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.

CEEMD annual sunspot numbersFigure 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.

CEEMD annual sunspot numbers periodogramFigure 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:

CEEMD SOI and nino3.4CEEMD SOI and nino3.4 periodogramsFigures 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,


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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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].

Willis Eschenbach

Thanks, Leif. I don’t think that the 11-year cycle is being modulated by the 100-year cycle, although anything is possible. I say this because the CEEMD analysis method functions as a bank of empirically selected bandpass filters. As a result, the empirical mode that contains the ~ 11-year cycles (intrinsic mode C3) will not show the effects of the ~ 90-year cycles shown in intrinsic mode C6.
Or that’s my naive view, so now, I need to go and test it … hang on … … well, I made some synthetic data and ran a CEEMD analysis on it. I couldn’t make the intermittent 90-year cycle interfere with the ~ 11-year cycle, but that may reflect my own inability.

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:

george e. smith

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.

george e. smith

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.

george e. smith

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

Peter Sable

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.

Peter Sable

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.comment image?dl=0

100 year cycle may be simply due to change in the predominance of one or the other hemisphere.

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

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.

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.

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

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

“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?)

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.

Dr. Svalgaard
“Except there is no 22-year cycle in solar activity.”
from Dr. Svalgaard’s website

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

Steve Crook

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


The shape of the peak of the solar cosmic rays is a 22 year cycle.

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


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.

Solar activity is not a vector.


I love this action at a distance. We knew this wasn’t going to be easy.

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.

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


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.


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.

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.


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.

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.


Cycles in second order effects can add, perhaps even multiply.

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


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.

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


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.

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.


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.


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?

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.


Earth’s albedo doesn’t necessarily cancel, and probably doesn’t.

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


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.

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.


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.


Leif, I do very much appreciate your insistence on evidence. It is very grounding.


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

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.

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.


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?

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

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.

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

“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.

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

george e. smith

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.

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

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)comment image
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

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

Bob Boder

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.


Get your Sixty-Six Year Cycle here; big black headlines: PDO!

Pamela Gray

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


You don’t like my clock? Think how long it’s been ticking.

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


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.

When I looked at that some years ago, I found a modulating period of 122 years:
so my clock runs slower than yours. Perhaps the actual period is 104 years, which matches what you can simply see by eye
No sign here of 66 year cycle.

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 .

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.


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.

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.


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.

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.


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.

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


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.

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?


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.

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


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


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

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.


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

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.


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.

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.


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.

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.


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.

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.


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.

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.


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?

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.


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.

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


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

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:
No solar cycle here.


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

necessity is not necessary, sufficiency is sufficient.
Here is from a well-known paper about clouds:


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.

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.


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

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].


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

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.

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.


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.

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?


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

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:comment image
so much for your objection based on desparate conjecture
It seems you don’t really know much about these things.


Read the last sentence of your excerpt. I may shut up but your excerpt can’t.


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

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


Hint: For cloudiness the relevant metric is relative humidity.


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.

“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.


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?

Can you? you are the one making the dubious claim.
Perhaps it is time for a little tutorial:


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

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.


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?

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.


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

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:
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.


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.

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.


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.

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.


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

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


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.


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)

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


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.


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

“””””….. 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.

george e. smith

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

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.

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.


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


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.


“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

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.
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.

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”?

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

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


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 periodicitycomment image

Willis Eschenbach

Thanks, Greg. I also noted the 9-year cycles and like you I assigned it mentally to the moon, but I’ve not run the analysis.


That is the same periodicity that is found in Atlantic cyclone energy.comment imagecomment image
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.


The ACE thing was discussed on C.Etc.
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.


Here are the regions where there is a clear 9y cycle. The previous plot only showed those where there was also the 13y periodicity.comment image
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

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.


Hello, PDO.


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.
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.
I hope you take the time to look at this. I think it will be worth your time.

Jimmy Haigh

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…

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


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.

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.


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.

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


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.

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.

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.

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.


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

Vuk and greg are hilarious to watch.
Neither learn.

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.

Willis Eschenbach

bazzer1959 April 21, 2016 at 4:48 am

lsvalgaard: … At least try to be more understanding of others, and reign in your ability to be curt.

Celebrate the reign of the Svalgaard, and may he reign in curtness forever!

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

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

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.


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.


“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.

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

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.

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 .

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.

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

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.
Also, here’s a thought about your third question:
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

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

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.

” 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.


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.


‘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)


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 😉


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.


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.”

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.


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.

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

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

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

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.

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?? 😉


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
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:
The methodology used reduces high frequency noise, and thus you will not find cycles much shorter that 100 years in that data.

Willis Eschenbach

Javier, first, I love how you see a very occasional (once every few thousand years) and very irregular cycle that ranges from about one hundred years to about four hundred years as being something significant. For starters, the claim that it is a “208 year cycle” is completely contradicted by your graphic.
Second, I doubt greatly that the claims of statistical significance (black lines in your figure) have been calculated correctly, with appropriate allowance for autocorrelation. The results are obviously highly autocorrelated, but I could find no discussion of autocorrelation in your cited document.
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 …


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:
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

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. ”

Claude Harvey

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!

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
Big cheese there is the ‘dark energy’ man Adam Riess professor of physics and astronomy a Nobel laureate.

Willis Eschenbach

Claude Harvey April 21, 2016 at 4:45

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 …

“Little Willis”? The “svalgaard child”? Oh, that’s so imaginative, Claude! I see you’ve discovered the secret of success, that oh-so-clever names and puerile taunts like those make you look like such a thoughtful person, and they just buff up the fantastic luster of your world-renowned reputation for putting forth solid scientific arguments …

Claude Harvey

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.

Willis Eschenbach

Claude Harvey April 21, 2016 at 5:01 pm

I should have known you couldn’t take a joke, even when it included a left-handed compliment. O.K.

