Length of Day, modelling the lunar and annual effect

Posted: January 18, 2016 by tallbloke in solar system dynamics

Tim Channon’s LOD model output, for the interest of R.J. Salvador. Hopefully Paul Vaughan might find a moment to weigh in too.

Deadal Earth

As a result of helping someone out with lunar effects in Earth length of day I wondered if a slightly more comprehensive version would work.

The result  is an interactive spreadsheet which might be useful.

I would not usually  produce such a monster, this is an xls >30Mbyte but it does include reconstruction of the lunar LoD signal, subtraction from the raw LoD and decimation for plotting. It is live, you can turn on or off individual terms/factors and see the effect.

This needs a great deal of explanation, codas, and so on.

For now here is the file lod-work

Do not try this unless you have a fairly large computer. Checked it works with gnumeric, openoffice/libreoffice. Excel should not have a problem but recursion is used.

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  1. tallbloke says:

    R.J. Salvador asked over on our ongoing Phi-orbital parameters thread for some assistance with integrating the Lunar Apsidal and Nodal cycles into his LOD model. Paul Vaughan linked the post he had on WUWT back in 2011.
    This post is a reblog of a post by Tim Channon, who assisted Paul with his modelling and then produced his own model, making a huge (30meg) xls spreadsheet available. Tim has kindly made the synth software he developed to identify the underlying frequencies and amplitudes available to all.
    Tim isn’t around much at the moment, and Paul’s busy too during the week, so we’ll just have to make the best of it.
    I’ve largely stayed out of LOD discussions for a few years, because I’m more interested in the underlying causes of the multi-decadal to centennial variation, which I believe involves the gas giant planets. I got shouted down about that at the time, but I think that with the progress we’ve made with our understanding of solar system harmonics and dynamics, the tide is turning in my favour. Or maybe it’s a conflation with Lunar orbital parameters which mirror the wider solar system’s organisation. Perhaps once R.J. Salvador has built LNC and LAC into his model dynamically, we’ll be able to extend the time period over which the model runs and decide.

    Here’s the output from R.J.’s model

  2. oldbrew says:

    Re ‘integrating the Lunar Apsidal and Nodal cycles into his LOD model’ – might one way to tackle that be to use the lunar wobble period, which ties the two cycles together and is just under 6 tropical years?

    Again, see the de Rop paper and our post.

  3. R J Salvador says:

    Thanks Guys.
    There is a lot to look at here so I will get after it.

  4. tallbloke says:

    A way to start that is to download Tims spreadsheet, analyse the model output, and see if the 6yr wobble that OB mentions is obvious in the data.

    A quick look indicates that all the periods are short and combine to produce the longer term cycles. it’s obvious to me that there’s a multi-decadal component missing, just by looking at the divergence of the model from the data over the period of record.

  5. R J Salvador says:

    As you know the moon has a very complicated motion and finding a way to improve my rough model of the moons tidal LOD influence in a clean way will be challenging. This could take awhile. Thanks for the ideas.
    In the meantime the LOD prediction for 2016 will provide a test of the basic structure and its dependence on the two gas giants plus Venus. FYI if I add in SEV, UEV and NEV the fit goes up to r^2=0.925 but the moon is the key actor to get this model to improve.

  6. tallbloke says:

    R.J. You have mail.

  7. pyromancer76 says:

    A New Year’s wish for health and happiness for all tallbloke’s bloggers and commenters. What courage you have, and a tremendous work ethic for science and the scientific method. As only a reader (no relevant expertise), I am deeply appreciative every day.

  8. tallbloke says:

    Thank you for that, we’re pushing on with our voyage of discovery and making strides towards understanding the wobbly solar system and Earth’s wobbles within it.

  9. R J Salvador says:

    If the crude lunar ecliptic two frequency model is removed from the model and replaced with the Channon/Vaughan 5 frequencies from the WUWT post in 2011 the fit goes up to r^2=0.95.

  10. Also Tim says:

    Tim appears. Been offline, blocked WiFi. Trying to use a tablet, people use these things?

    Back home so we popped out for some winter air, cold and sunny all day. Ho-ho, spotted solar panels on a roof… covered in frost, shaded by trees this take of year. 😀

    You need more information to help with figuring out what I was trying to do.

