intellect, you have grown up lacking certain social skills, and you seem to delight in parading that fact. That is not something to exhibit, if you have the choice. At least try to be more understanding of others, and reign in your ability to be curt. We can all act in a brusque manner, but many of us choose not to do so, as we have been schooled that it is impolite.

April 21, 2016 5:10 am

Well, science is a blood sport, and politeness often gets in the way of progress. There comes a point where the unwillingness to learn anything [e.g. in Vuk’s case] becomes intolerable and I simply express that. As for Greg, he continued on about TSI [and climate] even after I several times had stressed that there were many other drivers in play. I consider such attitudes to be impolite. The truth should not be sugarcoated.

rbabcock
April 21, 2016 5:38 am

Many of you evidently didn’t know the Sheldon character in “The Big Bang Theory” is based on lsvalgaard.

April 21, 2016 6:38 am

Vuk and greg are hilarious to watch.
Neither learn.

April 21, 2016 9:22 am

Hi Steven
It goes something like this:
“One thing that interferes with my learning is my education. Education should not be learning of the facts, but training of the mind to think.” A.E.

April 21, 2016 11:27 am

I, for one, admire Dr Svalgaard’s quality of telling it straight, like it is – so much better than slinking away and whispering behind someone’s back. I get utterly fed up with the current ‘Progressive’ politically correct stupidity of “Oh, you can’t say that… someone might be offended”. Poppycock!

Bob Boder
April 21, 2016 8:36 am

Steve
“Vuk and greg are hilarious to watch.
Neither learn.”
That coming from the model of flexibility and open mindedness himself.

don k
April 21, 2016 1:45 am

It’s certainly interesting. A couple of thoughts:
1. You understand CEEMD a lot better than I do. But it makes me nervous that C1 and C2 are “weaker” than C3. How do you know there isn’t a meaningful component that has been pushed off to C11? what’s your critereon for “complete”?
2. The CEEMD components certainly present interesting visualizations. But how do you know that you’re not looking at artifacts of processing similar to Mann’s infamous Hockey Stick?
3. Is it even possible to find cyclic components that don’t show up clearly in in Fourier analysis? I think that’s asking if Fourier decompositions are unique. I’ve always assumed they are. But maybe there are multiple different sets of Fourier components that yield the same result? I’d sort of think there would have to be if CEEMD is going to tell you anything new. But that’s way beyond my pay grade.
4. Not all cyclic phenomena are well behaved. An example — earthquakes. Presumably the stresses that cause quakes accumulate at a steady pace. But the release of the stored energy looks to be a complex process that happens when it’s damn well ready to happen. Consequence — if you have a big earthquake in 1763 and another in the “same” spot in 1963, you should not say with any confidence that the next big quake there will be in 2163. I think that’s an aperiodic oscillator. I know next to nothing about those. I should think that Fourier or EEMD or any other periodic analysis is going to end up with spurious terms when applied to an aperiodic oscillator.
5. In addition to aperiodicity (Is that a word?) there can also be ringing. You whack a system. It responds in a cyclic fashion. But the cycles are damped over time. Is it possible that some of the things we are trying to analyze as cyclic are actually aperiodic events followed by a ringing (damped oscillation) response? I suspect that Fourier/EEMD aren’t going to handle those all that well.

Greg
April 21, 2016 2:01 am

IIRC , CEEMD is just a series of band-pass filters. If you added all the separate frequency plots you’d end up with something close to the full FT. I suspect there is danger of some intermediate frequencies getting attenuated quite strongly if they happen to lie mid way between two of the frequency bands used.
The decomposition is a useful visualisation tool. It helps see what is going on and relative magnitudes etc.

rabbit
April 21, 2016 4:01 am

“I suspect there is danger of some intermediate frequencies getting attenuated quite strongly if they happen to lie mid way between two of the frequency bands used.”
I’m no great expert on Empirical Mode Decomposition, but I do know it is not a series of bandpass filters. One does not choose pass bands to examine. Rather the EMD (and its many variations) “chooses” the decomposed modes empirically — thus the name. If there are intermediate frequencies with strong amplitude then they will form part of the decomposition. And although the modes often resemble bandpassed versions of the data, it is not a true bandpass filter.

