*This article is a repost with permission of* “Two new connections between the Planetary and Lunar Cycles” on Ian’s blog.

**Two new connections between the Planetary and Lunar Cycles**

1. The Connection Between the Lunar Tidal Cycles and the Synodic Period of Venus and the Earth.

The first direct connection between the planetary orbital periods and the lunar tidal cycles can be found in a previous blog post that is located at:

http://astroclimateconnection.blogspot.com.au/2015/09/the-rate-of-change-in-tidal-stresses.html

In this post it was found that:

If you take the minimum period between the times of maximum change in the tidal stresses acting upon the Earth that are caused by changes in the direction of the lunar tides (i.e. 1.89803 tropical years), and amplitude modulate this period by the minimum period between the times of maximum change in tidal stresses acting upon the Earth that are caused by changes in the strength of the lunar tides (i.e. 10.14686 tropical years), you find that the 1.89803 year tidal forcing term is split into a positive and a negative side-lobe, such that:

Positive side-lobe

[10.14686 x 1.89803] / [10.14686 – 1.89803] = 2.3348 tropical yrs = 28.02 months

Negative side-lobe

[10.14686 x 1.89803] / [10.14686 + 1.89803] = 1.5989 tropical yrs

N.B.

10.146856 tropical years = 3706.059873 days = 9.0 Full Moon Cycles (FMC) and

1.0 FMC = 411.78443029 days = 1.127428 tropical years.

1.89803 tropical years = 693.2401518 days = 2.0 Draconic Years and

1.0 Draconic Year = 346.62007588 days = 0.949014 tropical years.

The time period of the positive side-lobe is almost exactly the same as that of the Quasi-Biennial Oscillation (QBO). The QBO is a quasi-periodic oscillation in the equatorial stratospheric zonal winds that has a mean period of oscillation of approximately 28 months.

Even more remarkable is the time period of the negative side-lobe. It is almost exactly the same as that of the synodic period of the orbits of Venus and the Earth (i.e. 583.92063 days = 1.5987 tropical years), agreeing to within an error of only ~ 1.8 hours.

2. The Connection Between the Lunar Tidal Cycles and the Synodic Period of Jupiter and Saturn.

The second direct connection between the planetary orbital periods and the lunar tidal cycles comes from a relationship that links the period of the QBO to the lunar and planetary cycles.

(8/19.8592) + (8/18.6000) + (4/8.8505) = 3/(2.3348)

where

19.8592 tropical yrs = the synodic period of Jupiter and Saturn.

18.6000 tropical yrs = time for the lunar line-of-nodes to precess around the Earth w.r.t. the stars.

8.8505 tropical yrs = time for the lunar line-of-apse to precess around the Earth w.r.t. the stars.

2.3348 tropical yrs = 28.02 months approximately equal to the average length of the QBO.

This can be rewritten as:

(8/19.8592) + (8/9.0697) = 3/(2.3348)

Where 9.0697 tropical years is half the harmonic mean of 17.7010 ( = 2 x 8.8505) tropical years and 18.6000 tropical years. This is close to the 9.1 tropical year spectral peak that is known as the the quasi-decadal oscillation.

Hence, we have an expression where the first term on the left is a bi-decadal oscillation, the second term on the left is a quasi-decadal oscillation and the denominator of the first term on the right is near to, but not precisely at, the nominal QBO oscillation period of 2.371 tropical years.

Remarkably, however, the denominator of the first term on the right-hand side is exactly that of the positive side-lobe produced by the amplitude modulation in part 1.

Hence, we have established two new connections between the synodic periods of Earth/Venus and Jupiter/Saturn that directly link into the variations in the stresses placed upon the Earth’s atmosphere and oceans by the luni-solar tidal cycles

— Original post http://astroclimateconnection.blogspot.com.au/2015/11/two-new-connections-between-planetary.html

Thank you Ian for alerting us.

Posted by Tim

Tim,

Thank you for the incredible speed at which put up this post. We have bolts of lightening here in Australia that are slower than your phenomenal editing skills.

It would be good if we transfer some of the incredible postings that Paul Vaughan putting up at Suggestions 15 to here [with his permission, of course] as it would help show his original and outstanding work on this important topic.

First of all, with a sense of urgency & expedition I’m asking all sensible, honest people for help combating unacceptable vandalism of recorded nature:

https://tallbloke.wordpress.com/suggestions-15/comment-page-1/#comment-109341

I would really appreciate it if I started seeing people ACTIVELY answer that deliberately simple, deliberately black-&-white litmus test both here and at other blogs. It’s simple: DO YOU ACKNOWLEDGE YES OR NO??? I’m not actually sorry for being so blunt because it’s really important …and since it’s so dead simple (

literally subtract one column of numbers from another) there’s NO acceptable reason — NONE WHATSOEVER — why it should have dragged on for almost a year.By now there should be thousands upon thousands of forceful acknowledgments from HONEST people of ALL political stripes.Now, if Ian can tolerate that important aside, can we also discuss lunisolar pattern?

Sure. Beneath my ERSSTv4 bias request in Suggestions-15, Michele (

deserved hat tip) triggered my commentary on Sidorekov (2014). That’s what Ian’s referring to above. Just follow the link I’ve given and scroll down.Regards

Paul,

What you have pointed to needs to have its own posting [if the hosts would generously allow that to happen] but I would prefer that you keep any comments here to the topic at hand.

