Guest post by David Archibald
With respect to the month of minimum, it is very likely that Solar Cycle 24 has started simply because Solar Cycle 23 has run out. Most solar cycles stop producing spots at about nineteen years after solar maximum of the previous cycle. Solar Cycle 23 had its genesis with the magnetic reversal at the Solar Cycle 22 maximum. As the graph above shows, Solar Cycle 23 is now 19 years old. Only 9% of the named solar cycles produced spots after this.
The graph also shows the position of Solar Cycle 24 relative to its month of genesis. Solar Cycle 24 is now the second latest of the 24 named solar cycles. January is 105 months after the Solar Cycle 23 maximum. Only Solar Cycle 5, the first half of the Dalton Minimum, is later. This lateness points to Solar Cycle 24 being very weak.
This graph shows the initial ramp ups of six solar cycles that were preceded by a vey low minimum. The ultimate trajectory of Solar Cycle 24 should be apparent by late 2009. If Solar Cycle 24 is going to be as weak as expected, the monthly sunspot number should remain under 10 by the end of 2009.
lgl (08:03:40) :
Vukcevic,
From the 22 yr solar cycle. According to Leif’s FFT the 11 yr is clearly there.
It is not where I first searched for it, but that’s another story ..
Yes, we know it is there, but question is why is it there? 11.86 and 19.6 are outside factors, so they can be considered to be part of the driving system, 11 is a consequence, cause and consequence have to be on the opposite sides of any proper equation.
Guiding principle here has to be: ‘the nature is adverse to a coincidence; it is ruled by a cause and the consequence’.
lgl (00:19:47) :
So you agree then that the 10 and 12 y cycles are real
What is real are the side peaks generated by the 100-yr modulation. The only ‘real’ cycle in the neighborhood of 11 years is the 11-yr ‘cycle’, even with its varying length and shifty phase, because it is not a ‘cycle’ in the strict meaning of that word.
Your modulation is not that interesting […] I believe this modulation has nothing to do with reality.
The modulation is an observed fact over the past 300 years. It even has a name: the Gleissberg cycle [varying between 75 and 125 years].
How does it work? How does the Sun manage to multiply two frequencies?
There are people out there believing that there are Grand Minima and Maxima, and that the solar cycle is modulated by a 172 yr, or 179, or 166, or such some, ‘process’, so there seems to be general agreement that the Sun can manage amplitude modulation. In fact, I don’t know any reasonable and knowledgeable person that questions that.
How is this modulator constructed?
In my test case the amplitude of the 11-yr cycle was set to follow a 100-yr period [you know, to be small in ~1700, ~1800, ~1900, ~2000] because that is what the data shows.
And how can you achieve the observed cycle length variation (mainly from 9.5 to 12.5 or so) by this modulation?
The modulation does not control the cycle length to vary. And BTW, if you add the 10 and 12 yr waves, the length becomes smaller when the amplitude of the result is small, contrary to observed behavior, further evidence that the Sun does not add those cycles.
All your cycles on page 7 are very close to 11 years.
Makes no difference. A varying length just broadens the peak and make the side peaks harder to see, as is observed [page 4, compare page 8]
But you still did not acknowledge that there is a lot of [most, in fact] power at 11 years rather than at 10.2 and 11.8 [with not much at 11] as you claimed. I think we all would take no response as a positive acknowledgment.
vukcevic (02:07:57) :
with a proviso you change phase every 250 or so years.
You formula has two COS functions. Which one or both has the phase change? And where do you add [subtract?] the phase?
Here is your formula:
SSN=100*ABS(COS(6.2832/4+6.2832*(t-1941)/(2*11.862))+COS(6.2832*(t-1941)/19.859))
modify it with the phase change added. I would assume that you change ‘t’ by 90 degrees, but how do you translate 90 degrees into time since that depends on the period [12 yrs or 20 yrs]?
Leif Svalgaard (10:00:42) :
Do you have a good (is there a definitive?) explanation of the Gleissberg cycle – it seems to be interpreted in numerous ways?
Have you written specifically on the Gleissberg cycle?
Is the Gleissberg cycle remotely relevant to solar/earth climate changes in all your learning?
As ever greatly appreciate any thoughts/learnings you can give.
PaulHClark (12:07:47) :
Do you have a good (is there a definitive?) explanation of the Gleissberg cycle – it seems to be interpreted in numerous ways?
