Length of Day: Ancient eclipse obs and modern analysis indicate cycles at planetary frequencies

Posted: July 27, 2014 by tallbloke in Celestial Mechanics, Cycles

I found a book by Peter Hubers which uses Length of Day (LOD) variation as a case study in data analysis. It contains information which may be relevant to our ongoing investigation of the effects the spatio-temporal distribution of the planets may have on solar variation and terrestrial rotation and climatic variation.

Hubers cites a 1995 paper by Stephenson and Morrison and his own Hubers 2006 paper which reconstructs the long term variation and decadal in LOD from ancient and modern astronomical records of eclipses in the figure below, which I have annotated in red to show the inexact nature of the periodicity of the ‘cycle’.



The Moon is responsible for the secular +2.3ms/cy in LOD with the post glacial rebound responsible for approximately -0.6ms/cy




Hubers goes on to test whether this apparent ‘cycle’ could in fact be Brownian motion but finds this unlikely. Noting that a careful inspection of the periodicity implies a quasi periodicity of around 1463 years, I think we might find a connection with the generally accepted average period of 1470 years attributed to the ‘Bond cycle’. It’s also worth noting that Tim Cullen highlighted a paper: Millennial scale cyclicity in the geodynamo inferred from a dipole tilt reconstruction – Andreas Nilsson, Raimund Muscheler, Ian Snowball http://www.lunduniversity.lu.se/o.o.i.s?id=12683&postid=2345020 which found a 1350 year cycle in geomagnetic axial tilt. Tim also noted this 1350 year period was found to have a strong presence in Keeling (yes, THAT Keeling) and Whorf’s lunar study.


Hubers also finds a decadal 1.3ms/cy (RMS) fluctuation of around 45 years which puts us in mind of the inner planetary periods involving Jupiter which have whole number multiples and submultiples around 44.77 years, close to two solar Hale cycles. Also of the ~45 year periodicity of the staircase of uplifted beach ridges around Hudson bay and the Siberian coastline. Hubers notes that the amplitude difference between these two quasi-cyclic periods is such that it is likely they have a different origin. I have Jupiter (or its influence on the lunar orbit) as number one suspect in both.

28 × SVE = 44.763 years
69 × SVJ = 44.770 years 
41 × SEJ = 44.774 years 
20 × SMJ = 44.704 years 


SVJ  = synodic period of Venus/Jupiter
SEJ  = synodic period of Earth/Jupiter
SMJ = synodic period of Mars/Jupiter



  1. Ian Wilson says:


    “Tim also noted this 1350 year period was found to have a strong presence in Keeling (yes, THAT Keeling) and Whorf’s lunar study.”

    The 1350 period in Keeling and Whorf papers (1997 & 2000) refere to the Ice Rafting Debris Events (IRD)


    “Spectral analysis of the IRD records, from 1- to 31-kyr BP, reproduced in Fig. 4 from Bond et al. (2), show broad peaks centered at 1,800 and 4,670 years (Fig. 4A), in contrast to an average pacing between IRD events of 1,470 +/- 532 years.”

    Keeling and Whorf constantly referred to a 1800 year tidal period not a 1470 year tidal period.

  2. tallbloke says:

    Hi Ian, yes indeed. Maybe you could tell us what the 1350 period on that plot is, since there’s no ‘peak’ in the solid curve.

  3. Ian Wilson says:

    The Keeling and Whorf study that you link to in the article above has a quote:

    “The IRD events identified by Bond et al. (1, 2) show high spectral power density in a broad band centered at about 1,800 years (0.55 +/- 0.15 cyclesykyr). The authors do not explain why this period is so much larger than the 1,476-year average pacing of cool events, but the time-distribution of pacing (ref. 1, Fig. 6c;
    G. Bond, private communication) suggests that a majority of the events were about 2,000 years apart, with occasional additional events occurring about half-way between, evidently too infrequent to cancel out a dominant spectral peak near 1,800 years. Bond et al. (2) in addition found a spectral peak near 5,000 years whose possible cause was also not explained.”

    Keeling and Whorf believed that there 1800 year tidal data better fitted the peaks (at 1800 and ~ 5000 yrs) seen in the spectral analysis of the IRD data, so they discounted the 1476 periodicity.