“Take a joke”??? If you truly think that calling me “little Willis” and calling Leif the “Svalgaard child” is a joke, then you need much more help than I can give you, my dear little Claude. If you were grown up you might understand it was not a joke of any kind, but then you’re still the Harvey child, so I guess it might take years for you to grasp what a joke is …
Does it seem all hilarious now?


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.
Please continue.

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.

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.

What about harmonics?
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.

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.

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.

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

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.

John Loop

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.

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

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……..

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

Bob Boder

or CO2

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

Willis Eschenbach

Steven Mosher April 21, 2016 at 12:32 pm Edit

Is it settled science that science is never settled?

It would would be settled, but I make it an absolute rule to avoid absolute statements.

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 .

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

Thank you Dr Svalgaard – very kind of you.

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.

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.

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.

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

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?

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

Bob Boder

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

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

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.

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.

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.

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.

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

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

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.

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

but very apt.

The sun is not a CRT.

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

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.

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.

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:
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

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.

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:

addressed to Bob Boder
for climate effects see graph further up the thread at

Bob Boder

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

Bob Boder

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.

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.

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’:
The blue curve has this FFT spectrum:
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

Your welcome, keep plugging away and I will keep reading.

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.

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

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

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.

Good discussion!

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

Dr. Deanster

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??

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


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

What you would see is the feedback effect caused by the earth having oceans, and thereby a modulating cloud layer that attenuates the TSI resulting in a surface variation.
Supposedly we once had a dim sun eons ago, and apparently not much real difference on earth surface climate. With the negative feedback due to clouds (affecting how much solar energy reaches the deep oceans for storage (deep)) the dim sun did not give much overall difference.
Expected earth mean Temperature, deduced from black body considerations, and known (from satellites) TSI measurements of about 0.1% amplitude over the sunspot cycle, should only produce about 70 milli deg. C Temperature change, which we don’t see, because the cloud feedback wipes that out.
Solar activity does affect TSI and other solar energy measures; but our atmosphere and oceans, end up erasing most of the evidence of such changes.
Our Goldilocks location is not quite so special as we think. The presence of liquid water oceans on earth greatly widens our Goldilocks happy place.

Brett Keane

Of course, we are watching the lowering Solar Flux proxy of SW closely for oceanic and delayed Air T effects, are we not?


Taking the findings that solar cycles of all types have negligible effect on global climate as given, there remains the question of regional and hemispheric effects on climate. Are there different results from this version of the question? Unless you assume global climate is perfectly uniform like the energy signature of the big bang, it requires a look.

george e. smith

There is no expectation of uniform global climate.
Southern winters are more severe than northern winters, because the earth is closer to the sun at Northern winters, so solar insolation is lower for SH winters, and then as Kepler’s Laws show, the earth spends more time in the southern winter zone, than in the northern winter zone so SH winters are longer and colder. Couldn’t possible be globally uniform.
The reader can look up Kepler’s “equal areas in equal times” orbital law for himself.

Brett Keane

Then, dang it all, the excess of northern dirt area has to go and muddy the waters….

The sun is not a CRT.
The sun is in point of fact very similar to a CRT.
Like the sun, the CRT has a hot filament with a similar surface temperature, which emits energetic particles into a vacuum. These particles are modulated by the yoke coils of the CRT in a similar fashion to the solar magnetic field. And like the solar magnetic field, the yoke coils oscillate positive and negative. And like a spot of phosphorus, the particles from the sun strike targets like the earth and in this fashion deliver energy and matter than is not dependent upon the average magnetic field.

No, that is not how it works. The solar wind expands to hit the Earth because the solar atmosphere is very hot. It is hot because electric currents caused by magnetic fields of different polarities annihilate. The strength of the solar wind does not depend on the sign of the overall magnetic field. So, no 22-year cycle.

george e. smith

Well you need to revisit the laws of electro-magnetism. A magnetic field does not alter the energy of a charged particle moving through it. It can neither add, nor subtract KE to the charged particle. It only deflects the path of the charged particle, and I would NOT refer to that as “modulation”.
So both solar and earth magnetic fields can and do alter the path of charged particles arriving on earth, and to the extent that the earth has a somewhat bar magnet like field with prominent magnetic poles, those incoming charged particles can spiral around earth field lines, so a lot of them reach the surface bunched near those poles. To the extent that these fields change from time to time, the resulting distribution of where CRs arrive on earth and more importantly get detected (where detectors are) will fluctuate.
So cyclic variations in detected CRs where detectors are, does not exactly reflect the total number of CRs reaching earth; just their distributions.
The vector force on a charged particle, by a magnetic field, is perpendicular to the magnetic field vector, and also perpendicular to the charged particle velocity vector, to there is ZERO resultant force on the particle in the direction of its motion which would result in an acceleration or deceleration of the particle, and hence change its KE.
Charged particle accelerators, like synchrotrons et al, use ELECTRIC fields to change particle energy, and MAGNETIC fields to steer them.
Gee !! I think CRTs are sort of like charged particle accelerators (electrons). They don’t accelerate phosphor dots, those are fixed on the CRT screen surface.
Don’t they teach electro-magnetism any more in schools ? is it all just computer science and how to write a tweetle ??

but very apt.
the pot calling himself black.

us two pots then play well together

Der Ganzumsonst

Signals could behave this way if they were harmonics of an elliptic fundamental.
Low frequency and high amplitude at aphelion, high frequency and low amplitude at perihelion.

