Ian Wilson PhD – June 2013
Earth’s climate Moon Jupiter Venus/Earth & Jupiter/Saturn
2×CW = QBO = 2 ½×DY = (2/10)×TJ = (2/10)×SJS – SVE
The line of nodes of the lunar orbit appears to rotate around the Earth, with respect to the Sun, once every Draconic Year (DY = 346.620076 days). This means that the Earth experiences a transition from maximum to minimum meridional tidal stress (or vice-versa), at times separated by:
¼ DY______________ = 86.65002 days
5 × ¼ DY = 1 ¼ DY__= 433.275095 days _= 1.18622 years
5 × 1 ¼ DY = 6 ¼ DY = 2166.375474 days = 5.93111 years
Remarkably, these time intervals are precise sub-multiples of the sidereal orbital period of Jupiter (TJ) = 4332.82 days = 11.8624 sidereal years, such that:
[N.B. The sidereal orbital period is the time for the planet to complete one orbit of the Sun with respect to the stars.]
The Earth has two distinct short-term wobbles. The first is the annual wobble which is a forced motion caused by the seasonal variations in the Earth’s atmosphere, oceans and hydrosphere. The second is a periodic wobble of the Earth’s polar axis with an average period of 433 days known as the Chandler Wobble (Gross 2000). This wobble is thought to be a free oscillation of the Earth’s rotation axis caused by the fact that the Earth does not rotate about its figure axis.
Dissipation processes associated with wobble-induced deformations of the solid Earth should cause the Chandler wobble to freely decay on a timescale of about 30-100 years (Plag et. al. 2005), unless some force is acting to reinvigorate it. The fact that there has been no noticeable decay in the Chandler Wobble has raised questions about the source of excitation for the wobble. Gross (2000) proposed that the wobble was excited by a combination of atmospheric and oceanic processes, with the dominant excitation mechanism being ocean-bottom pressure fluctuations.
The Chandler Wobble also suffers from a sinusoidal variation in its amplitude that has a period of roughly 6.4 years (Kosek 2005). It is generally believed that the 6.4 year amplitude modulation period is most likely just a beat period produced by the interaction the annual oscillation and Chandler Wobble (Kosek 2005) but what if the source of excitation for the Chandler Wobble had an extra-terrestrial origin?
There is a remarkable near-resonance condition that exists between the orbital motions of the three largest terrestrial planets with:
where:
[N.B. The synodic period is the time required for a faster inner planet to catch up to a slower outer planet.]
Source: JPL ephemeris http://ssd.jpl.nasa.gov/horizons.cgi?s_body=1#top
[N.B. the point in the Earth’s orbit that is 1 ¼ DY’s after the position of the Earth on January 1st, subsequently rotates around the Sun (with respect to the stars) once every 6.3699 years. This is just over three hundredths of year less than the time required for the realignment of the positions of the three largest terrestrial planets].
In addition:
where:
This means that these four planets return to the same relative orbital configuration once every 44.77 years.
There is a possibility that the 6.40 year realignment period for the terrestrial planets has interacted with the sidereal orbital period of the Earth/Moon system over the eons, to produce a side-lobe modulation that it has slowly nudged the precession rate of the line-of-nodes of the lunar orbit towards its current value. Hence, we now have a precession rate that varies on a time scale of 1 ¼ TD = 433.2751 days = 1.18622 years. The fact this so close to the nominal 433 day period of the Chandler Wobble, suggests that the variations in lunar tides produced by the precession of the line-of-nodes of the lunar orbit could, in fact, be the source of the ocean-bottom pressure fluctuations that are thought to be responsible for the excitation of the Chandler Wobble.
[N.B. This means that Venus, Earth and Jupiter, in particular, form alignments at sub-multiples of the 179 year Jose cycle i.e.:
½ × 179 yrs = 89.50 yrs
¼ × 179 yrs = 44.75 yrs
1/8 × 179 yrs = 22.38 yrs
1/16 × 179 yrs = 11.19 yrs
These alignments only change slowly over hundreds of years and they closely match the well known Schwabe (~ 11.1 yrs), Hale (~ 22.2 yrs) and Gleissberg (~ 90 years) solar cycles.]
