Cheeky Pukitee: nicking knowledge without acknowledgement

Posted: September 10, 2015 by tallbloke in ENSO
Tags: ,

Last week I told Paul Pukite where he was going wrong with his ENSO model:

This week, he’s ‘discovered’ that The Moon and the tides it raises underlie both The El Nino Southern Oscillation (ENSO) and  the Quasi Biennial Oscillation (QBO), which he previously thought was the driver of ENSO along with the Chandler Wobble (CW), as seen in the tweets above. He hastily added ‘tides’ though they get no mention in his original post.

Today he’s even accused me of being ‘secretive’ 🙂

Long after I alerted him to this post on the relationship between Sun, Moon, and El Nino which I put up last year. In that post, I did a rough plot using Ian Wilson’s Lunar data, plus some solar data I overlaid which shows that as well as the peaks of El Nino coinciding with Lunar alignments as Ian discovered, El Nino is initiated by reversals in the TSI trend at the end of solar Max and start of solar min:

Luni-Solar forcing of El Nino

I don’t mind people taking ideas from this blog and developing them further. In fact, I encourage it. It’s a bit thick when someone does that, then claims prior art, calls you a denier, and says you’re secretive though. 🙂

Pukite has a spectrum plot of ENSO on the new post he has put up.


I think the ~0.425 year peak relates to the 19yr Metonic cycle, but I’m double checking that – update as I have time.


Attribution: Meton of Athens 432BC

  1. tallbloke says:

    The discussion continues… 🙂

  2. Ian Wilson says:

    Paul Pukite is doing his own original investigations and much of what he has done is excellent work.
    However, he should be much more willing to acknowledge that others have been proposed similar ideas that he now claims his own. Much of his work has been already been investigated and discussed by Nikolay Sidorenkov, Paul Vaughan, Rog Tallbloke and myself [amongst others].

    For example, here is a quote from Paul Pukites web page:

    “What’s intriguing is that the driving force isn’t at this monthly level anyways, but likely is the result of a beat of the monthly tidal signal with the yearly signal. It is expected that strong tidal forces will interact with seasonal behavior in such a situation and that we should be able to see the effects of the oscillating tidal signal where it constructively interferes during specific times of the year. For example, a strong tidal force during the hottest part of the year, or an interaction of the lunar signal with the solar tide (a precisely 6 month period) can pull out a constructively interfering signal.”

    This is what I [and others e.g. Paul V. and Nikolay Sidorenkov] ] have be saying for quite some time! I have tried to point out that the strongest lunar tides are most likely to have their greatest impact when they are synchronized with the seasons. This by its very nature means that we must look for long term lunar tidal cycles that synchronize with the seasons.

    The long term cycles which should play a role are:

    1. The 18.6 year Nodal (Draconic) Precession Cycle

    This is the time that it takes for the lunar line-of-nodes to make one circuit of the Earth with respect to the stars. It is important to not that the nodes move is a retrograde (backward) direction with respect to the revolution of the Earth around the Sun.

    2. The 8.85 year Apsidal Precession Cycle

    This is the time that it takes for the lunar line-of-apse to make one circuit of the Earth with respect to the stars. It is important to not that the apse move is a pro-grade (forward) direction with respect to the revolution of the Earth around the Sun.

    3. The 20.293 year Perigee-Syzygy Cycle

    This is the time it takes for a new moon at closest perigee to return to the next new moon a closest perigee. This particular tidal cycle re-synchronizes the phase of the Moon with the Apsidal Precession Cycle.

    Of course, these long-term long-term tidal cycles are modulations that are the result of long term beats between the monthly lunar tidal cycles:

    A. The Draconic Month (27.21222 days) and the Sidereal Month (27.32166 days)
    [i.e. the beat between the time it takes the Moon to return to the same node and the time it takes the Moon to return to the same point in its orbit with respect to the stars.]

    (27.32166 x 27.21222) / (27.32166 – 27.21222) = 6793.52 days = 18.6 years.

    B. The Anomalistic Month (27.55455 days) and the Sidereal Month (27.32166 days)
    [i.e. the beat between the time it takes the Moon to return to the perigee of its orbit and the time it takes the Moon to return to the same point in its orbit with respect to the stars.]

    (27.32166 x 27.55455) / (27.55455 – 27.32166) = 3232.58 days = 8.85 years.

    C. Synodic Month (29.5305889 days) and the Anomalistic Month (27.55455 days)
    [i.e. the beat between the time it takes the Moon to return to the same phase each month and the time it takes the Moon to return to the perigee of its orbit.]

    (29.5305889 x 27.55455) / (29.5305889 – 27.55455) = 411.784448 days = A Full Moon Cycle

    One Full Moon Cycle is the time for the lunar line-of-apse to re-align with the Sun.

    and 18 Full Moon Cycles = 20.293 years

    Hence, it would make sense that if you are looking for a possible influence of these long-term tidal cycles on say the QBO then we should look at sub-multiples of these tidal cycles.

    20.293 years/ 8 = 2.537 years = 30.4 months
    18.60 years / 8 = 2.325 years = 27.9 months
    8.850 years / 4 =2.213 years = 26.6 months

    It know from observation that roughly half the QBO events have periods of ~ 26 months
    and the other half periods of ~ 30 months giving an average QBO length of ~ 28 months.

    Nikolay Sidorenkov has pointed out for decades that this must mean that there is a link
    between the Chandler Wobble, the QBO, the ENSO and sub-mutiples of the long-term
    lunar tidal periods.