If you were to place you obvious concerns – which I think we will all eventually all share, then place it in context and submitted to Rog as a separate post.

Cheers,

Ian

Ian writes:

“changes in the direction of the lunar tides (i.e. 1.89803 tropical years)”That’s a spatial polarity cycle the tropical year aliases from the lunar synodic month:

(29.530589) / 2 = 14.7652945 days

nearest harmonic of tropical year:

(365.242189) / 25 = 14.60968756 days

aliasing:

(14.7652945)*(14.60968756) / (14.7652945 – 14.60968756) = 1386.289965 days

(1386.289965) / 365.242189 = 3.79553624 tropical years

i.e.

spatially alternating(3.79553624) / 2 = 1.89776812 tropical yearsLast time you mentioned that I was in too much of a rush and too severely exhausted from excessive overtime at paid-work to notice that’s just half of a cycle familiar even to lunisolar newcomers.

….i.e. sometimes we’re

just unlucky enoughto catch people at an unreceptive moment …and so it’s unlucky miss where hit should have been easily guaranteed.Sometimes phoning back with the same inquiry on a different day you reach a more helpful agent.

Paul,

Can I put your post at Suggestion 15 for

November 6, 2015 at 11:29 pm

November 7, 2015 at 12:23 am (with corrections)

November 7, 2015 at 3:48 am

as a starter. I would really appreciate it.

Thanks

Ian

Paul,

I have found a 372 year “weave” that you might find interesting. It is not easily explained in a few words so I won’t be able post it here for a short while. I believe that it may be linked to the detailed temporal structure that I am finding in the Bi-Decadal oscillation. I hoping that someone like yourself could shine a little light upon the situation.

TB, OB: I’m not looking for a dedicated post. We already did that months ago. Periphery’s more appropriate than spotlight in this case.

Ian:

Do you see IPO on the graph?? Do you realize it’s relation to multidecadal polar motion amplitude (the subject of Sidorenkov (2014)??

This is

anything butoff-topic. They’re messing with recorded lunisolar patterns and judging by the lengthy correction delay, it decisively looks to me like the precedent hasalreadybeen set that skepticscan’t subtract one column of numbers from anotherto stopeven the most trivialbureaucratic vandalism.Have you considered that maybe you’ll discover the holy grail and not be believed because — poof! — bureaucrats rewrote climate history so it no longer matches lunisolar pattern??

Some people might even take an interest in your work

becauseof this.Paul,

I beg of you – I do not want to discuss conspiracies here, I want to discuss science. I still think that what you have posted is critical and needs to be discussed, do not get me wrong. I am sure that there are many on here [including me] who would appreciate a well explained posting on this topic to help reveal what is going on behind the scenes.

I am struggling to get even the most basic of scientific issues out to the wider public and so I would really appreciate it if you could give it the full attention that is deserves by having its own post.

🙂 Ian

P.S. I known that the very very important science underlies the wrong-doing by the warmists but I would still like to keep on topic if that is possible.

Ian Wilson (November 7, 2015 at 6:43 am) wrote:

“Paul,I have found a 372 year “weave” that you might find interesting. It is not easily explained in a few words so I won’t be able post it here for a short while. I believe that it may be linked to the detailed temporal structure that I am finding in the Bi-Decadal oscillation. I hoping that someone like yourself could shine a little light upon the situation.”

severely excessive overtime at paid-work, but I hope to look at it if/when ripe timing arises naturally

no conspiracy Ian — just a

reallyclumsy accidentthey got attached to v4

beforethey realized how serious the accident was…so they’re having trouble admitting their epic blunder

it’s going to be so embarrassing for them

they might not be able to face iti’m quite serious

i don’t have time to do any write-ups and don’t want a spotlight because I don’t have time to deal with it — only have time to point in passing

we can leave it there for now

I’ll see if I can find any more commentary to volunteer on the topic that has your focus…

Ian, as far as I’ve noticed you haven’t defined what 13 synodic months, 4 draconic years, and 9 FMCs are closest to. Those would have to be nearest-subharmonics of something crucial to not be arbitrary. If you can specify, it might incline me to think deeper exploration isn’t going to take more time than I have.

Ian, you can quote those calculations with acknowledgement. (The 2.37 calculation is something I’ve presented

countless timesfor years. I think most people have known about that for a long time now.) Don’t you think November 7, 2015 at 3:20 am says what’s most important even more clearly?By the way there’s something crucially important totally missing in Sidorenkov (2014). This has to do with phase reversals in the relationship between decadal-multidecadal IPO & polar motion amplitude. It’s something I’ve pointed out before in an important question I raised for NASA JPL.

Important:

The 2.37 year aliasing was brought to my attention by Piers Corbyn on Nov. 29, 2009. If anyone tries to frame it as a 2015 Paul Pukite original, I’m withdrawing the permission I’ve given to quote me and I’ll boycott further discussion on this thread.