Wilson (2011) showed that the following relationship links the rate of procession of the lunar line-of-node to the sidereal orbital period of Jupiter:
It can also be shown that the sidereal orbital period of Jupiter and Saturn can be linked to the sidereal orbital periods of Venus and the Earth through the following near-resonance relationship:
SJS – TJ = 5 × SVE
If we combine these two relationships, we get the following expression which links the rate of precession of the line-of-nodes of the lunar orbit with the orbital periods of Venus, the Earth and Jupiter:
Finally, it can be shown that this implies that to a high degree of precision:
2 × CW = QBO = 2 ½ × DY = 2/10 × TJ
These last two relationships indicate that there may be a link between the relative orbital configurations of Jupiter, Venus and the Earth and variations in the terrestrial lunar tides. They also indicate the tidal variations could be responsible for setting the periods for the Chandler Wobble and the QBO.
References:
Cuk, M. 2007, Excitation of Lunar Eccentricity by Planetary Resonances, Science, 318, 244.
Gross, R.S., 2000, The excitation of the Chandler wobble, Geophysical Research Letters, Volume 27, Issue 15, p. 2329-2332.
JPL ephemeris: http://ssd.jpl.nasa.gov/horizons.cgi?s_body=1#top
Kosek W., 2005, Excitation of the Chandler wobble by the geophysical annual cycle, Proc. ECGS Chandler Workshop, ed. H.-P. Plag, European Center for Geodynamics and Seismology, Luxembourg-city, 2005.
Plag, H.-P., Chao, B.F., Gross, R.S., and Van Dam T., 2005, Forcing of Polar Motion in the Chandler Frequency Band: An Opportunity to Evaluate Inter-annual Climate Variations, Eos, Transactions American Geophysical Union, Volume 86, Issue 3, p. 26-26.
Tallbloke's Talkshop 
This is really starting to pull things together, excellent work Ian!.
To amplify the point I made about earlier authors, the text on this page from the Encyclopedia of Climatology is worth straining your eyes for:
This work would not have been possible if Rog Tallbloke had not reminded me that I had sent an email to him in 2012 that included the [approximate] relationship:
Synodic(JS) – Period(J) = 5×Synodic(VE)
I had forgotten that I had mentioned this relationship to him and I cannot be certain that others may have come up with the same relationship before I proposed it to Rog. My apologies if there is someone out there who has mentioned this relationship prior to 2012.
Rog’s reminder spurred me onto flesh out the details of the post above. Thanks Rog for highlighting this speculative work.
This is just the starter, main course needs some time to get the presentation right so the huge dish doesn’t overface people!
‘This means that Venus, Earth and Jupiter, in particular, form alignments at sub-multiples of the 179 year Jose cycle ‘
There’s also a very close J-E-V alignment at a bigger scale:
510 Earth = 829 Venus = 43 Jupiter
319 V-E = 467 J-E = 786 J-V
In TB’s ‘oliver-page’ link it says the 556 year period was more prominent until 3000 B.P. when the 178/356 year periods came more into play.
Note the 556 year period = 28 Jupiter-Saturn conjunctions and the 178/356 look like the Jose cycle period (9 J-S/ 9×2). As 28 is 9×3 plus 1 maybe that was – for whatever reasons – the ‘shift’ i.e. from 28 J-S to 27 (9×3)?
Wow . I love to see the order in our climate!! and solar system..
Maybe a point of interest IAN is that global temperature decline.. inflection point ..was in 2005.
click link below
That is the same time there was a major perturbation or period of change/disorder/fractal bifurcation?
in the Chandler wobble
Apparently the 7 yr cycle was cut anomonously short at this time due to some cyclic or regime shift
Certainly the earth responded at that time Coincidence?.
This site has has an exact date for the Chandler wobble anomaly
http://www.michaelmandeville.com/earthmonitor/polarmotion/2006_wobble_anomaly.htm
graph best shows the anomaly well
http://rabbithole2.com/presentation/news/earth_changes_news/chandler_wobble_has_major_anomoly.htm
quote
AS PREVIOUSLY OBSERVED: For the time being I am going to stay with my earlier guess: a phase shift of AT LEAST 3.5 months has occurred. The wobble may actually have abruptly ended its normal cycle ….in November 2005…
after a large hop in the average location of the Spin Axis which began in December 2004
….
This gradual return to what the track was during 2005 will not normalize the Earth’s Wobble. The old, normal wobble cycle has “lost” at least 120 days, that’s four months out of a 14 month cycle. Thus it is likely that a major phase shift has occurred in both the 14 month wobble cycle and the primary 7 year cycle in the “Chandler Amplitude”, known here as the Primary Axis Cycle.
—————–
Also a point of interest or coincidence
Your one quarter of the JOSE cycle ( 44.8 yrs)
divided by the
(The Chandler Wobble also suffers from a sinusoidal variation in its amplitude that has a period of roughly 6.4 years (Kosek 2005)).