  3. tallbloke says:

    Thanks Ian for the excellent work you’ve done in this area, and for freely sharing it. A few more references to your work Mr Parakeet should look at and list on his website:

    Wilson, I.R.G., Long-Term Lunar Atmospheric Tides in the
    Southern Hemisphere, The Open Atmospheric Science Journal,
    2013, 7, 51-76

    Wilson, I.R.G., 2013, Are Global Mean Temperatures
    Significantly Affected by Long-Term Lunar Atmospheric
    Tides? Energy & Environment, Vol 24,
    No. 3 & 4, pp. 497 – 508

    Lunar Tides and the Long-Term Variation
    of the Peak Latitude Anomaly of the Summer Sub-Tropical
    High Pressure Ridge over Eastern Australia
    The Open Atmospheric Science Journal, 2012, 6, 49-60

  4. tallbloke says:

    Of course, something that hasn’t sunk into Parakeet’s brain yet is that since he now realises that we were right about the lunar influence on ENSO, and the predominance of El Nino over La Nina during ‘the global warming years’ (and the positive phase of the PDO), calling us ‘deniers’ is now looking a little, how shall I put this delicately?, – stupid?

  5. Chaeremon says:

    @Ian Wilson said (September 10, 2015 at 11:33 am) … then we should look at sub-multiples of these tidal cycles.

    Some time ago I began to look at 1039 synodic / 37 (37 synodic being 3 years and part of the anomalistic / draconic wobble) which gives the continued fraction 28; 12, 3 synodic. The 1039 synodic is commensurate with anomalistic and draconic (yields eclipses in long series), it is on the full-moon cycle (etc) and returns to equinox like Metonic (indispensable for seasonal happenings).

    FWIW I think the Chandler Wobble, with its reported irregularities, it a bit to high the bar IMHO.

  6. gymnosperm says:

    The really crazy thing about Ninos is their relationship to sea level.

    Credit forgotten, not my work.

    You can’t just increase GMSL by sloshing water from one side of the Pacific to the other whether by tidal forces or Rossby and other reaction waves. To raise sea level NEW energy is required, possibly thermal causing a temporary expansion that is rapidly dissipated to the atmosphere, or a gravitational effect that physically lifts the oceans.

  7. A C Osborn says:

    Does this guy have a website where we can all go and call him out?

  8. Paul Vaughan says:

    @ gymnosperm (September 10, 2015 at 4:28 pm)

    I’m always surprised to discover that some climate commentators are unaware that ENSO is also a cycle of precipitation over continents.

    Folks: Thinking of ENSO only temporally doesn’t cut it. It’s spatiotemporal.

  9. Paul Vaughan says:

    The classic piece of work on this is Dickey & Keppenne (NASA JPL 1997) and we are all just slowly waking up to what that illustrious paper leaked graphically (with no mention whatsoever in the text).

    The lunar signals are trivial and easily modeled near-perfectly using nothing more than conventional (e.g. fourier) methods. This is well-documented in mainstream literature …and uncontroversially verified by skeptics.

    Timing on the seasons…

    Why this matters:
    1. water physics — e.g. latent — e.g. you heat ice but some of the variables like temperature don’t change, so multivariate spatiotemporal conceptualization is needed
    2. nonlinear terms in the physical relationships
    3. asymmetric planet which thus guarantees physical aliasing due to 1 & 2.

    ENSO is the great distorter of simple solar & solar system pattern. It’s just an expression of the finger-pattern (chord) on the strings being strummed by the sun.

    What’s (GROSSLY) insufficiently appreciated:

    Take ANY given variety of physical set ups

    You’ll get different spatiotemporal output pattern.

    The challenge is probably the greatest unsolved problem in physics & math:
    aggregate asymptotic stats of turbulence

    Where you have the COLLECTIVE turbulence CLEARLY shaped by something as simple as THE YEAR, you canNOT sensibly pretend it’s ONLY turbulence. In aggregate it’s NOT turbulence. In components it IS turbulence. SO WE’RE DEALING WITH A SCALED PARTITION OF UNITY.

    The thing that changes is the sun and IT scales the unit through integration.

    …but be careful:
    It’s a spatiotemporal integral disturbed by a chord pattern (the fingers on the string) that has a simple asymmetry due to the present distribution of continents.

    Imagine a fan blowing from a fire to a freezer.
    Imagine that fan has ADJUSTABLE SPEED.

    Now imagine 2 fans.

    One fan is blowing from equator to north pole
    The other from equator to south pole.

    There’s a wind and pressure ring wall over ocean surrounding the south pole.
    The north in contrast has 2 western boundary streams that penetrate. ONE of them makes it all the way to the ice margins where the lion’s share of global downwelling occurs.

    …so global thermohaline circulation IS COUPLED TO the Atlantic western boundary fan speed.

    How do we measure that fan speed? That’s simple. That’s SCD (solar cycle deceleration).

    Recognition of global spatiotemporal integral is thwarted by ignorance of such WATER CYCLE ASYMMETRIES & NONLINEARITIES.

    As Dickey & Keppenne have also illustrated, ENSO is another aberration of the unit. (Keep in mind that I’m using the term “unit” in the sense of “scaled partition of unity”.)

    We cannot sensibly discuss the aggregate statistics of turbulence until people deeply understand firsthand the implications of asymmetric variable fire-to-freezer fan speed. (Remember: Years ago I derived the implications ALGEBRAICALLY. That was a GEOMETRIC PROOF — in the mathematical sense — of the long run aggregation & aliasing implications.)

    I see absolutely zero scope to sensibly discuss ENSO before we get this fire-to-freezer fan speed algebraic proof — and long run aggregate turbulent differintegral structure more generally — deeply understood and acknowledged firsthand by community members. Acknowledgment of a simple geometric proof is prerequisite for intellectual trust.

    Lukewarmist agents of devilishly dark ignorance &/or deception ARE EXPOSED if they’re unable &/or unwilling to acknowledge what’s IMPLIED by the LAWS of large numbers & conservation of angular momentum.

    In other words they can run but they can’t hide.

    In order to be sensible, they NEED to acknowledge the role of fan speed bounding aggregate turbulence.

    The ONLY weasel room available: They can suggest that CO2 plays a role in SCALING unity. Of course the problem is that observations do not support such a suggestion …and I believe that is EXACTLY WHY NOAA has boldly gambled by hinging their credibility TO A SINGLE STRATEGIC POINT in this boldly genius mirror-trick:

    Who would DO such a thing??