I think there is no physical cycle. All the way back to Rudolf Wolf himself in the 1870s it has occurred to people that there was a rough 75-125 year cycle in the size of the 11-yr cycle. This was studied in particular by Gleissberg in the middle of the 20th century and a length of some 90 years was suggested. With half a century more data, the ‘cycle’ looks more like ~100 years. Dynamo models can ‘explain’ this long cycle [or to be more correct, one can find parameters that can accommodate the cycle], but the true cause is unknown.
Have you written specifically on the Gleissberg cycle?
No, apart from mentioning it briefly as it is also seen in the interplanetary magnetic field:
http://www.leif.org/research/IDV-Index%20JGR-version.pdf
section 6, paragraph [20]
Is the Gleissberg cycle remotely relevant to solar/earth climate changes in all your learning?
I don’t think so, but many people fool themselves into believing otherwise 🙂 as in: It’s the Sun, Stupid!
vukcevic (09:57:23) :
Guiding principle here has to be: ‘the nature is adverse to a coincidence; it is ruled by a cause and the consequence’.
But humans are easily fooled by coincidences into believing weird things. There is actually evolutionary survival value in this: it is better to believe wrongly most of the time that the shadows in the grass is a tiger and take evasive action than to dismiss it as ‘mere coincidence’ and be eaten the one rare time it is not.
Leif,
I was hoping you could understand this so you will not shoot from your hip every time these real 10 and 11.8 y components will be mentioned in the future, but I realize that is mission impossible.
You are wrong on every point. What you are proposing, like you said, is amplitude modulation, where the 11 y is the carrier frq and the 100 y is the modulating frq, the ‘voice’. In AM the carrier frq does not change when modulated, contrary to observed behavior where there are peaks around 10 y and 11.8 y
The Gleissberg cycle in not an observed fact of AM, it is an observed fact of the envelope created by adding the 10, 11, 11.8 (and others) components.
Your claim that you get the wrong result when adding the components of ‘the real thing’ opposed to your flawed method just speaks for itself.
We just have to agree to disagree and move on to your next point.
At the time I didn’t have a real FFT of the signal so I took a look at this:
http://personal.inet.fi/tiede/tilmari/sunspots.html Table 3, and guessed it would tell something similar to FFT. I know it’s quick and dirty and I apologize if I have misled people, but I still find it strange that there is a dip at 11 y. Maybe if we had data back to say 1500 there would be a peak also at 11.
Paul,
Yes it’s amazing. Could it be the 22 y solar cycle over time forcing the inner planets into this 11 y sync. When their orbit times are whole years the Sun will give them an extra push at the same position in their orbit every time.
vukcevic (02:07:57) :
………….with a proviso you change phase every 250 or so years.
Leif Svalgaard (10:38:00) :
……………modify it with the phase change added. I would assume that you change ‘t’ by 90 degrees, but how do you translate 90 degrees into time since that depends on the period [12 yrs or 20 yrs]?
Are you taking some of my ideas seriously ( ? ! ), or just suspecting that I am trying to send-up the solar establishment?
No sir, it would not work the way you suggested by changing the time factor, as you rightly realise the magnitude of the angle is a function of frequency. Why I do this: explanation is the one you thought was an absolute nonsense, so we may discus it at some other time.
This is an oscillating back-forward change of 90 degree.
If you suspect my numbers here are the critical Excel entries.
If you start with A2=1000, A3=A2+1, then copy and past along A column .
Start with year 2000 (you could start with 2060)
Year 2000=100*ABS(COS(2*PI()*(A1001-1941)/19.859)+COS(2*PI()/3+2*PI()*(A1061-1941)/23.724))
Then going backwards change at the critical points
Year 1810=100*ABS(SIN(2*PI()*(A810-1941)/19.859)+SIN(2*PI()/3+2*PI()*(A810-1941)/23.724))
Year 1560=100*ABS(COS(2*PI()*(A561-1941)/19.859)+COS(2*PI()/3+2*PI()*(A561-1941)/23.724))
Year 1300 =100*ABS(SIN(2*PI()*(A312-1941)/19.859)+SIN(2*PI()/3+2*PI()*(A312-1941)/23.724))
Year 1160=100*ABS(COS(2*PI()*(A61-1941)/19.859)+COS(2*PI()/3+2*PI()*(A61-1941)/23.724))
And hey presto: You got Grand Minima as per NASA’s numbers. That must be worth at least a bit of help on my project.