Joe Born
April 21, 2016 4:55 am

I’m speaking from a wealth of ignorance here, but I’m of the opinion that, although I see what you mean by bandpass, it may be more helpful to consider the technique as akin to applying high-pass filters in succession.
My understanding is that each component into which empirical-mode decomposition teases a signal can be thought of as the difference between the residue the previous components left and that residue’s local-in-time “DC component,” defined as the average of a spline though the residue’s local maxima and one through its local minima. For each component, therefore, it’s like a respective high-pass filter having a time-location-dependent cutoff.
To make the time locality of the residue, i.e., the “DC component,” fairly uniform throughout the signal record, red noise is added to the residue. To attenuate the resultant noise error, the process is repeated a number of times for the same residue with different red-noise signals, and the average is taken as the component.
So I’d say that the CEEMD approach can (only very crudely) be compared to the results of a sequence of decreasing-cutoff high-pass filters operating on the residues of the previous components. Consequently, I’m not so sure how great the danger is of which you speak.

george e. smith
April 21, 2016 11:03 am

Well hold on there pardner !
This donnybrook started with Willis doing an analysis of sunspot 11 year cycle information.
So we have a signal that shows a significant 11 year periodicity; as in it’s a PERIODIC signal.
And what we all know about Fourier analysis, is that for a STRICTLY PERIODIC cyclic signal, Fourier decomposition yields ONLY harmonically related DISCRETE frequencies.
So there ARE no intermediate things lurking in the shadows between Willis’s modes.
Only when the signal is aperiodic, does Fourier analysis lead to a continuous spectrum of frequency components.
So in no way are Willis’s modes the outputs of any kind of band pass filters. Now any sort of wow or rumble in the nice 11 year period, will result in spectral broadening of Willis’s lines, and his computed plots show such things quite clearly.
DFT’s are just special case methods, but they are just substitutes for what is really an integral calculus problem, and for general signals, it requires the full Fourier Integral form of the mathematics to get a valid answer.
The basically 11 year periodicity of sunspot cycles and the related solar activity variations, is well established and makes the simpler case of harmonic modes valid, as Willis’s nifty plots demonstrate.
When I do optical diffraction patterns, I seldom use the FFT solutions, which my software can give me, because my systems contain aberrations (which I am trying to reduce), so I always end up doing the full Fourier integral approach in the end, before I put my signature on it. Takes a heck of a lot more time to do, than FFTs, but it is considerably more accurate.
G

April 21, 2016 3:30 pm

When I do optical diffraction patterns, I seldom use the FFT solutions, which my software can give me, because my systems contain aberrations (which I am trying to reduce), so I always end up doing the full Fourier integral approach in the end, before I put my signature on it. Takes a heck of a lot more time to do, than FFTs, but it is considerably more accurate.

I don’t understand why that should be . It’s been 30 years since I looked at Cooley Tukey and considered implementing it as reductions across the data expressed as an array in the prime factors of the number of data points , optimally a power of 2 , and thought I saw additional redundancies it didn’t capture . But all the algorithm does IIRC is compute points where multiple harmonics have the same value just once instead of once for each harmonic . It should produce exactly the same results for highly factorable numbers of points . I don’t know what it does if you give it , say , a prime number of data points .
The ability to write definitional ( not FFT ) Fourier transform in one line of APL contributed to my exit from grad school w/o a PhD .

Joe Born
April 22, 2016 4:57 am

I don’t understand why that should be.
Appropriately so.
The “full Fourier integral” thing makes no sense. If all you have is a sequence of samples, the DFT contains all of that sequence’s information, as I explained above. “Full Fourier integral” means nothing unless you somehow have the continuous function from which the samples were taken. The FFT is merely an efficient algorithm for calculating the DFT, in n^(3/2) time instead of n^2 time. The FFT is not a somehow-reduced transformation; it is a way of efficiently obtaining the full transformation.

Joe Born
April 22, 2016 4:59 am

Oops! The block indent should have ended after the first line.