The apparent ignorance of even undergraduate orthogonal function decomposition and the overall amateurish understanding of math and physics pervasive in the “climate science” global warming debates was a strong factor in getting me involved . Specifically it was the trivial case of getting people to understand the importance of the orthogonality of flat spectrum gray body temperature to which are added any non-flat spectral , ie : greenhouse effects . This continues to be the case when people mislabel a 255K value as some sort of fundamental “black body” temperature in our orbit when it is the result of a hypothetical step function spectrum . This causes them to fail to understand that the actual value of any computational significance is the flat spectrum value of , from Anthony’s recent post on TSI , about 278.3 . And it causes people to fail to understand the 180 year old observation this is the temperature of any gray , no matter how dark or light , body in our orbit , not just black .
If at some level in the upper atmosphere the absorption=emission spectra of the gases causes the temperature to decline from the gray body temperature to the 250s neighborhood , then that must be explained . But the “neutral” temperature which must be converged to as one leaves the atmosphere is the ~ 278 value .
NASA is complicit in promoting this ignorance by listing their step function calculated temperatures in their tables of planetary properties ( some absurdly irrelevant number in the 200s for Venus ) but not the computationally use gray body temperatures calculated simply by summing the total energy impinging on a point .
As I say , this is really trivial stuff . But until these fundamentals are settled understandings , you’re not talking physics .
I’d like to understand the history around Fourier’s insight . I have the impression that he was the first to realize that any pattern could be decomposed into , expressed in , other arbitrary orthogonal bases . I think it perhaps the next great leap after Descartes . But clearly the notion of decomposition into many other function sets rapidly evolved around the same time .


The earth is nothing like a grey body. It is a non-grey body that constantly changes reflectance in a semi-random fashion. Clouds make the whole situation even more complex.

You MUST understand the basics before you can understand the nuances . ALL real branches of applied physics follow this analytical approach . And it is the only way to start constructing a computational model providing an audit trail from the Sun’s output to our observed temperature .
And the gray body calculation explains 97% of our estimated surface temperature . So , in fact , we are very much like a gray body .
Furthermore , you give me a spectral map of the planet as seen from space , and I’ll give you back the additional couple of APL expressions to compute the equilibrium temperature for that map . But they will build on the computations for a gray sphere .


The basics are that if you observe earth ‘temperature’ over the equatorial pacific and do the same over the poles, you will find a difference. Earth does not have a uniform temperature. An average or mean temperature is a fictitious number. Neither the incoming energy from the sun is uniform on the surface and neither is the ‘blackbody’ radiation coming from the earth.
I feel you would have a problem looking at the spectral images centred on the two locations I mentioned.

Wein’s Law of Black Body Radiation.
Studied this 30 years ago as a CCNY Meteorology major undergraduate.
The “neutral” temperature was defined as 277K.
Not sure why NASA would use anything else. Odd.


Switching the wires on a speaker doesn’t seem to effect the sound volume.

george e. smith

Well Wien’s law is well known to give the wrong answer. Only the Planck Law gives the correct answer.
But in fairness Wien’s Displacement Law IS perfectly valid. lambdamax T is constant.
Black body radiation is a function of the single variable T x lambda (wavelength)

Dr. Deanster

In my opinion, this analysis on sunspots is not relevant to any discussion on sun-climate relations. TSI is equally useless, as if there is any sun-climate relationship, it will be due to an interaction. Thus, you could hold TSI constant, and still see fluctuations related to some cycle etc.
It would seem to me the more relevant metric would be short-wave rad received at the surface. Only then can you begin to compare any cycles in the sun’s energy output, magnetic output, etc with what is happening at the surface of the earth.
So there ya go Willis …. just gave you another fun project. Run your CEEMD on surface short wave data, or some proxy of short wave received at the surface, and get back to us with what you find! 🙂

Tom in Texas

just a foot note, Solarham is used by ham radio operators on a regular bases for many obvious reasons. And of course the short waves movement should have a variable heat effect. if my brain functions correctly here.


Short wave radiation as in under 1 micron wavelength or short wave radio?

george e. smith

The term “shortwave” as used in climate references, almost invariably means SOLAR SPECTRUM radiation, which contains 98% of its energy between 250 nm and 4.0 microns wavelength which is between 0.5 and 8 times the peak spectrum wavelength of 500 nm (for a roughly 6,000 K black body spectrum.
I wish people would say solar spectrum instead of short wave. LWIR of course usually refers to the BB like radiant emission from an earthlike body at about 288 K (for earth surface mean)
Earth’s surface Temperature can be found anywhere between about -94 deg. C in the midnight Antarctic highlands, to +60 deg. C in the hottest tropical northern deserts (all at the very same time, so maybe 150 deg. C range
And TSI cycling might be able to change that by about 0.07 deg. C. based on a simple BB based calculation, and neglecting cloud modulation which will wipe most of that out completely.

george e. smith

Well sunspot data is known to be periodic with an 11 year period. That’s why Willis’s analysis works. If you want to add all of the as yet not accurately modeled earth climate variations to that, you should take on that task yourself.
Given that the biggest terrafloputers are incapable of modeling that, you should hardly expect Willis’s X-box to do it for you.

Don V

It seems that the majority of the discussion on this post has devolved into various arguments about the what and how of the sun’s contributions to our planet’s _______ (fill in the blank with weather, climate, earthquakes, clouds, cycles and their attributions, etc.)
I, on the other hand, am a lot more interested in the mathematical analytical technique (that I had never heard of before) rather than the solar and ocean temp. applications that Willis has chosen to apply it too. That has got me wondering whether this analytical technique could be applied to some more practical things in life like:
Rapidly Identifying someones speaking, singing, or phone voice based on the timbre created by how their vocal chords propagate sound through various oral and nasal physical cavities.
Rapidly identifying spoken phonemes based on the changes in sound frequency spectra.
Rapidly identifying someone by using this analytical technique on the pattern of changes in intensity and color of one’s iris when scanned circumferentially around the pupil.
And more . . . .
Wish I had the time to learn the mathematical technique and then try some of these ideas out.