  11. R J Salvador says:

    Tim, your frequencies are a great help. I need a good fit of the moons influence and your analysis provides it. The idea I am following is that the day level changes in the LOD are like the little serrations or teeth on a key. If I can get the model to fit the these serrations then there is a chance that the large frequency terms based on JEV etc will be close to the truth. So far it looks interesting. I have a graphic of historical LOD back to 1890 but no source for it. I would like to compare how the model predicts the past but I am still searching.

  12. tchannon says:

    Actually online on my main computer, briefly, too cold up here.

    I note the output version is V1B so that is elderly. Shouldn’t matter.

    Was done rapidly as I recall and not as a real article.

    Export to XLS was done to assist others, native is Open Office famility. No real effect but hence the large file.

    Normally I would not produce anything so huge. In this case dealing in daily data and not wanting to lose information it was shown verbatim.

    You can change the output data rate to say monthly but be careful over aliasing of fast data. The lunar data is fast, faster than IER data can represent well.

    Lots and lots of codas.

  13. Paul Vaughan says:

    R J & Tim will probably be able to handle most everything.
    I’m quite overextended, but I’ll be monitoring this thread as the weeks unfold.
    I’m quite curious to see what R J ends up doing with JSUNEV after deep consideration.
    I can probably dig out links to different LOD data sources sometime relatively soon.

  14. tallbloke says:

    I have the Richard Gross annuals back to ~1836 somewhere on another computer. I used it to produce this plot, but I might have detrended the LOD data, can’t remember by what factor though.

    Ian Wilson has used Sidorenkov’s reconstruction which goes much further back (1600s) it looks only slightly different to Gross. Download link for Ian’s paper is on this page http://gsjournal.net/Science-Journals/Essays/View/3811

    Ian did a post on it here http://astroclimateconnection.blogspot.co.uk/2015/04/will-pdo-turn-positive-in-next-few-years.html

  15. Paul Vaughan says:

    Gross’ 1832+ LOD data:

    By web-search for the first 6 lines of data for the 1623+ series this link comes up:
    That page links to one with plainer format:

  16. Paul Vaughan says:

    Another paper on the 6 year LOD cycle we’ve discussed a number of times:

    Recovery of the 6-year signal in length of day and its long-term decreasing trend (2015)

    Click to access s40623-015-0328-6.pdf

  17. R J Salvador says:

    Thanks Paul.

  18. R J Salvador says:

    The model of the LOD is now at a stage where I am happy with it “but” and a big “but” it does not predict the LOD past beyond say 1890 in terms of the historical reconstructed LOD data. Now here is the weird part the model has a very strong coherence to the historical Pacific decadal oscillation. The model matches the shape of the PDO and leads it. Below is a the source for a graph of this from 1854 onward. I don’t have the numerical data but a visual check of a graphic by Ian Wilson tells me that the same relationship exists back to 1700. I also had the model forecast LOD out to 2100 which on the graph would imply that the PDO is starting a strong reversal out to at least 2050 to 2060 before reversing again.
    Is it possible that the historical LOD data is just wrong? Could they actually get some kind of measurement in milliseconds of the earths rotation in 1700 or even 1800?

  19. tallbloke says:

    Hi R.J.
    So far as I know, historical LOD is calculated from astronomical observations (transit and eclipse times etc). It’s certainly not an easy thing to et right. But your model seems to cohere with the gas giant effect on the solar motion quite nicely! I’d like to learn more about what you’ve done.

    http://www.livescience.com/38083-earth-core-day-length-pattern.html has some perplexed scientists doing some waffling about the ~6yr LOD changes.

  20. R J Salvador says:

    The smaller frequencies in this model enable the fitting of the larger frequencies like a key in a lock.
    The small frequencies are the earth at 1 year and 0.5 year for the seasonal change.
    Thanks to Tim and Paul, I was able to discard my crude model and use their frequencies to get the lunar LOD effect. There are four lunar frequencies in years =:
    half the sidereal orbit of 0.037402114 yrs and
    very close to half the draconic of 0.037327206 yrs which gives a beat of 18.6 years.
    two other frequencies which are very close to the tropical and anomalistic but not an exact match
    of 0.074359156 and 0.075442014.
    These frequencies above allow the model to place the gas giant frequencies to optimize the fit. (r^2=0.947)
    The narrative of why these gas giant frequencies work is not yet completely clear.
    The three smallest ones are :
    9.007246722 = SEV
    5.018891421 = UEV
    4.492694707 = NEV
    I think they model and eliminate any six year residual oscillation:
    The three biggest frequencies drive the curve which all the other frequencies ride.
    Two times the JEV =11.06964992 X 2 =22.13929985
    And then the beat of the axial period of jupiter and saturn with the two times JEV =13.6823310418865
    Finally the beat of the the jupiter orbit with half the jupiter saturn synodic = 61.04648218
    The last three control the big picture. All that the others supply is the ability to place and scale the magnitude of the three cosines.
    It seems amazing to me that working on LOD without PDO data produces a curve that matches and leads the PDO. Of course Ian Wilson has already shown there to be a relationship.