Joe Born
April 21, 2016 4:36 am

I don’t comprehend CEEMD, either. But here’s a possible answer to your first question.
If I remember the procedure correctly, each component’s generation starts with a residue that results from subtracting the previous component from the previous residue. So eventually you run out of any significant residue.
I’m no scientist, so take this for what it’s worth, but it seems as a matter of logic that a given time sequence’s discrete Fourier transform (“DFT”) is unique and contains all of that sequence’s information. That is, an n-point time sequence is a location, expressed in one set of coordinates, in an n-space, while the DFT is that location expressed in a different set of coordinates. Therefore, if a CEEMD component is a function of the time sequence, it must be a function of the DFT, too.
There’s a latent ambiguity in the question, though. When people are talking about a given quantity, such as temperature readings at a given site, they are not always talking about the same subset of those readings. This crops up in expressions like “spurious” in Mr. Eschenbach’s “This greatly increases the odds that it is a spurious signal.” (Actually, either it’s a signal or it isn’t; it all depends on which part of the record you’re looking at.) In this sense the DFT isn’t unique–because the original time sequence isn’t, either.

Don K
April 22, 2016 12:33 am

Thanks Joe. I reckon you folks are right about the first question. Still, though, as george smith points out below, Fourier decompositions can have no amplitude at some frequencies, so for FT, you can’t just stop when you see the first zero coefficient. I think CEEMD is different in that respect, but I’ve been wrong about things like that so often in the past eight decades that I’d be happier with a solid proof.
Wrt the third question, I would think that if transforms between frequency and time domains were not unique, it would be impossible to tune a radio to isolate one frequency band from the multitude of signals present at the output of a broadband antenna. But that’s an opinion, not a fact.
And wrt “spurious” signals, I was under the impression that FT, for example, introduces imaginary (spurious) high frequency signals in order to accommodate what it sees as transitions between no signal and signal states at the start and end of the sample. I’m not remotely competent with FT. so maybe that’s only if you do it wrong. But still … I think we should know from the hockey stick fiasco and the disastrous results of applying Li’s Cupola to security analysis a decade ago that not fully understanding tools can lead to quite dreadful results.

george e. smith
April 21, 2016 10:42 am

The reason you do the analysis is for the purpose of finding out just which components ARE significant. There is no expectation that the amplitude of higher order components should monotonically diminish with higher order.
Square wave decompositions for example contain no even order harmonics for a cyclic signal. only odd order components are present..
Willis’s finding of a prominent third order component, is just the sort of useful information that such analysis is used for.
G

oebele bruinsma
April 21, 2016 1:52 am

” When cycles come and go like that, it is hard to draw any firm conclusions. I mean, the ~ 80 – 100 year cycle is definitely there … but it’s only there when it is there, and the rest of the time, well, it’s simply not there.” The human brain apparently is wired to construct patterns from observations, with or without a physical base. This mechanism seems comforting to probing minds.
Thanks Willis.

Greg
April 21, 2016 2:08 am

The point is to look for possible cycles and if there is anything interesting seek a physical cause. It is not proof of something just to find a wiggle.
We are always trying seek underlying order in the chaos of the world to anticipate what will happen next and to be better prepared to handle it. The key is to know when our model is working and when to drop or modify it.
The temperature rise from 1975 to 1997 looked like it could be a problem. Sounding the alarm was reasonable at the end of the last century. Continuing to harp on about a broken model and refuse to modify it is totally irresponsible.

ClimateOtter
April 21, 2016 3:20 am

‘I love humans. Always seeing patterns in things that aren’t there.’ ~ Doctor Who
(I disagree with that observation though, as I believe it was political nonsense inserted by the writers)

Greg
April 21, 2016 4:05 am

Perhaps the pattern he was referring to was the steady rise arbitrarily attributed to AGW, a pattern which lasted for about 20 years in a very selective part of the last century 😉

Greg
April 21, 2016 4:10 am

It’s actually a pretty fair comment. We do have a tendency to see patterns , especially faces or animals in almost anything. Clouds, inkspots, shadows on Mars…
If we could communicate better with animals we’d probably find they do the same. It’s a fairly obvious survival trait.

