Orbital resonance and the celestial origins of Earth’s climatic changes – Why Phi?

Posted: October 30, 2021 by tallbloke in Analysis, Astrophysics, Celestial Mechanics, climate, COP26, Cycles, Ice ages, modelling, moon, Natural Variation, Phi, research, Solar physics, solar system dynamics
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A year after I wrote the original ‘Why Phi’ post explaining my discovery of the Fibonacci sequence links between solar system orbits and planetary synodic periods here at the Talkshop in 2013, my time and effort got diverted into politics. The majority of ongoing research into this important topic has been furthered by my co-blogger Stuart ‘Oldbrew’ Graham. Over the last eight years he has published many articles here using the ‘Why Phi’ tag looking at various subsystems of planetary and solar interaction periodicities, resonances, and their relationships with well known climatic periodicities such as the De Vries, Hallstatt, Hale and Jose cycles, as well as exoplanetary systems exhibiting the same Fibonacci-resonant arrangements.

Recently, Stuart contacted me with news of a major breakthrough in his investigations. In the space of a few hours spent making his calculator hot, major pieces of the giant jigsaw had all come together and brought ‘the big picture’ into focus. In fact, so much progress has been made that we’re not going to try to put it all into a single post. Instead, we’ll provide an overview here, and follow it up with further articles getting into greater detail.

One of the longest known climatic periods is the ~413,000 year cycle in the eccentricity of Earth’s orbit. This period has been found in various types of core sample data and discussed in many paleoclimatic science papers, along with cyclicities around 95, 112 and 124kyr, and shorter periods such as Earth’s obliquity variation, ~41Kyr and Earth’s equinoctial-precession periods of ~19 and ~23kyr. Stuart has discovered how all of these periods are related to each other and to the planetary orbits and their synodic conjunctions.

We’ve also been able to link these Earth Orientation Parameters and climatic periodicities to the planetary orbital and synodic conjunction periods which we believe are key to modulating solar activity. The basis for these were laid out in my 2011 post on Jupiter and Saturn’s motion and further developed with the valuable input of many Talkshop contributors, culminating in the solar variation models published by Rick Salvador and Ian Wilson in the 2013 special issue of Pattern Recognition in Physics.

Solar Total Solar Irradiance (TSI) prediction model hindcast created by Rick Salvador using planetary periods discussed at the Talkshop in 2013

Figure 1 below scratches the surface of what we have discovered. These relationships are all precise whole number ratios, not approximations. The red ‘Graham Cycle’ is a novel addition to previously known cyclic periods which connects the three areas of the figure; Solar-Planetary at the top, climatic periods bottom left, and Earth Orientation Parameters bottom right. Of note, are the ratios between the 60kyr Graham Cycle period and the periods in the three groups. They are mostly ratios of Fibonacci numbers or combinations of them. We know from a previous investigation that Fibonacci and phi (Golden Section) related periodicities tend to be stable and minimally resonant. It could be that the reason the 60kyr period hasn’t been found previously is due to it not showing up strongly in periodograms and other spectral analyses. Nonetheless, it’s an important period for our ‘Why Phi’ investigation and has a lot more connections than we wanted to clutter up Figure 1 with, as it already looks pretty busy!

Figure 1. Spatio-temporal diagram showing solar system dynamical arrangement with particular reference to solar modulation, climatic periods and Earth Orientation Parameters affecting Milankovitch cycles.

Solar cycles

Starting with the upper ‘Solar planetary’ section of figure 1, Ian Wilson’s 2013 PRP paper noted that the Hale cycle and Jupiter-Saturn synodic (J-S) have a 193 year beat period, which is evident in Oxygen18 isotope data as well as Group Sunspot Numbers and 10Be ice core data. This was picked up by the Helmholtz Institute research lab and covered in our earlier post on the Solar Magnetic cycle. What they didn’t pick up on is the fact that the same 193year beat period can also be derived from the 178.8yr Jose cycle and the 2403yr Solar Inertial Motion (SIM) period.

This second route to the 193 year solar magnetic cycle is a novel result revealed in this post. Using the beat period formula of (A*B)/(A-B) = period, the solar inertial motion cycle (A) proposed by Charvatova of ~2403 tropical years and the Jose cycle (B) produces the same 193 year result. It was then possible to tie all this together in the 60 kyr cycle shown in the diagram.

There are 336 Jose and 25 SIM in 60 kyr which means the beat period produces 336-25 = 311 solar magnetic cycles of 193 years each. The number of Hale cycles in 60 kyr is given by the number of J-S minus the number of solar magnetic cycles. i.e. 3024-311 = 2713. It’s notable that 311 and 2713 are both prime numbers. Coupled with the fact that the number of J-S in 60Kyr is the Fibonacci multiple 144×21, we think this is a strong indicator that both 193yr and 60kyr periods are significant solar-planetary cyclic periods.

Support for the 60kyr period comes from Russia, where in 2017 A. S. Perminov and E. D. Kuznetsov produced a paper at at Ural Federal University, Yekaterinburg, entitled ‘Orbital Evolution of the Sun–Jupiter–Saturn–Uranus–Neptune Four-Planet System on Long-Time Scales’. This paper shows inter-related variations in the orbital parameters of the gas giants including antiphase changes in the eccentricities and orbital inclinations of Jupiter and Saturn at ~60kyr and in-phase changes in those parameters at ~400kyr, antiphase to Uranus. These ~400kyr variations are likely to be drivers of Earth’s 413kyr eccentricity cycle.

ISSN 0038-0946, Solar System Research, 2018, Vol. 52, No. 3, pp. 241–259. © Pleiades Publishing, Inc., 2018.
Original Russian Text © A.S. Perminov, E.D. Kuznetsov, 2018, published in Astronomicheskii Vestnik, 2018, Vol. 52, No. 3, pp. 239–259

Planetary-climatic cycles

Moving on to the lower left ‘climatic and planetary cycles’ section of Figure 1,

The de Vries cycle is half of 21 J-S and is a prominent climatic cycle. It also links to other cycles through resonant harmonics: Hallstatt = 11 de Vries, J-S synodic precession cycle = 12 de Vries. 6 de Vries is 7 Jose cycles. 33 de Vries is 7 Eddy cycles. See also Why Phi? – Jupiter, Saturn and the de Vries cycle.

The lunar-terrestrial year (L-T) is 13 lunar months. Earth’s tropical year is used throughout this post. Whole numbers of both occur at 353 tropical years and 363 lunar years, forming 10 beats (363-353) of 35.3 years. An important period is 13 L-T, which is 2 Hallstatts and 11 de Vries cycle pairs (22 de Vries). This is 1/9th of the obliquity cycle. It is also 3x7x11 J-S. It follows that the 41kyr obliquity cycle is 3x7x11 Jose cycles, because the Jose cycle is 9 J-S. 3,7 and 11 are all Lucas numbers. We will post a separate article on the inter-relation of the Fibonacci and Lucas series, as they relate to orbital resonance. See also Sidorenkov and the lunar or tidal year (2016)

An explanation for the effect of the motion of the gas giants on these and other climatic periods is found in Nicola Scafetta’s 2020 paper ‘Solar Oscillations and the Orbital Invariant Inequalities of the Solar System’ discussed here at the talkshop.


At the lower right of Figure 1 we find Earth orientation parameters and associated cycles. To understand how these link to planetary periods we need to look at the motions of Jupiter and Saturn in particular. Kepler gives us this useful graphic in his book De Stella Nova (1606).

Kepler’s trigon showing the ~60 year cycle in the longitude of the Jupiter-Saturn synodic conjunctions. This may be linked to the ~60yr cycle of Earth’s major oceans, giving rise to the 30 year global cooling scare 1960-90 and the subsequent global warming scare 1990-2020.

From an earlier post: ‘As successive great conjunctions occur nearly 120° apart, their appearances form a triangular pattern. In a series every fourth conjunction returns after some 59.8 years to the vicinity of the first. These returns are observed to be shifted by some 7–8°’. Wikipedia. [2019 version]. After 3 J-S the conjunctions have nearly described an exact triangle, but the start position has moved (precessed) slightly, by 60/7 degrees of precession of the J-S conjunction axis. It takes 42 of those (42*3 J-S) to complete the precession cycle in 2503 years. (41×61.051 y = 41×360 degrees movement of the axis).

The 413kyr eccentricity cycle is equivalent to 55*3 of these J-S synodic precession periods, and 6765 or 55×123 (Fibonacci and Lucas numbers) of the 61.051 360 degree periods. Additionally 413 kyr = 10 obliquity periods.

In the brown triangle: the 19 kyr and 23 kyr periods have a beat period of the 112kyr perihelion precession.
23 kyr is 10 Hallstatt cycles.

In the blue triangle: the 95 kyr (5×19 kyr) and 124 kyr (3 obliquities) have a beat period of 413 kyr i.e. Earth’s eccentricity cycle (mentioned in various research papers). Since our 95 kyr = 353×270 and our 124 kyr = 353×351, we find: (351×270) / (351-270) = 1170, and 1170*353 = 413010 years (the obliquity period).


The 95 and 124kyr eccentricity cycles are linked with glacial periods. From Park and Maarsch (1993) paper ‘Plio—Pleistocene time evolution of the 100-kyr cycle in marine paleoclimate records’: “The DSDP 607 time scale is more favorable to an abrupt jump in amplitude for the 95-kyr δ18O envelope, but not in the 124-kyr envelope. Rather, long-period δ18O fluctuations appear phase-locked with the 124-kyr eccentricity cycle some 300-400 kyr prior to its growth in amplitude and phase-lock with the 95-kyr eccentricity cycle in the late Pleistocene.” Because the 124kyr period is 3x41kyr (obliquity period), this may help explain the change from glacial periods around 41kyr to around 100kyr.

The bi-modality of glacial cycles and the 95 and 124kyr cycles is one of the modes of variation mirrored between celestial cyclic motion and Earth climatic events. There are also many periods which are ‘quasi-cyclic’ and vary in length within bounds whose attractor nodes fit our phi-Fibonacci scheme. We are not claiming to have elucidated a deterministic and predictable system with our precise whole-number orbitally resonant ratios. We are offering this scheme as a potentially useful roadmap for further investigations into the intriguing numerical links between planetary orbits, synodic timings, planar inclinations, eccentricities, energy transfers and other celestial mechanical and orientation data.

As an example of how our scheme links shorter to longer term cycles, there are exactly 9 Jupiter Saturn conjunctions in the period of the Jose cycle of 178.8 years. There are 55x21x2 Jose cycles in the 413kyr eccentricity period. Experienced researchers like Paul Vaughan will immediately see that this product of multiple Fibonacci numbers resolves to the product of the first 6 prime numbers 1,2,3,5,7,11.

The solar system is organised by the forces of gravity and electro-magnetism into a log-normal distribution of which the Fibonacci series and Lucas series are examples which maintain the stability of the system. Resonance is minimised, but also utilised to transfer energy between orbits in order to resolve inequalities through resonance-forced changes to the eccentricity and inclination of orbits. These changes give rise to the cyclic changes in climatic factors on Earth observed at all timescales from the ~22yr Hale and ~60yr J-S trigon to the ~100kyr and 413kyr glaciation in core sample data and other indices.

Data sources and acknowledgements

Planetary data used is from NASA JPL which gives the Seidelmann values for orbital periods. Our thanks to Paul Vaughan for insisting on their use.

The periods we have calculated can all be reproduced using the ratios we have provided on Figure 1 and the NASA JPL values for the Jupiter, Saturn and Uranus orbital periods.

  1. Paul Vaughan says:

    1 = (1/2)*2

    “There’s a11LADI … CO[$]…sum timeswords halve*II meanings” — LZ

    May peace and tranquility be with you as you revel in super, natural beauty today and always.

    K Tune SST all

  2. PM says:

    If true, what would this tell us about the earth’s climate for the remainder of this century?

  3. tallbloke says:

    PM, welcome. Our orbital resonance based solar prediction model did well with the peak of solar cycle 24, but it remains to be seen how well it does with the current cycle 25. If it is somewhere near, then I expect to see temperatures down by 2030, with ongoing lower temperatures until late in the century.

  4. Paul Vaughan says:

    Keep vigilantly in mind that Salvador (2013) did not model observed solar cycle phase.
    Also: “Solar” proxies are being misinterpreted.

  5. Paul Vaughan says:

    “Planetary data used is from NASA JPL which gives the Seidelmann values for orbital periods. Our thanks to Paul Vaughan for insisting on their use.”

    Keplerian not in isolation but in concert (compare, contrast, relate) with fits, tropical, etc.

    This is were cross-disciplinary “experts” failed to efficiently guide at other sites, costing 6-7 years – maybe a decade.

    Recently I suspended my explorations totally and completely after realizing we were (maybe deliberately) misguided. Suddenly everything fit. The interest in further exploration and reporting vanished. No doubt real experts (not the decoy ones online) have had full models for many decades.

  6. tallbloke says:

    That’s just a touch of paranoia. We all get it from time to time. The last 18 months have been tough, especially for people living on their own.

  7. gbaikie says:

    2020 to 2060 AD would seem like bad years to explore Mars- and start towns on Mars.

  8. Paul Vaughan says:

    To be more forthcoming: going through my first switchover from Windows to MacOS (major destructive impact on efficiency, seasoned orientation, and productivity).

    Based on how easily lunisolar insights came after overcoming longstanding hurdles recently, I believe (confidently) that detailed geophysical models exist in high-level security circles. I suspect the details will be kept secret for as long as possible for well-founded reasons.

    Necessarily I will be more selective and casual about what I explore and how I contribute moving forward.

    Quick note on OB’s introductory summary: I do recall seeing most of the notes piece-wise over time. OB stressed 60k on a number of occasions. OB: if you have a link to a non-paywalled full version of the Russian article, please share it.

  9. Paul Vaughan says:

    For convenience, here’s a list including the NASA “factsheet” fits:

    0.240846697327135	0.240845995893224	Me
    0.615197263396975	0.61519780971937	V
    1.00001743371442	1.00001642710472	E
    1.88084761346252	1.88084873374401	Ma
    11.8626151546089	11.8619822039699	J
    29.4474984673838	29.4571389459274	S
    84.016845922161	84.0120465434634	U
    164.791315640078	164.788501026694	N
    Keplerian	fits	
  10. tallbloke says:

    Paul V: “Quick note on OB’s introductory summary”

    I wrote this post using Stuart’s notes on the numerics.

  11. oldmanK says:

    One needs to keep in mind that the cycle that dominated human fortunes in the last 8kyrs is the Eddy. And ancient texts, Akkadian and Indian, say the moon had its hands in the ‘pie’ up to the elbows.

    PV says “I suspect the details will be kept secret –“. Ancient literature from Egypt (Maqrizi) say the priests had found the 400 something astro relationship, and recorded it in obfuscated ways to keep it from the people. It served for no good, that known from the recorded laments – “sage Ipuwer described the anguish of the period: “Lo, the desert claims the land. Towns are ravaged. . . . Food is lacking. ” Somewhere there there’s a lesson for us.

  12. Nicola Scafetta says:

    Nice post.

    For those who may be interested, I am coediting a special issue on the harmonics of the solar system.


    Contact me directly for information.

    By the way, I had a new paper just published which also may be of general interest:

    Scafetta, N. Testing the CMIP6 GCM Simulations versus Surface Temperature Records from 1980–1990 to 2011–2021: High ECS Is Not Supported. Climate 2021, 9, 161.

    Abstract: https://www.mdpi.com/2225-1154/9/11/161

  13. tallbloke says:

    Hi Nicola, thanks for commenting here. Keep an eye on your inbox for an email from me.

  14. oldbrew says:

    Note re. our Figure 1 – Spatio-temporal diagram:
    The 19kyr:23 kyr ratio of 65:54 means 65*353 TY (23 kyr) and 54*353 TY (19 kyr), i.e. lunar-terrestrial cycles.

  15. Paul Vaughan says:

    If anyone can, please provide a link to a free, full version of the 2017 paper mentioned in TB’s article.

  16. Paul Vaughan says:

    oldmanK, I have tried repeatedly (by linking to 2 graphs back-to-back) to help you realize that 980 year cycle amplitude varies with the extremes of the 6ka cycle.

    That’s an important 1-sentence comment.

    Now there is something I would like to ask you since you appear to worry so much about the 980 year cycle: are there some measures you think societies and civilization should take to mitigate against its hazards (even if you presently lack the capacity to say exactly when it might hit a double or pull a 1470+980+490 phase twist on your planning team)?

  17. oldmanK says:

    PV, that fact did not escape me. However I think I still miss the devil in the detail you are pointing to.