10 years ago I bought a DVD with on it a “multimedia” database containing text, graphics, photos and acoustic records about over 500 birds. You can select a bird name and get all of it. That’s top-down search.
What I nevertheless miss since beginning is the inverse path! A cheap but good directional microphone together with a software working like you seem to describe would so prettily help in finding bottom-up the corresponding bird’s description 🙂

george e. smith

Are you living under a haystack ?? such analytical methods have been in use for eons, for all kinds of practical and impractical uses.
And you can actually buy text books that show you how to do it yourself.

Don V

george e. smith –
Although EMD and EEMD were available earlier, CEEMD was only published as a novel enhancement to the technique in 2011.
Torres, M. E., Colominas, M. A., Schlotthauer, G., Flandrin, P. (2011). A complete ensemble empirical
mode decomposition with adaptive noise. 2011 IEEE International Conference on Acoustics,
Speech, and Signal Processing, pp.4144-4147, doi: 10.1109/ICASSP.2011.5947265.
An eon is a billion years. 5 years ago is not an eon.
No, I do not live under a haystack although I have mucked cow and sheep barns in my youth. Was that meant as some kind of an insult? I did not wish for a textbook. I wished for the free time to explore this.


Well, that settles it. The Sun has absolutely nothing to do with the earth’s climate except in the fevered imagination of true believers.

‘Absolutely nothing’ is not correct either. There is a 0.1 degree solar cycle variation of global temperature, but this effect is so small that it drowns in the noise and is very difficult to dig out.

george e. smith

I think about 70 mDeg. C, from a dumb BB calculation assuming 0.1% TSI cycle amplitude.

I have read in the past that temperature is not the main effect of the ~11 year cycle, but that the effect is mostly on regional cloud/rain patterns.
The main effect in the cycle is in the UV range – ozone production in the lower stratosphere – increased temperature (~1°C) in the tropical stratosphere at high solar activity – jet stream position pushed towards the poles, including the accompanying rain patterns.
The link to the scientific report about the effect of the sun cycle on the lower stratosphere is gone now, but another alludes to that research, without mentioning the jet streams:
http://onlinelibrary.wiley.com/doi/10.1029/2005GL024393/abstract stratosphere – troposphere interaction
And a few reports on clouds/rain/wind patterns still do exist:
http://onlinelibrary.wiley.com/doi/10.1029/2005GL023787/abstract rainfall Portugal
http://ks.water.usgs.gov/pubs/reports/paclim99.html stream flow Mississippi delta
http://venus.unive.it/rubino/paper/JGR08.pdf river Po discharge (Italy)
rainfall in Kenya
And some more here:
Still the global effect of the ~11 year cycle may be small (even less on longer term), but the regional effect may be quite important.

may is a weasel word.
As Tweedledee said:
“if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t”

OK let’s reformulate:
Still the global effect of the ~11 year cycle probably is small (even less on longer term), but the regional effect is confirmed as quite important. including implied “AFAIK” as always in science…

That goes for you too…
So whatever you claim is only as far as YOU know.


Hi Ferdinand,
It is appalling that a serious response as yours based on a lot of published research is brushed aside with the excuse of your words choice.
I respect your efforts to educate others on atmospheric CO2 changes and the carbon budget. I want you to know that the effort you put on writing a serious response to Leif Svaalgard has not been a complete waste of time.
The link to that publication that you were looking for could be this one:
Crooks, S. A., & Gray, L. J. (2005). Characterization of the 11-year solar signal using a multiple regression analysis of the ERA-40 dataset. Journal of Climate, 18(7), 996-1015.
That was later updated here:
Frame, T. H., & Gray, L. J. (2010). The 11-yr solar cycle in ERA-40 data: An update to 2008. Journal of Climate, 23(8), 2213-2222.
You are corrected that the solar variability influence on climate appears linked to atmospheric changes that drive changes in cloud cover and precipitations, and only secondarily on temperatures. The link of cosmogenic isotope variation to speleothem records in the monsoon area has been highlighted multiple times, and can be seen clearly in the figure in my previous post:
https://wattsupwiththat.com/2016/04/20/ceemd-and-sunspots/comment-page-1/#comment-2195306 (green curve in A)
We find the fingerprints of the solar effect on climate all over the Holocene. For example the 2.8 Kyr BP event, that coincides with Bond event 2, shows very clear correspondence between solar activity, precipitations and temperatures. This was probably one of the worst periods for mankind of which we have evidence, that plunged the Mediterranean world into the Greek Dark Ages.
Bibliography for this figure:
Kaniewski, D. et al. 2013. Environmental Roots of the Late Bronze Age Crisis. PLoS ONE 8(8): e71004.
Bond, G. et al. 2001. Persistent Solar Influence on North Atlantic Climate During the Holocene. Science Vol. 294, pp. 2130-2136
Geirsdóttir, Á. et al. 2013. Abrupt Holocene climate transitions in the northern North Atlantic region recorded by synchronized lacustrine records in Iceland. Quat. Sci. Rev. 70, 48-62.
Shapiro, A.I. et al. 2011. A new approach to the long-term reconstruction of the solar irradiance leads to large historical solar forcing. Astronomy & Astrophysics 529, A67.
I think researchers are finally starting to look at the right place to find the solar-climate effect, and reanalysis looks like a powerful tool for the task.

Shapiro, A.I. et al. 2011
The general feeling is that Shapiro et al. are not correct and that their reconstruction is seriously off. So relying on them is hazardous. We can enter into a discussion of that if we must.


Also you were referring to this article in your first link:
Shindell, D., et al. “Solar cycle variability, ozone, and climate.” Science 284.5412 (1999): 305-308.


“The general feeling is that Shapiro et al. are not correct and that their reconstruction is seriously off. So relying on them is hazardous. We can enter into a discussion of that if we must.”
It is not necessary, Leif. The main point for the figure is the existence of the two grand solar minima at 2950 and 2750 years BP. Those lows in solar acrivity at 1000 and 800 BC are also present in Steinhilber reconstruction so it is not easy to dismiss them:


Some people are heliocentric and some are geocentric. ‘ It’s the CO2,stupid’. ‘It’s the sun,stupid’. Others just like to argue.