Joel O’Bryan
April 21, 2016 8:35 am

It is also why it was the innocent child in the Emperor’s New Clothes that forced the townsfolk to openly admit the lie they all knew inside.

“But he hasn’t got anything on,” a little child said.
“Did you ever hear such innocent prattle?” said its father. And one person whispered to another what the child had said, “He hasn’t anything on. A child says he hasn’t anything on.”
http://www.andersen.sdu.dk/vaerk/hersholt/TheEmperorsNewClothes_e.html

Which of course is widely regarded as the reason it was an obscure 26 yr old Swiss patent clerk who changed the course of physics.

ClimateOtter
April 21, 2016 3:18 am

lsvalgaard ~ Question if I may. Would that recent theory of ‘two dynamos’ inside the sun possibly play any role in those ‘twin peaks’ or the idea of a 22-year-cycle?
I am just going off of what little I know, in regards to the above conversation.

April 21, 2016 3:22 am

The ‘two-dynamo- scenario has been thoroughly debunked: http://arxiv.org/pdf/1512.05516.pdf
“A two-wave dynamo model was recently proposed by Zharkova et al. (2015, Zh15 henceforth), which aims at long-term predictions of solar activity for millennia ahead and backwards. Here we confront the backward predictions for the last 800 years with known variability of solar activity, using both direct sunspot observations since 1610 and reconstructions based on cosmogenic nuclide data. We show that the Zh15 model fails to reproduce the well-established features of the solar activity evolution during the last millennium. This means that the predictive part for the future is not reliable either.”

Bob Boder
April 21, 2016 6:31 am

Leif;
interesting evaluation of the merits of this model, could you please pass on your insight about modeling to others in the scientific community.

April 21, 2016 6:55 am

The scientific community is already well-versed in modelling. But any model is no better than the assumptions that go into the model. If those are wrong or inaccurate the model will not perform well. A model based on numerology usually fails.

Bob Boder
April 21, 2016 7:12 am

My comment was mostly sarcasm not directed at you, but this comment “We show that the Zh15 model fails to reproduce the well-established features of the solar activity evolution during the last millennium. This means that the predictive part for the future is not reliable either” does apply equally well to climate models which have zero backwards predictability.

April 21, 2016 4:32 am

An actual paper in addition: http://www.nature.com/articles/srep23961 (open). A sentence in the abstracts is some kind of strange: “This has led to some climate sceptics misrepresenting this literature to argue strongly that solar variability drove the rapid global temperature increase of the twentieth century.”
A paper for/versus “climate sceptics”? Are there some guys who are sceptic about the climate?? 😉

Javier
April 21, 2016 4:36 am

Mode C6 has a couple of strong cycles with a period of around 90 years at about 1800, and it then kind of tails off to nothingness. This makes it obvious why it has been so hard to discuss the existence or non-existence of the so-called “Gleissberg Cycle”, which Gleissberg claimed was ~ 80 – 100 years. When cycles come and go like that, it is hard to draw any firm conclusions. I mean, the ~ 80 – 100 year cycle is definitely there … but it’s only there when it is there, and the rest of the time, well, it’s simply not there.

The ~100 year cycle is likely to be half of the de Vries 208 year cycle. We know that it comes and goes but it does so as part of a larger cycle, the ~2500 year cycle. The 208 year periodicity is very visible within ±500 years of the ~2500 years cycle lows. In between it appears to be attenuated by higher solar activity. You can see it in this figure from Steinhilber et al., 2012
http://www.pnas.org/content/109/16/5967/F4.large.jpg
http://www.pnas.org/content/109/16/5967/
If you run that 9400 years of solar activity data reconstructed from 14C and 10Be records through your CEEMD analysis you should see it more clearly. The data is at:
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/solar_variability/steinhilber2012.txt
ftp://ftp.ncdc.noaa.gov/pub/data/paleo/climate_forcing/solar_variability/steinhilber2012.xls
The methodology used reduces high frequency noise, and thus you will not find cycles much shorter that 100 years in that data.