    Answer: Someone brilliantly conscience of how to LEVERAGE ENSO pattern to distort the appearance of unity scaling. It’s very impressive that they even figured this out.

  10. tallbloke says:

    gymnosperm, that’s a nice correlation. This appears to be the source

    I would hazard a guess that a drop in cloud cover would be the primary culprit. Nothing else can make such a difference to the number of Joules absorbed by the ocean.

  11. Paul Vaughan says:

    conscious rather — conscience didn’t deter the strategic vandalism

  12. Paul Vaughan says:

    @ tallbloke (September 10, 2015 at 8:53 pm)

    SST, pressure pattern, cloud cover, OLR, wind, evaporation, sea surface height (SSH) precipitation over land (where the water goes) — it’s all coupled together as Bill Illis has illustrated countless times — NASA has a very effective short video of ENSO SSH, SST, & wind vectors that makes it all easy to perceive at least for that trivariate subset of variables involved in the multivariate coupling

    dog chases tail without sufficient awareness of whole self is conceptual risk

  13. Paul Vaughan says:

    Let me state this explicitly so I can observe how it provokes:
    ENSO affects the partitioning of unity but not the scaling of unity.

    Any objections to this statement are sure to be informative.

  14. tallbloke says:

    Paul V, I’m not sure what you mean by unity. Surface climate over some long period?

  15. Paul Vaughan says:

    Not just the surface but certainly that’s a cross-section from which we alias our samples.

    I’m encouraging focus on quantities which are conserved in long run tuned spatiotemporal aggregate versus those which are turbulently stirred on shorter spatiotemporal scales and aliased.

    For example diagnostics based on geometric axioms and laws of large numbers & conservation of angular momentum point to something simple about Abreau+ (2012) which I’ve outlined in a series of points converging towards clearer awareness here:

    The butterfly’s wings are flapping, but there’s something systematic about the course it’s flying; there are attractors directing its flight. You might even call them nature’s flowers.

  16. Paul Vaughan says: September 11, 2015 at 12:10 am

    “Not just the surface but certainly that’s a cross-section from which we alias our samples.”

    Do you have a consistent definition “with examples” of what you term UNITY?

    “I’m encouraging focus on quantities which are conserved in long run tuned spatiotemporal aggregate versus those which are turbulently stirred on shorter spatiotemporal scales and aliased.”

    What is a long run spatiotemporal aggregate? If fourspace, is it long ‘time’ integration, as in power to energy, or aggregation into an ever decreasing time interval, Planck’s constant?
    What does turbulently stirred mean? How is that associated with “those”?

    For example diagnostics based on geometric axioms and laws of large numbers & conservation of angular momentum point to something simple about Abreau+ (2012) which I’ve outlined in a series of points converging towards clearer awareness here:

    Geometric axioms. Of what kind, in how many dimensions?
    Laws of large numbers. RMS variance = root (large number)! What else?
    Conservation of angular momentum. Over what volume must the vector sum remain zero? Is angular separate from linear, or just the same expressed in an orthogonal direction?
    Point to something simple about Abreau+ (2012). What is this ‘something’, that is simple, to any except you?

    What is “it” that you claim awareness thereof? Can “it” be expressed in earthling terms?
    All the best! -will-

  17. tallbloke says:

    Paul V: I’m encouraging focus on quantities which are conserved in long run tuned spatiotemporal aggregate

    Such as?

  18. Paul Vaughan says:

    Will, the lukewarmists will love your style of deflection.

  19. tallbloke says: September 11, 2015 at 5:26 am

    (“Paul V: I’m encouraging focus on quantities which are conserved in long run tuned spatiotemporal aggregate”)

    “Such as?”

    Will he ever answer?

    Paul Vaughan says: September 11, 2015 at 5:28 am

    “Will, the lukewarmists will love your style of deflection.”

    I take it that you have no answers to Roger’s or my questions!
    Paul is the only one in this thread deflecting questions just like his “lukewarmists”.

  20. TLMango says:

    In my work I found that there is a 19 year cycle that keeps emerging.
    This 19 year cycle appears to be almost as strong as the 61 year signal.
    I’d like to hear more about the metonic cycle, they may be one and the same.

  21. Paul Vaughan says:

    Busy week at work, but I managed to take a quick look at some of the stuff Pukite has been doing.

    I’ll never have time to comment on everything, but I suggest caution with one thing …and Tim Channon might be someone who could look at this from a different angle.

    Pukite considered calendar month aliasing of higher-frequency components of QBO. That’s the kind of stuff that’s really interesting, especially when we’re dealing with turbulent media and spatial dimensions beyond just time.

    The software spit out a clear suggestion of the lunar synodic month …and that suggested a lower-amplitude modulation of what Piers Corbyn showed us years ago, meaning (if you understand and follow what I’m saying with minimal words) that the QBO would have an 18.6 year envelope (something Tim Channon could explore using a different tool set if he has time & interest).

    But here’s the caution — and I’m going to say this with numbers because that’s how it’s best said (some people won’t get it because of this, but they can take independent responsibility for developing direct firsthand awareness, as that’s the responsible option):

    The average calendar month length is the harmonic of the terrestrial year nearest the length of the lunar synodic month:

    (365.24219) / 12 = 30.43684917

    But the harmonic of the terrestrial year nearest the length of the lunar draconic & tropical months is:

    (365.24219) / 13 = 28.09555308

    What I learned from Piers Corbyn years ago (I’ve shown this countless times over the course of years, so it should be nothing new to anyone):

    (28.09555308)*(27.212221) / (28.09555308 – 27.212221) = 865.5209286
    (865.5209286) / 365.24219 = 2.369717826

    Now let’s compare 2 other quantities:


    (30.43684917)*(29.530589) / (30.43684917 – 29.530589) = 991.7881379
    (991.7881379) / 365.24219 = 2.715425997


    (28.09555308)*(27.321582) / (28.09555308 – 27.321582) = 991.7876522
    (991.7876522) / 365.24219 = 2.715424667

    So there you can perhaps recognize the need to think very carefully about the difference between what’s happening at high frequency what’s in measurements due to calendar month aliasing, polynomial dissipation, &/or whatever else.

