Tim Channon: A non-linear solar cycle exploration

Posted: August 24, 2013 by tallbloke in Analysis, Cycles, Dataset, Electro-magnetism, Forecasting, Natural Variation, Solar physics, solar system dynamics

Reposted from co-blogger Tim Channon’s own blog for continuity of pre-running discussion here at the talkshop. In Ian WIlson’s Halstatt cycle thread, R.J. Salvador created a model of solar cycle evolution using Ian’s tidal/torque JEV theoretical periods, and has achieved an r^2=0.85 correlation. Here, Tim pares back the complexity to a minimum, so we can see what we can see. Over to Tim:

Preamble, do not take this work too literally. the intent is food for thought.

Figure 1

Recent very long free thinking discussion (paged comments) on Tallbloke’s Talkshop evolved into trying to create a model of astronomical effect on the sun of planetary parameters, a longstanding tantalising problem where “ought to” and reality throw buns. Probably fits the tales of the farmer of old leaning on the farm gate chewing straw watching fools trying to get the cart under the bridge. Won’t fit but watching is fun. Lets hope that one day more is learnt.

I can play too, know a bit about the local bridge.

Figure 1 is a result of some novel work but explaining what I have done is going to be tough. (spreadsheet supplied[2] for the brave)

I have written some unique software which approximates a non-discrete Fourier Transform or similar where the driving input is a discrete dataset. The output can produce datapoints for any time and therefore produce a new discrete time series on any scale. Validity is a different matter, why we have brains, computers just try and fit carts under bridges, can’t know it won’t go.

In this case I have played some further tricks since I know sunspot data is more than just cantankerous. (and is known inaccurate anyway)

Figure 2

The data is transformed (preprocessed) from SIDC published monthly sunspot count into the form shown figure 2 and this was the input to the software.

Data has been roughly turned into bipolar more akin to solar polar magnetic data but not offset to the apt 90 degree phase shift. (irrelevant here). In addition root 1.4 has been applied, pre-distorting the wave, perhaps into a more friendly shape for analysis. Power 1.4 is sometimes mentioned as a possible sunspot parameter. [1]

For exploitative analysis KISS (keep it simple, stupid) is generally the most likely to lead to insight so in this case I restricted the software to two terms but selected complicated versions, variable amplitude modulation, adding two more parameters plus modulation depth.

The software was left on automatic defaults. (apart from setup, turnkey)

A final twist was almost hide part of the input data from the software, for which there is a good reason.

Those familiar with sunspot data know there is a severe problem circa year 1790 when the sun seems to have behaved very strangely, although this is uncertain, disputed but either way the data is questionable. We are not even certain whether an additional short sunspot cycle was present around 1895. There is also cloud over post 1800.

I used the software “confidence” function to make the merit function almost ignore year 1780 through 1829. Engineers have a rule: if it looks hard, run away very fast. Lets see what the software assumes happened.

Analysis ran normally and complete promptly, a good sign.

One version of the output can be dropped into some spreadsheet software and implements an interactive model in the spreadsheet. This is used.

For this instance the preprocessing transform has to be reversed, output raised to power 1.4, spreadsheet can do this.

Figure 1 is one result. R2 of 0.57 but that includes the ignore section of data. I consider this quite good given no attempt is made to closely model. (could with many more terms be raised very high but only over the input period) In this case I am not interested in party tricks.

I won’t discuss the detail results, can leave that for any blog comments, you have eyes.

I’ve also produced a second result on a much longer timescale. Tallbloke is particularly interested in whether any models match the Maunder minimum.

Figure 3

Figure 3 shows a longer timescale running far outside the input data period. Treat with extreme caution because it is wrong. Illuminating, you decide.


These are machine output, no input or guidance from me. (which could be done)

Read as column associated.

period -var- 22.030288 19.884901
frequency -const- 0.045392 0.050289
phase -var- 1.224153 1.502501
amplitude -var- 116.826859 13.364567
aux -var- 0.182192 0.683620
am_period -var- 132.283608 44.080613
am_freq -const- 0.007560 0.022686
am_phase -var- 3.070491 4.132502
am_amplitude -var- 0.089202 0.415502

The software chose the above parameters.