Javier
April 21, 2016 12:58 pm

Willis,
I am not the only one to see it. The de Vries cycle is one of the cycles that appears more often in climate records, and one of the least disputed cycles. It appears regularly in the literature since the mid-70’s. Its climate link is quite strong.
In this graph you can see the last two instances of the de Vries cycle that coincide with the two coldest periods of the last 350 years:
http://i1039.photobucket.com/albums/a475/Knownuthing/Scafetta2c_zpsit66xrpm.png
The cycle shows up for about 5-6 periods and then disappears for about a millennia and a half. The graph posted here shows why. The level of activity becomes too high to significantly alter cosmic ray generation or climate. The graphic posted in the previous post does not contradict anything that I have said, nor the existence of the irregular de Vries cycle.

Finally, the analysis uses the 10Be records, which as both Leif and I have pointed out to you have serious problems as a solar proxy …

The analysis correlates 14C and 10Be records and as they have different climate contamination the correlation, if properly done, should theoretically be better than any of the isotopes independently. That it uses 10Be should be no excuse.

george e. smith
April 21, 2016 1:18 pm

Willis, You are hard to catch in flight.
Funny how stumbling over a rock can reveal hidden defects that maybe were not intended. I see you caught a live one.
e.g. “The Reign in Speign falls mainly in the Pleign. ”
G

Claude Harvey
April 21, 2016 4:45 am

These solar water-gun battles are always amusing. No matter who starts the fight, the Isvalgaard child rushes onto the field carrying the largest gun, loaded with acid. I notice little Willis started this one and then stepped aside to watch all the other children get smoked. Good job, Willis!

April 21, 2016 5:45 am

Don’t forget ‘Big bang’ threads, they are lot of fun too
Spring 2016: Johns Hopkins University astrophysicists seek to find out what happened after the Big Bang
I thought they knew, science was settled, or was it not ?
Science made simple from J H U
http://hub.jhu.edu/magazine/2016/spring/class-telescope-chile
Big cheese there is the ‘dark energy’ man Adam Riess professor of physics and astronomy a Nobel laureate.

Claude Harvey
April 21, 2016 5:01 pm

I should have known you couldn’t take a joke, even when it included a left-handed compliment. O.K. You’re “BIG Willis”. Kinda’ screws up the imagery I was going for, but “BIG Willis” it is.

3x2
April 22, 2016 10:13 am

The only thing I would suggest, and who am I anyway, is that you ‘plough on’.
You will probably make at least one babbling enemy every time you look at something a little too closely. Sun worshipers, sixth extinction believers and, hell, those that believe CO2 governs Planetary climate.

April 21, 2016 5:21 am

As matter of interest, how does Dr Svalgaard’s recently reconstructed/corrected sunspot record fit with the consensus position which argues that an increase in solar activity explains (partly/largely?) the rise in temps from the LIA upto the early/mid 20th C?
Presumably, climate models were (still are?) partly based on the old SSN version.

April 21, 2016 5:25 am

This may partly answer your question. On the other hand, some people are clinging to the old version because of its perceived role in Global Warming in the pre-SUV period.

April 21, 2016 5:37 am
ferdberple
April 21, 2016 6:08 am

Isn’t that a weakness of CEEMD. It doesn’t show the underlying frequencies of the physical process. It shows one of an infinite number of possible decomposition.
So for example, a physical 11 year and 22 year cycle both of constant amplitude will be reduced via CEEMD to a mathematical 11 year cycle of varying amplitude.

April 21, 2016 6:12 am

The physics of the situation dictates that there is no 22-year cycle. In every 11-year cycle we get activity from both negative and positive solar magnetic fields, so no 22-year activity cycle.

ferdberple
April 21, 2016 6:22 am

there is clearly a 22 year cycle for the magnetic field orientation, when the world “cycle” means returning to starting point.
“activity cycle” depends of the activity of interest. sunspots are not caused by TSI, so it would seem meaningless to look for an explanation of sunspot cycles within TSI.