    In fact the 1470 year periodicity is present in the Lunar tidal data if you consider the peak tidal events that are aligned with the Earth seasonal calendar, as is the 1800 year peak.

  4. tallbloke says:

    Ian: Thanks for the further reply. So do you think the ~1470 year LOD oscillation derived from the timing of eclipse events could be due to these tidal maxima, and that the period is perhaps modulated by the weaker, longer periods?

  5. Ian Wilson says:


    If you look at Figure 7c of:

    Bond, G., Showers, W., Cheseby, M., Lotti, R., Almasi, P., deMenocal, P., Priore, P., Cullen, H., Hajdas, I. & Bonani, G. (1997) Science 278, 1257–1266.

    You have the following accompanying quote:

    “Finally, spectral analysis of the time series of hematite-stained grains by the multi-taper method of Thompson (29) reveals that power is concentrated in two broad bands. One is centered at ;1800 years, near the mean of Holocene-glacial events, and the other is centered at ;4700 years (Fig. 7C). Cycles close to both have been noted previously in spectra from other paleo-climate records from the last glaciation (30).
    In addition, F variance ratio tests reveal lines with .95% probability at 4670, 1800, and 1350 years (Fig. 7C).”

    Maybe they are picking up the slight bump on the lower side of the 1800 year peak?

  6. Ian Wilson says:


    I believe that there is a link between the seasonally aligned strong Perigean Spring tides and the climate. This link is both direct through atmospheric and oceanic lunar tides as well indirect through long-term variations in the Earth’s LOD. I may be wrong, but I would attribute the ~ 1500 year oscillation in LOD to the 1470 year seasonal lunar peak tidal cycle.

    I refer the readers to the associated link to one of my blog pots cited above at the bottom of your article: :

  7. tallbloke says:

    Ian: Maybe they are picking up the slight bump on the lower side of the 1800 year peak?

    Maybe so. I confess I don’t know how to interpret the height of the dashed peak at 1350 years. Is it higher than the two longer period’s ‘F variance ratio tests’ because it exhibits tighter coherence, or what?

    And why is it 1350 years rather than 1470?

  8. Ian Wilson says:

    The poor spectral resolution means that it is 1350 (+/- a large error) years and any F Test would based on how significant a spectral peak was compared to the underlying red(?) noise background. The red (?) noise decreases quickly as you move towards higher frequencies i.e. towards the right in the diagram, and hence smaller peaks would increase in statistical significance.

    Though, I just as perplexed as to why that little bump is so significant? I do not think that we have the whole story here?

  9. Ian Wilson says:

    Here is an extract from my blog post that I have cited:

    B. Evidence that the Precession of the Lunar Line-of-Nodes and the Lunar Line-of-Apse are linked to the orbital period of the planets.

    NB: The following arguments use these mean planetary orbital periods:

    V = 224.70069 days = 0.615186 sidereal years
    E = 365.256363004 days = 1.0000 sidereal year
    J = 4332.75 days = 11.862216 sidereal years
    Sa = 10759.39 days = 29.4571 sidereal years

    1) The Lunar Lines-of-Apse

    If we look at the realignment period between the half pro-grade synodic period of Jupiter and Saturn (1/2 JS cycle) with the retrograde realignment cycle of the inferior-conjunctions of Venus and Earth with the Terrestrial year (VE cycle) i.e.

    1/2 JS cycle = 1/2 x 19.859 years = 9.9295 sidereal years [pro-grade]
    VE Cycle___= 7.9933 sidereal years [retro-grade]

    we find that:

    (9.9295 x 7.9933) / (9.9295 + 7.9933) = 8.8568 sidereal years

    This is extremely close to the time of precession time of the lunar line-of-apse with respect to the stars, which is 8.8501 sidereal years – error = 0.007 years or 2.56 days

    Greg Goodman has proposed an alternative commensurability over at WUPSYDO – but it was deleted because it was some speculating about cycles:

    18.031 sidereal years = period of the Saros lunar eclipse cycle
    8.8501 sidereal years = period of precession of lunar line-of-apse with respect to the stars

    2 /[(1/18.031) + (1/8.8501)] = 11.872740 years

    If we use the 11.862216 sidereal years orbital period this is error of 3.844 days.