22 year might be related to solar system magnetics, only some planets are magnetically active, dominated by Jupiter. 132 year makes no sense to me.

19.9 year suggests gravitational sum of force on the sun. In this case the modulation period is I think very interesting, circa 45 years is strongly present in some solar asymmetry data and in the past I have contended a pseudo 45 year in various terrestrial datasets. (note: there is no pure frequency, is an approximation)

The modulation depth (figure “aux”), is present relatively strongly, zero is none, one is full and can exceed one. Wikidpedia might help a little, assume partially suppressed carier.
A web search might help further or discuss.

1. A paper which might be of interest, by a veteran,

Title: Three-halves law in sunspot cycle shape
Authors: Bracewell, R. N.
Journal: Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 230, Feb. 15, 1988, p. 535-550.
Bibliographic Code: 1988MNRAS.230..535B

2. Spreadsheet in OpenOffice .ods format inside a zip, this is large and may pose speed problems with LibreOffice. Plots are unlikely to survive to your software. Ask if you need help or other file versions.

Updated zip file here containing ods and xls versions of files

Reason for update, apparently when Excel imports ods it imports formula as literal values, supposed to be a live spreadsheet (no macros), zip now contains an additional simple xls file which does import formula. I’ve also added the analysis remainder data.

(1.4M 2.7M hosted at Tallbloke’s where paid for extra of zip storage is present, part of what donations provide)

  1. tallbloke says:

    Nice work Tim.

    22.030288*19.884901/(22.030288-19.884901)=204.19 It is very encouraging that the software found two fundamental periods so close to a planetary (Jupiter Saturn synodic 19.86) and a Solar magnetic period (Hale cycle) which is also the average full Jupiter Earth Venus alignment cycle (22.14 years). It’s even more encouraging that the two values it chose have a longer term harmonic at 204.19 years, very close to the De Vries cycle at 207-8 years.

    Very roughly speaking, the output is mirror imaged either side of 1860, from the end of the forecast back to 1590 Yet there is no very long term frequency in the periods chosen by the software. Is there a natural harmonic developing? What might it’s period be? If we ran the forecast further forward, we might get a clue as to its wavelength.

  2. ren says:

    This cycle may be flatter than those of the early twentieth century.

  3. tallbloke says:

    Ren: Yes, both R.J. Salvador and Tim’s models get SS24 bigger than it is. I suspect there is an additional mechanism at work which is operative now and during the Dalton and/or Maunder minima but not so much at the start of the C20th. I hope Geoff Sharp might drop by with a view on that.

  4. tallbloke says:

    Tim : “132 year makes no sense to me.”

    3x44yr inner planet returns and perhaps
    2x66yr shows another influence (J-S tri-synod ~60yrs returns J&S to same point against fixed stars). Also 132 is
    4x33yr which is three schwabe cycles and the half period of the AMO. And of course 132 is also
    6x22yr Hale cycles, which is also
    12x11yr Schwabe cycles

    There’s also a strong ~396yr repetition in the output
    (3x132yr = 6x66yr = 9x44yr = 11x36yr = 12x33yr).
    If the model reflects reality, a Maunder type minimum is upon us.

  5. tallbloke says:

    Here’s a curiosity. I’ve never been very impressed by the fit of the C14 carbon isotope proxy to solar data. The plot on Wikipedia is a joke, putting the Maunder minimum in the 1740’s for example http://upload.wikimedia.org/wikipedia/commons/5/5c/Carbon14_with_activity_labels.svg No wonder they don’t dare show the solar data alongside it.

    However, when you take that C14 curve and invert it, it fits Tim’s model a good deal better. Upside down mud anyone? Where’s Mikey?

