Robert M Wilson: On The Distribution of Sunspot Cycle Periods

Posted: March 5, 2015 by tallbloke in Analysis, Astrophysics, Celestial Mechanics, innovation, Solar physics, solar system dynamics
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Back in 1987, Robert M Wilson of NASA’s Space Science Laboratory in Huntsville published this paper in the Journal of Geophysical Research. It’s important to our solar-planetary theory because it shows that the Sun is bi-modal in terms of its solar cycle lengths. They cluster around  periods of a little over ten and a little under twelve years. These periods correlate to the periods of Jupiter-Earth-Venus syzygy cycles and Jupiter’s orbital period respectively. Leif Svalgaard vehemently denied this correlation when I pointed it out to him a few years ago.

rob-wilson-bimodal-sun

The same correlation was noted by independent researcher Timo Niroma in 1989, who conducted his own survey and analysis of solar cycle lengths. He produced this simple ascii-art graphic to present his results.

solar cycle lengths

Ray Tomes and later, our own fellow researcher Ian Wilson determined the exact length of the J-E-V syzygy cycle to be 10.39 years. Jupiter’s orbital period is 11.86 years.

Also in 1989, french independent researcher Jean-Pierre Desmoulins created a simple program in Turbo-Pascal to calculate the ‘most aligned days’ for J-E-V (green curve) and compared the results graphically with the signed sunspot series (red curve), producing this graphic.

Venus Earth Jupiter alignments vs The solar cycles

Venus Earth Jupiter alignments vs The solar cycles

The out of phase epochs on this plot in the late 1700’s and late 1900’s presage the Dalton minimum and the current Landscheidt minimum getting under way with the anomalously low solar cycle 24. However, Desmoulin’s planetary index, whilst accurately predicting the epochs of solar minimum in most cycles, cannot predict their amplitude accurately. That’s something we’ve been working on here at the Talkshop, and I’ll outline our progress in another post soon.

Comments
  1. oldbrew says:

    A J-E-V period with whole numbers of conjunctions is around 110.3 years as has been shown before:

    69 Venus – Earth = 110.3125y
    101 Ju – Earth = 110.298y
    170 Ju – Venus = 110.304y
    (69+101=170)

    That approximates to five ‘average’ Hale cycles of 34 J-V.

    The ‘short’ J-E-V cycle (~10.38y) discussed by Ray Tomes, Ian Wilson, Timo Niroma etc. is 16 J-V.
    It’s also close to 9.5 J-E and 6.5 V-E.

    These periods don’t correspond to a ‘regular’ number of Jupiter orbits though.
    Has anyone matched Jupiter perihelion dates to sunspot cycles?

  2. ren says:

    Sunspot number: 43 – New regions: 0

  3. tallbloke says:

    OB: The ‘short’ J-E-V cycle (~10.38y) discussed by Ray Tomes, Ian Wilson, Timo Niroma etc. is 16 J-V.
    It’s also close to 9.5 J-E and 6.5 V-E.
    These periods don’t correspond to a ‘regular’ number of Jupiter orbits though.
    Has anyone matched Jupiter perihelion dates to sunspot cycles?

    The full cycle of the JEV syzygy is 2×10.38yr so you’ll get whole numbers of J-E and V-E for that.
    We wouldn’t expect whole numbers of Jupiter orbits because that solar cycle length of ~11.9yr is the other peak of the bi-modal distribution.

    Vukevic analysed Jupiter-Saturn separation angle in relation to solar cycles and found something very interesting that appears to back up my own observation that JEV alignments along the curve of the Parker Spiral yield better correlations than direct straight line alignments.

    I think that suggests there’s something electromagnetic happening here, not just tidal or angular momentum related effects.

  4. oldbrew says:

    ‘The full cycle of the JEV syzygy is 2×10.38yr so you’ll get whole numbers of J-E and V-E for that. We wouldn’t expect whole numbers of Jupiter orbits because that solar cycle length of ~11.9yr is the other peak of the bi-modal distribution.’

    7 Jupiter = 4 JEV syzygy cycles

  5. tallbloke says:

    So 7 x Jupiter = 8 x 10.38 = 83yrs, which is ~a year short of Uranus’ orbital period, and ~half a year longer than the Uranus-Neptune conjunction/opposition period. Neat.

    7:8 relationships have cropped up elsewhere in our investigations too.

  6. Paul Vaughan says:

    long-run average JEV = 11.07, but events cluster around 10.4 & 12 (not 11.86)

    dotplots vary with aggregation criteria, but bimodal 10.4 & 12 appears in narrow-extent-wavelet SCL dotplot (with frequency ratios similar to Niroma’s)

    it’s important to be aware that the distributions are not independent of time
    When time & resources permit (possibly never) I’ll more deeply explore osculating JEV, which has properties sure to fascinate talkshoppers.

    I know of no historical (observational, not model) parker spiral records to explore what vukcevic has done.