    A 6ka cycle has ugly connotations. Next in the Eddy 980 cycle is a peak. Past two peaks were mild. Not only variations in amplitude but also frequency of triggering. Or phase shift? No, shift in trigger yes but not in cycle peak; clear over 8k. Anyway, 6 peaks ago (=~6ka) from the next, the Sahara dried abruptly, Otzi froze abruptly in a location that was ice-free with temperate fauna growing, and nearby here a second calendar was built with reduced equinox to solstice angle from the adjacent older one. One can speculate about the first two, but not the third.

    Next to your PV request. Two things learned in life, out of necessity. First, early in life, to plough a field behind a wooden plough. Then from late teens, engineering; power generation and out of interest its history. Two observation: 1: In today’s highly integrated world, covid showed the food chain was the first to fail, and fast. 2: In a disturbance the widespread grid is the last thing to rely on. In spite of the great advantages of electrical technology, which is now considered as a god-given human right, that will be one of the first of the biggest let-downs. There needs for there to be Plan ‘B’ that is real, installed and fully functional. The era of the wooden plough is gone (those who are still there will never leave the dark ages); its replacement needs fossil fuels, widely available and decentralised.

    A take on a part quote from Theodore Dalrymple (with my changes) : “When people are forced to remain silent when they are being told the most obvious ‘misconceptions’, or even worse when they are forced to repeat ‘them’ themselves, they lose once and for all their sense of probity.” My view: some techno/scientific sacred cows are worse than the docile but ungody ones emitting methane.

  18. tallbloke says:

    oldmanK, if I understand this correctly, a reduced equinox to solstice angle implies an increase in obliquity, or a shift in the surface relative to the spin axis. Isn’t either of those more likely to be due to a cataclysmic impact than a cyclic change in EOP?

  19. pochas94 says:

    Amazing. Congratulations, fellows! Looking forward to more.

  20. Poly says:

    Re your post about the 6ka and Eddy cycles.
    When is the next Eddy cycle peak, and how may it affect us?

  21. oldmanK says:

    tallbloke: No, the opposite. Equinox to solstice angle at equator equals earth tilt angle. That angle increases with latitude, and reaches (theoretically for sphere) 90deg at arctic circle.
    See http://www.land-navigation.com/direction_of_sunrise_and_sunset.html

    No crustal shifts, and -likely- no impacts. (Ancients say when there is no moon at night, and same, when the sun and moon are together)

    At latitude 35.8N angle is ~29deg (as today at Mnajdra, but design started at 18deg – the Dodwell change at 2345bce). 6ka ago change ~23 to 18. Calendars don’t give date of change. Those disturbances appear sharp in certain proxies (see https://melitamegalithic.wordpress.com/2019/08/12/searching-evidence-deaths-tsunamis-and-earth-dynamics/ )

    Reduced angle means more insolation between new tropics and colder beyond.
    See fig 5 here https://www.terrapub.co.jp/e-library/ecp/pdf/EC0301.PDF

  22. oldmanK says:

    Poly: Follow fig 122 here https://judithcurry.com/2018/06/28/nature-unbound-ix-21st-century-climate-change/ Its from June 2018, from when other dates/events began to fall in place.

    Last two peaks, Roman warm period and Medieval WP were mild but still disruptive, mainly from what data I find, as climate shifts.

  23. Paul Vaughan says:

    Making a crude & quick effort to aid learning & discussion by compiling a few links here.
    My interpretation of these curves is consistent with neither conventional nor unconventional views.

    Be careful using “fig 122” as a general guide as it is idealized:

    Figure 122. Solar Grand Minima distribution during the Holocene. Thirty Solar Grand Minima (SGM) from solar proxy records during the Holocene, identified in the literature, are indicated by black boxes of thickness proportional to their duration. The ~ 2450-year Bray solar cycle (black sinusoidal) and the ~ 980-year Eddy cycle (red sinusoidal) identified in solar proxy records are displayed at their proposed time-evolution that best matches both solar activity and climate changes consistent with their periodicity. Periods where any of the cycles are at the lowest 20% of their relative sinusoidal function are marked in red, and comprise 54% of the Holocene. Present position is indicated by a dashed line. SGM show a bias towards clustering at the red areas. RWP: Roman Warm Period. DACP: Dark Ages Cold Period. MWP: Medieval Warm Period. LIA: Little Ice Age. MGW: Modern Global Warming. Source for SGM data: Usoskin et al., 2007; Inceoglu et al., 2015; Usoskin et al., 2016.

    Ray Tomes reported on 6ka at the talkshop years ago.

    It takes only a few minutes to isolate this crude view (no special tools needed) from 14C:

    Extremes: on average every ~3ka but that’s a crude number (use peaks & troughs as better guide).
    Nonlinear aliasing: mostly discrete seasonal “exists” / “does not exist” circulatory aliasing.

    oldmanK, thanks for sharing the interesting commentary.

  24. Paul Vaughan says:

    that was a rare occurrence – 2 people quickly & efficiently agreeing across-disciplines on something important on a climate blog – “unbelievable” (a moment of celebration)

  25. oldmanK says:

    A comment on PV’s third graph – holocene drift ice-. It is/appears in Bond et al 2001 and refers to record (core) MC52-VM29-191. It has been used also by others as in my link above.

    Here https://www.researchgate.net/publication/11616606_Persistent_Solar_Influence_on_North_Atlantic_Climate_During_the_Holocene
    Page 3 first col says “We increased sampling resolution to 20yrs in places and still resolved abrupt shifts—“. It is the curve at bottom of fig 2 in paper.

    As presented two dates are critical. At 5k2bce and 3k2bce since they appear to correlate to abrupt tectonic events (and for some reason they are precise Eddy roots). However something appeared not right to my mind (which could be my own misunderstanding of the sampling and its presentation). At those two dates I expect the sampling percentage to rise sharply not fall. I also have an impression of reading somewhere that its represented inverted, or that the scale has to be inverted.

    Maybe someone can throw light on this.

  26. Paul Vaughan says:

    “Others ask why such a well-established and functional system should be replaced, arguing that the existence of two competing abbreviations is likely to cause confusion.”

    In case it wasn’t obvious: my calculations are in Julian years, not Gregorian.

  27. Paul Vaughan says:

    Drive a pickup major who’ll low hone?

    “At those two dates I expect the sampling percentage to rise sharply not fall.”

    14 sea DO scree

    rearrange f(ace or macro fool ’em)

  28. oldbrew says:


    The North America temperature spectrum contains significant oscillations with periods 210a and 230a, which appear as the 10th and 11th harmonics of the 2300a Hallstatt cycle.

    – – –
    From our Figure 1:

    Hallstatt = 2294.5 TY (‘2300’) = 11 de Vries
    Ratio 1:11 gives 11-1 beats, or harmonics = 10
    2294.5/10 = 229.45 TY (‘230’)
    1 de Vries = 208.5909 TY (‘210’)

  29. tallbloke says:

    Side note on the importance of solar prediction.

  30. Paul Vaughan says:

    “However I think I still miss the devil in the detail you are pointing to.”

    “solar” “1500” PRfound www esst urn guise

    “NATO centre of excellence to study the security threats posed by climate change”

    “The Pentagon and British defence departments have been developing climate security plans for more than a decade, but Friday’s announcement appears to entrench that thinking in the 30-country NATO military alliance.”

    “It’s not just conspiracy theorists and marginalized, angry people online […] It’s state actors, too, using disinformation, propaganda, and cyberwarfare to harm our economies, our democracies, and undermine people’s faith in the principles that hold us together.”

    Cairn ease$peak climb IT:

    The only language you need to know is money.”

  31. Ned Nikolov says:

    This is indeed a great new paper by Svensmark et al (2021): https://www.nature.com/articles/s41598-021-99033-1

    We have also used CERES-measured reflected solar radiation to show that its annual variations are 100% consistent with independently observed global surface temperature fluctuations over the past 20 years. In other words, changes of global surface temperature in recent decades are completely and fully explainable by the observed variations in Earth’s cloud albedo. No room left for a “CO2 forcing”! For details, please watch this video presentation we made at the 101st AMS Meeting last January:

  32. Paul Vaughan says:

    oldmanK, which of the following patterns is most geographically consistent with your 980 readings?

  33. tallbloke says:

    Paul V, shouldn’t those temperature keys be marked as Kelvin rather than Centigrade?
    For example, an average annual temperature of 270C for the Tibetan plateau seems a bit high, and 300C for the tropical oceans is somewhat implausible.
    Also, the absolute amplitude of the diurnal cycle of 7K seems low for the Sahara.
    “Saharan desert zone has the most discordant climate in the world. Being that here is almost constantly sunny weather, the air is very hot, especially in summer when the sun is high and the days are long. While daytime temperatures in the shade reach 30C, at night the air is very cool, especially in winter, and night temperatures fall below 0C.”

    Can you give me some help with interpretation please.

  34. tallbloke says:

    Ned, I’ve tweeted your presentation for you.

  35. oldbrew says:

    A 6ka cycle discussed earlier looks like a match between 35 U-N and 302 J-S. Maybe it could repeat but don’t have any dates to propose.

  36. Paul Vaughan says:

    TB: mouse-hover over image links paper, authors (if you’ve technical questions for them)

    vary image-search combos — e.g. “semi-annual” amplitude map
    other authors well-aware of same spatial pattern — e.g. compare:

    Mostly I’m curious to hear something about oldmanK’s 980 (homogeneous?) spatial-pattern-worries (and linking to maps opportunistically to reduce spatial pattern ignorance).

  37. Paul Vaughan says:

    There seems to be a “misunderstanding”, so let’s try this:

    Boris Johnson leads anglosphere climate too “sst up: id & con tag us” (320 = 163+67+43+19+28)

  38. oldmanK says:

    Paul V; cannot really answer; here’s why
    The evidence I’ve been collating was not related to climate. It is in two primary aspects: 1) what appear to be tectonic changes in the central Med, and 2) what appear as obliquity changes, from a number of calendars in their main dimension, that is the horizon sunrise equinox to solstice angle.

    That the dates of the above mentioned changes, as perceived and correlated from a number of proxies, corresponded to the 980 cycle roots (from 7ka bce to 2ka bce; and on to the last 2kyrs) meant this is not simple coincidence. So did the cycle peaks, eventually found to correspond to historical social changes. In all cases, climatic conditions and climatic change were a collateral event, and not exactly repeatable. (Eg. tectonic change was permanent – until the next. The resulting desiccation of the Sahara in 3550bce ~6ka ago, up to now was permanent.)

    [Some examples – short excepts: cycle roots and peaks:
    1 — evidence for prolonged winter shamal seasons around 4,200 years ago –2k2bce. — could explain why Akkadian crop production dramatically decreased and the empire’s irrigated fields underwent salinization, leading to widespread famine that triggered the state’s dissolution. (at root)
    2 — Reading the history of the Punic Wars, —- sprinkled salt on her land so that nothing else grew– we will not find any information about the salting of the land, but only mention that the city was full of ruins; 146bce – salinization – root.
    3 — Tall el-Hammam is biblical Sodom, ending ca. 1700 BCE, — and that changed to allow civilization to return 600-700 years later. (collapsed post peak of 1750bce and re-inhibited pre following peak of 800bce]

    I don’t think one can put a climatic pattern to any situation. What may be the reality is that certain changes alter the climate pattern permanently. Eg the said 6150/6200bce root corresponding to the sinking of Doggerland could have had a permanent effect on the climate of continental europe.

  39. tallbloke says:

    Misunderstandings arise when people don’t give straight answers and speak in riddles.

  40. Paul Vaughan says:

    “I don’t think one can put a climatic pattern to any situation.”

    I appreciate the source of exasperation, as deeper mutual understanding could (under unfavorable circumstances) take lifetimes and teams of true expert communication (including terse statement of classification theorem role in spatiotemporal chaos) …but at least recognize a few basics for now:

    1 year
    0.5 years
    2.37 years
    Wilfully ignoring building blocks (& nonlinear including discrete circulatory aliasing) is physically unreal.

    Followers of recent arctic ice thread no. “AMO’$keyDO” (Nirvana).

    proximate (lunisolar) & distal (broader system)
    all “fit” (the part missing until late summer) together (nearly-decade delay CO[$]buy “experts”)

    I see enough of the pattern (as of late summer) to know a team of talented communicators exists.
    It’s up to them (not me) when (& weather) they’ll communicate.

  41. oldmanK says:

    Cont: The link as in above re sea level may be downloaded as pdf. See fig 4 of pdf.

    At the 8k2BP (6150bce) abrupt change. Post event Gisp2 d2O increases rapidly >> temp increase.
    Correlating, same temp rise happens at Vostok (polar), but a reverse at Kilimanjaro (equatorial).

    The TS line is of interest, in the period between 8k2 (6150bce) and 4k2BP (~2200bce) when events appear to stabilise. Is the elevated TS -total sulfur – indicative of elevated volcanic activity? That would be in keeping with the other evidence, tectonic and “more”.

  42. Paul Vaughan says:

    Copy/paste of notes drafted (con$script$yuan Kurt – Mars yell) a few months ago:

    Jupiter-Earth-Venus (JEV) NASA “factsheet” fits

    basic stuff

    1.59869582147101 = beat(1.00001642710472,0.61519780971937)
    0.799347910735507 = 1.59869582147101 / 2
    0.399673955367753 = 1.59869582147101 / 4

    0.380883168073026 = axial(1.00001642710472,0.61519780971937)
    0.190441584036513 = 0.380883168073026 / 2
    0.0952207920182565 = 0.380883168073026 / 4

    0.761766336146052 = harmean(1.00001642710472,0.61519780971937)

    generalized-Bollinger axial set-up

    0.814043513256406 = beat(11.8619822039699,0.761766336146052)
    0.407021756628203 = 0.814043513256406 / 2
    0.203510878314101 = 0.814043513256406 / 4

    0.715798377497214 = axial(11.8619822039699,0.761766336146052)
    0.357899188748607 = 0.715798377497214 / 2
    0.178949594374304 = 0.715798377497214 / 4

    base-level slip-cycles (base of slip-hiearchy construction)

    44.2788229093651 = slip(1.59869582147101,0.814043513256406)
    22.1394114546826 = slip(1.59869582147101,0.407021756628203)
    11.0697057273413 = slip(1.59869582147101,0.203510878314101)

    6.84829603928923 = slip(1.59869582147101,0.715798377497214)
    3.42414801964461 = slip(1.59869582147101,0.357899188748607)
    24.1412003962475 = slip(1.59869582147101,0.178949594374304)

    a few things to note from the hierarchy

    146.05776369693 = slip(44.2788229093651,1.59869582147101)
    73.028881848465 = slip(22.1394114546826,0.799347910735507)
    208.23504902444 = slip(73.028881848465,44.2788229093651)
    208.235049024445 = slip(44.2788229093651,0.399673955367753)
    104.11752451222 = slip(36.5144409242325,22.1394114546826)

    3651.64416767031 = slip(44.2788229093651,0.0952207920182565)
    3651.64416765971 = slip(349.986741261455,44.2788229093651)

    Recall 73 = average(19,43,67,163) is the lowest prime congruent to 1 mod 24.
    50 ~= 3651.64416767031 / 73.028881848465

    This is to contrast with (analogUS) Keplerian 5256 = 7920-2400-240-24.
    Nothing to do with “bore us” politics, but naturally more interesting — and beautiful.

    1.59869582147101 = beat(1.00001642710472,0.61519780971937)
    0.761766336146052 = harmean(1.00001642710472,0.61519780971937)
    60.9470469878813 = slip(29.4571389459274,11.8619822039699)
    0.814043513256406 = beat(11.8619822039699,0.761766336146052)
    0.771408028343905 = beat(60.9470469878813,0.761766336146052)
    0.7523626882775 = axial(60.9470469878813,0.761766336146052)
    22.0696489390603 = slip(1.59869582147101,0.771408028343905)
    12.7997594036608 = slip(1.59869582147101,0.7523626882775)
    6.39987970183041 = slip(1.59869582147101,0.37618134413875)
    3.19993985091521 = slip(1.59869582147101,0.188090672069375) ~= 3.2

    11.0697057273413 = slip(1.59869582147101,0.203510878314101)
    11.0696157491919 = slip(1.59868955949705,0.203510096933728)

    Recall 28 = s(28) (no other way to get there).
    320 = 28+292 “fits” “744 levels”

    Can be made easy-to-understand by average member of General Anglo$Fear less Angela$and (i.e. Gore) UN? No. idea, but we’re all sick and tired of the politics.