General note to readers: the 10.14686 tropical years (9 full moon cycles) period that Ian W refers to is half of this:

‘The equivalence of 14 synodic months is an approximation that will accumulate an error of one synodic month after 18 [full moon] cycles:

18×FC = 251×SM = 269×AM

whereas 18×14 = 252

The equality of 269 anomalistic months to 251 synodic months was already known to Chaldean astronomers’

http://en.wikipedia.org/wiki/Full_moon_cycle#Matching_synodic_and_anomalistic_months

[269-251 = 18]

Paul, given the recent thread I posted concerning Paul Pukite (AKA Web Hub Telescope) and his plagiarist, non-acknowledging tendencies, you can rest assured that we won’t be giving him credit for knowledge discovered by sceptics years ago.

Regarding your issue with ERSSTv4, please email me with a summary, because I’ve also been busy (and will continue to be) with UNPAID work in the cause of defending science, and don’t have time to hunt through many links to old comments which themselves make elliptical references to other linked comments, leading to a confusing maze. If it’s as simple as subtracting one dataset from another, then please find the time to tell us WHICH 2 DATASETS, with links to their sources. Thanks.

Edit to add;This is the most comprehensive comment from Paul I’ve found on the issue:https://tallbloke.wordpress.com/2015/09/10/cheeky-pukitee-nicking-knowledge-without-acknowledgement/comment-page-1/#comment-107091

When it comes to weather/climate, about is pretty good. The first time I became aware that there was more to the lunar cycle than meets the eye was I had a canteen from the Ute Indians. It had 9 and a quarter turns on it. The devil is in the details. How far out do you go with the decimal places. How accurate is that. How many days is a quarter? The hours, the minutes, the seconds? Where is Venus? Who in their right mind would know that Venus transits the face of the twice in one year every 76 years? Why would you want or need to know something like that? Almost as important, how would they know something like this? What’s your job? To go look if Venus has tansited the face of the sun.

The moon has a very big effect here. Biology, people’s behaviour, travel before street lights, tides. How could the position of the moon with respect to climate/weather not be important?

The rest I’d have to start visualizing as patterns of waves with reinforcing and cancelling effects. So even though the moon may be in the exact same spot, 37 years later, other forces, … planets,solar cycles, … would either add or subtract to the effect. Throw in changes in shorelines, somebody or something cut down a tree or a bunch, volcanoes, dust, cycles inherent on earth itself…. most ridiculous statement ever made, in modern times…. the science is settled.

Another planetary link: 25 x 1.89803 tropical years or 50 draconic years = 4 Jupiter orbits.

The basic match between full moon cycles and draconic years is 250 FMC = 297 DY.

The difference of 47 is the number of ‘lunar wobbles’ in the period.

It fits into this chart as a multiple of 7 i.e. 1750 FMC = 2079 DY = 1973 tropical years (TY).

Discussion: https://tallbloke.wordpress.com/2015/01/06/two-long-term-models-of-lunar-cycles/

—

At 186 years you have approximately:

196 draconic years

10 lunar nodal cycles (196 – 186)

165 full moon cycles (196 – 165 = 31 = 186 / 6)

21 lunar apsidal cycles (165 + 21 = 186)

31 lunar wobbles (RLA in diagram) (10 + 21)

157 Chandler wobbles (CW)

157 CW = 13 x 12, +1

196 DY = 13 x 15, +1

Difference: 196 – 157 = 39 = 13 x 3

So CW:DY ratio is ‘almost’ 12:15 or 4:5 as Ian Wilson and Paul Vaughan have pointed out in other Talkshop posts and comments, e.g. here:

https://tallbloke.wordpress.com/2013/08/05/ian-wilson-linking-the-orbital-configuration-of-jupiter-saturn-venus-earth-to-lunar-tides-earths-climate/

Tallbloke

This maybe what your looking for.

https://tallbloke.wordpress.com/2015/06/05/noaa-tries-to-make-global-warming-slowdown-vanish/

oldbrew says:

November 7, 2015 at 9:30 am

oldbrew, thank you for outlining the 9.0 Full Moon Cycles (FMC) period. It is just half the time it takes for new moon at closest perigee to return to the same situation (= 20.2937 tropical years). As you say, it comes about because 251 Synodic months (which governs the time it takes to return to a new moon) is almost the same as 269 anomalistic months (which governs the time it takes the moon to return to perigee).

i.e. 18 FMC = 251 Synodic = 269 anomalistic.

Paul Vaughan says:

November 7, 2015 at 7:55 am

Paul,

1. The explanation for the 9.00 FMC is given above. As you know, the mean FMC is just the time required for the lunar line-of-apse to realign with the Sun = 1.12743 tropical years = 411.7844303 days and it related to the beat period between the synodic and anomalistic months.

(29.5305889 x 27.554550) / (29.5305889 – 27.554550) = 411.784448 days

My next post at my site will fill you in on how the lone term lunar anomalistic and draconic cycles.

2. 13.0 synodic month = 383.8977 days is not just some number plucked out of the air. I talk about its physical origins extensively in one of my recent blog post:

http://astroclimateconnection.blogspot.com.au/2015/10/part-b-are-lunar-tides-responsible-for.html

The ~ 384 day period appears prominently in the peak differential luni-solar tidal force that is acting across the Earth’s diameter, that is parallel to the Earth’s equator.