    Either way:

    (2.715424667)*(2.369717826) / (2.715424667 – 2.369717826) = 18.61343046

    …and the whole point here is that we know what that is from base elements:

    (27.321582)*(27.212221) / (27.321582 – 27.212221) = 6798.410105
    (6798.410105) / 365.24219 = 18.61343046

    That’s the beat of tropical & draconic lunar months, no matter how it gets aliased by measurement systems and/or aggregated by summary systems.

    Are higher-frequency measurements going to resolve this?

    We already have them in earth orientation parameters …and for anyone who knows how to sensibly measure cyclic volatility therein, we already have the answer.

  22. Paul Vaughan says:

    Other points I’ll quickly note:


    Pukite refers to some 2.9 year earth-moon oscillation. That’s a loose end I’m leaving for now because I haven’t yet had time to figure out what he referred to only vaguely. If someone can shorten my investigation with a useful note or link, please do share.


    Pukite shows a calculation of 2.3 from Sidorenkov that isn’t consistent with the observations I’ve seen, so I’d recommend hard-headed scrutiny before buying into that.


    Pukite isn’t clear on where the factor 2 (as in 2 Chandler = 1 QBO) comes from. That’s simple. Earth has 2 hemispheres that are asymmetric and the oscillation is about the equator …so really you need complex numbers to represent it since the polarity (north vs. south) alternates.

    Maybe others are confused about this too and this could have been a source of many past misunderstandings.

    This is an excellent opportunity to make a more general point:

    My instinct about what goes wrong in general is that climate physical modelers start from false assumptions about geometry and then get caught in flawed circular reasoning about the geometry.

    = = = = = = = =
    No matter what physics an experimenter is dealing with it can be reconfigured geometrically to produce different spatiotemporal patterns, so it makes no sense when physical modelers assume the same spatiotemporal patterns will result no matter what the geometric set-up of the physical apparatus.
    = = = = = = = =

    Arguments based on false geometric assumptions (almost always subconscious but implicit from context and never stated explicitly) are widespread and seriously problematic in the online climate discussion.

    Just remember Polya’s simple, effective problem-solving tip:
    Use symmetry.

  23. Paul Vaughan says:

    This is probably an ideal opportunity to remind of the nonlinear importance of asymmetric wind and ice geometry:

    Bill Illis’ classic on Drake Passage status (open vs. closed):

    Jose Rial’s differintegral classic:


  24. Paul Vaughan says:

    eau (french) = water (english)

    Because of spatiotemporal memory, equator-pole & interhemispheric heat engine dissipation is asymmetrically polynomial …so now with a little way-past-due revelation the host of Climate Etc. can wave goodbye to some of her confusion & silly notions about chaos …if she understands a basic lesson seemingly framed especially for her correction (very clever):

    “demonstrates how the memory effects strangle the chaotic”
    “chaotic sequences which are presented in the system without any memory are squeezed out”

    Click to access 1111.3214.pdf

    Chaos is “washed out because of the memory effects.”
    “As the memory mounts, chaos and its traces disappear.”

    (Let’s just hope she doesn’t again forget tomorrow what she learned today as we’ve seen happen so many times before.)

    Generalize from temporal to spatiotemporal.

    intergyre (subtropical-subpolar) context:

    Sea-level fluctuations show ocean circulation controls Atlantic multidecadal variability

    Click to access McCarthy_NA_session_Mon_1145_EGU2015.pdf

    It’s a lot simpler with fractional differintegral calculus (…as I generalized years ago with a simple algebraic proof).

  25. Paul Vaughan says:

    more quotes from the correction paper:

    “Fractional calculus occupies an appreciable place in order to describe various kinds of wave propagation in complex media […]

    The fractional operator is a natural generalization of the ordinary differentiation and integration. When the operator depends on time, it is characterized by long-term memory effects.

    Appearance of long-term memory effects […] makes the coupling among states stronger. This feature is plainly directed against the development of the chaotic dynamics.

    […] fractional chaotic attractor”

  26. Paul Vaughan says:

    Roger is concerned with confounding, perhaps if for no other reason than to encourage very careful thinking. I can support that goal easily, so I choose to do so now with what follows.

    For those ready & able, hypercomplex numbers provide a superior conceptual framework for exploring long-run confounding. I’ve already outlined parts of this before, so this is a combination of reminder, synthesis, & extension:

    27.03 days = long-run average equatorial solar rotation period

    (27.212221)*(27.03) / (27.212221 – 27.03) = 4036.561832
    (4036.561832) / 365.24219 = 11.0517403 (indistinguishable from average solar cycle length)

    (365.24219) / 27 = 13.52748852
    (27.212221) / 2 = 13.6061105

    (13.6061105)*(13.52748852) / (13.6061105 – 13.52748852) = 2341.031097
    (2341.031097) / 365.24219 = 6.409530885 (polar motion envelope)

    – –
    Recall annual ecliptic geocentric z-axis 6.4 year aliasing tip, complete with simple Horizons recipes:
    – –

    harmonic mean:
    (6.409530885)*(5.525870152) / ( (6.409530885 + 5.525870152) / 2 ) = 5.934988744 years

    That’s not actually a G oscillation but rather an estimate of G that oscillates (with the concert of gravitational & thermal tides) in some observing systems.

    Similarly (it’s a direct analogy) I’ve outlined the geometric backbone of a 208 year circulation (& therefore deposition) anomaly expected from seasonal (physical) orbital aliasing. See the Suggestions-13 thread and I’m still waiting for someone sensible to get serious about discussing the geometry.

    The challenge is to carefully discern the role of the proximate & the distal in aggregation criteria specifying the morphology of observations.