  43. Paul Vaughan says:

    “What may be the reality is that certain changes alter the climate pattern permanently. Eg […] sinking of Doggerland could have had a permanent effect on the climate of continental europe.”

    Yes. Tipping points are observed. Bill Illis’ classic graph again since it underscores discrete circulatory reorganization fantastically:

    Cycles are observed too.

    Those cycles are always there.
    Other cycles we’ve discussed manifest over a more limited domain.

    Gravitational & thermal tides (proximate) is what I’ve explored in distal context. I wouldn’t even try (at this point in time) to have a discussion with anyone about why I suggest “solar” proxies are being (severely) misinterpreted. I simply note that (better rightly said than left silent).

    Tallbloke mentioned circulatory “cell structure” recently. I usually write “circulatory topology” with accompanying water transport & phase-transformations central in mind.

    Severe miscommunications arise because most climate commentators (whether in person or online) are totally and completely ignorant of the basic circulatory building blocks.

    In person I always quiz people on basic gyre structure awareness before I decide what to discuss (sometimes then deciding to totally change the subject immediately).

    If they don’t even know about heat engines (equator-pole & interhemispheric) but they consider themselves well-informed about climate I do other checks (on their judgement and willingness to learn) before deciding whether to promptly change the subject or politely exit the conversation.


    Solar cycle deceleration simply indicates interhemispheric throttle.
    Confounded lunisolar structure exists.

    I’ve worked out most of my Windows-to-MacOS migration issues so I may restart exploration. I reached “the starting point” in late summer this year and then stopped (with good reason).

  44. oldmanK says:

    PV says “If they don’t even know about heat engines—“.

    Not only heat cycles, but dynamics of the gyroscope under external ‘gravitational’ forces. Our ancestors had discovered (way before the tensor calculus – whatever that was in my earlier days) that ‘when sun and moon come together’, they meet sometimes like brazen lovers and create a disastrous mess.

  45. oldmanK says:

    For after the friday booze: video

    Just the first minute, and note the series of dates.
    7500bce > peak
    6200 ” > root
    5500 ” > peak
    5200 ” > root
    2200 ” > root
    Missing 3550bce -peak- the time of abrupt desiccation of sahara, and 3200bce -root- tectonic shift, similar to 5200bce.

    Info on their dating is missing.

  46. Paul Vaughan says:

    oldbrew wrote “A 6ka cycle discussed earlier looks like a match between 35 U-N and 302 J-S. Maybe it could repeat but don’t have any dates to propose.”

    73500 = slip(6000,1470)
    Mozart Symphony No. 40

  47. Paul Vaughan says:

    73500 = slip(6000,1470)

    What does it mean? Spelled out simply:

    ⌊ 6000 / 1470 ⌉ = ⌊4.08163265306122⌉ = 4
    6000 / 4 = 1500
    i.e.harmonic of 6000 nearest 1470 is 6000 / 4 = 1500
    73500 = (1500)*(1470) / (1500 – 1470)

  48. Paul Vaughan says:

    7920 (M11)
    4370 (B)
    4270 = s(4370)

    3650 = 7920-4270 = 146 * 25
    Suggestion: Repeat calculations at link for Keplerian.
    Thus concretely (in mathematical sense) find 5256 = 7920-2400-240-24.

    178 (B)
    836 smallest untouchable weird no.
    2400 ~= beat(418,356) — (E8)
    96 ~= axial(209,178)

  49. Paul Vaughan says:

    oldmanK wrote in good spirits: “For after the friday booze”

    No booze over here — and no alcohol consumption ever. This is my real taste:
    Vivaldi RV 411 – Cello Concerto in F Major : Ofra Harnoy

    Beyond that I have lots of acts, but the real me is clean and pure (minus whatever the toxic workplace politics of our incomprehensibly expensive city subtracted from my life mercilessly).

    There can be no controversy about this:
    2.36966735541038 = slip(0.999978614647502,0.0745030006844627)
    9.0943796900619 = slip(2.36966735541038,0.499989307323751)
    96.1613372617316 = slip(9.0943796900619,0.999978614647502)

    Exploring beyond that:
    207.339942322963 = beat(179.333839550924,96.1613372617316)
    179.333839550924 = beat(207.339942322963,96.1613372617316)
    65.6935817497354 = axial(207.339942322963,96.1613372617316)
    131.387163499471 = harmean(207.339942322963,96.1613372617316)
    103.669971161481 = beat(179.333839550924,65.6935817497354)
    96.1613372617316 = harmean(179.333839550924,65.6935817497354)
    96.1613372617316 = beat(207.339942322963,65.6935817497354)
    179.333839550924 = beat(103.669971161481,65.6935817497354)
    80.4240535631612 = harmean(103.669971161481,65.6935817497354)
    The latter’s a candidate for SAOT (stratospheric aerosol optical depth) tower translation symmetry.

  50. oldmanK says:

    PV OK. Good to know always sober. Maybe most would be on sunday morning, perhaps with some time to spare.

    Suggest (in line with thread)
    https://www.youtube.com/watch?v=cWjY0RpUDd0 good for background

    The question remains: what aligns with those dates (or near). If one likes watching music concerts – of the sane kind-, every so often the conductor stops to re-arrange the score, and his musicians. ‘Nodes’ in the music score. The solar system seemingly does so too. Those dates look like nodes, and the silence is a time of fear.

  51. Paul Vaughan says:

    Slowly getting back in the exploration groove (suspended for 2.5 months) while overcoming Windows-to-MacOS hurdles 1 by 1.

    As I’ve repeatedly reminded obtuse “energy doom & gloom” fans (who seem curiously unable to discuss natural climate variation sensibly, but perhaps able II accidentally CO[$] WWIII inequality), this is for sure observed clearly:

    2.36966735541038 = slip(0.999978614647502,0.0745030006844627)
    9.0943796900619 = slip(2.36966735541038,0.499989307323751)
    96.1613372617316 = slip(9.0943796900619,0.999978614647502)

    We all know this (lunar tropical month) is observed (with crystal clarity) in LOD:
    0.0748024157783867 = axial(0.999978614647502,0.0808503463381246)

    Simple step from there:
    208.076918907664 = slip(96.1613372617316,0.0748024157783867)

  52. oldbrew says:

    Some interesting-sounding concepts here.

    The Structure of Climate Variability Across Scales (2020)

    Plain Language Summary

    Climate variables are related over long times and large distances. This shows up as correlations for averages on long intervals or between distant areas. An important finding is that the majority of correlations in climate can be described by a simple mathematical relationship. We present such correlations for temperature on long times. Similarly, the intensity of precipitation events depends on their frequency in a simple manner. A useful concept is scaling where a scale denotes the width of an average. Scaling says that averages on different scales are related by a simple function—mathematically, this is a power law with the scaling exponent as a characteristic number. Scaling has impacts on predictability, temperature trends, and the assessment of future climate changes caused by anthropogenic forcing.
    – – –
    Not sure about the ‘future climate changes’ bit 🙄

  53. Paul Vaughan says:

    Ignorance “Fits”

    semi-annual equivalents of LNC & LAC (lunar nodal & apse cycles)


    0.0748024157783867 = axial(0.999978614647502,0.0808503463381246)
    0.0695963307732714 = axial(0.499989307323751,0.0808503463381246) ~= 0.07

    18.6129709123853 = beat(0.0748024157783867,0.0745030006844627)
    1.05675245596013 = beat(0.0745030006844627,0.0695963307732714)
    14.994646953627 = slip(1.05675245596013,0.0808503463381246) ~= 15 ($USDollars)


    0.0748024157783867 = axial(0.999978614647502,0.0808503463381246)
    0.0695963307732714 = axial(0.499989307323751,0.0808503463381246) ~= 0.07

    8.84735293159855 = beat(0.0754402464065708,0.0748024157783867)
    0.89843260443588 = beat(0.0754402464065708,0.0695963307732714)
    8.00090645270494 = slip(0.89843260443588,0.0808503463381246) ~= 8 (OCTopUS0?07)

    30.0144661920487 = slip(14.994646953627,5.99685290323073) ~= 30
    9.99363750860884 = beat(14.994646953627,5.99685290323073) ~= 10
    5.99685290323073 = beat(0.0754402464065708,0.0745030006844627)

    6.8554199096208 = harmean(8.00090645270494,5.99685290323073)
    171.38549774052 = 25 * 6.8554199096208
    171.389290439286 = beat(164.788501026694,84.0120465434634) — NASA “factsheet” fits

    0.761766336146052 = harmean(1.00001642710472,0.61519780971937) — NASA “factsheet” fits
    0.814043513256406 = beat(11.8619822039699,0.761766336146052)
    44.2788229093651 = slip(1.59869582147101,0.814043513256406)
    22.1394114546826 = slip(1.59869582147101,0.407021756628203)
    22.1397155269176 = 8.45661883002872 * φφ
    8.45661883002872 = axial(29.4571389459274,11.8619822039699) — NASA “factsheet” fits
    2.61803398874989 = φφ

    There were 378 comments on the last Scafetta thread. The last 2 comments exactly noted concrete (in the mathematical sense) properties of NASA “factsheet” fits not possessed by Keplerian elements.

    build in a mystery
    22.07 (JSEV)
    11.07 (JEV)
    10-0.07 = 9.93 ~= 9.92943862566537 = beat(29.4571389459274,11.8619822039699)/2
    9.07 harmonic mean of LAC & LNC/2 (matrix attractor – use different year-lengths)
    6.57 ~= axial(s/2,j) = 6.57038000192319 = axial(14.7285694729637,11.8619822039699)
    2.37 QBO
    0.07 ~= axial(semi-annual,lunar synodic)
    42 = 19.86 + 22.14
    4.2 = 6.57 – 2.37

  54. Paul Vaughan says:

    Timin’D(ice seas)19 & 247

    audio$11ave. no. 242 = 71+171 = average(ΣΔ(220),Σδ(220)) ?

    142 = ΣΔ(220) = 2 * 71
    342 = Σδ(220) = 2 *171

    71 = Top moon sstir f(actor)
    220 = lowesst amicable no.

    19 = y mod 24 where y = 19,43,67,163
    247 = average(-163,C) = average(Σφ(323),ΣΦ(323)) = ΣΦ(490)

  55. oldbrew says:

    This 2020 Geophys. Review article proposes splitting weather/climate timescales into regimes…

    The Structure of Climate Variability Across Scales

    The proposed regimes are as follows:

    1. the weather regime with time scales from 6 hr up to 20 days with an exponent of β≈1.8
    2. the macroweather regime with time scales between 20 days and 50 years and β=0.2
    3. the climate regime with time scales between 50 and 80,000 years (includes glacial-interglacial cycles) and β=1.8
    4. the macroclimate regime between 80,000 and 500,000 years and β=−0.6
    5. the megaclimate regime for time scales larger than 500,000 years which takes us to the limit of reliable proxies (Lovejoy & Schertzer, 2013) and β=1.8.

    – – –
    The climate regime minimum period is longer than the satellite record promoted by the IPCC alarm crowd.

  56. oldbrew says:

    Some of the periods shown in our Figure 1, lower right sector.

    Credit: A. Berger (1994)

  57. Paul Vaughan says:

    No. 11edge of….

    “-wan tag url with US$word$ Kurt?”cake

    The tree lisird guardian node out tropico[II].

    J: -11/II
    S(at)turn: +11/II+07
    U: +07
    N: -07
    LA N/A buzz ‘fits’

  58. Paul Vaughan says:

    “1800 year” Jupiter-Venus “fits”

    0.648849058984626 = beat(11.8619822039699,0.61519780971937)
    1.16972993301468 = harmean(11.8619822039699,0.61519780971937)

    42.1273789033386 = slip(11.8619822039699,0.61519780971937)
    571.728713687145 = slip(42.1273789033386,0.648849058984626)

    1.17212805162319 = beat(571.728713687145,1.16972993301468)
    6.05665191901057 = slip(1.17212805162319,0.648849058984626)
    18.1090542796984 = slip(6.05665191901057,0.648849058984626)
    1800.94544758387 = slip(18.1090542796984,6.05665191901057)

    208 & 3000 year Jupiter-Earth “fits”

    1.09208381849802 = beat(11.8619822039699,1.00001642710472)
    1.84453091657695 = harmean(11.8619822039699,1.00001642710472)

    85.8241422239818 = slip(11.8619822039699,1.00001642710472)
    208.060899534332 = slip(85.8241422239818,1.09208381849802)

    1.86102957924381 = beat(208.060899534332,1.84453091657695)
    6.28957264698494 = slip(1.86102957924381,1.09208381849802)

    0.273020954624506 = 1.09208381849802 / 4
    170.175183513687 = slip(6.28957264698494,0.273020954624506)
    3000.4570621401 = slip(170.175183513687,6.28957264698494)

  59. oldbrew says:

    Ice Would Suffice
    A geophysicist detects the celestial rhythms that govern the fate of the earth.

    Like Milankovitch, Rial likes to think big. Lately he’s been studying the Earth’s orbital variations. Earth’s solar orbit constantly expands and contracts, oscillating in shape between an almost perfect circle and an ellipse. This continual cosmic waltz is known as the Earth’s eccentricity. The whole cycle-from greatest to least eccentricity, and back-takes roughly 95,000 years.

    But eccentricity has a second component-as Earth’s orbit shrinks and stretches, it also rotates. A full cycle lasts 413,000 years (see illustration).

    – – –
    Illustration link (one-page pdf) says:

    The 95,000-year cycle occurs simultaneously with a second, longer cycle in
    which the degree of eccentricity itself fluctuates. In figure 1, the maximum
    eccentricity is very elliptical. In figure 2, maximum eccentricity has become
    more circular. After 413,000 years, the cycle is complete (figure 3).

    Click to access orbits.PDF

    More re. 413,000 years…

    And the missing 413,000-year eccentricity signal? FM theory can explain that, too. In frequency modulation, the modulator — in this case, the 413,000-year signal — doesn’t show up in the final signal. Rather, it widens the signal’s frequency by creating sidebands, or peaks distributed symmetrically on both sides of the carrier.

    That, Rial says, is why heavy oxygen signals often show multiple peaks — and why some of those peaks are not directly related to Milankovitch frequencies.

  60. Paul Vaughan says:

    ENSO cure deluge yuan TropiCO[II]

    utmost fear roc-river
    B -26˚CO[TooII]in’ _rain washin’ tune
    fear caste$SSTin’ “out”
    $0 C air “down” poor

    sew word$ “soak air fully” or “$0 care folly?” love$era miss$sstory 2-1 vision

    Dove “hide & concur” buy done? NO way: west-torn climbIT bully up$ET urban morgue II central lies CO[UNtry] life.

    46 = (72^5-67^5-43^5-19^5-47^5)^(1/5) ——– n = 5

  61. Paul Vaughan says:

    CO[$] LOCAL west-torn how-sing inequality
    WORSE than TropiCO[II]in Can.: no. DO
    -26˚C secret$awes B11inkUN reelUS $state
    $0 deluge yuan means$ DO lose UN

    4278 = 4370 – 46*2 = ⌊slip(164.788501026694,84.0120465434634)⌋ —— fits

    UN can sell north earn -26˚C 0[$] TooII “DO:whatITache$JUST[in]getTH[_]ru…..MI sh! add DO….In$soak Eur. deluge yuan”

    4270 = ⌊slip(164.791315640078,84.016845922161)⌉ = s(4370) —- Keplerian

    World climate bullies (financially) assault “selfish” Can. aid UN pour.
    Rich just ice: UNflyway over -26˚Code-who?bri$in TropiCO[II] deluge yuan.