April 21, 2016 6:25 am

No, there is only a 22-year cycle in each hemisphere and because we get energy from both hemispheres the two opposite cycle cancel out. And variations of TSI and sunspots are formed from the same phenomenon: the sun’s magnetic field, to TSI and sunspots are intimately connected.

george e. smith
April 21, 2016 11:13 am

For a given signal and a Fourier decomposition, there is only one solution that fits a given signal.
So there is not an infinite number of possible decompositions.
There are many ortho-normal mathematical functions that are suitable for doing decompositions, but each one yields a specific result for a specific signal.
G

John Loop
April 21, 2016 6:18 am

I am “simply” a lay physicist/engineer following this discussion as best I can. I appreciate Dr Svalgaard’s frankness and knowledge. Nevertheless, who is to say we have all the evidence? This sounds suspiciously like saying the science is settled. It is never settled right? Or am I reading the wrong blog…. We may discover new evidence with new techniques and science, which may necessitate changes in our models and perceptions. We are always stuck with models of “what we think corresponds to the evidence.” It is all magic I fear-we can only approximate the truth. I would feel better if everybody said “AFAIK” at least.

April 21, 2016 6:37 am

Nevertheless, who is to say we have all the evidence
We have to base our conclusions on the evidence we have, and EVERYTHING a scientist says is ALWAYS AFAIK, so that is always understood. It would be too cumbersome to qualify every single statement by an AFAIK.

John Loop
April 21, 2016 6:43 am

Thanks. Feel better. I am overwhelmed by people claiming to know the truth in this day and age and need (occasional) reminding that we are all very fallible human beings. I fear those who don’t know this. Must be a gene for this……..

April 21, 2016 6:42 am

who is to say we have all the evidence?
Ya it might be unicorns or aliens

Bob Boder
April 21, 2016 8:56 am

or CO2

April 21, 2016 12:32 pm

“This sounds suspiciously like saying the science is settled. It is never settled right? ”
is it settled science that science is never settled?

April 22, 2016 6:39 am

I dislike this “science is never settled” meme .
It’s Junk science that’s never settled .
Maxwell is settled . Planck is settled . It’s integral , Stefan-Boltzmann , is settled .
Einstein is settled . Schrodinger is settled .
Our world runs on settled science .
Only extreme edge conditions are in doubt .

April 22, 2016 6:43 am

I agree.
But even settled science can be [and has been] improved. In the meantime, as you say “the world runs on settled science”.

April 21, 2016 6:27 am

Thank you Dr Svalgaard – very kind of you.

ferdberple
April 21, 2016 6:37 am

http://www.leif.org/research/Solar-Polar-Fields-1966-now.png
this waveform clearly shows a 22 year period. Look for example at 1975. The “darker” pole is strongly positive, while the lighter poles is strongly negative. roughly 10 years later in 1985, the situation is reversed, with the darker pole strongly negative and the lighter pole strongly positive.
However, after roughly 20 years, in 1995 we have returned to the starting point of our cycle, with the darker pole again positive and the lighter pole again negative.
The difference is one of semantics. You are considering the average energy of the system, while disregarding the orientation. This is the problem with averaging.
If you have 1 foot in the freezer and 1 foot in the oven you are on average comfortable.

April 21, 2016 6:40 am

No, what we actually get from the sun is the sum of both polarities, and the magnetic energy is given by the square of the field so we the energy we get does not depend on the sign of the field. Hence no 22-year cycle in the amount of activity.

ferdberple
April 21, 2016 6:57 am

the energy we get does not depend on the sign of the field
=====================================
that is dependent on the form of energy. atom smashers and cathode ray tubes both depend on the sign of the magnetic field to deliver energy to a target.

April 21, 2016 7:01 am

No, the energy is the same. The direction depends on the sign, not the energy. Try to look at http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html

Bob Boder
April 21, 2016 6:49 am

Ferd;
However to Leif’s point it doesn’t matter whether you have your left foot in the freezer or your right foot the result for your body is the same. Switch feet back and fourth would make no difference.
What’s much more interesting is the weakening and lengthening towards the end of your graph, may be just my eyes but sure looks like a change of some sort is happening. Leif?

April 21, 2016 6:58 am

small sunspot cycles [such as the current one] usually last a bit longer than strong cycles, hence the lengthening.