L.S.
….but humans are easily fooled by coincidences into believing weird things.
You are misinterpreting my ideas again! I invented that motto to protect my ideas from being declared “just a coincidence” as Dr. H. put it. What I am saying is there are no coincidences, only causes and appropriate consequences. In the grass were I grew up, there are no tigers, but there are poisonous snakes, and when I here or see grass move, I can assure you, I take evasive action.
I do not believe in “just a coincidence”, there is a cause to everything.
If either cause or consequence assumption is wrong, that is an illusion, if cause and consequence are linked together correctly, that is science.
Corrections for typing errors in the entry:
vukcevic (14:41:37)
should be:
then copy and paste, (A811-1941) twice , (A301-1941) twice
Another gem from my cyclopaedia of cyclographs (or is it cyclograms):
I hope one day that solar scientists, in the interest of accuracy, will stop talking about 11 year long cycles. That is for press releases and general public. As learned Dr.S. has shown in many of his pages, each cycle last longer, it is cycle overlaps that are causing confusion.
Guess that should have been; when they make a number of full orbits in sync with the solar max the Sun will…
lgl (14:06:29) :
mission impossible
Yes, indeed, it has become clear that the learning curve is too steep for you, so I’ll you be.
Leif,
There are more flaws.
With AM the sidebands will be symmetrical around the carrier. The FFT of the observed shows they’re not, 10 y much higher than 11.77 y. And you cant fix it by adding more frqs to the modulation. It only makes things worse, adding more frqs symetrically around the carrier.
Paul,
… or sticking to my belief. The inner planets and Jupiter will line up pretty well every 11 years… So there we have all three big players:
10 J/S
11 Me/V/E/Ma/J
11.8 J
lgl (16:53:15) :
There are more flaws.
With AM the sidebands will be symmetrical around the carrier. The FFT of the observed shows they’re not, 10 y much higher than 11.77 y. And you cant fix it by adding more frqs to the modulation. It only makes things worse, adding more frqs symetrically around the carrier.
I recalculated the FFT using monthly data for 1700.042 to 2008.625 with the highest resolution the data allows and find the following frequencies and periods:
0.08392334 11.91563634 left band
0.09155273 10.92266719 main peak
0.09918213 10.08246143 right band
The exact midpoint of the two side bands [add frequencies, divide by 2] is at
0.091552735 10.92266659
which is indistinguishable from the observed middle peak above.
Of course, all the many decimals are not really significant, but as far as the data goes, the side bands are symmetrical.
lgl (16:53:15) :
There are more flaws.
With AM the sidebands will be symmetrical around the carrier. The FFT of the observed shows they’re not, 10 y much higher than 11.77 y.
The asymmetry in height is due to the cycles being asymmetric themselves and also that shorter cycles generally are larger than longer cycles adding power to the low-frequency ‘wing’ of the peak. All this can be demonstrated by playing around with simulated cycles of various shapes and properties. Scientists have long ago [incl. myself] explored all of that. You are welcome to fiddle with it yourself to be convinced.
high-frequency ‘wing’ of the peak, of course.
vukcevic (14:41:37) :
Are you taking some of my ideas seriously ( ? ! ),
Not necessarily [most ideas including my own turn out to be junk in the end], but I always look at the data and let them speak. Here http://www.leif.org/research/Vuc-SAM.pdf is some of my analysis of your graphs, and of Carl’s Angular momentum data set.
Leif,
Yes there are two ways. The scientist’s way, fiddling with dusins of complicated functions and tweaking and tuning until you get close, like the climate modellers are working, and there are the nature’s way, simply adding the different frequencies together.
The first is the one you are forced to follow until you understand what is really going on.
But if you insist, there is a planetaty modulator. 4 Saturn orbits is 118 y, 10 Jupiter orbits is 119 y, so they line up well every 118 years.
Leif Svalgaard (21:37:33) :
to
lgl (16:53:15) :
……….All this can be demonstrated by playing around with simulated cycles of various shapes and properties. Scientists have long ago [incl. myself] explored all of that.
I assume, that means that my equations are new to the scientists who ”have long ago explored all of that”, otherwise you wouldn’t have bothered with it. If nothing else, that it is a small but notable achievement in itself. After all, even if it is all “junk”, in these days of “re-cycling” even some of the higher quality junk could be reused.
lgl (00:40:00) :
But if you insist, there is a planetary modulator………….