  62. Paul Vaughan says:

    selection from today’s informal slip-cycle exploration

    Jupiter-Uranus fits
    (alert readers compare carefully with Jupiter-Saturn Keplerian)

    13.8121761933365 = beat(84.0120465434634,11.8619822039699)
    6.90608809666827 = 13.8121761933365 / 2
    3.45304404833414 = 13.8121761933365 / 4
    20.7887248306405 = harmean(84.0120465434634,11.8619822039699)
    10.3943624153202 = axial(84.0120465434634,11.8619822039699)
    5.19718120766012 = 10.3943624153202 / 2
    2.59859060383006 = 10.3943624153202 / 4
    1018.7884154919 = slip(84.0120465434634,11.8619822039699)
    4247.89838274149 = slip(1018.7884154919,13.8121761933365)

    generalized Bollinger set-up
    20.8909627934705 = beat(4247.89838274149,20.7887248306405)
    10.4454813967353 = 20.8909627934705 / 2
    5.22274069836763 = 20.8909627934705 / 4
    20.6874826760404 = axial(4247.89838274149,20.7887248306405)
    10.3437413380202 = 20.6874826760404 / 2
    5.1718706690101 = 20.6874826760404 / 4
    42.8535516856396 = slip(20.8909627934705,13.8121761933365)
    42.8535516856396 = slip(13.8121761933365,10.4454813967353)
    38.8661803403201 = slip(13.8121761933365,5.22274069836763)

    41.560206288534 = slip(20.6874826760404,13.8121761933365)
    41.1913683891299 = slip(13.8121761933365,10.3437413380202)
    41.9357092032815 = slip(13.8121761933365,5.1718706690101)

    noteworthy findings
    (alert readers will readily note number theory tie-ins)

    417.707237123125 = slip(42.8535516856396,13.8121761933365)
    208.853618561562 = slip(38.8661803403201,13.8121761933365)
    208.853618561562 = slip(42.8535516856396,6.90608809666827)
    104.426809280781 = slip(38.8661803403201,6.90608809666827)
    104.426809280781 = slip(42.8535516856396,3.45304404833414)

    2433.40320912782 = slip(41.9357092032815,20.7887248306405)
    1216.70160456391 = slip(41.9357092032815,10.3943624153202)
    608.350802281956 = slip(41.9357092032815,5.19718120766012)
    304.175401140978 = slip(41.9357092032815,2.59859060383006)
    152.041769532922 = slip(38.8661803403201,3.45304404833414)

    349.059353015345 = slip(42.8535516856396,10.3943624153202)
    149.003701341377 = slip(38.8661803403201,10.3943624153202)
    698.11870603069 = slip(42.8535516856396,20.7887248306405)
    298.007402682754 = slip(38.8661803403201,20.7887248306405)

    239.056088301519 = slip(104.426809280781,42.8535516856396)
    355.799519579182 = slip(slip(42.8535516856396,5.19718120766012),38.8661803403201)
    2400.67054947816 = slip(698.11870603069,42.8535516856396)

    selected recall
    349.002324320085 = ⌊(e^√17π)^(1/2)⌉^2 – e^√17π
    s(496) = 496 = s(652) = s(s(608))
    29.4474891061275 = 1/(1/104+1/298)/φ^2 — ~Keplerian


    semi-major elements

    19.8815827583247 = beat(29.4525211998593,11.8693295447839)
    61.1813294227419 = slip(29.4525211998593,11.8693295447839)
    791.61563705865 = slip(61.1813294227419,19.8815827583247)

    17.2894874414117 = beat(791.61563705865,16.9199430202764)
    16.5658652544205 = axial(791.61563705865,16.9199430202764)

    99.3316290158022 = slip(19.8815827583247,16.5658652544205)
    25888.1275003765 = slip(99.3316290158022,19.8815827583247)
    ^ compare v
    25887.2073732037 = harmean of following sidereal-tropical beats
    25780.5804579468 = beat(29.4571389459274,29.42351935) —- S
    26586.2998478743 = beat(84.0120465434634,83.74740682) —- U
    25326.0015186278 = beat(164.788501026694,163.7232045) —- N

    starting point reached: late summer this year
    rich arrays to explore with parameter variation
    no doubt varying degrees of awareness exist in geostratigraphy community (some cases patchy)
    a few sensible climate students aren’t cancelling in mad-panic for inverted totalitarian lockdown

  63. Paul Vaughan says:

    OB wrote “413,000 years”

    readers may be aware: 413k estimate published 1978
    more recent estimate: ~405k

    sensible: comparative diagnostics, probe slip-cycle sensitivity to parameter variation

  64. oldbrew says:

    The ratios radiating from the de Vries cycle can be tested by putting 208.59091 in the memory of an 8-digit calculator, and using this cut from the main diagram of the post (brown circle added).

  65. Paul Vaughan says:

    regarding the magnified diagram (discussed years ago without the diagram)

    983 should be neither confused nor conflated with 980
    the 2 are distinct and strictly related to one another mathematically

    of the other quantities in the diagram only 2 are necessary (and important ones are omitted)

    this may indicate a fundamental difference in what each of us is exploring — i.e. we have different exploratory objectives …and that is neither wrong nor right – it simply is

    I’ve reoriented exploration (tropical, fits, semi-major elements, whatever else + relations between)
    note well for example: last comment doesn’t feature any Keplerian elements

    there’s a lot of stuff I never noted — too time-consuming and for no reward ($0 income for 1.5 years — meanwhile I knew a wealthy individual living for free in a big house collecting benefits during the same interval while researching offshore investments – weird qualification systems our western governments design …indeed)

  66. tallbloke says:

    Paul V. José Rial’s 2013 paper uses 413kyr. What citation has the 405kyr?

    “Here we show that climate oscillations over the past four million years can be explained by a single mechanism: the synchronization of nonlinear internal climate oscillations and the 413,000-year eccentricity cycle. ”


  67. oldbrew says:

    This paper was published 2 weeks ago and mentions both periods.

    Middle Ordovician astrochronology decouples asteroid breakup from glacially-induced biotic radiations

    Precession filter output tuning option

    Another tuning was performed using a large bandwidth precession filter output (0.04–0.1 cycles/cm) and setting up an average duration for this orbital component at 20 kyr according to ref. 25 (Supplementary Data 4). This tuning option logically enhances the power of the 20 kyr and erases any expression of frequency and amplitude modulations of the precession but highlights the presence of a significant periodicity at 413 kyr that matches fairly well the expected 405 kyr component (Fig. 4d). [bold added]

    – – –
    They expected 405 kyr but found 413.

  68. oldbrew says:

    This one’s from January 2021.

    A New Theory of Change in the Insolation of the Earth over Millions of Years against Marine Isotope Stages
    J. J. Smulsky

    Oscillations in the parameters of orbital and rotational motions of the Earth and various insolation components, as well as their periods and amplitudes, are considered for the last 5 Myr. Orbit eccentricity e varies with periods of 94.6 kyr, 413 kyr, and 2.31 Myr, while the periods of perihelion rotation relative to the equator are nonuniform and vary from 13.8 to 41.8 kyr. These periods can also be found in changes in the obliquity and insolation.

    – – –
    Some other papers refer to 405 kyr but not sure what the origin of the number is. 413 kyr derives from 124 kyr (3 obliquities) and 95 kyr (5*19 kyr) in our diagram, ratio 3:10:13.

  69. Paul Vaughan says:

    quoting TB: “José Rial’s 2013 paper uses 413kyr. What citation has the 405kyr?”

    g_2 – g_5 :

    405113.811661464 = beat(304399.417131486,173804.240903943)
    405568.048748278 = beat(304405.279928371,173889.708842077)
    405691.196375825 = beat(304407.424910486,173913.043478261)


  70. Paul Vaughan says:

    the suggestion I consistently make:

    explore output sensitivity to parameter variation
    i.e. do analyses with all possible combinations of parameters of all types from all sources

    compare, contrast, benefit from awareness thus derived
    e.g. “Charvatova 2400 year trefoil” is from Keplerian elements but does not exist with NASA “factsheet” fits-to-observations

  71. Paul Vaughan says:

    “semimajor axis” appears twice on each NASA “factsheet”:
    1. “Earth Mean Orbital Elements (J2000)”
    2. “Orbital parameters”

    generalized Bollinger method on latter
    19.7966520147419 = beat(29.663446337819,11.8729429230374)
    16.9582581219409 = harmean(29.663446337819,11.8729429230374)
    9311.85469245949 = slip(59.5164858493412,19.7966520147419)
    axial +/-
    16.989197952262 = beat(9311.85469245949,16.9582581219409)
    16.9274307787351 = axial(9311.85469245949,16.9582581219409)
    top level result
    119.798661842894 = slip(19.7966520147419,16.989197952262)
    top-base slip
    2327.9636731148 = slip(119.798661842894,19.7966520147419)

  72. tallbloke says:

    Paul V. An inpage search doesn’t find 405. Fig.2 indicates g_3 and g_4 are also involved in Earth’s eccentricity, so it’s not clear to me why the beat period of g_2 and g_5 would produce a definitive value. Time is short, and a clear explanation would be welcome.

  73. Paul Vaughan says:

    Review (stuff I always assume everyone memorized long ago – perhaps my bad assumption)

    La2011 Table 6 & La2004a
    173913.043478261 = 1 / g_2 = 360*60*60/7.452
    304407.424910486 = 1 / g_5 = 360*60*60/4.257452

    La2011 Table 6 La2010a
    173889.708842077 = 1 / g_2 = 360*60*60/7.453
    304405.279928371 = 1 / g_5 = 360*60*60/4.257482

    La2011 Table 5
    173804.240903943 = 1 / g_2
    304399.417131486 = 1 / g_5


    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    2384110.34604552 = beat(74626.0277273697,72361.0252351259)

    La2011 Table 6 & La2004a
    74619.9907876555 = 1 / g_3 = 360*60*60/17.368
    72337.575351641 = 1 / g_4 = 360*60*60/17.916

    La2011 Table 6 La2010a
    74619.9907876555 = 1 / g_3 = 360*60*60/17.368
    72337.575351641 = 1 / g_4 = 360*60*60/17.916

    La2011 Table 5
    74626.0277273697 = 1 / g_3
    72361.0252351259 = 1 / g_4

    This is all conventional-mainstream stuff – widely- & well-known.

  74. Paul Vaughan says:

    for anyone deep-diving the history

    Berger 1978

    Berger-Loutre 1991

    source: Table 1 p.114 (pdf p.8)

  75. Paul Vaughan says:

    Here’s a fantastic example relating the different sets of parameters – note that Seidelmann’s (1992) parameters hit an exact match:


    68753.3156498674 = 1 / s_3 = 360*60*60/-18.85
    68760.6112054329 = 1 / s_3 = 360*60*60/-18.848

    A very helpful paper:
    Hinnov, Linda 2013. Cyclostratigraphy and its revolutionizing applications in the earth and planetary sciences.

    TB: see Table 1, note “g2-g5” under “orbital eccentricity”

  76. tallbloke says:

    Paul V, thanks for the notes and links. I admit I don’t have this stuff commited to memory. I still don’t get why the beat period of g_2 and g-5 tells us anything, but I’ll leave that for now.

  77. oldmanK says:

    A quick comment (lengthy reading following the many links; but interesting)

    Gail Combs says: May 26, 2014 at 11:35 am asks a very particular question: “So the question becomes what else kicks the earth into glaciation?”
    That’s easy. An obliquity swing to ‘very low’. (Remember Dodwell changed the goalposts). And to a high, with large polar masses (Iz becoming larger than Ix Iy), fast ice melt.

    There is something else I question. But – caveat- I may need to be corrected; too rusty on the maths.
    Eccentricity is dictated by planetary influences (?). However obliquity may be intrinsic to planet, though maybe change is extraneously triggered. The third, precession, depends on obliquity, in that an abrupt change in obliquity triggers a precession change in both frequency and phase.

    Secondly, the extreme changes to the geology don’t seem to feature. If looking at cycles of near 1/2M years, there were very big geologic changes.
    See video below at 04:30 , the Sahara was an open sea.

  78. tallbloke says:

    OldmanK, changes in eccentricity are accompanied by changes in inclination of the orbital plane relative to the invariant plane (roughly the plane through the centres of the Sun and Jupiter). I suspect obliquity will then be affected too, due to a gyroscopic effect imposed mainly by Jupiter. The clue is in the 3:1 whole number ratio between the 41kyr obliquity period and the 124kyr eccentricity period.

  79. Paul Vaughan says:

    Hydrologic Luna: Sea Atmosphere Rock River


  80. Paul Vaughan says:

    filter caught 28 dayspacing

  81. Paul Vaughan says:


    I had noticed that the weekend deluge was exactly 5 lunar months after the 4 day heat wave.
    It next occurred to me that autumn hiking trail washouts had been about a month apart.

    These events were of a notably discrete nature (intense, short duration) — thus easy to recall distinctly.

  82. Paul Vaughan says:

    something in response to TB’s last comment – recall

    Cuk, M. – excitation of lunar eccentricity by planetary resonances
    explores Jovian evection resonance, resonance with Venus – seminar video:

    “This guy isn’t like climate modelers bluffing about the extent of what’s known. He’s upfront, clear, & honest about what’s not known.”

  83. tallbloke says:

    Paul, good reminder. I did watch that video at the time, and should watch it again when I have bandwidth.

  84. Paul Vaughan says:

    a little elaboration on the last graph
    more discrete than usual switch in weather here this year from summer drought to wet fall
    flips like switch every year but difference this year:
    events were discrete sharp impulses
    from memory – some of it sharp – and some of it vague I began suspecting lunar scheduling
    figured out some exact dates from recall – then got data and verified others
    events considered as a set were more powerful than usual – on lunar schedule
    resonance appears to have played powerful role that should not be ignored – work to be done (governments, universities, etc.) – e.g. discerning combinations of other factors permitting such circulatory expression – a problem too challenging for most, but even assuming CO2 problems are far worse than UN & MSM say, there’s crucial work (needed for infrastructure resilience planning etc.) demanding exceptional awareness of circulatory topology and good programming skill
    better rightly said than left silent, but this message is written for very few people

  85. Paul Vaughan says:

    405 kyr Jupiter-Venus driven Earth eccentricity cycle linked to paleoclimatic variation
    Posted: July 10, 2019 by tallbloke”

    seems like forever ago

    “assigned a 412.885- ky periodicity based on a now-legacy analytical astronomical solution, BRE74/BER78 (6, 7). Since the 1990s, there have been dozens of reports for strong 405-ky scale cycles in stratigraphic sequences from around the world that appear to bear out this astronomical calculation […]”

  86. Paul Vaughan says:

    nominal “400ka” review
    interpretive note: the high-frequency is calendar-month aliasing from the online calculator set up by insolation authors – tracking the max day gives a smooth curve

  87. Paul Vaughan says:

    watching the Cuk seminar video pay attention to his commentary about:
    tide-modelling on earth (with specific attention to geography)
    tidal dissipation – 95% versus “naive” (tidal-bulge) conception
    he mentions plates, but doesn’t talk about circulatory reorganization
    (ocean-wise our best teacher on that was Bill Illis)

    raising question, but not expecting public alphabet answers:
    which climate models (secret or otherwise) include tides well enough for sam, enso, nam, do, etc.?

  88. tallbloke says:

    Paul V, thanks, in the hurley burley of running the Yorkshire region general election campaign, I forgot all about making that post. Food for thought.

  89. Paul Vaughan says:

    Dear Friends,
    Weather IT left & right.

    “nothing stands between us hear” — “Possession

    NASA “factsheet” sidereal fits with Seidelmann (1992) tropical
    24833.7230131724 = beat(0.61519780971937,0.61518257)
    26449.9240047265 = beat(1.00001642710472,0.99997862)
    25691.7257904301 = beat(1.88084873374401,1.88071105)
    25771.8797028462 = beat(11.8619822039699,11.85652502)
    25780.5804579468 = beat(29.4571389459274,29.42351935)
    26586.2998478743 = beat(84.0120465434634,83.74740682)
    25326.0015186278 = beat(164.788501026694,163.7232045)
    25764.8962196266 = harmean

    Seidelmann (1992) Keplerian sidereal with Seidelmann (1992) tropical
    25763.987503107 = beat(1.00001743371442,0.99997862)

    NASA “factsheet” sidereal fit with NASA “factsheet” tropical
    25762.0064305964 = beat(11.8619822039699,11.8565229295003)

  90. Paul Vaughan says:

    NASA “Mirrorball”

    Seidelmann (1992) Keplerian sidereal with Seidelmann (1992) tropical
    25811.3691836373 = beat(0.240846697327135,0.24084445)
    25757.05496809 = beat(0.615197263396975,0.61518257)
    25763.987503107 = beat(1.00001743371442,0.99997862)
    25902.4692609995 = beat(1.88084761346252,1.88071105)
    26114.2236547808 = beat(84.016845922161,83.74740682)
    25259.6956047041 = beat(164.791315640078,163.7232045)
    25765.5344057459 = harmean

    another day of knowing – SM – “cashew sew herd”

  91. Paul Vaughan says:

    Given some of the (unexpected) confusion that surfaced in discussion, I’m going to post some basic calculations (next day or 2).