  6. tchannon says:

    Updated to a new data file after Rog found Excel imported formula as literal numbers, now contains an export to xls too.

  7. ren says:

    You can see that already the previous cycle was weaker. This is not the case.

  8. tallbloke says:

    Ren: which cycle numbers are you referring to?

  9. tallbloke says:

    Acoording to http://booty.org.uk/booty.weather/climate/1700_1749.htm the late 1720s-1730’s decade was unusually warm, as CET confirms. Reading reports there, it looks like the high solar values resulting in a thumping big El Nino following solar min in the mid 1730’s followed by an equally big La Nina at the end of the decade near solar max of the following cycle. That fits the pattern I’ve identified, with big El Nino’s following solar min unless a volcano has already caused a heat release from the ocean during the solar cycle.

  10. tallbloke says:

    Right, so 23 was weaker than 22 and 21, and 24 is a lot weaker than all of them. The model also shows that. So I don’t understand what you mean by “This is not the case”.
    Where the model does fail is by getting cycle 23 lower than cycle 20, which is too high in comparison to the surrounding cycles.

  11. ren says:

    What I tend visible at Vukcevic, a gradual reduction of magnetic activity the Sun.

  12. ren says:

    And it still happens, I do not believe that this activity will increase.

  13. tallbloke says:

    ren: Now I understand what you are trying to say. We agree. 🙂

  14. tallbloke says:

    The long repeat in the model output at around 396 years (3x132yrs)

  15. J Martin says:

    Tim said “132 year makes no sense to me.”

    but from;


    But lets remember what Bart actually said:
    “I observed four significant peaks in the PSD of the SSN process at 10 years, 11.8 years, 10.8 years, and 131 years ”

  16. tallbloke says:

    JM: Good reminder. The interesting thing about that is the 131 figure dropped to 122 when I shifted Bart’s original figures to the planetary periods in my followup post:
    “The fourth ‘necessarily apparent’ period of ~131 years is given by Bart’s equation T1*T2/(T2-T1) years. When we use the actual orbital periods rather than the DSP analysis estimates this works out at 122 years, which is within error for the spectral analysis,”

    Which means we need to think some more about the periods Bart found in the DSP analysis you quoted: “10 years, 11.8 years, 10.8 years, and 131 years”
    132 can be derived like this:

    But, 9.983 is quite a long way from 9.93 – half the Jupiter-Saturn synodic. Good puzzle. 🙂

  17. tchannon says:

    The strange solar activity seems to point more to 1776/7 when a remarkably abrupt rise occured.

    This link points to data problems around then, with the death of an observer compounding things.

  18. tchannon says:

    This 1998 paper adds further weight to the dire state of sunspot data during early years but ads a new string I have not come across before, relating the observation days to seeing and cloud cover.

    Robert M.Wilson

    Click to access 19980237265_1998361105.pdf

  19. suricat says:

    tallbloke says: August 24, 2013 at 9:28 pm

    Do you include ‘stabilising attractors’ in your “puzzle”?

    Consider the gravitational influence that formed the gaps between Saturn’s ‘rings’. This principle also applies to the orbit preference for stellar systems and planetary ‘satellites’ (moons).

    Gravity has a tendency to generate order from chaos, and shows this by modifying a local resonance towards unity. Earth’s ‘satellite’ (the Moon) is currently undergoing a transition from an orbital ‘chaotic resonance’ to an orbit of ‘harmonic unity’. All orbiting mass bodies are also governed by this ‘harmonic interaction’ that is propagated by gravitational influence.

    Best regards, Ray.