Sure, that the Sun has little to do with Earth’s climate is settled. As settled as the overbearing influence of CO2 on climate.
Meanwhile research on solar influence on climate continues:
Mitchell, D. M., et al. “Signatures of naturally induced variability in the atmosphere using multiple reanalysis datasets.” Quarterly Journal of the Royal Meteorological Society 141.691 (2015): 2011-2031.
“A multiple linear regression analysis of nine different reanalysis datasets has been performed to test the robustness of variability associated with volcanic eruptions, the El Niño Southern Oscillation, the Quasi-Biennial Oscillation and with a specific focus on the 11-year solar cycle. The analysis covers both the stratosphere and troposphere and extends over the period 1979 – 2009. The characteristic signals of all four sources of variability are remarkably consistent between the datasets and confirm the responses seen in previous analyses. In general, the solar signatures reported are primarily due to the assimilation of observations, rather than the underlying forecast model used in the reanalysis system. Analysis of the 11-year solar response in the lower stratosphere confirms the existence of the equatorial temperature maximum, although there is less consistency in the upper stratosphere, probably reflecting the reduced level of assimilated data there. The solar modulation of the polar jet oscillation is also evident, but only significant during February. In the troposphere, vertically banded anomalies in zonal mean zonal winds are seen in all the reanalyses, with easterly anomalies at 30◦N and 30◦S suggesting a weaker and possibly broader Hadley circulation under solar maximum conditions. This structure is present in the annual signal and is particularly evident in NH wintertime. As well as the ‘top-down’ solar contribution to Northern Annular Mode variability, we show the potential contribution from the surface conditions allowing for a ‘bottom-up’ pathway. Finally, the reanalyses are compared with both observed global-mean temperatures from the Stratospheric Sounding Unit (SSU) and from the latest general circulation models from CMIP-5. The SSU samples the stratosphere over three different altitudes, and the 11-year solar cycle fingerprint is identified in these observations using detection and attribution techniques.”
As someone said, observation trumps theory.

Since the ‘finding’ is the result of “A multiple linear regression analysis of nine different reanalysis datasets” it is statistics and not observation.

Jim G1

It’s the World Wrestling Federation of solar science. I love it! Thank you, Leif, for all of your insights. You live up to your aka ” the Donald Trump of solar science”, but with more factual information.


So oceans and heat storage don’t count. Oh.


On the sun?

Jim G1

Not only storage but circulation and redistribution into the atmosphere.


Yes, a multistage problem with cycles

Steve Fitzpatrick

Hi Willis,
I think a CEEMD of the Hadley temperature history might be very interesting.

be careful of any signal analysis of a variable that is, strictly speaking, non physical and an index only.
we call it the land ocean INDEX .
That said, if you go hunting for signals you will find them.
Pushing data through meat grinders is a poor excuse for science.
Start with a physical theory.
Explain why you think that theory should result in a signal in the temperature record.
Then you might be on solid ground looking for it


My point is that there are known and suspected causes for short term temperature variation (like ENSO), of varying time influence, where this kind of decomposition might help to isolate and define short and longer term variation. The ‘secular change’ in temperature versus shorter term changes is important if you want to understand the influence of GHG forcing.


Thanks to Willis Eschenbach for this very interesting guest post and of course also to Leif Svalgaard for his accurate (and very, very patient) reactions.
I read about the amazing fight of LS and his colleagues worldwide to reestablish a correct SSN evaluation after Waldmeiers lone hand play.
A little question alongside this post: does the correction have an effect even on WE’s CEEMD plot, or is its influence restricted to evaluations of the sun’s activity during the XXeth cy?

There are corrections throughout the series, but the largest one from 1947 on.

Steve Oregon

Is this accurate too?
There may be a 0.1 degree influence on the variation of global temperature from adding 100 PPM in CO2, but this effect is so small that it drowns in the noise and is very difficult to dig out.

Most climate scientists would put the increase to something like 0.5 degrees for a 100 ppm increase in CO2. Whether that is accurate, I don’t know, but that is what the data show.

Don V

Has there really been a verified cause/effect experiment done to confirm that 100 ppm change in CO2 concentration will cause a half a degree change in world-wide air temperature? or when you say “that is what the data show” do you really mean “that is what various theoretical computer models show”?
If you know this to be true, I would like to read the paper that has actually VALIDATED the cause/effect relationship between CO2 and world-wide air temp with “data” not modeling. IMHO the “data” shows nothing of the kind. The “data” shows no substantial change in temp for the last 18 years even though the concentration of CO2 has gone up 44 ppm. I will continure to believe the actual “data” until the models are validated.

I would also like to see your ‘data’ that you believe.
I don’t think there is any way to VALIDATE the result. How would you do that?

Don V,
On laboratory scale, the absorption effect was measured at different air pressures and CO2-water-CH4 levels. That was combined in an overall model based on the average 1976 atmosphere with the cloud/rain patterns of that year. The line by line calculations were done by the US military in the HITRAN model, later simplified in the MODTRAN model, which can be found in interactive form here:
You can change the CO2 levels for the “1976 US standard atmosphere” with fixed relative humidity and look at the “Upward IR Heat Flux” for 280 and 380 ppmv, keeping the other variables constant. Then for 380 ppmv, give the ground offset a stepwise increase until the outgoing IR equals that at 280 ppmv. That is what the warming of the surface would need to cancel the 100 ppmv CO2 extra, based on its absorption characteristics.
Of course that is the physical base only, without any positive or negative feedbacks to the increased temperature.
Climate models add a lot of positive feedbacks like water vapor and clouds, while reality shows no water vapor feedback and clouds are a negative feedback…

Jeff L

In looking at input signal (solar) vs potential output signal (ENSO, PDO, temps etc), everyone seems to assume that the earth-atmosphere-ocean system doesn’t act as a filter or that the filter is essentially white.
I would say that is a very large & untested assumption. In geophysics, we never see natural earth filters with a white spectrum. Understanding how the earth-atmosphere-ocean system acts as a filter on input is essential before you can do any interpretation on output signal.
This may (or may not ) be a fruitful line of investigation.

lsvalgaard April 21, 2016 at 9:08 am says
“Your ‘Hale Cycle’ is nowhere in the data. You made it up by making every other solar cycle have negative solar activity”
If this is not Hale cycle, it must be Mosher’s unicorns.