  92. Paul Vaughan says:

    Basics — Part I

    translation from angles
    to periods:
    La2011 Table 6 La2004a

    231842.576028623 = 1 / g_1 = 360*60*60/5.59
    173913.043478261 = 1 / g_2 = 360*60*60/7.452
    74619.9907876555 = 1 / g_3 = 360*60*60/17.368
    72337.575351641 = 1 / g_4 = 360*60*60/17.916
    304407.424910486 = 1 / g_5 = 360*60*60/4.257452
    45884.2272968667 = 1 / g_6 = 360*60*60/28.245
    419695.778851413 = 1 / g_7 = 360*60*60/3.087951
    1925645.70793482 = 1 / g_8 = 360*60*60/0.673021
    3703492.02720466 = 1 / g_9 = 360*60*60/-0.34994

    231842.576028623 = 1 / s_1 = 360*60*60/-5.59
    183829.787234043 = 1 / s_2 = 360*60*60/-7.05
    68753.3156498674 = 1 / s_3 = 360*60*60/-18.85
    72993.5229512813 = 1 / s_4 = 360*60*60/-17.755

    49188.0648348793 = 1 / s_6 = 360*60*60/-26.347855
    433078.958481195 = 1 / s_7 = 360*60*60/-2.9925259
    1873547.13358854 = 1 / s_8 = 360*60*60/-0.691736
    3703068.74678553 = 1 / s_9 = 360*60*60/-0.34998
    La2011 Table 6 La2010a

    231842.576028623 = 1 / g_1 = 360*60*60/5.59
    173889.708842077 = 1 / g_2 = 360*60*60/7.453
    74619.9907876555 = 1 / g_3 = 360*60*60/17.368
    72337.575351641 = 1 / g_4 = 360*60*60/17.916
    304405.279928371 = 1 / g_5 = 360*60*60/4.257482
    45884.3897482377 = 1 / g_6 = 360*60*60/28.2449
    419696.458422524 = 1 / g_7 = 360*60*60/3.087946
    1925651.43034595 = 1 / g_8 = 360*60*60/0.673019
    3702116.71951324 = 1 / g_9 = 360*60*60/-0.35007

    231016.042780749 = 1 / s_1 = 360*60*60/-5.61
    183569.40509915 = 1 / s_2 = 360*60*60/-7.06
    68760.6112054329 = 1 / s_3 = 360*60*60/-18.848
    73009.9712692243 = 1 / s_4 = 360*60*60/-17.751

    49188.090971097 = 1 / s_6 = 360*60*60/-26.347841
    433078.972953216 = 1 / s_7 = 360*60*60/-2.9925258
    1873536.29976581 = 1 / s_8 = 360*60*60/-0.69174
    3702857.14285714 = 1 / s_9 = 360*60*60/-0.35
    La2011 Table 5

    232283.957100594 = 1 / g_1
    173804.240903943 = 1 / g_2
    74626.0277273697 = 1 / g_3
    72361.0252351259 = 1 / g_4
    304399.417131486 = 1 / g_5

  93. Paul Vaughan says:

    Basics — Part II

    combinations of part I pieces

  94. Paul Vaughan says:

    Basics — Part II — La2011 Table 6 La2004a

    18954.7215653296 = axial(72337.575351641,25685)
    19107.8673985264 = axial(74619.9907876555,25685)
    22379.7610632674 = axial(173913.043478261,25685)
    23123.257932709 = axial(231842.576028623,25685)
    23686.4105892345 = axial(304407.424910486,25685)

    405691.196375825 = beat(304407.424910486,173913.043478261)

    22379.7610632674 = axial(405691.196375825,23686.4105892345)
    23686.4105892345 = beat(405691.196375825,22379.7610632674)

    2364963.50364963 = beat(74619.9907876555,72337.575351641)

    18954.7215653296 = axial(2364963.50364963,19107.8673985264)
    19107.8673985264 = beat(2364963.50364963,18954.7215653296)

    94885.6349884336 = beat(304407.424910486,72337.575351641)
    98851.7032239995 = beat(304407.424910486,74619.9907876555)
    123853.211009174 = beat(173913.043478261,72337.575351641)
    130697.862041146 = beat(173913.043478261,74619.9907876555)

    94885.6349884336 = beat(23686.4105892345,18954.7215653296)
    98851.7032239994 = beat(23686.4105892345,19107.8673985264)
    123853.211009174 = beat(22379.7610632674,18954.7215653296)
    130697.862041146 = beat(22379.7610632674,19107.8673985264)

    405691.196375825 = beat(23686.4105892345,22379.7610632674)
    2364963.50364959 = beat(19107.8673985264,18954.7215653296)

    28885.0726711513 = beat(231842.576028623,25685)
    29856.6153692987 = beat(183829.787234043,25685)
    39630.0395794302 = beat(72993.5229512813,25685)
    41002.9713449516 = beat(68753.3156498674,25685)
    41726.4103344458 = beat(2364963.50364963,41002.9713449516)
    53754.4977286943 = beat(49188.0648348793,25685)

  95. Paul Vaughan says:

    Basics — Part II — La2011 Table 6 La2010a

    18954.7215653296 = axial(72337.575351641,25685)
    19107.8673985264 = axial(74619.9907876555,25685)
    22379.3746087485 = axial(173889.708842077,25685)
    23123.257932709 = axial(231842.576028623,25685)
    23686.3976020646 = axial(304405.279928371,25685)

    405568.048748278 = beat(304405.279928371,173889.708842077)

    22379.3746087485 = axial(405568.048748278,23686.3976020646)
    23686.3976020646 = beat(405568.048748278,22379.3746087485)

    2364963.50364963 = beat(74619.9907876555,72337.575351641)

    18954.7215653296 = axial(2364963.50364963,19107.8673985264)
    19107.8673985264 = beat(2364963.50364963,18954.7215653296)

    94885.8433982369 = beat(304405.279928371,72337.575351641)
    98851.9294203326 = beat(304405.279928371,74619.9907876555)
    123865.048265316 = beat(173889.708842077,72337.575351641)
    130711.04387292 = beat(173889.708842077,74619.9907876555)

    94885.8433982369 = beat(23686.3976020646,18954.7215653296)
    98851.9294203326 = beat(23686.3976020646,19107.8673985264)
    123865.048265316 = beat(22379.3746087485,18954.7215653296)
    130711.04387292 = beat(22379.3746087485,19107.8673985264)

    405568.048748277 = beat(23686.3976020646,22379.3746087485)
    2364963.50364964 = beat(19107.8673985264,18954.7215653296)

    28897.9541450021 = beat(231016.042780749,25685)
    29863.4951755413 = beat(183569.40509915,25685)
    39625.1928264671 = beat(73009.9712692243,25685)
    41000.3769972924 = beat(68760.6112054329,25685)
    41723.7236350429 = beat(2364963.50364963,41000.3769972924)
    53754.4665144806 = beat(49188.090971097,25685)

  96. Paul Vaughan says:

    Basics — Part II addendum

    these belong in last group of last 2 comments:
    40304.1903450548 = axial(2364963.50364963,41002.9713449516) —- La2011 Table 6 La2004a
    40301.6836680027 = axial(2364963.50364963,41000.3769972924) —- La2011 Table 6 La2010a

  97. Paul Vaughan says:

    Basics — Part II — La2011 Table 5

    18956.3312608245 = axial(72361.0252351259,25685)
    19108.2632249266 = axial(74626.0277273697,25685)
    22377.9583670246 = axial(173804.240903943,25685)
    23127.6410355152 = axial(232283.957100594,25685)
    23686.3621038729 = axial(304399.417131486,25685)

    405113.811661464 = beat(304399.417131486,173804.240903943)

    22377.9583670246 = axial(405113.811661464,23686.3621038729)
    23686.3621038729 = beat(405113.811661464,22377.9583670246)

    2384110.34604552 = beat(74626.0277273697,72361.0252351259)

    18956.3312608245 = axial(2384110.34604552,19108.2632249266)
    19108.2632249266 = beat(2384110.34604552,18956.3312608245)

    94926.7650262257 = beat(304399.417131486,72361.0252351259)
    98863.1425160258 = beat(304399.417131486,74626.0277273697)
    123977.271216256 = beat(173804.240903943,72361.0252351259)
    130777.916695678 = beat(173804.240903943,74626.0277273697)

    94926.7650262257 = beat(23686.3621038729,18956.3312608245)
    98863.1425160258 = beat(23686.3621038729,19108.2632249266)
    123977.271216256 = beat(22377.9583670246,18956.3312608245)
    130777.916695678 = beat(22377.9583670246,19108.2632249266)

    405113.811661464 = beat(23686.3621038729,22377.9583670246)
    2384110.34604549 = beat(19108.2632249266,18956.3312608245)

    no node periods in La2011 Table 5, so no obliquity periods

  98. Paul Vaughan says:

    Basics — Part III

    for comparison

    “Figure 2. Earth’s orbital parameters from the La2010d astronomical solution […] (A) The orbital eccentricity variation, 0–10 Ma. (B) Periodogram of the orbital eccentricity variation shown in (A). (C) The orbital inclination variation relative to the invariable plane, 0–10 Ma (Note: Fig. 6 […] La2004 orbital inclination relative to the ecliptic plane). (D) Periodogram of the orbital inclination variation shown in (C). […]”


    La2011 Table 6 La2004a
    172849.434938392 = beat(68753.3156498674,49188.0648348793)
    121064.922933209 = beat(183829.787234043,72993.5229512813)
    1183561.64383561 = beat(72993.5229512813,68753.3156498674)
    109849.126970673 = beat(183829.787234043,68760.6112054329)
    106535.141800247 = beat(231842.576028623,72993.5229512813)
    97752.3004978126 = beat(231842.576028623,68760.6112054329)

    La2011 Table 6 La2010a
    172803.663437665 = beat(68760.6112054329,49188.090971097)
    121223.458984192 = beat(183569.40509915,73009.9712692243)
    1181403.82862352 = beat(73009.9712692243,68760.6112054329)
    109942.314217849 = beat(183569.40509915,68760.6112054329)
    106745.737583395 = beat(231016.042780749,73009.9712692243)
    97899.9848919776 = beat(231016.042780749,68760.6112054329)

  99. tallbloke says:

    Paul V. One of things I’m having difficulty understanding is why, when spectral analyses are ‘tuned’ to 405kyr, they’re still getting the 413kyr spike.


  100. Paul Vaughan says:

    Perhaps 413 Might

    Authors measured 14, 15.6, 19, 283 and perhaps misinterpreted.
    Their “1/20” expectation might mislead some.
    Suggested exercise: Compare errors for 405ka (3 variations) & 413ka.

    18968.7769128273	19123.4907382544	22363.1896235437	23667.8484048724	95540.1800459198	99598.6480311155	124970.765543333	132006.789762337	405691.196375825	2344646.50206282	FOR 405691.196375825
    18954.7215653296	19107.8673985264	22379.7610632674	23686.4105892345	94885.6349884336	98851.7032239995	123853.211009174	130697.862041146	405691.196375825	2364963.50364963	La2011 Table 6 La2004a
    0.0741522234931415	0.081763911179418	-0.0740465444505892	-0.0783663877319498	0.689825238104729	0.755621585420129	0.902321809061103	1.00149130272598	0	-0.859083091787828	%error
    18954.7215653296	19107.8673985264	22379.3746087485	23686.3976020646	94885.8433982369	98851.9294203326	123865.048265316	130711.04387292	405568.048748278	2364963.50364963	La2011 Table 6 La2010a
    0.0741522234931415	0.081763911179418	-0.0723209896956726	-0.0783116010458243	0.689604080280548	0.755391032994111	0.892679003077824	0.99130559363939	0.0303642330620824	-0.859083091787828	%error
    18956.3312608245	19108.2632249266	22377.9583670246	23686.3621038729	94926.7650262257	98863.1425160258	123977.271216256	130777.916695678	405113.811661464	2384110.34604552	La2011 Table 5
    0.065654328527416	0.0796907241047769	-0.0659968315189778	-0.0781618507704194	0.646198171321414	0.743963317745508	0.80135198761018	0.939664048570346	0.142524075393413	-1.65528596644679	%error
    18976	19155	22428	23716	94945	99590	123297	131248	412885	2035441	Berger 1978
    -0.0380643295359243	-0.164496276406214	-0.288970824220958	-0.203034217944118	0.6268682352096	0.00868363401493495	1.35750711155385	0.57813434287496	-1.74232622259824	15.1910815426642	%error
    18963.0189375615	19117.6857995821	22356.4012737567	23660.6640257036	95511.1788089858	99568.4148455754	124932.830647464	131966.719080191	405568.048748278	2343934.78424214	FOR 405568.048748278
    18954.7215653296	19107.8673985264	22379.7610632674	23686.4105892345	94885.6349884336	98851.7032239995	123853.211009174	130697.862041146	405691.196375825	2364963.50364963	La2011 Table 6 La2004a
    0.0437746985795721	0.0513840757368143	-0.104379083604455	-0.108697615596668	0.659260825549022	0.72503720037257	0.871692893137342	0.970832283886494	-0.0303550159942798	-0.889177332971089	%error
    18954.7215653296	19107.8673985264	22379.3746087485	23686.3976020646	94885.8433982369	98851.9294203326	123865.048265316	130711.04387292	405568.048748278	2364963.50364963	La2011 Table 6 La2010a
    0.0437746985795721	0.0513840757368143	-0.10265405264196	-0.108642845541049	0.659039734857333	0.724806717930777	0.862053014229361	0.960649666673524	0	-0.889177332971089	%error
    18956.3312608245	19108.2632249266	22377.9583670246	23686.3621038729	94926.7650262257	98863.1425160258	123977.271216256	130777.916695678	405113.811661464	2384110.34604552	La2011 Table 5
    0.0352793831512226	0.0493115179784413	-0.096331814164491	-0.108493140722365	0.615647001768807	0.713382471566966	0.770753721091869	0.909023797403744	0.112125796193252	-1.68513852012011	%error
    18976	19155	22428	23716	94945	99590	123297	131248	412885	2035441	Berger 1978
    -0.0684077910968735	-0.194801359529488	-0.319238123075324	-0.233327602869035	0.596322933262191	-0.021674017898007	1.32674002405872	0.547603834108347	-1.77215235518897	15.1561152714393	%error
    18941.7803155694	19096.273950372	22331.3620562503	23634.1640311101	95404.2060833131	99456.8980068163	124792.905608457	131818.916071013	405113.811661464	2341309.57224282	FOR 405113.811661464
    18954.7215653296	19107.8673985264	22379.7610632674	23686.4105892345	94885.6349884336	98851.7032239995	123853.211009174	130697.862041146	405691.196375825	2364963.50364963	La2011 Table 6 La2004a
    -0.0682745442373714	-0.0606736895988835	-0.216262393866731	-0.220576089093842	0.546522236946284	0.61222494208871	0.758716380161948	0.857744734580467	-0.142321233371462	-1.00018166751008	%error
    18954.7215653296	19107.8673985264	22379.3746087485	23686.3976020646	94885.8433982369	98851.9294203326	123865.048265316	130711.04387292	405568.048748278	2364963.50364963	La2011 Table 6 La2010a
    -0.0682745442373714	-0.0606736895988835	-0.214539294942624	-0.220521380380804	0.546301393876646	0.611994717787748	0.749087297939075	0.847573521920674	-0.112000215060377	-1.00018166751008	%error
    18956.3312608245	19108.2632249266	22377.9583670246	23686.3621038729	94926.7650262257	98863.1425160258	123977.271216256	130777.916695678	405113.811661464	2384110.34604552	La2011 Table 5
    -0.0767603448941711	-0.0627439260881098	-0.208224137385847	-0.220371843231838	0.502957260742499	0.600583266604433	0.657890260206246	0.796005473735504	0	-1.79525137641767	%error
    18976	19155	22428	23716	94945	99590	123297	131248	412885	2035441	Berger 1978
    -0.180331389284119	-0.306583396648241	-0.430880790751317	-0.345066490512435	0.483654835234169	-0.133649958011525	1.21325385731807	0.434990301576268	-1.88216775580034	15.0271401746756	%error
    19305.1353483089	19462.5925925926	22759.7385159011	24087.5317875841	97234.3190846973	101364.752697842	127186.774059447	134347.562574493	412885	2386222.27855155	FOR 412885
    18954.7215653296	19107.8673985264	22379.7610632674	23686.4105892345	94885.6349884336	98851.7032239995	123853.211009174	130697.862041146	405691.196375825	2364963.50364963	La2011 Table 6 La2004a
    1.84868863291689	1.85643529268771	1.69786197251836	1.69346552884606	2.47527889395476	2.54224195626413	2.6915434998499	2.79247148832379	1.77322152623458	0.89890498813696	%error
    18954.7215653296	19107.8673985264	22379.3746087485	23686.3976020646	94885.8433982369	98851.9294203326	123865.048265316	130711.04387292	405568.048748278	2364963.50364963	La2011 Table 6 La2010a
    1.84868863291689	1.85643529268771	1.69961812518164	1.69352128702149	2.47505381451243	2.54200731563286	2.6817297055552	2.78210516405108	1.80412418441359	0.89890498813696	%error
    18956.3312608245	19108.2632249266	22377.9583670246	23686.3621038729	94926.7650262257	98863.1425160258	123977.271216256	130777.916695678	405113.811661464	2384110.34604552	La2011 Table 5
    1.84004005144836	1.85432534341359	1.70605442469248	1.69367369270102	2.43087822263198	2.53037696167751	2.58878325979001	2.72954789998839	1.91827286921293	0.0885836727120304	%error
    18976	19155	22428	23716	94945	99590	123297	131248	412885	2035441	Berger 1978
    1.73448223181352	1.60580836644527	1.479126609154	1.56658706183228	2.41120552393202	1.782059140317	3.15480024611071	2.36160747172788	0	17.2336745968835	%error