I would be surprised indeed, if Dr.S. is seriously suggesting there is any kind of planetary modulation, or do we have a conversion on the road to Damascus ? !
There is no way you can get a regular beat out of angular momentum. Not even close. It doesn’t follow a strict on then off again pattern. It varies as the planets orbits do, in relation to one another.
The only background “beat” is the conjunction of N+U and varies on the strength of the alignments of J+S. There are periods thousands of years ago that differ very much from recent times. When the conditions are right, the angular momentum disturbance can be dominate, widening the window on solar influence substantially.
I will have a new graph showing that very soon.
Vukcevic,
No no, Leif never suggested any kind of planetary modulation, heaven forbid, but he is insisting on a kind of modulator and I suggested the planets.
vukcevic (04:38:16) :
I assume, that means that my equations are new to the scientists who ”have long ago explored all of that”, otherwise you wouldn’t have bothered with it.
I bother with many things. wrong or right, but that sort of equations are not new, here is Rudolf Wolf’s [from 1859]:
SSN(t) = 50.31 + 3.73 * [1.68 sin (586.26° t) + 1.00 sin (360° t) + 12.53 sin (30.35° t) + 1.12 sin (12.22° t)]
and very many others can be found.
email sent to me from Vuk:
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Dr.S.
Thanks for the graphics. I do not really believe that spectral analysis will get us anywhere closer, although interesting. If the system is driven by gravitation alone (tides, momentum, etc.) whole thing would run as clockwork. I think the current/magnetic field feedback is the area where the answer lies. Jupiter magnetosphere is huge, currents and fields are at 360 degrees, and in addition, if the heliosphere on the forward side is ‘effective’ to only about 80 AU, it would be logical to expect that at 20AU & 10AU and possibly 5AU, would introduce effect of asymmetry. In this context, it appears to me that precise dates of conjunctions are most likely irrelevant.
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The idea of clockwork is alluring. Many scientists have been attracted to it. E.g.
Bracewell, R. N., Stanford University
(R. G. Giovanelli Commemorative Colloquium, Tucson, AZ, Jan. 17, 18, 1985) Australian Journal of Physics (ISSN 0004-9506), vol. 38, 1985, p. 1009-1025.
Abstract
The 1700-to-present sunspot number series R(t) is presently noted to be representable by an expression involving the angular frequency corresponding to a 22-year period, the instantaneous envelope amplitude, the instantaneous phase of a complex and time-varying analytic function, an undulation of low amplitude and period lasting for about 30 of the 22-year cycles, and a nonlinear operator whose primary effect is the introduction of a small amount of third harmonic with a period of about 7 years. The third harmonic is an expected consequence of minor nonlinearity in the dependence of the arbitrarily defined sunspot number series on the physical cause of sunspots. A complex envelope is discerned whose intrinsic behavior may be studied to reveal statistics bearing on the origin of the solar cycle. The results imply a deep monochromatic oscillator whose influence is propagated to the observable surface via a time-varying medium.
or:
The phase variations of the solar cycle
Dicke, R. H., Princeton University
Solar Physics (ISSN 0038-0938), vol. 115, no. 1, 1988, p. 171-181.
Abstract
It has previously been shown that the statistics of the phase fluctuation of the sunspot cycle are compatible with the assumption that the solar magnetic field is generated deep in the Sun by a frequency stable oscillator and that the observed substantial phase fluctuation in the sunspot cycle is due to variation in the time required for the magnetic field to move to the solar surface (Dicke, 1978, 1979). It was shown that the observed phase shifts are strongly correlated with the amplitude of the solar cycle. It is shown here that of two empirical models for the transport of magnetic flux to the surface, the best fit to the data is obtained with a model for which the magnetic flux is carried to the surface by convection with the convection velocity proportional to a function of the solar cycle amplitude. The best fit of this model to the data is obtained for a 12-yr transit time. The period obtained for the solar cycle is T = 22.219±0.032 yr. It is shown that the great solar anomaly of 1760 – 1800 is most likely real and not due to poor data.
http://articles.adsabs.harvard.edu/full/1988SoPh..115..171D
Dicke’s formula reads:
SSN(t) =A(t) {C0 + C1 cos (2pi v(t-1889) + psi(W(t,s,tau – W) + S1 sin[…] + C3 cos (3*[…]) + S3 sin (3*[…])}
Never mind the details, but you can perhaps recognize the general idea.
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Nothing has come of those various proposals.