Bob Boder
April 21, 2016 7:09 am

Leif
“small sunspot cycles [such as the current one] usually last a bit longer than strong cycles, hence the lengthening”
Why?

April 21, 2016 7:38 am

This is difficult question. A rough answer may be: the polar fields determine the size of the next cycle after they reverse at sunspot maximum. They reverse because magnetic flux from decaying sunspots migrate towards the poles [much as heat does in the Earth’s atmosphere]. In a weak cycle there are fewer spots and less flux migrates to the poles which then takes longer to reverse; then the polar field continues to build up to act as a seed of the next cycle, but the ‘damage’ is already done: the whole process now takes longer.

Bob Boder
April 21, 2016 8:01 am

Leif
Thank you, I have to chew on that one for a while so it sinks in correctly. I appreciate you taking time to answer questions as always.

April 21, 2016 7:17 am

What Dr. S. doesn’t want us to know is that the Earth has a magnetic shield, which is a kind of a ‘semi-conductor’ of magnetic field, it lets one polarity with less resistance than the other.

ferdberple
April 21, 2016 6:46 am

start in 1975 with your left foot in the freezer and your right foot in the over. this is the situation in the graph above. then slowly pull them out, so that in 1980 both feet are free, then turn over and start inserting them so that by 1985 they are fully inserted, but reverse such that your right foot is now in the freezer and your left foot in the over.
you have only completed 1/2 a cycle. now slowly pull your feet out so that by 1990 both feet are free and then flip over once more and start inserting them so that by 1995 both feet are fully inserted and you have returned to the situation of 1975, with your left foot in the freezer and your right foot in the oven.
This is a full cycle, because you have returned to your starting position. Over the entire roughly 20 year time frame there was no 11 year cycle because your average energy between your two feet remained roughly equal on average the whole time with only minor variance. However, the variance between your individual feet over that time was much more significant.

April 21, 2016 6:48 am

You seem especially dim today. The energy in a magnetic field is given by the square of the field and does thus depend on the sign.

April 21, 2016 7:04 am

As to being ‘polite’ as one commenter was whining about, here is a good example of somebody who simple will not learn.

April 21, 2016 7:06 am

And, sadly, it is usually the same small number of people who display their defect on every topic.

ferdberple
April 21, 2016 7:08 am

a CRT delivers energy to a phosphorus screen, dependent upon the strength and sign of the yoke coils. the energy delivered is not the magnetic field itself, it is the electron stream.
you are assuming that average magnetic energy is the important measure. But it we consider that the phosphorus screen on a CRT is space, and earth a single dot of phosphorus on the screen, then at earth we would see almost zero change in average magnetic energy. Yet depending upon that magnetic field, we would either be dark of light.
So for a CRT, the important measure for a dot of phosphorus is not the average magnetic field, which varies very little. It is the effect of this variation, which cannot be measured by considering averages alone.

ferdberple
April 21, 2016 7:10 am

You seem especially dim today.
=====================
the argument of a child.

April 21, 2016 7:16 am

but very apt.

April 21, 2016 7:15 am

The sun is not a CRT.

April 21, 2016 7:53 am
April 21, 2016 8:15 am

Which has nothing to do with the sun. Your ‘Hale Cycle’ is an artifact.

April 21, 2016 6:51 am

Once more time: the solar ‘freezer’ and the solar ‘oven’ have the same temperature as the energy powering them depends on the square of the field and not on the sign.

April 21, 2016 7:19 am

Not so.
the Earth has a magnetic shield, which is a kind of a ‘semi-conductor’ of magnetic field, it lets one polarity with less resistance than the other.

April 21, 2016 7:30 am

Not so. The interaction between the solar wind and the Earth’s magnetic field depends on the balance between the ram pressure of the solar wind and the square of the magnetic field of the Earth:
https://en.wikipedia.org/wiki/Magnetopause#Estimating_the_standoff_distance_to_the_magnetopause
Magnetic reconnection feeds energy into the magnetospheric tail [and does depend on the direction of the field], but the solar wind doesn’t ‘pour in’ in a ‘breach’. This happens because magnetic fields of opposite directions meet.