    Above: scroll over from the left to see whats in the far right column.


    avg(abs(%error))	405000	405691.196375825	405568.048748278	405113.811661464	412885	413000
    La2011 Table 6 La2004a	0.453842582875912	0.451667209395487	0.44545910254283	0.448349791145578	2.02701137797331	2.0554287491746
    La2011 Table 6 La2010a	0.448609034768862	0.452497576025584	0.440218213916148	0.443114772325428	2.02821885101099	2.05663655852723
    La2011 Table 5	0.497559295545652	0.521849130200924	0.509548716416127	0.492078788930631	1.93805363982683	1.9664462338144
    Berger 1978	2.04881647281473	2.0199166737023	2.02363833125262	2.04377189498121	3.33293512482162	3.361716232247

    example derivation with “405ka” from La2011 Table 6 La2010a

    20063.4370405509 = 1000*14/283*405.568048748278
    22356.4012737567 = 1000*15.6/283*405.568048748278
    27228.950269319 = 1000*19/283*405.568048748278
    405568.048748278 = 1000*283/283*405.568048748278

    18963.0189375615 = axial(2343934.78424214,19117.6857995821)
    19117.6857995821 = axial(405568.048748278,20063.4370405509)
    23660.6640257036 = beat(405568.048748278,22356.4012737567)

    95511.1788089858 = beat(23660.6640257036,18963.0189375615)
    99568.4148455754 = beat(23660.6640257036,19117.6857995821)
    124932.830647464 = beat(27228.950269319,22356.4012737567)
    131966.719080191 = beat(22356.4012737567,19117.6857995821)

    2343934.78424214 = beat(131966.719080191,124932.830647464)

    Stable peace and tranquility weather left and right (both puppets on inverted totalitarian strings).

  101. Paul Vaughan says:

    15.6 panel bclearly above “1/18 misinterpretation”

  102. Paul Vaughan says:

    Lunisolar 405ka


    2.36966735541038 = slip(0.999978614647502,0.0745030006844627)
    9.0943796900619 = slip(2.36966735541038,0.499989307323751)
    96.1613372617316 = slip(9.0943796900619,0.999978614647502)

    0.0748024157783867 = axial(0.999978614647502,0.0808503463381246)
    18.6129709123853 = beat(0.0748024157783867,0.0745030006844627)
    8.84735293159855 = beat(0.0754402464065708,0.0748024157783867)
    16.8627856518082 = beat(18.6129709123853,8.84735293159855)

    179.333323110834 = slip(18.6129709123853,8.84735293159855)
    491.132481334807 = slip(179.333323110834,16.8627856518082)
    245.566240667403 = 491.132481334807 / 2

    207.340632664648 = beat(179.333323110834,96.1613372617316)
    103.670316332324 = 207.340632664648 / 2

    245.715087562547 = beat(179.333323110834,103.670316332324)
    65.693651051301 = axial(179.333323110834,103.670316332324)
    131.387302102602 = harmean(179.333323110834,103.670316332324)

    405378.494928687 = beat(245.715087562547,245.566240667403)

    18954.1560286571	19108.7506026991	22345.9523706273	23649.6055380984	95466.5389296544	99521.8787010176	124874.439718211	131905.040662135	405378.494928687	2342839.27932606	FOR 405378.494928687
    18954.7215653296	19107.8673985264	22379.7610632674	23686.4105892345	94885.6349884336	98851.7032239995	123853.211009174	130697.862041146	405691.196375825	2364963.50364963	La2011 Table 6 La2004a
    -0.00298361899232734	0.00462220170498978	-0.151068157271712	-0.155384670874586	0.612214842943918	0.677960475298569	0.824547624333596	0.923640679454771	-0.0770786869253174	-0.93549960874356	%error
    18954.7215653296	19107.8673985264	22379.3746087485	23686.3976020646	94885.8433982369	98851.9294203326	123865.048265316	130711.04387292	405568.048748278	2364963.50364963	La2011 Table 6 La2010a
    -0.00298361899232734	0.00462220170498978	-0.149343932551743	-0.155329926417319	0.611993855585284	0.677730100579334	0.814912250898552	0.913462821378996	-0.0467378582153743	-0.93549960874356	%error
    18956.3312608245	19108.2632249266	22377.9583670246	23686.3621038729	94926.7650262257	98863.1425160258	123977.271216256	130777.916695678	405113.811661464	2384110.34604552	La2011 Table 5
    -0.0114749638921969	0.00255061261572336	-0.14302464895313	-0.15518029156746	0.568621403330824	0.666311193663589	0.723655629095238	0.861861080934799	0.0653355327822297	-1.7310887806815	%error
    18976	19155	22428	23716	94945	99590	123297	131248	412885	2035441	Berger 1978
    -0.115113676975806	-0.241448171761631	-0.365826776229351	-0.279956408760208	0.549306366479949	-0.0684017461415346	1.27938207597211	0.500610037589408	-1.81806194734922	15.1022937695594	%error

    Summarizing avg(abs(%error))
    La2011 Table 6 La2004a 0.436500056654335
    La2011 Table 6 La2010a 0.431261617506748
    La2011 Table 5 0.492910413751669
    Berger 1978 2.03204009768186

    Overall lunisolar gives the best fit.
    Too much sedimenttide too – inverted totalitarian (IT) strings weather left or right no doubt.

    Turn IT a round(too,sea?) what measurements models simply predict:

    13.98799707	15.61155982	19.05465729	283	(14,14)	(15.6,15.6)	(19,19.1)	(282.5,283.5)	La2011 Table 6 La2004a
    13.99245442	15.61603049	19.05963966	283	(14,14)	(15.6,15.6)	(19,19.1)	(282.5,283.5)	La2011 Table 6 La2010a
    14.00922478	15.63255074	19.07572924	283	(14,14)	(15.6,15.7)	(19,19.1)	(282.5,283.5)	La2011 Table 5
    13.76797552	15.37261949	18.79068758	283	(13.7,13.8)	(15.3,15.4)	(18.8,18.8)	(282.5,283.5)	Berger 1978

    supplementary (to facilitate model-ratio summary checks)

    La2011 Table 6 La2004a
    27315.5714207149 = beat(123853.211009174,22379.7610632674)
    20052.3224982472 = beat(405691.196375825,19107.8673985264)

    La2011 Table 6 La2010a
    27314.4200179513 = beat(123865.048265316,22379.3746087485)
    20052.6234539743 = beat(405568.048748278,19107.8673985264)

    La2011 Table 5
    27306.8600163833 = beat(123977.271216256,22377.9583670246)
    20054.1711916695 = beat(405113.811661464,19108.2632249266)

    Berger 1978
    27414.8164054368 = beat(123297,22428)
    20086.8924770782 = beat(412885,19155)

    oldmanK: do sensible assumptions underlie the smooth obliquity curve in ref. 25?
    curious to hear your perspective on that

  103. Paul Vaughan says:

    Persistent Stability

    20054.0598197937 = 1000*14/283*405.378494928687
    22345.9523706273 = 1000*15.6/283*405.378494928687
    27216.2240411486 = 1000*19/283*405.378494928687
    405378.494928687 = 1000*283/283*405.378494928687

    18954.1560286571 = axial(2342839.27932606,19108.7506026991)
    19108.7506026991 = axial(405378.494928687,20054.0598197937)
    22345.9523706273 = 1000*15.6/283*405.378494928687
    23649.6055380984 = beat(405378.494928687,22345.9523706273)

    95466.5389296544 = beat(23649.6055380984,18954.1560286571)
    99521.8787010176 = beat(23649.6055380984,19108.7506026991)
    124874.439718211 = beat(27216.2240411486,22345.9523706273)
    131905.040662135 = beat(22345.9523706273,19108.7506026991)

    2342839.27932606 = beat(131905.040662135,124874.439718211)

    23092.5537318837 = harmean(27216.2240411486,20054.0598197937)


    Seidelmann (1992) Keplerian sidereal with Seidelmann (1992) tropical
    23094.6280196825 = beat(11.8626151546089,11.85652502)

    NASA “factsheet” sidereal fit with NASA “factsheet” tropical
    25762.0064305964 = beat(11.8619822039699,11.8565229295003)

    223051.949854934 = beat(25762.0064305964,23094.6280196825)
    20927.7815496935 = axial(223051.949854934,23094.6280196825)
    111525.974927467 = beat(25762.0064305964,20927.7815496935)

    compare with


    25760.4349434063 = beat(1.00001743371442,0.999978614647502)
    20934.9357937308 = beat(1.00002638193018,0.999978614647502)
    111759.01908408 = beat(1.00002638193018,1.00001743371442)
    111759.01908408 = beat(25760.4349434063,20934.9357937308)
    23098.3518513919 = harmean(25760.4349434063,20934.9357937308)

  104. Paul Vaughan says:

    panel b cryptic
    17.5545112781955 = 405378.494928687 / 23092.5537318837
    ally no.
    16.0927294142842 = 282.5 / 17.5545112781955
    16.1212121212122 = 283 / 17.5545112781955 ——- (16,16)
    16.1496948281401 = 283.5 / 17.5545112781955
    label less
    16.67 = 1 / 0.060
    16.39 = 1 / 0.061
    16.13 = 1 / 0.062
    15.87 = 1 / 0.063

  105. Paul Vaughan says:

    21466.317553582 = harmean(23092.5537318837,20054.0598197937)
    24985.3860049889 = harmean(27216.2240411486,23092.5537318837)

    g_5 ~= difference of frequency midpoints (& from there estimate other g_i)

    304821.709260864 = beat(23092.5537318837,21466.317553582)
    304821.709260864 = beat(24985.3860049889,23092.5537318837)

  106. oldmanK says:

    Paul Vaughan says: November 24, 2021 at 5:29 am; asked “oldmanK: do sensible assumptions underlie the smooth obliquity curve in ref. 25? curious to hear your perspective on that”.

    If the reference is to ‘Supplementary Fig 9 e’, to what looks like the extrapolated obliquity curve, it looks like the old secular ‘thing’. There is much in the material that I do not understand, nor familiar with techniques being used. Eg the scale for obliquity from -1 to 1 centred on 0.023 – ?? I would hazard a guess it is a formula-extrapolated obliquity curve. If that is so, it is the secular only. A second point I question is that, afaik from some research of mine some years ago, there is not a formula that can be relied on beyond 1My.

    See also https://www.researchgate.net/publication/229033144_Report_of_the_International_Astronomical_Union_Division_I_Working_Group_on_Precession_and_the_Ecliptic
    extract: “The effect of these changes on the higher-order terms in
    the precession theory was ignored. Ignoring the higher-order terms results
    in an error in the precession of about 6.4 mas cent−2in longitude and
    0.01 mas cent−2in obliquity. Thus, the precession theory was not consistent
    with dynamical theory”

    A second point in the paper fig 2 shows geological stratifications that indicate abrupt geologic changes. Of importance is what triggers the abrupt change. Nothing ‘uniformitarian’ there, so the slow orbital change is not the culprit, though a possible enabler.

    [compare to changes at a much shorter period. Link https://melitamegalithic.wordpress.com/2018/04/24/searching-evidence-2/ The link compares Med sediment analysis to North Atlantic ice rafting. The period is over the last 10kyrs. Both separately dated, and the dates correlate to other proxies, plus a clear indication of an obliquity jump in the secular mean (today’s 23) found from archaeology.]

    An incidental piece: the exposed face in fig2 appears to be a major scarp fault. A major scarp fault found 10days ago explains the odd orientation of an archaeological artifact, thus both dated to 5200bce. See similar here http://tectonic-culture.blogspot.com/2017/08/bronze-age-faulting-at-mycenae-greece.html

    The paper links its research to ‘Climate’. The apparent dominant factor there is not eccentricity, nor precession, but obliquity, on time-scales of ~0.5kyr.

  107. Paul Vaughan says:

    oldmanK, clarification — TB & OB pointed back to ~465 Ma:

    Middle Ordovician astrochronology decouples asteroid breakup from glacially-induced biotic radiations (“Published: 05 November 2021”)

    Reference 25 in that paper is:

    Waltham, D. Milankovitch period uncertainties and their impact on cyclostratigraphy. J. Sediment. Res. 85, 990–998 (2015).

    “oldmanK: do sensible assumptions underlie the smooth obliquity curve in ref. 25?
    curious to hear your perspective on that”

  108. oldmanK says:

    PV thank you for the clarification. A most welcome read.

    If you are referring the unnumbered figure ‘Obliquity versus Earth-Moon separation’, in my view it is wrong.
    The paper dates from 2015. Had they looked at Dodwell’s theory – and RR Newton – they might have considered also the possibility of abrupt jumps. (I was facing that dilemma in 2015, based on other evidence).

    In the abstract, important points re “observed sedimentary cycles”, that “(i) they drift through time; (ii) they overlap;” mentioned in connection to “eccentricity, obliquity and climate-precession”. My finding in archaeology on the subject I was researching, were evident obliquity jumps, three in a period of 3kyrs, last in 2345bce (Dodwell date) none evident since from measurements.

    An obliquity jump -for whatever reason- incurs also a precession phase shift, forward or backwards depending on the obliquity move (increase or decrease [not respectively]). Such would account for an observed drift as well as an overlap.

    Caution: my observed obliquity jumps are limited to dates 5200bce -2200bce. None appear to have happened since. But before 5200bce is unknown, in that there may have been long periods of no changes except for the small secular. Obliquity may be stable throughout a glacial period, until destabilised resulting in fast melt/interglacial, however that is a speculative point.

  109. Paul Vaughan says:

    Take Route 25…

    …CO[$]weather divide∫inequality.

    IT$ ‘west earn’ continent$seas buy or[well]$ease.
    CO[bane] UK=cross11UNdone seizeIT$not “$0 Great!” BRI10.

    can’t hear audience in seminar video, but
    at one moment Cuk responds dismissively – something like
    “quadrupole term?? NO, continents are in the way”

    The (ridiculous) assumptions underling ref. 25 curves are shamelessly unimaginative.

    980 = a(12) + 323
    360 = a(12) – a(11) = 9*40 = σ(323)
    180 = a(11) – a(10) = 5*36, etc. climb IT
    ! 1/2 prime + square
    323 = 196883 – 196560

    CO[$] for celebration no doubt…

    moleUN CO[V]ITch UNcertain Teaseveral $smooth curves$
    UNtug$pent “Time C ode” in hindsight rev verse sell:

    “in ch buy in ch$$ITback’nwat??chITgo”Sloan
    √25 s at 131 k

    D-vote quad drew
    dr.owe poll term
    weather deluge
    yuan-nil or DO lose
    UN no.11 ref. 25 with
    ~NO diss APace yuan

    “hi T!
    roc bought ’em?
    NObuddy nos. whatIT$SSTand$for

    tropiCO[II] ‘phase’: “when IT comes ‘down’ […] go write ‘out’ […] Till ITmean$more”

    Map 11 reins$
    call$IT$self “nature”
    “ad MIT ‘too your$self’ ” (better rightly$aid than left silent) weatherIT$myth or math$seaCO[NO]ME

  110. Paul Vaughan says:

    oldmanK, have you noticed the date (and estimated error bounds) in OB’s comment?

  111. oldmanK says:

    PV no I had not yet seen that post. Interesting, however it is one of, now, many. In this particular case, if one allows some delay, -just a couple of years-, for stalagmite deposition, it would be near to 2345bce. Both Dodwell, as well as the early tree-ring identified by Dr M Baillie, – and evident in the C14 isotope IntCal13,,,, (plus the interesting planetary alignment at 2348bce +/-x ), much food for thought.

    But go to my link above ( https://melitamegalithic.wordpress.com/2018/04/24/searching-evidence-2/ ), now those seem to tell what the spikes in the C/N ratio are. It is near to an Eddy cycle root. The 980yr cycle inflection points appear to be points of transition.

