If you review the conversation, you’ll realize we’ve barely grazed the surface of the ideas I have to introduce. A serious challenge I am facing is that many of the people I am writing to about my findings do not understand wavelet methods, let alone cross-wavelet & acoustic-cross-wavelet methods.

You are certainly right when you say, “lots to do now!”.

You will find lots of news releases from the early 00′s about Richard Gross’s work on the Chandler wobble. Gross’s work is fascinating – and it leaves questions for scientists in other disciplines about what is driving the atmosphere & the oceans. The cause of the Chandler wobble phase reversal in ~1931 is still considered a mystery.

Regarding the magnetic poles, one pub of which I know is:
Adrian K. Kerton (2009). Climate Change And The Earth’s Magnetic Poles, A Possible Connection. Energy & Environment 20(1-2), 75-83.
http://www.adriankweb.pwp.blueyonder.co.uk/Climate_Change/E-E_Clr_Abstracts.pdf

If you dig into references in Gross (2007), you’ll find more.

But you probably knew that, and were being elliptical when you said the atmosphere was the bigger driver than the ocean. I wonder though, whether the changes in the ocean’s retention of the heat of insolation I’m working on may also have an effect due to density changes. I know the effect on the polar motion caused by the Pacific Warm Pool calculated by Zhou et al are small in relation to the total, but The PWP isn’t the only place the oceans are storing heat if I am right. The north Atlantic anomaly has run particularly high in the later C20th, and being further from the equator, I would expect a greater effect. I wonder also if perhaps the pressure changes on the bottom of the ocean are large enough change the shape of the earth’s crust.

Speculative question: Could the polar motion on a longer timescale affect the position of the magnetic north pole? I remember Vukevic got excited about that and posted some maps on solarcycle24.com showing the path of the shifting magnetic north over the last 2000 years or so which had been produced by some researchers (from Canada I think).

I get what you mean about differencing now. It’s the same as the method I used to get the running cumulative total on the sunspot counts and sunspot area measurements.

If you dig around in directories like …
http://hpiers.obspm.fr/iers/eop/
…and in publications, you’ll find the info you need.
“mas” is the abbreviation for milli-arcseconds (angle).

You may find this site to be a useful gateway:
http://hpiers.obspm.fr/eop-pc/

Accessible from there, the following page gives a good overview of EOP:
http://hpiers.obspm.fr/eop-pc/earthor/orientation.html

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LOD & AAM:

When you have time, I encourage you to study:
a) figure 1a in Schmitz-Hubsch & Schuh (1999)
http://www.uni-stuttgart.de/gi/research/schriftenreihe/quo_vadis/pdf/schmitzhuebsch.pdf
b) Figure 6 in Sidorenkov (2005)
http://images.astronet.ru/pubd/2008/09/28/0001230882/425-439.pdf
c) figures 1, 2, & 3 in Zhou, Zheng, & Liao (2001)
d) everything Richard Gross has to say in Gross (2007)
ftp://euler.jpl.nasa.gov/outgoing/EarthRotation_TOGP2007.pdf

You will see that the PWP (Pacific Warm Pool) is something Zhou & associates are looking at to explain “left-overs” not explained by AAM (Atmospheric Angular Momentum). If you dig into Gross’s work, you’ll see that he looks at OAM (Oceanic Angular Momentum).

It is important to keep in mind that most experts agree that AAM accounts for a large proportion of LOD variation.

There is plenty of quantified speculation about polar motion, but my impression from digging in the literature is that it is not as well understood as LOD, even though certain aspects of it are certainly very well-understood.

The paper that originally drew my attention to polar motion was the following:

Yndestad, H. (2006). The influence of the lunar nodal cycle on Arctic climate. ICES Journal of Marine Science 63(3), 401-420.
http://icesjms.oxfordjournals.org/cgi/content/full/63/3/401

Over time I have developed the view that, while Dr. Yndstad’s research is a very important contribution, there are problems with his interpretations; I believe there are confounded-influences on polar motion (no simple matter to disentangle). There are different factors with very similar harmonic scales that show up in polar motion phase relations analyses (details will have to wait for another day).