Show a graph of the Hale Cycle ‘data’ that you computed the spectrum from.

you can do it, here is the data,
instructions : Extracting higher frequencies (shorter periods) can be achieved by using any of the known high pass filters. However, for the convenience and benefit of the easy reproducibility, the 21 year (cantered) average can be subtracted from the ‘raw ’ geomagnetic data. The obtained difference represents higher frequencies. Since the geomagnetic data is only available for the 1840-1990 period, the obtained result is truncated by 10 years at each end.

From your colleague Ken Schatten
Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models
published on line 1 July 2014
tell Ken he got it wrong ! there is no such a thing as “the 22-Year Activity Cycle”

They mean [and say in the paper] ‘the 22-year magnetic cycle’. This not the same as a 22-year cycle in solar activity. The clearest example is perhaps the butterfly diagram:
But you are evading the issue. Show us the Hale Cycle you used to calculate your spectrum.

No, that is not the solar Hale Cycle. Show the solar Hale Cycle, if you have one

“Except there is no 22-year cycle in solar activity.”
Solar Polar Fields and the 22-Year Activity Cycle: Observations and Models
“They mean [and say in the paper] ‘the 22-year magnetic cycle’.”
I think Mosher got it, sunspots are not magnetic activity, they could be unicorns.
I’m done, bye for now.

Running away and shirking to show the Hale cycle graph. This is your typical and standard reaction when cornered. Be a man and do what you need to do.

Jim G1

Leif says:
“but that is what the data show”
A spurious correlation. For years the US stock market correlated well with the height of ladies’ hemlines. And yes, one can come up with a mechanism for that, too, but I won’t get into that here. Spurious relationship.

Check out http://www.leif.org/EOS/Nagoya-Lean-2012.pdf and take up your opinion with Judith Lean.

Jim G1

Tried to download it several times. It gets to 41.09mb and stops. In any event, too many exogenous variables involved for anyone to buy the certainty of any such .5 degree quantification. A better statement might be that ” there is some data that indicates such a relationship”.

Well, it is 42 Mb, but is is based on Figure 2 of the following paper:
http://www.leif.org/EOS/2010GL045777.pdf and the more technical:
http://www.leif.org/EOS/LeanRindCauses.pdf and


“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.” – Willis
As a suggestion, if you use TSI from the PMOD composite ftp://ftp.pmodwrc.ch/pub/data/irradiance/composite/DataPlots/composite_42_65_1602.dat instead of SSNs you might get a different result.
Most people naturally use SSNs first instead of TSI as the sun’s energy proxy. They do track together annually over solar cycles, with an R2 of .87 (as does F10.7), but it’s the timing, duration, magnitude, and direction up or down of TSI that ultimately matters to the Earth’s response, not particularly exactly when SSNs are high, most of the time.
Using annual averages, PMOD TSI peaked in 2002, v2 SSN peaked in 1979, and F10.7cm peaked in 1989.
Secondly, SOI/MEI/ONI/OHCI ENSO parameters follow TSI in time, as it takes time for the build-up of TSI to do it’s work raising temps, OHC, and creating pressure differentials – meaning there’s a TSI response lag to consider.
2015 was the highest SORCE TSI year, and the highest since 2002, but the SSNs weren’t.
Year 1au TSI F10.7 v2 SSN
2015 1361.4321 117.5 69.8
2014 1361.3966 145.8 113.3
2013 1361.3587 122.8 94.0
2012 1361.2413 119.9 84.5
2016 1361.1986 99.1 56.2
2011 1361.0752 113.4 80.8
2003 1361.0292 127.4 99.3
2004 1360.9192 106.5 65.3
2010 1360.8027 80.1 24.9
2005 1360.7518 91.7 45.8
2006 1360.6735 80.0 24.7
2007 1360.5710 73.1 12.6
2009 1360.5565 70.6 4.8
2008 1360.5382 69.0 4.2
I’m not so sure FFT and CEEMD are exclusively the best ways to understand what we’re looking at – and you didn’t say they were, although CEEMD is interesting. Thanks.


“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.”
Obviously, speculation is a poor substitute for observations. The problem is that observations are missing that would show what caused the large climate cycles over the last few thousand years such as the Medieval Warm period and Little Ice age.
Due to the absence of observations, and the fact that the Sun has the most influence on climate, I speculate that changes in the sun are most likely the cause. If it is not the sun, then I would speculate that the next most likely possibility seems to be volcanic followed by speculation that the type of “variations” in the climate can combine in ways that reinforce trends that lead to periods of cold or warm as have been seen in the past.
In the absence of observations, I think speculation is healthy so long as those speculating understand that is what they are doing. Unlike the speculation on “catastrophic global warming” and “catastrophic climate change” which somehow became “holly writ” even as observations began to accumulate that made the “catastrophic” part very unlikely.

In the absence of observations, I think speculation is healthy so long as those speculating understand that is what they are doing.
And that they label it as SPECULATION, instead of pretending it is not.