Bob Boder
April 21, 2016 7:30 am

Vuk;
if you can show a clear 22 year affect on the earth in any way than you have made your point. The back and fourth between you and “Dr S.” is amusing but most of Willis’s investigations have shown that at least until this point Leif arguments are holding up. Demonstrate a irrefutable affect or the Null theory holds the field, and Leif with it.

April 21, 2016 7:40 am

Yes, it is clearly contained in the LOD (length of day) which has 25-30% strong component with 22 year cycle and synchronous with changes in the solar magnetic polarity.
I wrote a paper on it published here:
EVIDENCE OF LENGTH OF DAY (LOD) BIDECADAL VARIABILITY CONCURRENT WITH THE SOLAR MAGNETIC CYCLES
https://hal.archives-ouvertes.fr/hal-01071375v2/document

April 21, 2016 7:55 am

for climate effects see graph further up the thread at
https://wattsupwiththat.com/2016/04/20/ceemd-and-sunspots/comment-page-1/#comment-2195198

Bob Boder
April 21, 2016 7:57 am

Vuk
I read through your abstract and IMHO it is unconvincing at best.

Bob Boder
April 21, 2016 8:22 am

Vuk
The upstream plot is compelling except that I know Willis has pulled this apart before so it is not irrefutable. I am not trying to say you are wrong just unconvincing.

April 21, 2016 8:38 am

Thanks for the comment, at least you bothered to take a look. You asked for any evidence, I’ve shown what I found in the data, whether you are convinced or not it is your free choice. Data sources are there, procedure is simple and clearly described, if someone is willing to go beyond abstract. I am not in the business of changing anyone’s view or opinion, there are plenty of other people left right and centre, attempting to do that.

April 21, 2016 9:08 am

I’ve shown what I found in the data
Not so. Your ‘Hale Cycle’ is nowhere in the data. You made it up by making every other solar cycle have negative solar activity. And it doesn’t even have to be the sunspot number. Here I generate a series of random numbers [red curve] and another series [blue curve] where I have reversed the sign of the red data every other period of [a bit less than] 12 ‘years’:
http://www.leif.org/research/Vuk-Failing-37.png
The blue curve has this FFT spectrum:
http://www.leif.org/research/Vuk-Failing-38.png
As you can see, a beautiful spike at a bit less that 25 ‘years’, generated from random data. So ANY series [random or real data] subjected to your procedure will produce your Hale Cycle peak.
So, your ‘finding’ is completely spurious.

Bob Boder
April 21, 2016 8:59 am

Vuk;

April 21, 2016 9:40 am

You can’t be serious man, you created 22 year cycle, and than confirmed it has 22 year component, science has been advanced by leaps and bounds.

April 21, 2016 9:48 am

And you created your artificial Hale Cycle. Show us a graph of that cycle.

April 21, 2016 10:10 am

no need for me to do it, a far better scientist, Ken Schatten done it
“Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models”
published on line 1 July 2014

April 21, 2016 10:24 am

Ken is referring to the 22-year magnetic cycle. Either you don’t understand the issue or you are trying todig yourself out of your hole.

Tom Halla
April 21, 2016 7:16 am

Good discussion!

April 21, 2016 7:17 am

Yes, I hope you all learn something, regardless of the usual whiners who will never learn.

Dr. Deanster
April 21, 2016 7:16 am

Just my un-enlightened opinion, but if u want to tease out a cycle effect on the earths surface, u cannot use TSI!!! ….. The more appropriate metric would be short wave proxies at the earths surface.
The problem I see with this entire discussion is that it seems to be omitting that climate, at least from any perspective involving the sun, is a result of interaction between the earth and solar metrics. Thus again, TSI at the top of the atmosphere in isolation, i.e. Sunspot numbers, 10.7, etc. are meaningless.
Willis, try running your analysis on the proxies that would coincide with the amount of short wave rad reaching the surface. Wonder what u would see then??

April 21, 2016 8:17 am

The amount of UV varies just like TSI, the sunspot number, F10.7 and all the rest.

J
April 21, 2016 9:46 am

If we look at only short wavelength at the earth surface, we might miss effects on the earths atmosphere at higher altitudes that could affect the climate.

george e. smith