  27. Paul Vaughan says:

    I did a little digging on the 2.9 year oscillation. That’s a cycle in moon rotation rate or libration. Some of the articles mention the moon’s Chandler wobble equivalent and Roger (thinking of Norwegian Harald Yndestad’s work) will probably be thrilled to learn that it has a period of 74 years. I may post some links to material if/when I can find some time to go over the material a little more thoroughly. Noteworthy: Jean Dickey has published about this.

  28. Paul Vaughan says:

    2.369717826 & 6.409530885 were derived above.

    This was quick & nice:

    2*(6.409530885) = 12.81906177
    (12.81906177)*(2.369717826) / (12.81906177 – 2.369717826) = 2.907125974
    (12.81906177)*(2.369717826) / (12.81906177 + 2.369717826) = 2
    (12.81906177)*(2.369717826) / ( (12.81906177 + 2.369717826) / 2 ) = 4

    Now that answers a few questions about the annual interhemispheric heat engine (volatility weave)…

    Sometimes the stuff just falls together quickly.

  29. Paul Vaughan says:

    (12.81906177)*(2.907125974) / (12.81906177 + 2.907125974) = 2.369717826

    (2.907125974)*(2) / (2.907125974 – 2) = 6.409530885
    (2.907125974)*(2) / (2.907125974 + 2) = 1.184858913
    (2.907125974)*(2) / ( (2.907125974 + 2) / 2 ) = 2.369717826

    That was too easy.

  30. Paul Vaughan says:

    Probably tomorrow I’ll derive the frequency algebra for 2.9. Then if we’re lucky Ian Wilson will consult the libration literature and help us expedite an assessment of synchrony.

  31. Paul Vaughan says:

    What resonance keeps this 2.9 year thing from dissipating?
    Is that known?
    The high frequency component here?

    (1)*(0.542304542) / (1 – 0.542304542) = 1.184858913
    (2.907125974)*(0.542304542) / (2.907125974 – 0.542304542) = 0.666666667
    (2.907125974)*(1.184858913) / (2.907125974 – 1.184858913) = 2
    That would certainly simplify bidecadal oscillation (BDO) focus.

  32. Paul Vaughan says: September 13, 2015 at 12:20 am

    “Roger is concerned with confounding, perhaps if for no other reason than to encourage very careful thinking. I can support that goal easily, so I choose to do so now with what follows.”

    Paul, you are deliberately confounding for some political reason the balance ‘tween the conceptual of all, including your fantasy, and the physical/measurable ‘is’!

    “For those ready & able, hypercomplex numbers provide a superior conceptual framework for exploring long-run confounding. I’ve already outlined parts of this before, so this is a combination of reminder, synthesis, & extension:”

    Good God Paul.
    You insist on introducing your hypercomplex numbers that do indeed provide a superior conceptual framework for exploring long-run confounding that you have already outlined parts of this before, so this is a combination of reminder, synthesis, & extension:

    Paul; can you identify by name, any other that would claim understanding of your hypercomplex numbers that do indeed provide a superior conceptual framework for exploring long-run confounding? I can see some twinkling of concept, but nothing further, I wish only to cry!

  33. Ian Wilson says:


    Where do you get the 0.542304542 year value from – its roughly 198 days – is that a significant fraction of the annual cycle or lunar cycles?

  34. Ian Wilson says:


    If you are talking about the wobbling of the Moon that allows us to see round edges of the visible face of the Moon (sometimes called Lunar Nutation), this comes about because the Moon rotates a constant rate (once per Lunar sidereal orbit = 27.32166 days) but its tangential speed with respect to the Earth surface varies as the Moon moves nearer and further away from the Earth along its elliptical orbit (with the distance variations taking place over one anomalistic month = 27.55455 days).

    When the Moon is at the apogee of its orbit (i.e. furthest from the Earth) its tangential orbital speed is at its slowest – and so the Moon is rotating at too high a rate to keep the same face towards the Earth. Similarly, when the Moon is at the perigee of its orbit (i.e. closest to the Earth) its tangential orbital speed is at its fastest – and so the Moon is rotating at too low a rate to keep the same face towards the Earth.

    Hence, you would expect that this wobble to complete itself in one anomalistic month (27.55455 days) as it travels from (say) perigee back to perigee. However, the point of perigee in the Moon’s orbit precess towards the east (in a pro-grade direction) and so the wobble cycle will end at a slightly later point in the Lunar phase cycle (i.e. the synodic month = 29.5305889 days).

    If you want the wobble to roughly end at the same point in the phase cycle of the Moon you will have to wait until the perigee of the Lunar orbit returns to the same position in the sky with respect to the Sun. This will about one Full Moon cycle = 411.7844 days.

    However this is not an exact alignment since:

    14 Synodic months = 14 x 29.5305889 days = 413.42824 days
    15 Anomalistic months = 15 x 27.55455 days = 413.31825 days

    Now here is the desperate speculation need to get the 2.9 years:

    The beat period between ~ 413 days and the tropical year is 8.648 topical years
    And one third of this period is 2.88 years

    But I have no idea why it would be 1/3 of the beat period! Open to ideas.

  35. Ian Wilson says: September 14, 2015 at 10:28 am


    “Where do you get the 0.542304542 year value from – its roughly 198 days – is that a significant fraction of the annual cycle or lunar cycles?”

    Dr. Wilson,
    That is the nutation rate plus/minus a few cows!

  36. Paul Vaughan says:

    frequency algebra:

    1 / T = 1 tropical year = 365.242189 days
    1 / D = 1 lunar draconic (or nodal) month = 27.212221 days

    1 / 2.369718033 = D – 13T
    1 / 6.409527865 = 27T – 2D

    1 / 2.907013783 = 2D – 53T / 2 = 1061.805281 solar days

    “A recent analysis of the forced and free libration amplitudes, phases, and periods was made by Rambaux and Williams [1]. That study extracted a series of periodic terms by analyzing the numerically integrated DE421 physical librations [2] that resulted from a fit to Lunar Laser Ranging (LLR) observations.