Bob Boder

There are other possibilities like natural warming and cooling trends in the oceans regulated by their circulation and their ability to move warmer water to the north where it radiates to space more easily. Two different oceans with different warming and cooling cycles sometimes in sync sometimes not in sync, sometimes in sync for a little while some times totally in sync and so on, creating natural variability. Add to this warming tropical trends that alter cloud cover and its affect on albedo and varying ice cover and its affect on albedo in the south and the in the north lower ice cover equals higher thermal radiation to space and you have a pretty unpredictable chaotic system. Throw in volcanic activity, maybe large solar variability or not but at least small variability and the system gets more unpredictable. you can add in any other natural cycle you want and to complicate the system more and you don’t need any magic control knob to understand why with climatic change. over larger times scales the movement of the continents greatly alters the circulation of the oceans and the tilt of the earth on its axis affects how the system absorbs energy from the sun.

george e. smith

“””””….. like natural warming and cooling trends in the oceans regulated by their circulation and their ability to move warmer water to the north where it radiates to space more easily. …..”””””
Nothing could be further from the truth.
“Thermal” (BB like) electromagnetic radiation radiance varies as the 4th power of Temperature, so the very last thing that is going to happen to energy in warmer waters that move north, will be increased radiation to space.
The VERY HOTTEST tropical (high) deserts in the middle of the hottest summer days, is where you should look for efficient cooling of the earth; at rates almost twice that for the global nominal 288 K Temperature, but the very coldest places like the Antarctic highlands or the northern polar regions, can only radiate at rates as low as one sixth of the global mean rate.
The polar regions DO NOT COOL THE EARTH.

Bob Boder

Bad choice of words on my part, was trying to make the point that as the waters in the arctic warm and the ice melts this allows for a transfer of heat from the oceans to the atmosphere and then to space. When the arctic is frozen it acts as a valve limiting this path, creating a control valve the helps regulate the system. was not trying to imply that the arctic was the main source of heat transfer in the system.

off topic but this one surprised me.
“The average temperature on Venus makes it the hottest world in the Solar System, with its thick atmosphere trapping heat and giving rise to scorching temperatures of 460°C (860°F) on the surface.But measurements taken by Venus Express at an altitude of 130 to 140 kilometers (81 to 87 miles) above the surface have revealed the atmosphere near the poles has temperatures far below that on Earth. In fact, the polar atmosphere on Venus drops to -157°C (-251°F), which is 70 degrees colder than expected.”

Bob Boder

Where is this quote from?


A quick search finds this …5th para. From there it’s a short hop to doi:10.1038/nphys3733, available here: http://phys.org/pdf380286576.pdf


Arrgh! Not the actual paper unfortunately but a lot more detail. Sorry about that.


The sun definitely is in complete control of the weather & climate.
High TSI in 2015 directly caused high temps in 2015, and all the extreme weather events in 2015.
Observe in the TSI data I posted before that TSI in 2015 was the highest since 2002. The 2015 ENSO started in Feb/March just as TSI for SC24 peaked, driving 2015 temps up to record levels.
Since the final ENSO temp peak in Feb/Mar this year, SSTs and OHC have dropped. People are now calling for a strong La Nina this year – but the La Nina will just be the response to present and future lower TSI this year. 2016 will not be a record temperature year because falling TSI won’t support it.
OHC started dropping right after last year’s second SORCE TSI peak in November, accelerating its drop as TSI has dropped off more recently:
2015.042 1361.5359
2015.123 1361.8859
2015.204 1361.6749
2015.288 1361.6690
2015.371 1361.4732
2015.455 1361.3152
2015.538 1361.4622
2015.623 1361.1664
2015.707 1361.1063
2015.79 1361.3139
2015.874 1361.3646
2015.958 1361.2527
2016.042 1361.2892
2016.124 1361.3051
2016.206 1361.1865
2016.292 1360.8044
In spite of the fact of the lagged TSI response to SSN, we can use SSNs going back in time to get a fairly good general idea of the sun’s influence on temps post-1865.
The modern maximum in solar activity occurred during the 70 years from 1935 to 2004, when the annual average v2 sunspot number was 108.5, versus the previous 70 years since 1865, when the SSN annual average was 65.8 (lower than this year’s 69.8), a 65% sustained higher sunspot level for 70 years.
That means TSI was on the whole higher for those 70 years than the previous 70 years, making the sun’s TSI the only realistic viable candidate for the cause of ‘global warming’ since 1850. Remember the Dalton minimum cold years? It was low SSNs and low TSI.
I try not to call what the sun does a trend or a cycle, such as the Gleissberg, but clearly, there was an overall major energetic step change upward in solar output in the 20th century that has already peaked.

You are just playing your usual cherry-picking games. A better comparison would be the years 1712-1798 SN=83.2, 1823-1901 SN=81.6, 1933-2015 SN=98.5, a meager 20% higher than the two other periods.
You have to consider the temperature variation from 1700 to now. Part if the Dalton minimum low temps were due to volcanic activity [e.g. ‘the year without a summer’]


You’ve already played these cards on me, including your ‘cherry’ picking argument, many times.
The modern period was more active. Using annual v2 SSNs for three consecutive 9 solar cycle periods
1712-1809 ave = 78.7, 18.4% less than the most recent 9 cycles
1810-1913 ave = 71.7, 22.4% less than the most recent 9 cycles
1914-2009 ave = 95.1
‘Cherry’ picking:
You have always attempted to cover the actual variation in SSN and TSI with the broadest hand-wave ever seen, with your repeated assertion to only use variation from 1700 onward, as though the actual real solar variation within that time frame didn’t matter. Very unscientific of you.
Clearly, Dr. Leif Svalgaard, you are not being scientific at all if you’re going to make this statement in contradiction to the facts:
“Part if the Dalton minimum low temps were due to volcanic activity [e.g. ‘the year without a summer’]”
From http://berkeleyearth.lbl.gov/auto/Global/Complete_TAVG_summary.txt
The year without summer occurred in 1816; Tambora erupted in 1815.
Temperatures fell for years as solar activity dropped long before Tambora erupted. 1816 saw a minor temperature decrease given the amount the hype Tambora generates wrt it’s supposed cooling effect. The cooling effect from zero sunspots in 1810 was as deeper and longer than the Tambora cooling effect.
Year BEST v2 SSN
1800 0.027 24.2
1801 0.116 56.7
1802 0.127 75
1803 -0.027 71.8
1804 0.308 79.2
1805 0.008 70.3
1806 -0.152 46.8
1807 -0.268 16.8
1808 -0.992 13.5
1809 -1.509 4.2
1810 -1.619 0
1811 -1.687 2.3
1812 -1.519 8.3
1813 -0.845 20.3
1814 -1.006 23.2
1815 -1.356 59
1816 -1.624 76.3
1817 -1.593 68.3
1818 -0.729 52.9
Dr. Svalgaard, you really ought to check your facts first before giving wrong unsupported unscientific opinions. Any discussions with me from now on should reflect this new knowledge. Your education is costing me a lot of time.