In this post, I point out that I have been saying for some time that we should be looking at tidal stresses upon the Earth that are in resonance with the seasons. (i.e. annually aliased). If we do just that, we find that the peaks in luni-solar differential tidal stressing every 13 synodic months (= 383.8977 days) will realign with the seasons once every:

(383.8977 x 365.242189) / (383.8977 – 365.242189) = 7516.06.07 days = 20.58 tropical years.

I indicated that the 20.58 tropical year period is close to the period of the Bi-Decadal oscillation.

3. I have talked about the seasonal anomalistic 4.0 year lunar cycle many times. Here is the explanation that I give for this cycle:

“The underlying reason for the four year cycle is the fact that for short term periods of a few years, the specific FMC period i.e. the average of 14 Synodic months (= 413.428244 days (J2000)) and 15 Anomalistic months (= 413.318248days (J2000)), which is 413.373246 days (J2000) or 1.131778 tropical years, should be used rather than the long-term mean FMC period i.e. 411.784430 days (J2000). Hence, 3.5 specific FMC’s = 3.96122463 tropical years ~ 49 Synodic months. This falls short of exactly four tropical years by 14.16 days which is very close to half a synodic month. Thus, if we start with a new moon at perigee on a given day of the calendar year, we end up with a full moon at or close to perigee (3.5 specific FMC’s + 0.5 Synodic months) later = 4.001651 tropical years or 4 years and 0.602895 days (J2000).”

I disagree strongly, but Ian chooses to regard ENSO “bias” adjustments as OT even though they force lunisolar exploration to track

moving targets.…so out of respect for Ian’s stated wishes and with reference to Per Strandberg’s tide-based ENSO modeling, I’ve answered TB’s request (quoted below) for a v4-bias

cookbook recipeelsewhere:https://tallbloke.wordpress.com/suggestions-15/comment-page-1/#comment-109422

tallbloke (November 7, 2015 at 9:32 am) requested:

“If it’s as simple as subtracting one dataset from another, then please find the time to tell us WHICH 2 DATASETS, with links to their sources. Thanks.”done Aug. 30, 2015 — (link takes you there)

I’ll watch for any follow-up on Suggestions-15.

Regards

Strategic pause for broader perspective on annual physical aliasing:

Important Reminder (August 19, 2015 at 8:08 am):

https://tallbloke.wordpress.com/suggestions-13/comment-page-1/#comment-105803

86, 104, 148, 208 (de Vries annual circulatory topology aliasing), 506

Ian, I was inquiring about 4 draconic years (not 4 tropical years).

There’s something alien in the way you & OB are framing 9 FMC and the way you’re framing 13 synodic months and your suggested BDO, so that means there will be an indefinite delay (months, years, maybe never) until I have sufficient time to do all of this very carefully firsthand via NASA JPL Horizons online ephemerides. I have an order of magnitude less free time now than I’ve had at any other time during the past 5 years, so I probably won’t ever do this. It will be up to others. We have to share the load with an efficient division of labor.

Just to clarify: any numbers I put forward are not necessarily climate-related, although they might be.

Paul,

For the sake of those following the conversation, Paul is asking about the physical meaning of 4.0 Draconic years = 3.796 tropical years.

The Draconic year is the time required for one of the two lunar line-of-nodes to realign with the Sun. Its mean value is = 346.62007589 days = 0.949014 tropical years. [note: extra decimal places are retained to minimize propagation error].

The 4.0 Draconic year cycle is related to the lunar Synodic month (i.e. the position of the Moon with respect to the Sun) relates to the tropical year. Here is quote from my 2012 paper describing its derivation.

“Higher than normal spring tides occur once every semi-synodic month (Msf), whenever the Sun, Earth and Moon are co-aligned at either New or Full Moon. It turns out that 12.5 synodic months are 3.890171 days longer than one tropical year (N.B. from this point forward, the word “year” will mean one tropical or seasonal year = 365.2421897 days (J2000) (McCarthy and Seidelmann [11], unless indicated). Hence, if a spring tide occurs on a given day of the year, 3.796 tropical years will pass before another spring tide occurs on the same day of the year. This occurs because: (0.5 synodic months)/(12.5 synodic months – tropical year) = (14.7652944 days/3.890171 days) = 3.796 years.

In addition, it can be shown that multiples of half of the lunar synodic cycle (Msf) are almost exactly equal to whole multiples of a year, for 4.0 years, 4.0 + 4.0 = 8.0 years, 4.0 + 4.0 + 3.0 = 11.0 years, 4.0 + 4.0 + 3.0 + 4.0 = 15.0 years, and 4.0 + 4.0 + 3.0 + 4.0 + 4.0 = 19.0 years.

Hence, spring tides that occur on roughly the same day of the year follow a 4:4:3:4:4 year spacing pattern (with an average spacing of (4 + 4 + 3 + 4 + 4)/5 = 3.8 years), with the pattern repeating itself after a period of almost exactly 19 years. The 19.0 year period is known as the Metonic cycle. This cycle results from the fact that 235 Synodic months = 6939.688381 days = 19.000238 Tropical years.”

ADENDUM

Interestingly, if you take the harmonic mean of the 9.300 trop. year (1/2 of the 18.600 trop. year precession cycle for the lunar line-of-nodes) and the 8.8505 trop. year (the precession cycle for the lunar line-of-apse) you get 9.0697 trop. years.