    Mantle Modes: The three modes for mantle+crust are familiar. (1) The libration in longitude is a sinusoidal speeding up and slowing down of the rotation about its polar axis, the axis corresponding to the largest moment of inertia. LLR data analysis finds a period of 1056.1 d and an amplitude of 1.30″, or 11 m at the equator [1]. (2) The wobble mode is analogous to the Chandler wobble of the Earth. Viewed from the rotating Moon, the mean axis of rotation appears to trace out an elliptical path about the polar axis, but equivalently, the pole can be considered to wobble about the axis of rotation. LLR finds semiaxes of 3.3″x8.2″ (28 m x 69 m) and a period of 74.6 yr [1]. (3) The latitude mode is a retrograde free precession of the pole in space. The period is 80.9 yr. Although [1] saw a small term when analyzing DE421 physical librations, the amplitude was small and it was considered uncertain.
    Longitude Libration Modes: Model calculations indicate that the 2.9 yr mantle mode involves mantle and inner core liberating in phase, but with different amplitudes. The inner core mode has a model period of roughly 2 yr with most of the motion in the core. Van Hoolst et al. [13] have developed a theory for the librations of an icy shell and a solid core, an analogous situation.”

    Williams, Boggs, & Ratcliff (JPL 2014). Free libration modes of a structured Moon.

    Click to access 1579.pdf

    Note the Earth-Moon angular momentum match (J+N ~= JEV):
    (12.81855828)*(11.06602004) / (12.81855828 – 11.06602004) = 80.93998719
    Recall that the long JEV cycle has period N and that from daily resolution LOD the intersection of cyclic volatility of barycentric annual interhemispheric & heliocentric semi-annual equator-pole heat engines has period N/2, so this bundle appears to (unsurprisingly) satisfy a near-resonance condition.

    Ian, this link answers your question about 0.54:

    That’s just J+N J-N beating with the year:
    (12.78279303)*(1) / (12.78279303 – 1) = 1.084869521
    In absolute frequency deviations (off-resonance whether above or below is off-resonance either way, so absolutes indicate the cycle of on- & off-resonance) it becomes:
    (1.084869521) / 2 = 0.54243476
    Alternatively it’s absolute solar barycentric radial acceleration period beating with the semi-annual equator-pole heat engine:
    (6.391396515)*(0.5) / (6.391396515 – 0.5) = 0.54243476
    The near-matching number I gave above is from the analogous lunar context.

    It looks like the period (stemming from absolute solar barycentric radial acceleration) rocks plus or minus 10 days across the sweet spot needed to prevent the 25ka damping estimated by Williams+ (2014).

  37. oldbrew says:

    PV says:
    ‘That’s just J+N beating with the year: (12.78279303)*(1) / (12.78279303 – 1) = 1.084869521’

    Yes, x 2604 = 2825 years = 221 J-N (2825 – 2604 = 221)

    I must do that J-N ‘Why Phi?’ post soon or PV will say I’m pinching nicking his numbers 🙂

  38. Paul Vaughan says:

    Point of clarification:

    This is about trying to understand Pukite’s 29.5 day (suggested from QBO input by his software) & his decision to put a 2.9 year term in his model. (Maybe some talkshop readers have not yet explored the links to the various pages at Pukite’s website?)

    Keep in mind that the beat of the tropical year and the lunar tropical month is 29.53 days.

    Here are some links that can help with 2.9 year libration in longitude background:

    Rambaux & Williams (2010). The Moon’s physical librations and determination of their free modes. Celestial Mechanics and Dynamical Astronomy. Springer Verlag (Germany). 109(1), 85-100.

    Williams & Dickey (2002). Lunar Geophysics, Geodesy, and Dynamics.

    Click to access williams_lw13.pdf

    A Summary of LLR Activity and Science Results

    Click to access Shelus_et_al_LLR.pdf

    Table II from an old book lists candidate resonance periods near 2.9 years

    That’s probably enough for now.

  39. Paul Vaughan says:

    welcome back OB!

  40. Paul Vaughan says:

    Thanks to Ian Wilson for pointing this out at contextearth:

    Bizouard, Zotov, & Sidorenkov (2014). Lunar influence on equatorial atmospheric angular momentum.

    Click to access 54fd6ae60cf2c3f52424b91a.pdf

    That’s a classic piece of work.

  41. oldbrew says:

    Note: I misread the data in the BZS Eckhardt paper so I’ve withdrawn the comment I made on it.

  42. Paul Vaughan says:

    OB, your comment was on the Eckhardt (1993) article, not BZS.

    I think we might benefit from consideration of the philosophical elements of this piece emphasizing 2.9 year earth-moon spin-orbit resonance:

    Bois (1995). Proposed terminology for a general classification of rotational swing motions of the celestial solid bodies.

    With the advantage of hindsight we see that Eckhardt’s (1993) proposal was off-track (less info was available then).

    I’ll have more commentary & calculations later in the week — just too busy to wrap this up today….

    Just one brief comment now: These librations are about non-uniform mass-distribution. Never mind point mass distortion artist BS!!

  43. Paul Vaughan says:

    Bizouard, Zotov, & Sidorenkov’s (2014) 25.82 hours:

    (29.530589) / 2 = 14.7652945

    (365.242189)*(14.7652945) / (365.242189 + 14.7652945) = 14.19158495 days

    24*(14.19158495) = 340.5980388 hours

    (340.5980388)*(24) / (340.5980388 – 24) = 25.81934166 hours

    frequency algebra:
    ( 1 – (T+2Y) ) / 24

    1 / T = 365.242189 days (tropical year)
    1 / Y = 29.530589 days (lunar synodic month)

    period = 1 / frequency
    24 / ( 1 – (T+2Y) ) = 25.81934166 hours

    The paper makes a simple point with implications that may look profound & unbearably inconvenient to reluctant mainstreamers who are willing and able to clue in. It will be informative observing the duration of mainstream ignorance.