    An earlier root is at 3200bce, corresponding to a sapropel (organic) layer in the Med in between the normal clayey deposits. Question: what washed that thick deposit? There is no growth before or after, all inert clay. ( If you recall my mention of the earlier spike at 3550bce (5500BP) when the Sahara abruptly dried in less than a century. Eddy peak at ~3700).

    If anyone want to read something for the weekend, here, re an earlier Eddy root the 8k2 event 6150bce, the sinking of Doggerland.

    Or https://www.preprints.org/manuscript/201902.0063/v1
    “Rapid, prominent events observed in both continental and marine palaeo-archives during glacial
    periods are also evident during the Holocene, although less pronounced. This persistent rapid
    variability is suggested to be in response to an internal rhythmic throbbing of the climatic system
    at centennial scales [141]. In the scope of this review, three reference Holocene events are reviewed: ca. 8200 years BP (referred to here as the 8.2 ka event), ca. 4200 years BP (4.2 ka event) and ca. 700 years BP (0.7 ka or LIA). These events are concomitant with major glacier advances in the Northern Hemisphere [32,142] (Figure 6B).”

  112. Paul Vaughan says:


    Rhythmic climate cycles […] recorded in sedimentary archives […] empirical confirmation that the unimodal 405-kiloyear orbital eccentricity cycle reliably paces Earth’s climate back to at least 215 million years ago […]”

    Empirical evidence for stability of the 405-kiloyear Jupiter–Venus eccentricity cycle over hundreds of millions of years

  113. oldbrew says:

    ‘The Earth’s orbit approximates an ellipse. Eccentricity measures the departure of this ellipse from circularity. The shape of the Earth’s orbit varies between nearly circular (with the lowest eccentricity of 0.000055) and mildly elliptical (highest eccentricity of 0.0679).[4] Its geometric or logarithmic mean is 0.0019. The major component of these variations occurs with a period of 413,000 years (eccentricity variation of ±0.012). Other components have 95,000-year and 125,000-year cycles (with a beat period of 400,000 years). They loosely combine into a 100,000-year cycle (variation of −0.03 to +0.02).’

    ‘Eccentricity varies primarily due to the gravitational pull of Jupiter and Saturn.’

    – – –
    ‘Eccentricity has two main periodicities, one cycle with an average of ~100,000 years and a longer cycle with a periodicity of ~413,000 years.’

    Is it Jupiter-Venus or Jupiter-Saturn? Or both?

  114. oldmanK says:

    Whether its 405k or 413k it is equivalent to about four glacial cycles. What is of concern is of far more shorter periods. Nearer 1k.
    From an ‘academic’ point of view, and going by mass-distance factor, it is Jupiter and Venus mainly. But then the mass-distance factor would add also the moon; and the latter already had a bad reputation with the ancients.

  115. Paul Vaughan says:

    Pea and Shell Game

    Wikipedia’s “413,000 years” is “calculated from Berger (1978)” (see Berger 2006). This is at the very end of a Berger 2006 article …but keep an eye on Berger 1991 …if your caught in that game.

    There needn’t be any confusion about the 2 models. They are clearly defined by their authors. (Just look at the tables in the articles.)

    ~465 Ma: fits 405 ka model, but NOT Berger (1978) …as I detailed above.
    The question rightly left: Did ~465 Ma authors (understand correctly and) misrepresent or simply misinterpret? (neither crave nor need an answer)

  116. Paul Vaughan says:

    Pea & Shell Game – part 2

    OB’s 2nd link trail leads here. The author does NOT specify the model …but anyone keeping track of the movement of the pea under the shells knows it’s the Berger (1978) model.

    Suggestion – again – make it this simple: do the calculations for each model, compare, contrast, and benefit from awareness thus derived. Lots of climate commentators (whether consciously or not) mix numbers derived from disparate models. Weather it’s hoodwink or ignorance YOU will know …silently with no need to debate the agents of inverted totalitarianism.

  117. Paul Vaughan says:

    oldmanK wrote: “Whether its 405k or 413k […] What is of concern is of far more shorter periods. Nearer 1k.”

    6000 year cycle launched from LIA, yet there’s (curiously and suspiciously) a monstrous obfuscation campaign burying that crucial point with “solar” discourse (“solar” being misinterpretation).

    I have a tendency to assume everyone has memorized things we already discussed. Just trying to be practical, not naive — and to avoid repeating, but maybe a few things will need to be repeated (e.g. what we already know about how g_2,3,4,5,6 & s_2,3,4,6 relate to one another in a collective sense).

  118. Paul Vaughan says:

    pea & shell games part 3

    Typo alert — note in 1991 Table 1
    but in the original 1978 publication

    Are you watching the pea? Note what a few shells from the original publication reveal:

    2030644.02234637 = beat(19155,18976)
    2035645.32831001 = beat(99590,94945)

    Another important typo.
    Remember the Seidelmann typo (that propagated into a bunch of books)?

    Missed herd what type O’Berger catch op?
    (maybe they do this stuff on purpose – not ruling out the possibility…)

  119. Paul Vaughan says:

    pea & shell games part 3+

    2035779.79276929 = beat(75259,72576)

    eu11oweBRI˚K CRowed: ‘why$airdavo$?’
    could 2305441 B-the-ant? ‘$sure!’

    18976.4179210901 = axial(2035441,19155)
    19154.5741760953 = beat(2035441,18976)
    94944.5554607872 = axial(2035441,99590)
    99590.4891043321 = beat(2035441,94945)

    Typo discovery triggered opportunistic, enhanced scrutiny of Berger 1978.

    An early highlight is that the “2.4 Ma” metronome is missing:

    1282622.04724409 = beat(41000,39730)
    2565244.09448819 = 2 * 1282622.04724409
    2565244 ≠ 2035441

    1282621.27286703 = beat(72732,68829)
    2565242.54573405 = 2 * 1282621.27286703
    2565243 ≠ 2035441

    For convenience – summaries based on Berger 1978:
    Berger 1988 Table 4 (planets) p.635 (pdf p.11) & Table 3 (Milankovitch) p.634 (pdf p.10)

    Check this (which is review) :
    36750 ~= 8 / (g_2 + 5*(g_3 + g_4) + g_6 + s_2 + s_3 + s_4 + s_6)

    La2004: 36750.3379015986
    La2010: 36749.7014379182
    Berger: 37209.6176613942 = piece of “413 ka package deal”; pleases 490, 735, 980, & 1470 fans?

    explore everything in parallel
    no need to pick a favorite
    just learn to recognize which narrative is using what model, know the properties of each model

    this was a (worthwhile) side-trail (but now behind schedule)

  120. Paul Vaughan says:

    Basics — Part IV — Berger 1978 (references in links give deeper historical sources)

    This is to help make it easy to compare models (a few loose ends have been left – managing time).

    Table 4

    25694 = 1 / k

    249275 = 1 / g_1
    176420 = 1 / g_2
    75259 = 1 / g_3
    72576 = 1 / g_4
    308043 = 1 / g_5
    49434 = 1 / g_6
    422814 = 1 / g_7
    1940518 = 1 / g_8

    230977 = 1 / s_1
    191404 = 1 / s_2
    68829 = 1 / s_3
    72732 = 1 / s_4

    49339 = 1 / s_6
    432023 = 1 / s_7
    1874374 = 1 / s_8

    18976 = axial(72576,25694)
    19155 = axial(75259,25694)
    22428 = axial(176420,25694)
    23293 = axial(249275,25694)
    23716 = axial(308043,25694)

    412883 = beat(308043,176420) — 412885 (supplementary below)

    22428 = axial(412885,23716)
    23716 = beat(412885,22428)

    2035780 = beat(75259,72576) — 2035441

    18976 = axial(2035441,19155)
    19155 = beat(2035441,18976)

    94945 = beat(308043,72576)
    99590 = beat(308043,75259)
    123299 = beat(176420,72576) — 123297
    131248 = beat(176420,75259)

    94944 = beat(23716,18976) — 94945
    99601 = beat(23716,19155) — 99590
    123289 = beat(22428,18976) — 123297
    131258 = beat(22428,19155) — 131248

    412968 = beat(23716,22428) — 412885
    2030644 = beat(19155,18976) — 2035441

    28910 = beat(230977,25694)
    29678 = beat(191404,25694) —
    39729 = beat(72732,25694) — 39730
    40999 = beat(68829,25694) — 41000

    41843 = beat(2035441,41000) —
    40190 = axial(2035441,41000) —

    53615 = beat(49339,25694)
    174241 = beat(68829,49339) — “173k”
    117308 = beat(191404,72732) — “121k”
    1282621 = beat(72732,68829) — “118k”
    107478 = beat(191404,68829) — “110k”
    106161 = beat(230977,72732) — “107k”
    98046 = beat(230977,68829) — “98k”
    supplementary — Table 3
    eccentricity: 18976, 19155, 22428, 23716, 94945, 99590, 123297, 131248, 412885, 2035441
    obliquity: 28910, 39730, 40521, 41000, 53615

  121. Paul Vaughan says:

    Check: 2*(g_4 – g_3) ~= s_3 – s_4 metronome

    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    1182481.75182481 = 2364963.50364963 / 2 ~=
    1183561.64383561 = beat(72993.5229512813,68753.3156498674)
    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    1182481.75182481 = 2364963.50364963 / 2 ~=
    1181403.82862352 = beat(73009.9712692243,68760.6112054329)

    2035779.79276929 = beat(75259,72576)
    1017889.89638464 = 2035779.79276929 / 2
    1282621.27286703 = beat(72732,68829)

  122. oldmanK says:

    Re Berger-1988Rev-Geophys.pdf from above link https://www.researchgate.net/profile/Andre-Berger-2/publication/230890888_Milankovitch_Theory_and_Climate/links/5c3c6b3e92851c22a3737068/Milankovitch-Theory-and-Climate.pdf

    What is the curve for ’tilt’ in fig 11 based upon? At least, here, the time span was limited to within one million years.
    (Am presently collating of ancient writing referring to ‘permanent disturbances of the stars’. It is the only explanation that might account for the abrupt occurrences of interstadials. Also what mechanism controls the thermal energy needed for such fast glacial melt [to note: it takes 334J to melt a gram of ice but 4.186J to raise it by 1 degree.])

  123. Paul Vaughan says:

    Sustained, heavy, warm rain (from a tropical source).

    First-hand in real life that’s by far the quickest way deep snow goes (sun alone takes far longer).
    In a few hours strong winds rip up (local lingo) “rotten” ice, “rotted” by warm rain.

    Doing my first multivariate factor analysis on climate data way back whenever I remember how clearly the temperature and precipitation variables separated.

    Based on how bad online “climate” discourse was on other sites years ago I got the impression most of the commentators live in places where there is no water (never mind snow and ice). Contrasting perspective: repeatedly (dozens of times per year for decades) seeing hose relentlessly spraying warm equatorial (ocean-sourced) water poleward (& landward).

    The maps of diurnal temperature amplitude (above) may also be maps of climate-tribe water-communication breakdown. It seemed to me most commentators never conceived of local insolation and (outsourced) water-blasting following different curves. First-hand observation: tropical water cannon = fast ice sculptor (…& soil sculptor too).

    Locally here this year we have a persistent lunar hydrology schedule.
    begins with first spring temperature uprising
    28 days later: 4 day heat wave (made headlines)
    42 days later rain interrupted drought
    28 days later rain
    14 days later heavy rain
    28 days later heavy rain
    14 days later rain
    14 days later exceptionally heavy rain (made headlines)
    14 days later heavy rain (happening now – i.e. pattern continuing since I graphed it above)
    with a few other lesser-rains spaced 7 & 14 days in between
    only lesser-rains weren’t (at least not as obviously) on the lunar schedule
    media says nothing (except what you might well guess) = shallow discourse on important subject (natural hazards)
    rightly left wondering about nature’s role in official inverted totalitarian “resilience planning”
    moon’s a huge (& totally ignored) obvious signal presently — expecting academics to fully, totally, and clearly outline domains conducive (or not conducive) to such expression
    (basic nonparametric anova sorting to date is insufficient if they can’t separate expressive from non-expressive domains — optics: not recruiting (&/or not empowering) sufficiently-exceptional talent)
    if they dismiss it (or media-talk around it like “passing curiosity we ignore with an iron fist”), astute observers will have good reason to sideline them as delugeUNallyUNprepared to do their important job recognizing nature for a deserving public (fairness for their investments)
    better rightly said than left silent

  124. oldmanK says:

    I sense that a deeper question in my earlier comment went unnoticed. PV answered as to the mechanism “Sustained, heavy, warm rain (from a tropical source)”.

    But there may be a catch there. See link here https://nsidc.org/sites/nsidc.org/files/images//200901_Figure4.png

    The times of max tropical insolation (times of max tropical evaporation), at spring equinox > ice is at peak; at autumn equinox > ice starts to grow again. At those points thermal energy transport to pole is lost to space, adding ice to the pole. The time when ice decreases is when there is more direct sunlight. [which is the correct way to see it since it obviates the need of an intermediate process].

    Meaning that earth axial tilt matters. Meaning that today’s axial tilt is a little too much and would ultimately melt the poles.

  125. Paul Vaughan says:

    oldmanK asked: “What is the curve for ’tilt’ in fig 11 based upon?”

    model specification (weights, periods, phase) summarized in tables of earlier papers

    obviously they’re not modelling the detailed stuff you notice (next-level on perceptual hierarchy) — just major generalities stratigraphically observed (leaving residuals for patient observers like you)

    subject is too massive to pursue everything — requires capable team — narrowing individual focus as necessary now to manage time (NO time too 100% dissipate 465 Ma of lunar BS)

    “Basics” review was side-tangent to sort muddled discourse (gets so ridiculous) conflating narratives & models (weather right or wrong, a well-designed D-light left for $sumNOwe doubt).

  126. Paul Vaughan says:

    addessing misunderstanding (cross-posting) : response was to “fast glacial melt” (quoting oldmanK) – key word “glacial” interpreted as musing about glaciers (not sea ice) ; thus how commentary would have differed: thermal transport by gyre vs. atmospheric river (perhaps in geothermal ignorance)

    I have floods of exploration to share, but whenever back-and-forth erupts nothing productive happens and the discourse slides backwards (compounding lost opportunities).

  127. oldmanK says:

    PV, engineering taught me that “nothing is as it appears to be”; the devil is in the detail. The two recent points I raised relate to the tilt curve. They are pointers, one of several, that tell that the curve is only a minor fluctuation and is not what dictates the big changes.

    To flog the matter some (sorry), re ice, both sea ice and glacier require a massive amount of energy to change phase. There it is solar declination that appears to matter most, ie direct insolation. ‘Warm rain’ would have lost its ‘vapour latent heat – 2260J/gm’ to space (?) earlier; also an indication that insolation concentrated in tropical regions is mostly lost to space (ie at equinox the thermal engine appears to be still adding snow to the poles).

    As I also mentioned above, the ancients spoke of stars changing their course, or that they underwent a declination or deviation (allowing for what is lost in translation). To borrow a phrase, Dragon King events.

  128. Paul Vaughan says:

    Basics — Part V – simply

    Berger 1988 Fig. 10 simplifies.
    (a) climatic precession
    23715.850630886 = axial(308043,25694)
    (b) obliquity
    2035779.79276929 = beat(75259,72576)
    70223.1480968991 = axial(2035779.79276929,72732)
    40519.831263679 = beat(70223.1480968991,25694)
    (c) eccentricity
    1282621.27286703 = beat(72732,68829)
    76928.9576075447 = beat(1282621.27286703,72576)
    102535.642763153 = beat(308043,76928.9576075447)

    There is NO “2.4 Ma” metronome above, but there is in analogs below.

    23686.4105892345 = axial(304407.424910486,25685)
    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    70808.064251762 = axial(2364963.50364963,72993.5229512813)
    40305.4438005169 = beat(70808.064251762,25685)
    1183561.64383561 = beat(72993.5229512813,68753.3156498674)
    77046.5489566613 = beat(1183561.64383561,72337.575351641)
    103155.573568868 = beat(304407.424910486,77046.5489566613)

    23686.3976020646 = axial(304405.279928371,25685)
    2364963.50364963 = beat(74619.9907876555,72337.575351641)
    70823.5422700694 = axial(2364963.50364963,73009.9712692243)
    40300.4304463981 = beat(70823.5422700694,25685)
    1181403.82862352 = beat(73009.9712692243,68760.6112054329)
    77055.7108032582 = beat(1181403.82862352,72337.575351641)
    103172.24399153 = beat(304405.279928371,77055.7108032582)

  129. Paul Vaughan says:

    oldmanK, long ago we understood your concerns about model residuals — some of which are a monstrously much larger signal as you’ve repeatedly stressed.

    armies of climate commentators repetitively write descriptive, phenomenological paragraphs
    = unaffordable, unproductive time consumption

    If you have a model of the residuals, please share it as concisely as you can.