((9.0697 + 9.0697 + 9.0697) + 3.796) trop. years = 31.0051 trop. years.

So I think that the 4.0 Draconic year cycle is important in re-synchronizing the Draconic/Synodic alignment cycle with the 31/62/93/186 year anomalistic/Synodic alignment cycle.

Event series drift from long-run attractors, so if/when time/interest permits I’ll have to dust off some old tools I developed to handle Ulric Lyons’ various claims. Usually I restrain my annoyance but I think for once I should express it: You guys should do the work yourselves. The work doesn’t stop at identifying event series because the event series drift from the long-run attractors. The long-run attractors are the more fundamental object of aggregation. I apologize if that comes across as rude, but I think you can tell that I’m very frustrated at the time-compression I’ve been through in recent months. If v4 does not get retracted this month, I might resign.

IW says: ‘13.0 synodic month = 383.8977 days is not just some number plucked out of the air. I talk about its physical origins extensively in one of my recent blog post:

http://astroclimateconnection.blogspot.com.au/2015/10/part-b-are-lunar-tides-responsible-for.html

The ~ 384 day period appears prominently in the peak differential luni-solar tidal force that is acting across the Earth’s diameter, that is parallel to the Earth’s equator.’

—

If we assume 766 synodic months = 7 lunar apsidal cycles (see chart above: November 7, 2015 at 12:12 pm) then:

~~3 lunar nodal~~54 full moon cycles = 251 x 3 synodic months (= 753),therefore 7 lunar apsidal cycles take exactly

13 synodic monthslonger than~~3 lunar nodal~~54 full moon cycles (766 – 753 = 13).The other lunar chart in the post I linked to is all about multiples of 7, based on 766 SAROS cycles.

(12250 FMC = 1561 lunar apsidal cycles or 7 x 223 LAC)

One thing that’s becoming crystal clear to me as I try to plow uphill through all of this unaesthetically cumbersome and very unhelpful event series language is that conceptualizing in terms of event series absolutely (as in the mathematical sense) guarantees statistical aliasing.

What this means for example is that anyone trying to statistically analyze climate time series using event series is going to be drawing inference based on false assumptions. Their aggregations will be aliases rather than attractors.

Until I sort though the cumbersome, unaesthetic language, it’s something alien Ulric, Ian, or whoever is saying. But then always when it comes to me in a flash what they really mean to say (about the attractors, not the event series), it’s always like “Oh! Holy f**k, that’s too simple — why didn’t they just say so outright?? Man, that’s annoying — it wasted so much of my time! …and I thought there’s a mystery …but there’s none.”

A reason to note this annoyed reaction isn’t to be rude but rather to raise community awareness of communication barriers. There’s never any guarantee that everyone participating has the capacity and endurance to hang in there until their independent revelations kick in first-hand. It’s far more likely they’ll walk away thinking someone was wrong …and please just think for a moment of the damage that does. (For a good example look at wuwt & ce. The atmosphere is so sour that sensible people decide to leave.)

Now that I see what OB & Ian have been going on about with 9 FMC, there’s just no mystery at all. It’s just some plain, dull, and straightforward.

The attractor numbers are:

10.12692531 tropical years

20.25385063 tropical years

Now that we’re past that, moving on:

Ian, the 2.33 number that pops out when beat with 1.9 cycles through 2.37 roughly every Neptune cycle. That’s some pretty fast drift, so you Nikolay, & Paul P. have a narrative to develop about that. Please entertain us by adding some color to the story.

You are correct about a near-match with V-E: only 3.244420162 hours shy …and let’s not pretend we even have that level of measurement precision — effectively they’re equal to the best of our current awareness …but is this really any news? It’s ancient knowledge since the time of Mayans so far as I’m aware …but still ignored by climate scientists of course, which is why I advise their budgets be reallocated to the few agencies with a clue, like NASA JPL (…not to be confused with other branches of NASA (!) that think climate is a propaganda exercise, OB will be pleased to note I hastened to add).

OB, you got something wrong there. 3 LNCs don’t equal 60.88 years

[reply] thanks, correctedNow that Ian has clarified about 4 draconic years, I can verify that the attractor (not to be confused with

slippingevent series) is as I’ve outlined above:3.79553624 tropical years

Remember: To leverage the power of the law of large numbers, we

needthe attractor definitions. It doesn’t work with the event series.–

That’s 2 down.

1 to go…

I remain unsatisfied with the assertion that 13 lunar synodic months

exactlydefines the envelope spacing.Ian mentions the following components:

“[…] where R is the distance of the Moon and Dec(M) is the declination of the Moon.[…] where Rs is the distance of the Earth from the Sun and Dec(S) is the declination of the Sun.”

Ian: If you can’t derive the envelope spacing from the theoretical periods of these 4 variables, then your understanding can still (and needs to) go deeper.

This is the only remaining loose end.

The labeling on this graph is wrong:

There are 16 envelopes in 18 years.

That’s the full moon cycle (FMC) and it beats with the year to give the lunar apse cycle (LAC).

…

NOTthe bidecadal oscillation (BDO).That’s a wrap.