  44. Paul Vaughan says:

    Talkshoppers: This paper is a big deal.

  45. Paul Vaughan says:

    BZS14 is a conceptual game-changer — alternative link:

    Click to access Bizouard.pdf

    “Brezinski (1994) introduced the concept Celestial Equatorial Angular Momentum [CEAM] […] Whereas the diurnal band is squeezed in a frequency band around 24 h in the TRF [Terrestrial Reference Frame], the corresponding periodicities of the CEAM stretch from 2 days to several years with respect to the non-rotating reference frame: any diurnal component of frequency σ = -Ω + σ′ with σ′ ≪ Ω is mapped to a long periodic celestial component of frequency σ′.”

    a minimal outline for those trying to follow BZS’s perception in the celestial reference frame…

    1 solar day = 24 hours
    0.5 solar days = 12 hours

    List of principal tide constituents:


    derivation of 25.819 hours outlined above


    (365.242189)*(1) / (365.242189 – 1) = 1.002745426 days
    24*(1.002745426) = 24.06589023 hours


    (365.242189)*(1) / (365.242189 + 1) = 0.997269566 days
    24*(0.997269566) = 23.93446959 hours


    (14.7652945)*(0.5) / (14.7652945 – 0.5) = 0.51752505 days
    24*(0.51752505) = 12.4206012 hours


    (182.6210945)*(0.5) / (182.6210945 + 0.5) = 0.498634783 days
    24*(0.498634783) = 11.9672348 hours


    2Y+A = 1 / 9.613717876 solar days
    for a derivation see:

    (9.613717876)*(0.5) / (9.613717876 – 0.5) = 0.527431176 days
    24*(0.527431176) = 12.65834823 hours

  46. Paul Vaughan says:

    I’m repeating this (see 2nd graph on p.4 of ERSST EOF 1234) for those trying to solve IPO (including PDO & ENSO):

    The quality of (Chandler frequency) heliocentric-barycentric resonance cycles bidecadally.
    The proportion of time spent near-resonance oscillates with the BDO.

    There’s no heliocentric BDO so you don’t see thermal tide signature.
    This is barycentric BDO, so we do see gravitational tide signature (in the multivariate geophysical record).

    I’m confident that NASA JPL has this problem well-solved and classified.

    Now a little observation-based provocation to help stir a check of who’s willing & able to be sensible:

    Those suggesting the solar Hale cycle is the root of the BDO are (a) ignoring the observational evidence and (b) implicitly asserting that Jean Dickey, Richard Gross, Ian Wilson, Nikolay Sidorenkov, & Paul Pukite are all wrong.

    Finally, I’m obligated to squarely confront Ian Wilson as follows:

    Ian: Since they conclusively nailed QB ENSO and predate everything in the list of citations you recommended to Paul Pukite, will you begin recommending due citation of Dickey & Keppenne (1997)?

    Dickey, J.O.; & Keppenne, C.L. (1997). Interannual length-of-day variations and the ENSO phenomenon – insights via singular spectral analysis.

    Click to access 97-1286.pdf

  47. Paul Vaughan says:

    principal tide frequency algebra:

    T = 0.00273790933828841 / solar day = 1 / 365.242189 solar days (tropical year)
    D = 0.0367481948643589 / solar day = 1 / 27.212221 solar days (draconic or nodal month)
    A = 0.0362916469330836 / solar day = 1 / 27.55455 solar days (anomalistic month)
    Y = 0.0338631918245857 / solar day = 1 / 29.530589 solar days (synodic month)
    L = 1 / solar day

    1 / K1 = L+T
    1 / P1 = L-T
    1 / O1 = L-2Y-T
    1 / K2 = 2L+2T
    1 / M2 = 2L-2Y
    1 / N2 = 2L-2Y-A

  48. Paul Vaughan says:

    T = 1 / tropical year = 1 / 365.242189 solar days
    D = 13.421991134057 / tropical year = 1 / 27.212221 solar days
    A = 13.2552405682546 / tropical year = 1 / 27.55455 solar days
    Y = 12.3682663085386 / tropical year = 1 / 29.530589 solar days
    L = 365.242189 / tropical year = 1 / solar day

  49. Paul Vaughan says:

    23.9344695921965 hours = 1 / K1 = L+T
    24.0658902255828 hours = 1 / P1 = L-T
    25.8193416551304 hours = 1 / O1 = L-2Y-T
    11.9672347960983 hours = 1 / K2 = 2L+2T
    12.4206012010478 hours = 1 / M2 = 2L-2Y
    12.6583482264709 hours = 1 / N2 = 2L-2Y-A

  50. Paul Vaughan says:

    Zotov & Bizouard (2015). Regional atmospheric influence on the Chandler wobble.
    ” From the maps of regional contribution to atmospheric angular momentum (AAM) over the period 1948-2011 (NCEP/NCAR reanalysis data) time domain excitation in Chandler frequency band was extracted by Panteleev’s filtering method. This permits us to investigate the evolution of the regional atmospheric influence on Chandler wobble. It appears that the temperate latitudes bring the strongest inputs. For pressure term they are limited to continents, and highlight the role of Europe. For the wind term they mostly result from ocean area, encompassing in particular North Atlantic. A quasi-20 year cycle is found in the regional patterns of the atmospheric excitation. The integrated AAM is finally compared with the geodetic excitation reconstructed from the observed polar motion.”

  51. Paul Vaughan says:

    cautionary note: Zotov thinks BDO is from LNC. It’s not.

  52. Paul Vaughan says:

    Zotov, Sidorenkov, & Shum (2015).
    Multichannel Singular Spectrum Analysis of the Axial Atmospheric Angular Momentum.