  20. tallbloke says:

    Over on Ian’s thread, Paul V has made a long and interesting comment in which he points out an alternative to the interpretation of Tim’s software’ choice of 19.88. It is close to the period of the Jupiter-Saturn synodic, but can also be derived from the timings of Earth and Venus with these gas giants:

    J = 11.862615
    S = 29.447498
    JEV = 11.06964992 = +6V-10E+4J
    JEV/2 = 22.13929985 = +3V-5E+2J
    SEV = 9.007246722 = -6V+10E-4S
    SEV/2 = 18.01449344 = -3V+5E-2S
    2*(22.13929985)*(18.01449344) / (22.13929985 + 18.01449344) = 19.86503587
    We should at least consider emphasizing this when giving J-S model specs:

    I couldn’t agree more. Paul’s JSEV observations support Ian Wilson’s tidal/torque theory. J-S synodic is more in line with Wolff and Patrone 2010 and Jose 1965, relating to angular momentum theory and possibly electromagnetic concepts (Landscheidt 1981). Conflation or complimentarity? We don’t know yet.

  21. tallbloke says:

    Ray: “Consider the gravitational influence that formed the gaps between Saturn’s ‘rings’. This principle also applies to the orbit preference for stellar systems and planetary ‘satellites’ (moons).”

    Maxwell worked on the Saturn rings problem. It informed the development of his kinetic theory of gases later on. It’s thought that collisions and gravity is what causes the separation of the rings. If you can point me to any coherent theory which quantifies and generalises the tendency to ‘orbit preference’ I’d be delighted.

  22. ren says:

    Everything points to the future course of the current solar cycle.

  23. tallbloke says:

    Tim, I think it’s relevant that the 1790 strangeness is separated from the anomalously (though not according to the model) low cycle 20 around 1970 by around 179 years (Jose cycle). That’s one of the reasons I think there’s an additional mechanism not captured by the model, which has identified and used gravito-tidal frequencies. Consider my barycentric x-y and z axes model:

    See the black tick marks near the bottom? They line up with periods when the x-y axis barycentric motion has a hiccup near the solar surface (grey curve inside the yellow band). There’s one near 1790 and another near 1970. What effect those hiccups have varies because it depends on:
    What the phase of the solar cycle is at the time (Geoff Sharp)
    The timing of EV in relation to J at the time.
    To be investigated, but if we can add in a simple model of that to the main model and improve the correlation, it might be another indicator that there is more than one mechanism involved here.

    Note also that the time from the first hiccup of the earlier pair around 1790 near the start of the Dalton minimum to the second hiccup of the second pair around 2005 near the start of the present grand minimum is 215 years. This might be a source of confusion/conflation when identifying de Vries cycle length perturbations in the proxy record.

    Note also that if you go back 179 years from 1790 you get to 1611, which is pretty close to the start of the Maunder Minimum.

  24. tchannon says:

    I’m quiet because I don’t feel able to write anything useful.

  25. tallbloke says:

    Tim, you already did. Your amazing analysis software, and your introductory post. 😉

  26. suricat says:

    tallbloke says: August 25, 2013 at 8:40 am

    “If you can point me to any coherent theory which quantifies and generalises the tendency to ‘orbit preference’ I’d be delighted.”

    Sorry for the delay, I’ve been contemplating Mum’s memorial.

    Well, I ‘googled’ with TalkTalk’s Google engine for “orbital preferentiation” and came up with;

    Click to access 20110007944_2011006399.pdf



    Seeing as the second ‘hit’ is a personal dictionary ‘disambiguation’, does this constitute a ‘Googlewack’??? 🙂

    Seriously. The first link is an ‘observation’ and not a ‘theory’, but the evidence is there to enable the formulation of a theory.

    It’s easy to explain an ‘observation’, but the ‘theory’ behind the ‘evolution’ of the ‘observation’ requires more time to construct. However, Newtonian mechanics shows that ‘both massive bodies’ possess gravity, which again leads on to ratio-metric attraction and separation of orbital periodicity by mass product. Thus, frequential lag/lead and a ‘harmonic component’ dependant on the relevant ‘mass’, ‘central “G” force’ and ‘orbital vector’.

    Best regards, Ray.

  27. ren says:

    Is Cycle 24 will be similar to a 12?

  28. tallbloke says:

    ren: that is a question of how you count the sunspots.