Better clear this up:

(29.530589)*(27.55455) / (29.530589 – 27.55455) = 411.7844289 days

= 1.127428433 tropical years

beat with tropical year:

(1.127428433)*(1) / (1.127428433 – 1) = 8.847542139 tropical years

–

harmonic of 411.7844289 nearest 27.55455:

(411.7844289) / 15 = 27.45229526 days

beat with 27.55455:

(27.55455)*(27.45229526) / (27.55455 – 27.45229526) = 7397.56074 days

= 20.25385063 tropical years

–

harmonic of 411.7844289 nearest 29.530589:

(411.7844289) / 14 = 29.41317349 days

beat with 29.530589:

(29.530589)*(29.41317349) / (29.530589 – 29.41317349) = 7397.56074 days

= 20.25385063 tropical years

–

Interpretation:

The lunar anomalistic & synodic months cycle through the full moon cycle (FMC) bidecadally.

–

–

This is the one insight that has made participation in this thread worthwhile.

It isn’t the BDO Ian suggested, but it’s the one I found.

Because I think people will be curious, I include this:

(20.25306467)*(19.86503587) / (20.25306467 – 19.86503587) = 1036.850499 sidereal years

(20.25306467)*(19.86503587) / (20.25306467 + 19.86503587) = 10.02858686 sidereal years

(20.25306467)*(19.86503587) / ( (20.25306467 + 19.86503587) / 2 ) = 20.05717373 sidereal years

(20.25385063)*(19.86580677) / (20.25385063 – 19.86580677) = 1036.890737 tropical years

(20.25385063)*(19.86580677) / (20.25385063 + 19.86580677) = 10.02897604 tropical years

(20.25385063)*(19.86580677) / ( (20.25385063 + 19.86580677) / 2 ) = 20.05795209 tropical years

Paul Vaughan said:

November 8, 2015 at 3:00 am

“The labeling on this graph is wrong”

This is completely false. The numbers at the top of this graph have been very carefully measured and if anyone cares to check them they will find that that they are indeed correct.

If Paul had bothered to read the posting carefully, he would have found that I went to pains to point out that the 384 day spacing of the peaks was only true for the three peaks 384 day peaks that were near the longer term maxima at 4.53 years. Even a cursory look at the data shows that the spacing between the short term peaks is not the nominal 384 days that occurs for those that are closer to the long term maxima.

Paul,

You are correct in pointing out that the AVERAGE spacing between the short term peaks is:

~ (18 years/16 peaks) = 1.125 years per peak.

This is just the 1.12743 year Full Moon Cycle (FMC).

You have taken the nearest harmonic of the FMC to both the synodic and anomalistic months and then beat those harmonics with the respective lunar monthly cycle. From this you have correctly concluded that:

“The lunar anomalistic & synodic months cycle through the full moon cycle (FMC) bidecadally.”

and get a bi-decadal oscillation period of 20.2539 years.

However, the point that I was trying to make was that in the physical world, where you are dealing with the actual tidal stress being applied to the Earth, the spacing between the short-term peaks occur every 384.0 days, if these peaks in tidal stress are located near the long term maxima that repeat once every 4.53 years [N.B. This is very close to half the harmonic mean of the 9.300 year semi-LNC cycle and the 8.8505 year lunar line-of-apse precession cycle = 9.0697/2 years = 4.535 years].

The precise 384.0 day repetition cycle that occurs in the strongest part of the longer 4.53 year cycle is most likely 13.0 synodic months = 383.89766 days = 1.05108 tropical years.

If you beat the 1.05108 tropical year period with the tropical year you get:

(1.05108 / 0.05108) = 20.5771 tropical years ~ 20.58 tropical years.

The peak differential lunar force across that is parallel to the Earth’s equator includes changes that are caused by the anomalistic month (allowing for the precession of the lunar line-of-apse), the Draconic month (allowing for the precession of the lunar line-of-nodes), as well as the Synodic month (allowing for the contribution of the Sun to the lunar tides).

Hence, since Paul’s explanation only involves the anomalistic and Synodic months – it will by its very nature give an incomplete picture.

Paul,

A bit of pure speculation:

The arithmetic mean of 12 Synodic months (= 354.36707 days) and the FMC (411.784430 days) is 383.07575 days = 1.048827 tropical years. This beast with the tropical year to give 21.48 years.

Ian, the event spacing

varies. You can’t just pick the minimum-spacings and pretend there are no maximum-spacings.The minimum-spacings don’t endure long enough for the beats to be meaningful.Anyone can verify that visually. The spacing you’re getting is because of the cosine terms in the 2 equations. They FORCE SIGN CHANGES. You can easily verify that they dictate that the high-frequency be the lunar synodic month, soof courseyou’re getting integer-multiples of the lunar synodic month when you go PEAK-TO-PEAK. The radius-cubed terms in the denominator set the envelope to FMC and it beats with the year to give LAC.If you add a 384 day sinusoid to your graph you’ll see the 384 does NOT come into play in BEATS of the envelope with the year. You’ve blundered with your “20.58 tropical years”. It’s wrong fundamentally (

it’s BOTH strictly unphysical AND strictly incorrect mathematically) and you should acknowledge that. You need to differentiate in your mindconceptuallybetween event series and envelopes. Conceptually they differ fundamentally. The aliasing calculation you’ve done is fundamentally wrong. It doesN’T deal with EVENTS.If you want to alias from the event series, youYou can teach yourself. Once you do it, what you’ll learn is that the average aliasing is NOT 20.58. Go ahead and roll your sampling through every phase angle: You will NOT find 20.58.CANdo that, but it demands a DIFFERENT method.Ian, the only sensible option you have is to retract the 20.58 suggestion.