44.8 : 6.4 = 7
is the whole number ratio significant
————
was also interested particularly in the QBO relationship
this equality statement is profound
2×CW = QBO = 2 ½×DY = (2/10)×TJ = (2/10)×SJS – SVE
This shows the QBO is resonant with the relationship you describe in the above
2 X CW
In writing means
twice the chandler wobble = QBO mean
could you clarify what you mean by QBO mean?
the QBO is a biennial oscillation where the wind changes direction at the ~30mb layer of the upper atmosphere
every 24 months or thereabout l believe
Just trying to picture what is happening here
Does this relate to the phase of the chandler wobble?
How does QBO mean? relate to its oscillation of ~ 24 months
——–
regards
So very close to 12.5 Eclipse years per Jupiter orbit, neat.
These three are in a Phi ratio:
20 × SMJ = 44.704 years
28 × SVE = 44.763 years
41 × SEJ = 44.774 years
28-20=8
41-28=13
It looks good, I’ve already done the same, except with the entire solar system baring the asteroid belt, I found that Jupiter is the main player, but a coupled system of Neptune, Uranus and Jupiter from what I can see are the main planetary influence in the solar system, the other coupled system that has a minor role is Saturn, Mars, Earth and Venus.
Ian Wilson says:
This means that these four planets return to the same relative orbital configuration once every 44.77 years.
In theory they do if you go by the math, but in practice they do not, this is because of the ellipse of their orbits, Precession and continuous perturbations.
You can see this for yourself, if you have access to planetary simulation software find a date where the planets are aligned, then step forward or backward in time every 44.77 years, you will notice that the planets do not line up or have the same configuration.
Crickey said;
2 X CW In writing means twice the chandler wobble = QBO mean
could you clarify what you mean by QBO mean?
Yes, I meant the QBO mean period.
The QBO cycle can vary in length between 22 and 34 months with the average being about 28 – 29 months.
1.18622 yrs x 2 = 2.372 yrs = 28.469 months
The QBO signal in the outgoing long-wave radiation (OLR) from the equator has a 2.4 year signal
between about 1987 and 2002. However, it is clear that there are times when the QBO devaites from this long-term mean.
This is a Jupiter and Uranus Heliocentric 13.8 year step. it shows what I mentioned above.
Crickey said:
“Also a point of interest or coincidence.
Your one quarter of the JOSE cycle ( 44.8 yrs) divided by the (The Chandler Wobble also suffers from a sinusoidal variation in its amplitude that has a period of roughly 6.4 years (Kosek 2005)).
44.8 : 6.4 = 7
is the whole number ratio significant?”
No, it is not a coincidence – though you will have to watch my blog in the coming month or so to see why.
Oldbrew said:
“There’s also a very close J-E-V alignment at a bigger scale:
510 Earth = 829 Venus = 43 Jupiter
319 V-E = 467 J-E = 786 J-V”
Interesting! Could this be the underlying reason for the 506 year peak that Abreu et al. find in the planetary toques?
Ian, I suggest you read all my comments on this thread on JEV calc’s:
“(2/10)×SJS – SVE”
Ian Wilson (August 5, 2013 at 11:56 am) wrote:
“Synodic(JS) – Period(J) = 5×Synodic(VE)
[…]
Thanks Rog for highlighting this speculative work.”
– – –
Let me help with the “speculation”:
In frequencies:
E-[(SEV)+(JEV/2)]
E-[(-6V+10E-4S)+(3V-5E+2J)]
= 3V-4E-2J+4S
In period:
1.185033426 years
So the beat of 4/5 of that with the draconic year (346.6200854 days) is 910.9622211 years, which is pretty close to the long JS cycle of 907.2999052 years (…and we know these longer-period estimates are very sensitive to tiny changes in inputs, so we can’t say these differ).
Recall that Keeling & Whorf wrote about 1800 year tides.
copy & paste these into excel:
=(29.47303787)*(11.86630899)/(29.47303787-11.86630899)
=2*harmean(22.1092812464479,6.40444001524529)
they give the same number (J-S = 19.86377916) precisely
reminders:
average solar hale cycle period = 22.1
average absolute solar barycentric radial acceleration period = 6.4
shows up in Earth-Moon angular momentum with respect to sun & solar system barycenter – (no surprise)
interesting thing is what can knock CW off its rocker (flip it over)…
Well my take is that Earth’s climate is affected (in the short term) by gravitational factors that include 1, 12, 37 and 48 months along with the various harmonics and half cycles combinations (which nature always uses to compose longer series) to deliver what we see as temperature.