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Regarding wavelets:

It would take me weeks of heavy, more-than-full-time engagement to develop a good “Wavelets in Excel for Beginners” website. For now, I suggest you focus on getting the basics.

The simplest way to think of it is that the wavelet can shrink and grow —- at each size which it can assume, it takes a trip through the data, pausing at each time-step to measure how well its shape correlates with the data. As you know, correlations range from -1 to +1 – so if the wavelet records -1, that means it matched that data perfectly in a given time-step-window (& at a given size), but that it had to flip over to do it.

For each wavelet size (timescale) there is a string of measurements. In a wavelet plot the strings of measurements are stacked vertically on the timescale axis. Don’t confuse time (horizontal axis) with timescale (vertical axis) on wavelet plots.

What I’ve just described is for a real wavelet. To get at phase information, complex wavelets (with a real & an imaginary part) are used. The imaginary part is phase-shifted by 90 degrees (seahorse-shaped) so that it sees “uphill” vs. “downhill” (upside-down seahorse) while the real part (mexican-hat-shaped) sees “peak” versus “valley” (upside-down mex-hat). This enables one to know – from a pair of correlations – things like “going uphill & approaching a peak” or “in a valley bottom & about to go uphill”, etc. —- i.e. it takes you a step beyond just knowing “on a peak” or “on the side of a hill” — it puts these states into a richer context.

The mexican hat & the seahorse are cooperative traveling buddies. They have different shapes, but they always stick together & assume the same size. These explorers are always curious to see how well their complementary shapes match their surroundings on the time-series-landscape as they slide & change size together. Mathematicians call them a “complex pair” because of their relative appearance, but their view of the world is simple.

Wavelets come in other shapes. The Morlet wavelet gets lots of attention. It can be adjusted to control how many waves it has in its sliding window. This means it can be adjusted to achieve good timescale-resolution – but at the expense of lost time-resolution. For graphs that illustrate this point nicely, see here:
http://www.clecom.co.uk/science/autosignal/help/Continuous_Wavelet_Transfor.htm

If you get the basics from the tutorial at …
http://www.ecs.syr.edu/faculty/lewalle/tutor/tutor.html
…to the point where you can look at the regular timeplots on that site and see how they map onto the wavelet plots and vice versa, that will be enough to tide you over until you master wavelet transform calculations — i.e. at least you’ll be able to read others’ work while you are learning to write your own.

Advised: Go through the tutorial links in the order in which they are presented.

Wavelet concepts are simple, but since the edge-effect varies with timescale – i.e. the wavelet hangs further off the edges of a time series as it grows – computer-coding gets fussy. This is just a technical issue – so reading comes fast, but writing takes a little longer.

I don’t have multiple free weeks to explain all of the coding technicalities now – and “part-way” coding doesn’t cut-it with computers. I suggest moving at whatever pace you can, with the first priority being ability to read wavelet plots.

For now I’ll take questions on that. I’m hoping to be positioned to start posting graphs within hours-to-days (there is a technical issue – & I never underestimate them).

One other thought, once we have the radius plotted against time, we could also take the first and second derivatives to look at velocity and acceleration of the polar motion. It seems to me these might have some bearing on the excitation of atmospheric and oceanic phenomena and may lead to some insight into the relationship between the slopes of the AAM curves and the rate of motion of the pacific Warm Pool.

It might help if I understood the units. Presumably x and y are coordinates representing the offset of the pole from the reference frame.

I hope you don’t mind taking the time to get me through this step by step. I’m certainly willing to spend the time to try to replicate and corroborate your results.

Thanks

1.
Polar motion time series can be obtained here:
http://hpiers.obspm.fr/eop-pc/products/combined/C01.html
2.
Difference both x & y and find the root mean square. (This creates an index of polar motion radius with the trend removed.)
3.
Do a complex Morlet transform with wavenumber = 2pi on the interval (3.5a, 9.5a). [Note: a = annum.]
4.
Convert the real & imaginary arrays into modulus & argument arrays.
5.
Find the maximum modulus for each time and note the timescale. (If using Excel, use the functions “max” and “match”.) [Note: This gives a series of group-wave periods corresponding to the polar motion beats visible in the original x & y.]
6.
Find the beat period of this series of modulus-maximizing timescales with the annual wobble using the Helmholtz acoustic equation.
7.
Convert from years to days.
8.
Make a simple time-plot of the resulting series.