    “Earth’s variable rotation is mainly produced by the variability of the Atmospheric Angular Momentum (AAM). In particular, the axial AAM component, which undergoes especially strong variations, induces changes in the Earth’s rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the Length of Day (LOD) were described. We applied Multichannel Singular Spectrum Analysis (MSSA) to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-month, quasi-biennial, 5-year, and low-frequency oscillations. Principal components (PCs) strongly related to El Nino Southern Oscillation (ENSO) were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.”

  53. Paul Vaughan says:

    The bidecadal Chandler frequency resonance quality cycle matches both bidecadal SST & sea level:

    Compare with slide 10 here …and note the problem with slide 33:

    Click to access Zotov.pdf

  54. Paul Vaughan says:

    So the grey lines on that graph are from J-N beating with one kind of terrestrial year …but they get aliased by other kinds of terrestrial years in the multivariate geophysical system.

    The aliasing schedule is regular clockwork.

    It takes the form of physically aliased resonance frequency crossings with coupled Chandler wobble phase.

    The wake up call here is that excitation can be physically aliased.

    There’s an analogy here with the pervasive sloppiness in thinking about de Vries that I outlined on the Suggestions-13 thread. Deep ignorance of physical aliasing is the obstructing shortcoming underscored by that simple, clean, effortlessly illuminating example.

    Maybe because of anomaly-think, a lot of people are preconditioned to overlook and underestimate the capacity of the big annual swing to physically alias.

    The grey line on the graph above is folded (across the x-axis from below) from signed to absolute to show the proportion of time distant from resonance ….in absolutes, whether the signed anomaly from resonance is too positive or too negative.

    Conceiving alternately by looking at signed anomalies instead of absolutes, the high frequency component shoots across resonance in a different direction in alternating cycles and that switching from below-resonance-frequency to above-resonance-frequency and from above-resonance-frequency to below-resonance-frequency gets aliased (to Chandler frequency) by a different annual cycle.

    Remember that illustrated above is the barycentric year.

    The heliocentric year is NOT having these plus & minus 2 to 10 day cycle-length oscillations …so it has a different length in these years. If you check the heliocentric year’s length oscillations via NASA Horizons, you’ll see that although there’s a 22.14 year cycle (which I illustrated for the community in the past), the amplitude is a dwarfed fraction of the oscillations of the barycentric year.

    Learning Exercise:

    It’s actually a trivial exercise to check how the heliocentric (thermal) year aliases barycentric (gravitational perturbation) year resonance-crossings. What you’ll discover aliased: Chandler frequency.

    So again we’re reminded that the mainstream in it’s devoted attention to amplitude is weak on recognizing frequency effects — for example Rial has to counsel everyone on 100ka & DO, I have to counsel everyone on multidecadal solar cycle length & its derivative deceleration, and now BZS14 have to counsel climatologists on frequencies in different reference frames.

    Frequency effects on physical aliasing & aggregation can’t be ignored.

    When it comes to nonlinearities, asymmetries, & latent heat, physical aliasing is a dominant factor. (Ice is just the obvious example that comes to mind first.)

    typo alert:
    Above I wrote:
    ” That’s just J+N beating with the year:
    (12.78279303)*(1) / (12.78279303 – 1) = 1.084869521 “

    That should read:

    ” That’s just J-N beating with the year:
    (12.78279303)*(1) / (12.78279303 – 1) = 1.084869521 ”

    J-N, not J+N

    Anyone capable & willing can verify that via NASA Horizons while pursuing the easy learning exercise I’ve outlined a few lines above.

    Nipping efficiency-killing misrepresentations in the bud… some are all too eager to mischievously engineer sidetracking, intolerably time-consuming misunderstandings …so I’ll just preemptively clarify that what I’m saying about bidecadally oscillating resonance heliocentrically aliased from barycentric J-N does not conflict with what I’ve previously written about the following lunisolar aliasing:

    sidereal years, tropical years, frequency algebra
    2.369626074, 2.369718033, D-13T
    1.184813037, 1.184859016, 2D-26T
    6.409279139, 6.409527865, 27T-2D
    12.81855828, 12.81905573, 27T/2-D

    The next challenge is to explore spatial evolution of terrestrial BDO expression. I have a flood of ideas about this that I’ve never had time to express. There’s scope for a range of asymmetry diagnostics based on EOP (earth orientation parameters …not to be confused with earth orbital parameters, which are not the same thing).

    Of notable interest is the way the BDO sits across the ENSO spatial attractor with the evolution of time.

    I’ve planned an extensive multitude of investigations that with certainty will never happen since I have insufficient time & resources to write and implement the prototyped algorithms based on multivariate multidimensional generalization of unconventional (this is absolutely NOT Torrence & Compo!) wavelet methods that subsume all known types of fourier methods and afford exploration far beyond them (oldschool fourier methods are just a minute fraction of the space explored by the generalized methodology).

    By analogy the prototyped algorithms could be reconfigured for SSA (singular spectrum analysis). A team of talented programmers would be the way to go for efficiency. That would be the only feasible way to try to make up for lost time. Potentially it could be a challenging project to manage.

  55. oldbrew says:

    PV says:
    ‘So the grey lines on that graph are from J-N beating with one kind of terrestrial year …but they get aliased by other kinds of terrestrial years in the multivariate geophysical system.

    The aliasing schedule is regular clockwork.

    It takes the form of physically aliased resonance frequency crossings with coupled Chandler wobble phase.’

    There’s a close match between: 23 J-N, 294 years and 248 Chandler wobbles.
    That’s 1/5th of the well-known 1470 year cycle which is 74 Jupiter-Saturn conjunctions.

  56. Paul Vaughan says:

    E-(J-N) = E-J+N

  57. oldbrew says:

    Update (re: September 20, 2015 at 9:59 am) – using J-N/2 we get:

    46 x J-N/2 = 248 Chandler wobbles = 294 years.
    Inter-locking frequencies? 46 + 248 = 294
    If 1 QBO = 2 CW then 23 J-N = 124 QBO = 294 years.

    QBO – see part II here:

    Click to access soim.pdf