It seems to fit the UAH data. It would be interesting to see what it does to other series. So far I have found similar componenerts in CET and ENSO.
But everybody syas that that cannot be true.
Ian Wilson said: “…The QBO signal in the outgoing long-wave radiation (OLR) from the equator has a 2.4 year signal between about 1987 and 2002. However, it is clear that there are times when the QBO devaites from this long-term mean.”
There is a QBO ‘signal’ in the OLR? In my understanding, the QBO is a wind-shift generally above the tropopause & the OLR is usually shown as a satellite image showing where deep convection is occurring (the greater the areal coverage of convection, the less OLR is occurring). Is the QBO directly affecting tropical deep convection & if so, in what way? Is there a graphic where this signal can be seen?
Thanks in advance,
Jeff
Look at 24 QBO cycles from Jan 1955 to Dec 2010:
A tad under 2.333 years average over that section.
‘44.8 : 6.4 = 7’
Also, 6.4 x 5 = 32. There’s a J-E-V conjunction at 3904 years (122 x 32).
Push that further and we find 3904y x 32 = 27 Grand Synods (4627.1 years each).
Note also that 122 x 5 = 610, a Fibonacci number.
Awesomely mindboggling
The golden ratios and the Fibonacci series in the solar system and earths climate
This would revolutionise the concept of the chaos theory of climate
The implication is that the entire solar system is governed by the golden number system
This implies order of the highest structure and intelligent design
I assume you are all religious.
The concept of perfect order doesn’t sit well with atheists generally
Landscheidt did well in illuminating this concept.
If the solar system governs the earths climate. this infers forecasting future is completely predictable.
———————–
Another interesting ratio ‘Oldbrew’ from your post
The JEV conjunction of 3904 and the 6.4 yr of the CW and the re-alignment period for terrestrial planets
3904 : 6.4 = 610 ( Fibonacci number)
no coincidence l assume
order in the cosmos
————————-
Paul V said
“interesting thing is what can knock CW (chandler wobble)off its rocker (flip it over)…”
I am not sure what you mean by ‘flip it over’?
but l do know that Karin Labitzke has some excellent graphs for all things upper atmosphere
http://strat-www.met.fu-berlin.de/labitzke/
One interesting thing to note from her work is that the winter stratospheric warmings were arriving at regular peaks and troughs of the 10.7cm solar flux until about 1995 . Most commonly .
The east phase QBO at the troughs and the west phase QBO at the peaks of solar flux .
This relationship broke down in the 1995/1996 trough of the 10.7cm solar flux
The SSW failed to emerge …
From that time on the SSW events have been occurring as a continuous stream since around the year 2000
until 2011 when her data finishes for this series.
In 2006, the time of the CW anomaly and the time of the climate shift to declining global temps’
there was a swarm of SSW events
Now an SSW event is associated with large perturbations at the surface like a very large low pressure cell that extends convection of warm air right up to the upper layer
These things are soo large that the polar vortex slits in two for a period of time
This is a massive perturbation to the atmosphere vertically near the arctic and later themed latitudes as it is thought the cold upper air then descends down to surface for cold anomalies at mid-latitide
Associate with negative AO/NAO .. bending Jetstream behaviour and anomalously cold winters in parts of NH.
It would seem that at the global temperature shift of 2005. There was a change in phase of the 60 yr cycle? Some temporary chaos as the cycle bifurcates and settles into the new descending phase
The CW anomaly of 2005/2006 may be a signature of that disturbance and shift in phase of the 62.5 yr cycle . THe AMO and the thermohaline circulation phase change?
The increased frequency of SSW events at this change of phase from 1995- 2011 and ?
of the SSW/ QBO relationship may/should return?.
However..
I suspect the yr 2000 was a major shift as up to 4 cycles align constructively between 1992 -2005
qian and lu( 2010)
All 4 are in descending phase from end of solar max this year.?
21.1 yr, peaked 2002
62.5 yr peaked 1998
116yr peaked 1994
194.6yr peakedin 1998
Global cooling
Wondering where the longer cycles are sitting at the moment?
1000 yr?
1800 yr?
I believe the larger the cycle , the larger the forcing on global temp
coupled with the constructive interference ( additive)
and the positive feedbacks from downturn over time
The mindboggles
If you need references let me know and l chase them up
I think we are in a truly unique period of the earths climatic history of modern time ..In particular the entry into the downward phases of a number of cycles in alignment?
Crikey: Appreciating the beauty and order in the cosmos doesn’t require religion. An understanding of wholeness and its implicate order is useful though.