    2/[(1/11.862216) – (1/11.872740)] = 26764.9195 years ~ 26,000 year precession time for the Earth’s rotation axis.

  10. tallbloke says:

    Ian: Greg Goodman has proposed an alternative commensurability over at WUPSYDO – but it was deleted because it was some speculating about cycles

    Seems to be still there:

    As it happens, Oldbrew and I discussed that comment in email the other day. We weren’t quite sure where his periodicities were from, as they are slightly longer than the ones you and we use. This is the guts of his comment:
    pSaros= 18.0310284658705
    days_per_year = 365.25636
    print 2/(1/pApsides+1/pSaros)
    That is very, very close to Jupiter’s sideral orbital period. (fixed stars).
    pJ= 4332.589 / days_per_year # = 11.861775658061

    Now looking at how long these cycles take to drift in phase and come back into phase:
    print 2/(1/pJ-1/pApSaros) = 21322 years

    Your 0.5 J-S x V-E / (0.5 J-S – V-E cycle) calc gives 8.8568yrs and you compared this with the apsidal lunar cycle period 8.8501 years. If you work out the harmonic of the two in the same way you get 11699.03 years which is roughly half the precession of the equinoxes and is also 8 x 1462.4 years. I’m not sure if this is of any interest or just an oddity, such close harmonics are highly leveraged by tiny errors in the input numbers.

    Though, I’m just as perplexed as to why that little bump is so significant? I do not think that we have the whole story here?


  11. oldbrew says:

    At the risk of stating the obvious, 1350 years is 3/4 of 1800 years.

  12. tallbloke says:

    OB: Yes, I spotted that too. 1800 years is also 2:3 with 1200 (1199) years (The V-E cycle precession), and 2:1 with 3600 years (The U-N cycle precession). Not a million miles from 89 J-S either.

  13. oldbrew says:

    4 x 1350y = 3 x 1800y = 5400y
    Four of those = 21600y, looks like the precession of the equinoxes period – also 3600y x 6.


    ‘Not a million miles from 89 J-S either.’
    See draft post 😉

  14. Paul Vaughan says:

    I note that Bond+(1997) misreferenced Thomson (1982) as “Thompson (1982)”.

    ( not the same climate explorer:
    David J. Thompson (with “p”): spatial AO / NAM
    David J. Thomson (no “p”): spectral multitaper )


    Note the correspondence of A & B:


    (4670)*(1800) / (4670 – 1800) = 2928.919861 years
    (2928.919861) / 2 = 1464.45993 years

    or equivalently:
    4670 / 2 = 2335
    1800 / 2 = 900
    (2335)*(900) / (2335 – 900) = 1464.45993 years


    tropical year ~= 365.24219 days
    sidereal year ~= 365.256363 days

    harmonic mean
    = 2*(365.256363)*(365.24219) / (365.256363 + 365.24219)
    = 365.2492764 days

    beat with nearest subharmonic of terrestrial day
    = (365.2492764)*(365) / (365.2492764 – 365)
    = 534811.9792 days

    (534811.9792) / 365.24219
    = 1464.266708 years

  15. Paul Vaughan says:

    Bond+(1997) applied Thomson’s (1982) method, but didn’t interpret very well (middle paragraph 3rd column p.1263) it’s summary of the glacial vs. Holocene difference they noticed:

    2*(1800)*(1350) / (1800 + 1350) = 1542.857143 years
    (harmonic mean)

  16. oldbrew says:

    PV: re. ‘2*(1800)*(1350) / (1800 + 1350) = 1542.857143 years’

    9 Uranus-Neptune conjunctions = 1542.5 years = 34 Saturn-Uranus = 43 Saturn-Neptune (9+34=43)

  17. Paul Vaughan says:

    OB: Ulric Lyons comment on Cullen thread

  18. oldbrew says:

    PV: thanks.

    There’s some mention on the Scafetta thread of Svalgaard’s 1024 year period which looks a lot like 6 U-N.

  19. TLMango says:

    For whatever it is worth. I found a really nice relationship between
    the 2208 year Hallstatt, 1000 year Millennial and 1828 year Wave cycle.
    2208.027476 x 1000.061137 / ( 2208.027476 – 1000.061137 ) = 1828

  20. Paul Vaughan says:

    OB: Svalgaard’s article was an exercise in distortion artistry.