And your new cherry-picks [~20%] are a far cry from your previous 65%.
There were large volcanic eruptions in 1809 and 1812 [e.g. Maion].
I’ll show this again, so you can familiarize yourself with it:
Not much variation over the centuries.

Check out https://en.wikipedia.org/wiki/List_of_large_volcanic_eruptions_of_the_19th_century
“1808/1809 mystery eruption 1808 Greenland and Antarctic ice samples suggest an undocumented eruption roughly half the magnitude of Mount Tambora occurred, contributing to the 1810s being the coldest decade in at least 500 years.[1] Recent searches of documents suggest that it may have taken place in South Western Pacific Ocean around Dec 4, 1808 and observed in Colombia from December 11, 1808.[2]”
And Mayon was 1814, not 1812 [my bad]


You’re not learning anything Leif. All the comparison I made are valid, they just cover different time periods. What you want to do with your childish accusations of cherry-picking is prevent anyone from delving into the nuances of solar activity over time at all, so your viewpoint on the climate can prevail – an argument you have clearly lost.
You obviously have an incapacity to learn:
“There were large volcanic eruptions in 1809 and 1812 [e.g. Maion].”
So what? Temps started dropping in 1804. The deepest cold occurred after the year without sunspots, not after the volcanic eruption years 1809 or 1812. I just told you all that a few minutes ago and yet you come back with the same old same old. You didn’t learn a thing!

I think there is not much to learn from you. You how a graph with temperatures rising and solar activity [and thus TSI] falling. As I said: what more is there to say.
And you are certainly free to indulge in any flights of fancy you wish. As for me: you are not convincing.


You have to ignore the fact that PMOD was highest in the early 2000s in order to maintain your point of view. You are bordering on stupid here.
You said “temperatures rising and solar activity [and thus TSI] falling”
Get a clue – TSI rose until 2002, it did not fall, OK?! Those are the facts. Are you disputing them?
I showed you the PMOD rankings. Once again your hand-waving explanation comes up short.
You will continue to be shown by me how wrong you are about your opinion about the sun-earth climate connection, why you are wrong, and why your activist-like statement in your sunspot number paper about the trend in solar activity not causing global warming is not only wrong, but so easily proven wrong as to make me wonder how that ever made it through peer-review! It will be challenged.
You are clearly NOT AN EXPERT on the sun-earth climate connection, despite your claims.

Here is Claus Froehlich’s [maintainer of PMOD] latest composite of TSI:
Study it carefully.

Willis Eschenbach

Bob Weber April 21, 2016 at 11:04 am Edit

The sun definitely is in complete control of the weather & climate.

That means TSI was on the whole higher for those 70 years [1935-2004] than the previous 70 years, making the sun’s TSI the only realistic viable candidate for the cause of ‘global warming’ since 1850

Thanks, Bob, but consider the size of the variation in TSI. The TOA solar varies by 0.3 W/m2 (24/7 global average) from peak to trough of the sunspot cycle. The average difference over longer periods, of course, is much smaller than that, on the order of a maximum of 0.1 W/m2.
If you think that a 0.1 W/m2 change in TOA insolation is “the only realistic viable candidate” for global temperature variations, well … I’d say several things.
First, you are committing the “Error of the Excluded Middle”, meaning you have left out all kinds of possibilities. IF a change of 0.1 W/m2 can indeed change the global temperature, that is less than the change in forcing from the CO2 change over that time period, so that could be the cause of the warming. It is also equivalent to a change from a global average albedo of ~30% to ~ 30.03%, a trivially small change, so that could be the cause of the warming. Or an equally tiny change in the global average wind speed would reduce evaporation by that same small amount, 0.1 W/m2.
Next, given the size of the system, you are looking at a meaninglessly small change in forcing, far too small to make a difference. The average downwelling energy at the earth’s surface is on the order of a half a kilowatt per square metre. The TSI change that you think is the “only realistic viable candidate” is a tenth of a watt per square metre. That is a total change of 0.002%, a whacking great TWO TEN-THOUSANDTHS OF A SINGLE PERCENT variation in the forcing … sorry, but that is far too small to cause anything measurable.
Finally, IF the smaller long term TSI variations like your seventy year period above made a difference, then the larger 11-year variations would make a larger difference … but we do not see that in the record.


Willis: “Thanks, Bob, but consider the size of the variation in TSI. The TOA solar varies by 0.3 W/m2 (24/7 global average) from peak to trough of the sunspot cycle. The average difference over longer periods, of course, is much smaller than that, on the order of a maximum of 0.1 W/m2.”
That is the variation for the data available. The sun has been observed for too short of a time to know what variations are possible or what variations occur over several thousand years. The variations that happened for example between 1640 to 1700 are not measured variations. The graphs of TSI for that period of time usually are a relatively flat line. But that is a speculative estimate. I know, some may say it is based on theory and the theory they think is robust. I think it is not robust at all given it is not based on observations of TSI for the time in question.