This will draw undeniable attention to the Chandler wobble phase reversal.

Step 2 is to compare the resulting curve with precipitation series smoothed at 13 year bandwidth (the average period of the envelope of the polar motion group-waves). [Note: Be sure to check to see if the precipitation series need variance-stabilizing transforms - square root works well with the series I have investigated.]

In part due to the notes of Currie (1996, cited above) I have focused my attention on the heavy precipitation of the Pacific Northwest of North America, where the Pacific Ocean abruptly meets mountain ranges, resulting in heavy fall/winter rain/snowfall. A large anomaly in the 13a-time-integrated precipitation series matches the wavelet-derived Chandler period series. The spatial extent of the 1930s drought extended beyond the Pacific Northwest. I plan to expand the analysis to other sites & regions.

Good science is reproducible. I await feedback. If this result is already known to climatologists, I await references (and I have other clean results involving extreme monthly temperatures).

Note that the calculations do not (so far) depend on the solar system barycentre. Things get a lot more complicated. This is just an introduction.

It is worth going down every link-branch on that site in all detail. The site pitches at a truly introductory level. Someone with no background could spend weeks looking at other wavelet sites and get nowhere – and then get all the wavelet basics in a few hours on this site. There are a LOT of BAD wavelet sites that are just scrapes of other bad wavelet sites – it is epidemic.

The links between LOD, GLAAM, & ENSO are well-established and can be traced back decades in the literature. You might want to dig into the references listed in papers 1, 4, & 5 which I listed at Paul Vaughan (16:56:10). You may also have noted links provided by Richard Mackey (to Lambeck) & Ian Wilson (to Sidorenkov) during recent months — and the following (which includes tons of good references) is likely to be of interest:

R.S. Gross (2007). Earth rotation variations – long period (3.09). In: T. Herring & G. Schubert (eds.), Treatise on Geophysics, Volume 3, Geodesy, pp. 239-294.
ftp://euler.jpl.nasa.gov/outgoing/EarthRotation_TOGP2007.pdf

You may also be aware that Klyashtorin & Sharp make use of the polar motion harmonics I explained above:
ftp://ftp.fao.org/docrep/fao/005/y2787e/
ftp://ftp.fao.org/docrep/fao/006/y5028e/

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If anyone knows of any very concise summaries of the spatiotemporal extent & phasing of the 1930s drought (that affected at least North America), please let me know. Also, if anyone knows of any “respected” regional &/or global precipitation series, I will appreciate links.

Related:

“Currie (1996), who employs filtering techniques commonly used in electrical engineering, seems to contend that significant lunisolar components are detectable in a very wide variety of terrestrial time series, including virtually all climate series. He investigates terrestrial geographic sites individually (thousands of them) and cautions that zonal &/or global averaging masks locally detectable signals that are intermittently out-of-phase with those at different locations, even ones relatively nearby. [...] Currie (1996) suggests that “on decadal and duodecadal time-scales the spectrum of climate is signal-like rather than noise-like, as radically assumed by statisticians and mathematicians the past 70 years.”" (Vaughan 2008)

Currie, R. G. (1996). Variance contribution of luni-solar (Mn) and solar cycle (Sc) signals to climate data. International Journal of Climatology, Vol. 16, No. 12, 1343-1364.

With awareness of this, some of you should be able to pull several threads together (e.g. precipitation, length of day, polar motion, atmospheric angular momentum, SOI, NAO, solar variation, temperature [global, regional, minimum, maximum, average, extreme monthly minimum, & extreme monthly maximum], rate of change of carbon dioxide concentration, …)

I did take note of this post and await more details. :-)

One thing which may interest Paul with regard to this is that according to my solar activity cumulative running total method, the count reached a minimum in around September 1935 following a decline since around 1875, and rose to a peak around 2000. To me, this would indicate that the swiftly rising temperature 1920-1940 was the result of a terrestrial redistribution of energy, rather than having a direct solar energy emission cause. How much of the terrestrial redistribution of energy was due to motions induced by non-terrestrial sources I leave to Paul to elucidate and demonstrate.