PV says: ‘OB, you got something wrong there. 3 LNCs don’t equal 60.88 years’

Correct, thanks for noticing. The amendment reads:

’54 full moon cycles = 251 x 3 synodic months (= 753),

therefore 7 lunar apsidal cycles take exactly 13 synodic months longer than 54 full moon cycles (766 – 753 = 13).’

The 13 synodic month period fits in with something TB and I are working on but it’s not ready for publication yet.

PS it looks as if it could also validate the 20.58 year period or at least make it fit a period. It’s a question of overall timescales.

Paul V: You can’t just pick the minimum-spacings and pretend there are no maximum-spacings. The minimum-spacings don’t endure long enough for the beats to be meaningful. Anyone can verify that visually.The use of the word ‘pretend’ in this comment is out of order IMO. Ian has provided explanation and reasoning for his contention that the temporal spacings AT TIMES WHEN THE TIDAL STRESS IS NEAR MAXIMUM may produce an important resonant beat.

As an engineer who has hands on experience of the way resonance can produce more marked effects at times of maximum stress (attempting to produce fine surface finishes whilst machining five tonne asymmetric castings spinning at various speeds), I fully appreciate and endorse Ian’s reasoning, regardless of whether or not this particular hypothesis for the 20.58yr period stands or falls under further scrutiny.

Paul has himself complained vociferously about mainstream ignorance of annual and semi-annual variations and highlighted the importance of gas-giant ecliptic crossing timings in relation to them in his suggestions 13 comment regarding the Tomes-Tattersall Z-axis theory.

Please let us maintain courtesy, regardless of how pressed we are for time, or how certain we are of our own conclusions.

But TB it’s only an

instantaneousfrequency that rocks back & forth across LAC. Theinstantaneousfrequency hitting 20.58 only lasts afewyears (it’s not there 20 years later— it fluctuates with LAC) and then plummets so low that in central limit it’s back to LAC. This is a fact by geometric axiom. We cannot sensibly be reduced to debating the validity of geometric axioms.…but I’ve pointed Ian to what I think he’s really looking for …and I have more on that.

Paul, said :

1. “The radius-cubed terms in the denominator set the envelope to FMC and it beats with the year to give LAC.”

Yes – this is basically correct. That is why you get 16 short term peaks in 18 years.

2. Yes, you have correctly pointed out an error in my analysis. It was a basic mistake on my part that was innocently made because of my inattention to detail. There are no excuses for this silly mistake.

3. I will put a retraction on my web site explaining that the peak differential lunar force across that is parallel to the Earth’s equator does not produce an annually aliased signal with a period of 20.58 years. As soon as I post a retraction on my site, I will ask Rog to do the same with this post.

4. It would appear that if you annually alias the peak differential lunar force across the Earth’s diameter (that is parallel to the Earth’s equator) with the tropical year you get a period that is close to 8 tropical years. This might just be the LAC.

5. Paul, thank you for your time and patience in ferreting out this stupid error on my part.

However, as with many things in science, accidents and mistakes often led to new discoveries.

I will be putting up a post in the next day or so highlighting some interesting features about some of the potential candidates for the bi-decadal oscillation.

(20.25385063) / 2 = 10.12692531

(10.12692531) / 10 = 1.012692531

(1.012692531)*(1) / (1.012692531 – 1) = 79.78648954 (SAOT)

(79.78648954) / 80 = 0.997331119

(1)*(0.997331119) / (1 – 0.997331119) = 373.6889064

Ian wrote:

“However, as with many things in science, accidents and mistakes often led to new discoveries.”Exactly.

Ian wrote:

“This might just be the LAC.”It is.

Conclusion: I need to spend more time thinking about what geomagnetic indices are telling us about terrestrial core motions.

Thank you Ian.

Rog,

Thank you for coming to my defense. You are right in pointing out the rational that I used to propose that the regular appearance of 384 day peaks in the tidal stress might be responsible for a 20.58 year bi-decadal driven by the Moon. However, in this particular case Paul is correct – the aliasing would not be sustained.

A preliminary crude analysis on my part indicates that the actual annually aliased signal would be about 8.0 years but my data series is too short to really tie it down precisely.

The silly mistake that I made does not negate Part A of the two postings at my site. It does, however, invalidate the claim in part B [which you have kindly posted here] that the peak differential lunar force across the Earth (that is parallel to the Earth’s equator) produces an annually aliased signal with a period of 20.58 years.

I will update the post at my site for part B to include a retraction of my 20.58 year claim. I would appreciate it if that retraction could be placed at the front of my post here.

As, I have mentioned above, as with many things in science, accidents and mistakes often led to new an unexpected discoveries.

I will be putting up a post at my site in the next few days highlighting some very interesting features that I have found about the potential candidates for the bi-decadal oscillation. It looks as

though Paul has also come up with some new and interesting ideas on this topic – so hopefully our discussions here will end up doing some long term good.