  7. oldbrew says:

    ‘long-run average JEV = 11.07, but events cluster around 10.4 & 12’

    So we’re talking about 16 J-V (10.38~y) and half of 18.5 J-V (= 22 J-E = 15 V-E = ~24 years) there.
    11 J-E = 12.013y

  8. tallbloke says:

    Paul V: I know of no historical (observational, not model) parker spiral records to explore what vukcevic has done.

    There is a relationship between the solar wind speed and the rate of curvature of the Parker spiral. Granted th solar wind speed is not the same in all directions and so we only know the Earth directed speed. Assumptions have to be made, and reconstructions are derived from the F10.7 flux derive from sunspot numbers.

    Models all the way down.🙂

    However, given the good result I got from applying those models to JEV alignments along the modeled spiral in terms of solar cycle shape and cycle lengths, I still think there’s something going on with the electromagnetic hypothesis.

  9. E.M.Smith says:

    When Willis was declaring no 11 year period found in climate data, I pointed out the bi-modal nature of sunspots (courtesy of reading Timo…) and have done so a few times. Near as I can tell it just gets ignored. He keeps looking for 11 year cycles of fixed size in a bimodal variable world, and not finding them…

  10. tallbloke says:

    E.M.: Willisful ignorance.

    I’ll stop there.

  11. oldbrew says:

    A glance at the list of solar cycles shows there are none recorded between 10.6 and 11.2 years, so anyone looking for 11 year cycles is obviously wasting their and everyone else’s time.

    http://en.wikipedia.org/wiki/List_of_solar_cycles

    On the other hand, the last century included seven cycles between 10 and 10.5 years and two at 11.7 years.
    Cycles 9-14 averaged 11.7 years while the next five cycles (15-19) averaged 10.24 years.

    Looks bi-modal – five minutes work.

  12. Paul Vaughan says:

    OB: The summaries vary with the aggregation criteria.

    The reason people don’t find 11 year cycles is because they’re looking at the wrong variables and/or deliberately using the wrong aggregation criteria.

  13. Paul Vaughan says:

    The naive mainstream conventional theoretical assumption that the 11 year cycle shows up uniformly in SST harshly fails elementary diagnostics. That’s not where the 11 year cycle shows up. It does appear elsewhere with crystal clarity.

    I propose an illustrative cross-disciplinary exercise:
    1. Exhaustively list all the energy forms to which insolation energy can be transformed.
    2. Consider the evolving spatial distribution (including equator-pole gradients and gradients due to land-ocean geometry & physical property contrast).

    Given all the silly & egregious sun-climate obfuscation from lukes (that informatively actually works on their timid, functionally-innumerate followers), I think we’re more than way-overdue for this exercise.

    What belongs on this list?
    1. Exhaustively list all the energy forms to which insolation energy can be transformed.

  14. oldbrew says:

    I’ll start the ball rolling…

    ‘Labitzke and Van Loon (1997) …reported on statistically convincing correlations between the 11-year solar activity and selected parameters in the stratosphere and upper troposphere. A distinct 10-12 year period in height and temperature of certain isobar sheets was shown to be phase-locked to the solar activity cycle during the last three cycles. Although many meteorologists rejected the association, careful statistical tests demonstrated that the probability of the effect being just a coincidence is less than 1%.’

    http://www.tmgnow.com/repository/solar/lassen1.html

  15. oldbrew says:

    From the link above (lassen1):
    ‘The graph [Fig.7, lower frame] illustrates how the northern hemisphere land air temperature has varied with solar cycle length since the last decades of the sixteenth century (the second half of the seventeenth century excluded). The temperature decreases monotonically with increasing solar cycle length. The relationship is approximately linear with regression coefficient (-0.28+0.03)0 C/yr. The correlation coefficient is 0.83.’ [bold added]

    The authors say in conclusion:
    ’70-90 years oscillations in global mean temperature are correlated with corresponding oscillations in solar activity. Whereas the solar influence is obvious in the data from the last four centuries, signatures of human activity are not yet distinguishable in the observations.’ [NB written around 1990]

  16. Paul Vaughan says:

    It may not be clear to readers how this ties in with JEV. We each have different roles to play.

    All statistical inference depends on assumptions. I’m here to inform you that 2 of the regular distortion artists at wuwt deliberately base their statistical inference on false assumptions absolutely guaranteed to blind their “analyses” (actually tactically-designed false-front luke-thought-policing props that work quite well on a timid, functionally innumerate audience).

    It’s a turbulent system and the turbulence is proportional to the incoming energy. The more energy coming in, the more mixing (in contrast to silly, naive, & deliberately obfuscatory notions of static recording at the surface, as if insolation energy gradients don’t kinetically drive thermal mixing & energy form transformations).

    Signal distortion in naively-chosen static proxy-records is proportional to signal amplitude since turbulence is coupled to energy input. We know this from observations. How well do we know this? We have proof based on geometric axioms & laws.

    Reductionism as an operational modeling philosophy is mercilessly crushed in this context by impossible sampling requirements. The only sensible avenue available in this context is holistic.

    We can look at:

    1) the integral
    &
    2) pulse evolution, vigilantly keeping in mind that spatiotemporal pulse evolution will be highlighted by strong land-ocean geometry contrasts (such as between the northern & southern hemispheres).