  130. Paul Vaughan says:

    No doubt some material puzzlers aim to lose boundary conditions constraining multivariate spatiotemporal pattern evolution.

    (for source: review Tim Channon post from 2014)

  131. Paul Vaughan says:

    Metronome Commentary

    La2004 & La2010 don’t give exactly 2 times (close, but not exact).
    Curiosity: Look how long the model suggests waiting to observe 1 slip.
    1296000000.00196 = slip(2364963.50364963,1183561.64383561)

    Compare the following with corresponding values in b above.

    70809.9986340664 = harmean(72993.5229512813,68753.3156498674)
    40304.8170630404 = beat(70809.9986340664,25685)
    70821.6071477363 = harmean(73009.9712692243,68760.6112054329)
    40301.0570474577 = beat(70821.6071477363,25685)

    The frequency algebra reduces to the known metronome:
    k-s_4-g_4+g_3 ~= k-s_3/2-s_4/2
    2k-2s_4-2g_4+2g_3 ~= 2k-s_3-s_4
    s_3-s_4 ~= 2g_4-2g_3

    Berger 1978 analogs: same frequency algebra is vaguely suggested, but missing when checked.
    70726.6948947803 = harmean(72732,68829)
    40354.0517144827 = beat(70726.6948947803,25694)

    Striking qualitative model property changes from Berger 1978 to La2011 Table 5 arouse curiosity about what other simple properties will eventually be noticed by explorers simply looking carefully.

  132. Paul Vaughan says:

    COCOTune in nos.

    B78: 410142.57105261 = 4 * 102535.642763153
    L04: 412622.294275471 = 4 * 103155.573568868
    L10: 412688.975966121 = 4 * 103172.24399153

  133. Paul Vaughan says:


    Centerpiece of article linked by OB & TB is the number 17 circled in red, alerting readers to ref. 25.

  134. Paul Vaughan says:

    Press “$sure!”

    Out of curiosity googled: lunar rain cycle


    “People also ask
    Does the Moon cycle affect rain?
    They found that when the Moon is high in the sky, it creates ‘bulges’ in Earth’s atmosphere that cause a slight change in precipitation levels. The higher air pressure created by each oscillation leads to an increase in temperature, and because warmer air can hold more moisture, that means less chance of rain.”

    …and therefore more chance somewhere ELSE google?

    What a ridiculous “climate discourse” we have.
    The west has morphed into such a ridiculous joke (presumably a response to “The Party” pressure).

  135. Paul Vaughan says:

    Such B*** S***

    Shrewd folks note (from google’s FIRST “people also ask” search result) :

    “As far as I know, this is the first study to convincingly connect the tidal force of the Moon with rainfall,” — 2016

    Earth orientation parameter basics (effectively ancient knowledge now) :

    “Apart from all other reasons, the parameters of the geoid depend on the distribution of water over the planetary surface.” – Nikolay Sidorenkov

    What the **** is going on with the hydrology propaganda??? It’s not acceptable. Are we already subjects of “The Party“?

    WESTERNERS: SHOW SOME BRAVERY (through official channels and legally).
    Everyone who doesn’t have official authority: Please find peaceful ways to ensure the officials stop being official cowards. Beware tricks baiting you into bad behaviour. If you lack the needed tact, express yourself peacefully to someone with tact who is smart but not naive. Showing restraint is necessary. It’s the only way we’ll secure the right combination of good partners to do real good.

    Prediction: Russia and the west will exhibit a temporary alliance to reveal a full solution to the problem (before things revert back to a normal stability).

  136. Paul Vaughan says:

    1933 Muck-Clock Lune

    based on diverse parameter sets – same :
    110.812298918645 = harmean(163.723203285421,83.7474058863792)
    110.812300014126 = harmean(163.7232045,83.74740682)
    111.156022076987 = harmean(164.498657117277,83.9373297002712)
    111.287690909751 = harmean(164.788501026694,84.0120465434634)
    111.292543528394 = harmean(164.791315640078,84.016845922161)’
    111.36267477478 = harmean(164.883685549933,84.0727720535526)
    111.380010891351 = harmean(164.708162250495,84.1382639508332)
    Good news: “mow’s = US” Johnson-time
    index UN: harmonic mean
    mount sign-comm.
    and mean T
    nigh tune 111

  137. Paul Vaughan says:

    vortices off equatorial waveguide recently spaced ~5 every 60˚ — that’s lunar month
    gaussian-smooth field — amenable to spatial wavelet animation (need money, team, & stability …otherwise this is as clear as the communication will ever get)

  138. Ulric Lyons says:

    The two most important cycles are missing. Centennial solar minima, which occur at the first regular synodic harmony of Venus, Earth, Jupiter, and Uranus. And grand solar minima series, where a series of longer centennial minima occur at each half cycle of very stable 1726.62 years long synodic harmony of Venus, Earth, Jupiter, and Uranus. Which is on average every 863 (+/-20) years, e.g. from 2225 BC, 1365 BC, 500 BC, 350 AD, 1215 AD, and the next from around 2095 AD. More active series of solar periods occur at the same 863 (+/-20) year period.
    Every fourth one at 3453 years is clearly visible in the Greenland GISP2 series.

    If the planetary orbits were more circular, much of the variability of the intervals between centennial minima, and the variation in the lengths of centennial minima over the long cycle, would not occur.

    If the 4627 year Jovian cycle were to repeat 25 times without slipping out of sync, it would reach a harmony with the 1726.62 year cycle, at 115,684 years, that’s purely speculative, but it is apparent in the last 800 kyr of glacial sequence in places.

  139. oldmanK says:

    Paul Vaughan says: November 29, 2021 at 7:09 pm asks “If you have a model of the residuals, please share it as concisely as you can.” ‘residuals’?? Can you pls clarify?

    Here is something curious (belatedly). I was looking for something related to glacier ice growth/ablation. Came across this paper https://www.sciencedirect.com/science/article/abs/pii/S0277379114004776?via%3Dihub (from 2015 but is now free to download) and settled for figure 6 (proxy for glacier melt). Objective was to compare chronologically with dates obtained for apparent obliquity change from megalithic calendars plus as were evident in fig 4 here https://www.researchgate.net/publication/307704719_Glacier_response_to_North_Atlantic_climate_variability_during_the_Holocene

    The particular dates are 2345bce; 3550bce 4375bce, plus 3200 and 5200bce. Figure6 was copied to Photoshop and markers added. The dates corresponded to inflection points. However in error I had marked dates in bce on datum BP, so I shifted curve by 1950 years, and they corresponded again though inverted. The dates appear to be some ‘pacing’ signal. As I realised later 1950 is approx twice Eddy cycle.
    Seems the trigger for change may not be so erratic in timing.

  140. Paul Vaughan says:

    33.3 ka

    noticing tremendous equator & monsoon ignorance in online “climate discourse”
    digging in cyclostratigraphy, paleoclimate literature back past 600 Ma
    405 ka McLaughlin cycle reported in studies from all ages — but academic obliquity narratives leave a combination of curiosity, suspicion, & instinct to scrutinize fundamentally — first off:

    33308.1817153554 = axial(103172.24399153,49188.090971097) — latter = saturn node period

  141. oldbrew says:

    Milankovitch Cycles, Paleoclimatic Change, and Hominin Evolution
    Christopher J Campisano (2012)


    Animation 1: Earth’s orbital precession.
    Courtesy of NASA.

    Figure 3: Variations and schematic diagrams of Milankovitch cycles.
    a, Precession and precessional index with a periodicity of ~23,000 years, with the amplitude of the cycles modulated at eccentricity periods of 100,000 years and 413,000 years (“variability packets”). b, The tilt of the Earth’s axis with a periodicity of 41,000 years. c, The eccentricity of the Earth’s orbit with periodicities of 100,000 and 413,000 years. d, Present position of the Earth in its orbit at different times of the year. e, Position of the Earth in its orbit at different times of year ~11,000 years in the future.
    © 2012 Nature Education Graph reproduced from Kingston 2005, diagrams a–c reproduced from Lutgens & Tarbuck 2001, d–e reproduced from PhysicalGeography.net. All rights reserved.

  142. Paul Vaughan says:

    Not curious & not surprising: “413,000 years” does not come from the sources at the given link. Perhaps NASA educators start with wikipedia (…and then list in their article the reference for 405 ka).

    The “great” thing about 413 ka is that it gives none of the results OB showed us in the past about DO.

  143. Paul Vaughan says:


    ref. 25 plots smooth k assumptions
    another example: Table 1 in stability of the astronomical frequencies over the earth’s history for paleoclimate studies

  144. oldmanK says:

    Paper for PV’s link is here https://www.academia.edu/2450804/Stability_of_the_astronomical_frequencies_over_the_earths_history_for_paleoclimate_studies

    It asks a fundamental question: “But did orbital variations drive climatic oscillations in nonglacial times, as in the Cretaceous, which had no amplification from ice sheets?”

    Orbital variations are slow to very slow. What is evident is abrupt change; and in much shorter time spans. The points at which glacier grow or melt is sudden, as evident in the last ~15k years. Not only evident in the proxies, but when they advance they cover growing flora that is preserved under the ice. That flora can be readily dated.

  145. oldbrew says:

    On a closer look at another version of the paper above, there’s a large gap between the ‘NASA animation’ heading and Figure 3, so the animation may be missing and the figure may not be from NASA?

    Update — it’s not from NASA:
    © 2012 Nature Education Graph reproduced from Kingston 2005, diagrams a–c reproduced from
    Lutgens & Tarbuck 2001, d–e reproduced from PhysicalGeography.net. All rights reserved.

    But this still leaves us with the 2021 paper that found a ‘significant’ 413 kyr period, for example.
    See here: ‘https://tallbloke.wordpress.com/2021/10/30/orbital-resonance-and-the-celestial-origins-of-earths-climatic-changes-why-phi/comment-page-1/#comment-173347’
    – – –
    Forcing mechanism for intensive onset of the Northern Hemisphere
    glaciations (NHG) at ~2.75 Ma (An et al., 1999; Cane and Molnar, 2001;
    Haug et al., 2005; Lunt et al., 2008a; Nie et al., 2014; Raymo, 1994;
    Shackleton and Al, 1984) is one outstanding question in paleoclimate
    research. Numerous hypotheses have been proposed for this event but
    no consensus has been reached after decades of studies. Here we aim
    to narrow down forcing mechanisms hypotheses for this event by considering the Plio-Pleistocene 405-kyr (also called 400-kyr or 413-kyr) climatic variability.


  146. oldbrew says:

    For reference…

    Orbital control on the timing of oceanic anoxia in the Late Cretaceous (2016)

    For the Livello Bonarelli from Furlo (124 cm), a duration estimate is obtained from 2 cm spaced XRF spectrometry data. The MTM spectral analyses of SiO2 yield dominant periodicities of ∼ 40, ∼ 12, and ∼ 6 cm (Fig. 3a). We calculate the ASM using the results of MTM harmonic analysis (> 80 %), and obtain an optimal sedimentation rate of 0.286 cm kyr−1 for the Bonarelli in Furlo. Hence, we interpret the reported periodicities as the imprint of short eccentricity, obliquity, and precession and estimate the duration of the Livello Bonarelli at 413 kyr.
    ASM analysis of the Al2O3 data from the 82 cm thick Livello Bonarelli at Bottaccione suggests an optimal sedimentation rate of 0.208 cm kyr−1 (Fig. 5). The ∼ 8 cm thick cycles are interpreted as the imprint of obliquity, and the duration of Livello Bonarelli at Bottaccione is estimated at 410 kyr,
    comparable to the estimate of 413 kyr at Furlo.

    [bold added]

    – – –
    Published: 10 March 2013
    Synchronization of the climate system to eccentricity forcing and the 100,000-year problem
    José A. Rial, Jeseung Oh & Elizabeth Reischmann

    Over the past million years, glacial–interglacial cycles have had a period of about 100,000 years, similar to the 100,000-year period of change in the eccentricity of the Earth’s orbit. However, the change in incoming solar radiation—insolation—at this timescale is small, and therefore difficult to reconcile with the amplitude of the glacial cycles1,2,3,4,5. This issue, known as the 100-kyr problem, is compounded by a lack of explanation for the transition of the length of the cycles from 41,000 to 100,000 years at the mid-Pleistocene transition 1.2 million years ago6. Individual discrepancies have been explained, for example, through interactions between other orbital frequencies such as obliquity and the 413,000-year period of eccentricity3,4,5,6,7,8,9,10,11,12,13, but a unified explanation is lacking. Here we show that climate oscillations over the past four million years can be explained by a single mechanism: the synchronization of nonlinear internal climate oscillations and the 413,000-year eccentricity cycle. Using spectral analyses aided by a numerical model, we find that the climate system first synchronized to the 413,000-year eccentricity cycle about 1.2 million years ago and has remained synchronized ever since. This synchronization results in a nonlinear transfer of power and frequency modulation that increases the amplitude of the 100,000-year cycle. We conclude that the forced synchronization can explain the strong 100,000-year glacial cycles through the alignment of insolation changes and internal climate oscillations.


  147. oldmanK says:

    Keep in mind that 413kyrs is in excess of four glacial cycles. Great events are on much shorter time spans.

    Compare to this for example https://phys.org/news/2017-06-collapse-european-ice-sheet-chaos.html

  148. oldbrew says:

    oldmanK – there’s more than one type of eccentricity.

    See ‘https://tallbloke.wordpress.com/2021/10/30/orbital-resonance-and-the-celestial-origins-of-earths-climatic-changes-why-phi/comment-page-1/#comment-173247’

    That’s not to say the ‘100 kyr problem’ doesn’t exist.

    There’s also a 400 kyr problem according to some, or a change of frequency to ~100 kyr.

    Marine sediment records from the Oligocene and Miocene reveal clear 400,000-year climate cycles related to variations in orbital eccentricity. These cycles are also observed in the Plio-Pleistocene records of the global carbon cycle. However, they are absent from the Late Pleistocene ice-age record over the past 1.5 million years. Here we present a simulation of global ice volume over the past 5 million years with a coupled system of four three-dimensional ice-sheet models. Our simulation shows that the 400,000-year long eccentricity cycles of Antarctica vary coherently with δ(13)C data during the Pleistocene, suggesting that they drove the long-term carbon cycle changes throughout the past 35 million years. The 400,000-year response of Antarctica was eventually suppressed by the dominant 100,000-year glacial cycles of the large ice sheets in the Northern Hemisphere.


    400,000-year problem
    The 400,000-year problem is that the eccentricity variations have a strong 400,000-year cycle. That cycle is only clearly present in climate records older than the last million years. If the 100 ka variations are having such a strong effect, the 400 ka variations might also be expected to be apparent. This is also known as the stage 11 problem, after the interglacial in marine isotopic stage 11 which would be
    unexpected if the 400,000-year cycle has an impact on climate. The relative absence of this periodicity in the marine isotopic record may be due, at least in part, to the response times of the climate system
    components involved — in particular, the carbon cycle.

    Pdf from Wikipedia — https://courses.seas.harvard.edu/climate/eli/Courses/EPS281r/Sources/Glacial-cycles/Milankovitch-cycles-Wikipedia.pdf

  149. Paul Vaughan says:


    Whenever back-and-forth arises, the discourse slides decades backwards.

    oldbrew: The older publications went by 413 k because that was the “consensus” value back then.
    Berger: 37209.6176613942 = piece of “413 ka package deal”
    property of newer models contrasts (no need to judge and decide, just be aware)
    36750 ~= 8 / (g_2 + 5*(g_3 + g_4) + g_6 + s_2 + s_3 + s_4 + s_6)
    La2004: 36750.3379015986
    La2010: 36749.7014379182

    oldmanK: Boundary conditions exist whether expressed multivariately or not (with geographic material organization).

    We are not thinking about the same thing — at all.
    By declaration, it seems, k varies smoothly (in theory). That’s an inverted-totalitarian declaration.

  150. Paul Vaughan says:


    k snails past hare-paced deflection (ITseams logistic others hide bet).

  151. Paul Vaughan says:

    0.78 micrometers per hour

    with natural concentration: streams densely

  152. chickenhawk says:

    Whenever someone gets brave enough to translate this post to an executive summary for policymakers and idiots, I will happily read it.
    I’ve tried to follow the links and the discussions, but I’m requesting backup…

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