Another Conclusion: The solar wind (or something confounded with it) is affecting stratospheric circulation over the poles systematically.

How did I get that from this discussion? Didn’t. I’m combining what I’ve learned in the past few days with what I noticed in 2009 or 2010 about the integral of the solar wind. I now know why VEI does not always translate into SAOT and why the poles differ from IPO ~1940ish.

The central limit of the translation symmetry in SAOT is 79.78648954 tropical years.

These notes may appear disjointed, but this is how exploration looks and I can suggest disjointed notes are preferable to silence. Those inclined to piece puzzles together will. For example, I’ve no doubt Ian will be on the case even if I haven’t volunteered comprehensively due to real time constraints. But it’s enough to keep both exploration and discussion alive.

Thanks to TB for hosting and for being patient during the heightened moments of misunderstanding.

Ian: Intended or not you led me to 20.25 and for that I thank you.

Best Regards

(20.25385063) / 41 = 0.493996357

(0.5)*(0.493996357) / (0.5 – 0.493996357) = 41.14138221

2*(41.14138221) = 82.28276442

4*(41.14138221) = 164.5655288

Now if only NOAA had the decency to retract like Ian does….

(You see this is what they destroyed by infilling the Southern Ocean with physically unjustifiable tropical extrapolation across Earth’s biggest wall of pressure & wind….)

nodes on the z-axis …indeed TB…. indeed

Ian W says: ‘It would appear that if you annually alias the peak differential lunar force across the Earth’s diameter (that is parallel to the Earth’s equator) with the tropical year you get a period that is close to 8 tropical years. This might just be the LAC.’

In the context of ‘connections between the Planetary and Lunar Cycles’: it’s also close to the Venus-Earth ‘pentagram’ period of just under 8 years.

Good stuff, scientific progress and discovery live as it happens. Just what I want this website to be about. Thanks to all participants and particularly the main protagonists for the diligent scrutiny, insight and acceptance of error. And of course the hints of new ideas being formed as a result!

Just a reminder – the actual post above is still correct. What I am retracting only affects Part B of my earlier post here at Tallblokes Talkshop:

https://tallbloke.wordpress.com/2015/10/31/ian-wilson-are-lunar-tides-responsible-for-historical-temperature-anomalies/

And yes, Paul, 1.89803 (= 2.0 Draconic years) is half of 3.79606 tropical year (= 4.0 Draconic years) which is a well known lunar cycle that I (and many others) have commented on in the past as it is an importan sub-multiple of the 19.00 tropical year lunar Metonic cycle (= 19.0/5 = 3.8 years).

And a hat tip to oldbrew, whose posts along with Paul’s have opened up some new possibilities and potential discoveries.

Here is one of the specific posts by oldbrew which I’d like to emphasise.

“Another planetary link: 25 x 1.89803 tropical years or 50 Draconic years = 4 Jupiter orbits.”

This comes from my 2008 paper that eventually got published in 2010:

Wilson, I.R.G., 2011, Are Changes in the Earth’s Rotation

Rate Externally Driven and Do They Affect Climate?

The General Science Journal, Dec 2011, 3811.

http://gsjournal.net/Science-Journals/Essays/View/3811

In this paper I found that

5.0 Draconic years = 0.4 Jupiter orbits = 433.275 days = 1.0 Chandler wobble

(with 1 Jupiter orbit = 4332.75 days = 11.8627 tropical years)

Of course, this would give:

50 Draconic years = 4 x 11.8627 tropical years as per oldbrew’s post.

Thanks oldbrew for reminding every one of this additional connection between the Lunar Draconic cycle and orbit of Jupiter.

That should be:

50 Draconic years = 4 x 11.8627 tropical years as per oldbrew’s post.

[amended – mod]Please forgive my error prone posts – that should read:

In this paper I found that

5.0 Draconic years = 0.4 Jupiter orbits = 4 x 433.275 days = 4.0 Chandler wobble = 2.0 x QBO

(with 1 Jupiter orbit = 4332.75 days = 11.8627 tropical years)

Of course, this would give:

50 Draconic years = 4 x 11.8627 tropical years as per oldbrew’s post.

Thanks oldbrew for reminding every one of this additional connection between the Lunar Draconic cycle and orbit of Jupiter.

IW says: ‘So I think that the 4.0 Draconic year cycle is important in re-synchronizing the Draconic/Synodic alignment cycle with the 31/62/93/186 year anomalistic/Synodic alignment cycle.’

Here’s a small chart showing some links between observed lunar phenomena.

Real-world accuracy may not quite be 100% but as TB likes to say: ‘good enough for farmwork’🙂

Note: 196 draconic years = 149 x 4 DY (‘the 4.0 Draconic year cycle’)

@oldbrew said

… accuracy may not quite be 100% …I’m often curious why the observed interval lengths are not used; in the case here for draconic year one can see that 6939.69 days (Metonic) / 20 (# of draconic years) = 346.

9845and not 346.62007588, so where does such a huge yearly discrepancy come from.Chaeremon – 18.5992 sidereal years = 19.5992 draconic years = 1 lunar nodal cycle (Dr.Y – Sid.Y)

Then the Metonic cycle is 19 tropical years, as per the chart here:

https://tallbloke.wordpress.com/2015/11/09/why-phi-some-moon-earth-interactions/