    It’s like someone is turning the fan speed up and down on a schedule, but they’re not always punctual. When we measure their aberrations from punctuality, lo & behold the pattern that shows up exactly matches north atlantic aberrations from the integral.

    Too much for the functionally innumerate & politically invested, but earth orientation parameters prove it (in the rigorous sense) and it’s not going away unless someone f**ks with those records. I believe some very high-ranking administrators will be so tempted to mess with EOP records (once they understand) that they may not be able to resist. I don’t question that they (easily) have the means & the power to coerce scientists.

  17. oldbrew says:

    PV: ‘When we measure their aberrations from punctuality’

    Just wondering – how do we do that?

  18. Paul Vaughan says:

    OB, the spatial dimensions and energy allocation bins cannot be ignored. A full description of the spatiotemporal & energy-binning pulse aberration attractor existing due to land-ocean geometry needs both SCL & SCD (which aside from the secular are by mathematical definition necessarily orthogonal).

    What has been overlooked:
    global-scale eddy pulsing constraints — not only spatiotemporal eddies evolving with time in space, but also turbulence pulsing through the energy allocation bins, as kinetic energy stemming from insolation energy gradients pulses mass transport, thermal mixing, & energy form transformations

    Lassen seminally tried to summarize with real numbers alone what can only be fully summarized with complex numbers.

    Lassen used the real (as in real numbers (not as in not imaginary)) SCL.
    But a full description of the spatiotemporal & energy-binning central limit demands the complex pair SCL & SCD because the turbulence in the system is proportional to the forcing and the response is transient (not having time to equilibrate on decadal timescales).

    The signal is scrambled in naive cross-sections of time, space, & the energy bin spectrum by the turbulence that’s coupled to & coherent with the forcing.

    Laymen may have heard of the Doppler Effect. Well, this is analogous to a looping Doppler Effect, but timing on the looping schedule isn’t punctual and it’s the pattern of deviations from punctuality that governs how the more erratic north (due to land-ocean geometry) rocks about the more stable surface recording of the solar integral in the south.

    Any existing finer-scale spatiotemporal chaos is NOT FREE to remain deviant in global aggregate.

    For theoretical background, see the works of Rial on 400ka & 100ka.
    (I’m willing to dig for and share links — just ask.)

    A note for more technical readers:
    3 terms (SCL, SCL’ = SCD, & SCL”) account for almost all of the variance, so that’s all you’ll need to put into your system of differential equations when you start trying to model the global constraints properly.

  19. Paul Vaughan says:

    Correction:
    Turbulence in the system is proportional to the forcing and the response is transient (not having time to equilibrate on decadal timescales).

    (I accidentally wrote “multidecadal” above.) [amended – co-mod]

    oldbrew (March 6, 2015 at 6:23 pm) wrote:
    “PV: ‘When we measure their aberrations from punctuality’

    Just wondering – how do we do that?”

    Capable parties can do this (effortlessly) using multi-extent wavelets (or some other analogous tool sufficiently evolved that it doesn’t clumsily couple the extent to the grain) to measure SCL and then (numerically) take the derivative (which is SCD = solar cycle deceleration).

    oldbrew (March 5, 2015 at 1:07 pm) quoted & commented:
    “‘long-run average JEV = 11.07, but events cluster around 10.4 & 12′

    So we’re talking about 16 J-V (10.38~y) and half of 18.5 J-V (= 22 J-E = 15 V-E = ~24 years) there.
    11 J-E = 12.013y”

    JEV is a low-frequency component (with long-run attractor 11.07).
    The high-frequency content (which dominates by an order of magnitude the overall variance) is EV.

    Since I gained some background knowledge, I’m still in a position to comment strategically to augment JEV discussions when they arise. Unfortunately, my JEV explorations had barely begun in 2009 when I hit the limits of my time & resources. The project is permanently shelved (barring some kind of unexpected, miraculous financial support).

  20. Paul Vaughan says:

    Here’s an analogous illustration where orders of magnitude greater clarity is afforded by complex numbers:

    Rial (2012)

  21. Paul Vaughan says:

    @ TB (March 5, 2015 at 3:44 pm)

    OK, I’ve explored the orbital origins of the pattern in Vukcevic’s first illustration.
    From a naive first-order approximation one would expect:
    (11.06964992)*(9.932517933) / (11.06964992 – 9.932517933) = 96.69017963
    However, even a novice is aware of solar cycle asymmetry (shape in time).
    Assuming the basic shape can be corrected by including a harmonic
    (5.534824961)*(4.966258966) / (5.534824961 – 4.966258966) = 48.34508981
    then we could look on the solar axis of rotation for asymmetries with period
    (48.34508981)*(11.06964992) / (48.34508981 + 11.06964992) = 9.007246722
    This is SEV and indeed that’s exactly what’s observed.
    Now, vukcevic’s first illustration is not based on the parker spiral.
    So what do I find when I extend the calculations using the assumption suggested by TB?
    I think we had better check to make sure everyone has understood Rial & SCD before we proceed.