Two posts that might be of interest:
https://tallbloke.wordpress.com/2013/02/20/a-remarkable-discovery-all-solar-system-periods-fit-the-fibonacci-series-and-the-golden-ratio/
JKrob,
I was referring to this paper that uses equatorial OLR as a proxy for the wind-shift.
Quasi-biennial oscillation signals in outgoing long-wave radiation
of the equator.
L.H. Ma, Y.B. Han, Z.Q. Yin
Advances in Space Research 46 (2010) 1477–1481
Click to access 14.pdf
@ crikey
Correct – the ratios are not a coincidence, in most cases anyway. Sometimes a ratio turns out not to be one on closer inspection (or vice versa) 😉
A note for Crikey at August 5, 1:35pm re. Chandler wobble: “The wobble may actually have abruptly ended its normal cycle ….in November 2005” This was also about the same time as the step function change seen in the Ap magnetic index from the sun…Interesting
Crikey says: “3904 : 6.4 = 610 ( Fibonacci number) – no coincidence l assume”
Further point: 3904 x 32 = 27 grand synods (4627.1 years each).
Therefore: 610 x 32² = 27 x 5 grand synods.
(32 being 5 x the 6.4 years period discussed in the post).
Also: 3904 x (5/8) = 2440 = 610 x 4
There are 2442 Venus-Earth conjunctions in 3904.12 years (1.59874y each, close to 8/5).
Thanks for that observation Ian..
I google that anomaly and Anthony Watts did an article on that Chandler wobble anomaly
here
Would love to read the 300 odd comments sometime..phew!!
His Ap time series graph shows the anomaly well. However the anomlaies either up or down are quite common in that time series
I have overlayed that graph with the global temperature inflection points which are phases of the 60 yr cycle and run parallel with the AMO phases
Firstly here are the global temperature inflection points of the quasi 60 yr cycle
and here is where l have overlayed those inflection points on the AP index time series supplied by Anthony W
I would like to see the AP index with inflection points? Is there any such data?
You solar system guys like vukcevic and scafetta always use sine waves
How can you match steps in climate with steps in solar syatem data ?
Sine waves versus the linear trends don’t correlate well?
Can you convert your planetary / lunar/ solar data into step trends?
———————————————————————-
Here is the AP index series correlated with 60 yr global temperature cycle
RESULTS
3 AP index cycles = one 30 yr phase of the 60 yr global temperature record
there is a zoom feature on this link to see details
Interesting that the steps in global temperature especially the downward steps are announced by a steepe downward descent of Ap index. THe upward step of global temperature in 1975 was associated with an upward step in AP index.
Although there are many steps in AP index in the series
I agree it is interesting that the CW anomaly in 2005/2006 was coincident with the downward phase shift of global temp’ of the 60 yr cycle
As Anthony W has already observed . THe drop in AP in 2005 has never recovered.
The step down in AP index and step down in global temp’ and CW perturbation would suggests a regime shift in the suns activity and global temperature at this inflect point at 2005..with NO LAG?
A bifurcation at the point of phase change perhaps
One could argue that 2005 was a point where earths energy budget tipped negative.. An inflection point
But the fact that the AP index dropped synonomously ! with global temp inflection point? of the 60 yr downward phase of the 60 yr cycle? infers otherwise?
Ha.. Notice that 2 Ap index cycles ( peaks) exist between the 30 yr phases of the 60 yr cycle
| * * | * * |
IMPORTANT OBSERVATION
THe timing of the inflection point for 60 yr global temp change is exactly in the same position of the AP index cycle.
Always inflecting at 2 yr before solar minimum.. !!
The 60 yr global temp cycle is linked to AP index cycle by a ratio of 3 : 1
3 AP index cycles = one phase of the 60 yr global temperature cycle ( 30 yrs)
NOW..
What modulates amplitude of the 60 yr cycle?
oh Bugger.
No edit function
mistake!!
the 60 yr global temp’ cycle is linked to the AP index at a ratio of 6 :1
the 30 yr phases of the 60 yr cycle ratio is 3 : 1
see Archibalds graph on my link above
sorry not used to no edit function..
oldbrew
The best E-V resonance is from the transit cycle. 243yrs and 235yrs are very close, and 478yrs (235+243) is closer.
Thanks Ulric, definitely worth noting. 1020 years works well too but nothing obvious to link it to, except that it’s 34 x 30.
[…] as seen below. Using ~44.76 years as the base period, the inner planet return period identified in Ian Wilson’s post here, the number of synodic conjunctions […]
The cube of the solar sidereal rotation period is 44.76 years.
Blimey.