  21. tallbloke says:

    R.J. it’s great that you’ve come up with this just now. I assume you’ve noticed that the J-S axial, 13.68 and 22.139 are all in phi relation? 🙂

    Just for phun

    Also, Earth and Moon densities are very close to phi relationship too.

    We are at the start of a new paradigm of understanding in solar system dynamics.

  22. R J Salvador says:

    Rog, I did notice and that is just outstanding work on the phi thread. That thread is where I saw the frequencies that allowed this model.
    The implication of the model is that Jupiter Saturn and Venus are the major spinners of the Earth. Just three frequencies potentially explain hundreds of years of PDO data. The three frequencies can all be derived from the orbital frequencies of J S &V. which means the model could be expressed as the orbital frequencies of J S & V.
    Do your phi relationships allow and predictions about so called planet 9 if it exists?

  23. tallbloke says:

    R.J. Paul V has made major strides forward, occasionally finding bits and pieces OB and I come up with useful. What is good is we now have much fuller explanations of how he does his calcs, so we can join in the phun more productively.

    Planet 9 is in my view a speculative idea with little to prove its existence. We’ve only seen two Uranus orbits and less than a Neptune orbit since their discoveries. One model posits a 1.1 million year exchange of angular momentum between U and N but that isn’t well constrained either. So since planet 9 rests on tiny anomalies in U and N’s orbits, and the orbits of kuiper-belt objects, described by perturbation theory’s heuristic equations, which are not based on first principles derivations, we should be interested, but sceptical.

    In any case, its way too far out to have any obvious effect on our solar-planetary theory.

  24. oldbrew says:

    RJS says:
    5.018891421 = UEV
    4.492694707 = NEV

    UEV/NEV ≈ √5/2 (99.84% match)

  25. tallbloke says:

  26. tallbloke says:

    R.J. :These frequencies above allow the model to place the gas giant frequencies to optimize the fit. (r^2=0.947)
    The narrative of why these gas giant frequencies work is not yet completely clear.
    The three smallest ones are :
    9.007246722 = SEV
    5.018891421 = UEV
    4.492694707 = NEV
    I think they model and eliminate any six year residual oscillation:

    Why would you want to eliminate the six year oscillation?

  27. Fast says:

    That is interesting. I was not able to completely follow their work. When you mentioned this oscillation before, I did not look closely at the magnitude of the LOD effect that is involved with their 5.9 yr cycle. If I got it right they are looking at a variance in LOD that is ten times smaller than the levels described by my humble effort. I’m cutting with an ax and they are working with scalpels.

  28. tallbloke says:

    Here’s a 2013 paper on the discovery of the 5.9yr cycle in LOD

  29. Paul Vaughan says:

    RJ wrote: “And then the beat of the axial period of jupiter and saturn with the two times JEV =13.6823310418865”

    Keep in mind that twice this frequency is a factor of U-N along with 25 (as I’ve been pointing out primarily algebraically).

    13.68233104 / 2 = 6.841165521
    171.4062162 / 6.841165521 = 25.055119
    log_φ (6.841165521) = 3.996074109 ~= 4
    log_√5 (25.055119) = 4.002736773

    The 1/(U-N) solar system boundary is a product of 2 intersecting geometries:

    φ^4 = 6.854101966
    (√5)^4 = 25

    25*6.854101966 = 171.3525492

    TB wrote: “We’ve only seen two Uranus orbits and less than a Neptune orbit since their discoveries.”

    I think people may be at risk of thinking I’m pulling the boundary conditions out of a dreamy hat …but on the contrary, I’ve derived them systematically.

    Thanks for the update R J.

  30. oldbrew says:

    The lunar axial period of 25.42006 days = phi³ x 6 days (99.9856% match).

  31. […] sending me an updated prediction for changes in LOD during 2016. This plot has been produced using R.J.s model, which has been developed using the planetary periodicities we have been working on here at the […]