Semantic note:
When you say “invert” some might think you mean 1/x, as opposed “-x where x is negative” or |x|. If I understand what you did, you subtracted a ‘central’ value and then took absolute values (i.e. you removed negative signs from negative values). [Note: If the central value was the average, a statistician would call the resulting series of quantities "absolute deviations". Using the median as the central value would produce "median absolute deviations".]

Carl, Ian Wilson, & Geoff all had the right idea in following Jose’s advice to investigate alternate indices. Tip: Try wavelet transforms (as suggested by Landscheidt in his later years). My impression is that most people underestimate what can be done with wavelets.

[WORDPRESS HASHCASH] The poster sent us ‘0 which is not a hashcash value.

Please explain what columns B, C, D, E and I, J represent

REPLY: This is Carl’s original data, B= longitude, C= solar radius, D= AM, E= torque. I is a copy of D, J is a manipulation of I allowing a different method of viewing AM. Weak AM and strong AM (top & bottom of cycles) both account for strong solar cycle modulation. This method matches the weak with strong by assuming 2.0E+47 as the neutral point. ie all figures below 2.0E+47 are inverted.

Cheers

Rog

REPLY: Here is the adjusted AM spreadsheet, use column J
http://users.beagle.com.au/geoffsharp/ssb1873-2013.xls

-
The tides show up in the daily LOD series.

Related:
The following article is worth digesting thoroughly:

Harald Schmitz-Hubsch & Harald Schuh (1999). Seasonal and short-period fluctuations of Earth rotation investigated by wavelet analysis. Technical Report 1999.6-2 Department of Geodesy & Geoinformatics, Stuttgart University, p.421-432.
http://www.uni-stuttgart.de/gi/research/schriftenreihe/quo_vadis/pdf/schmitzhuebsch.pdf

I can provide other references if anyone is interested.

[WORDPRESS HASHCASH] The poster sent us ‘0 which is not a hashcash value.

Since the curves are constructed using a weighted average, it is possible to ’sharpen’ the view of the ‘wiggles’ with a distortion filter. Multi-timescale 3D-color-contour plots are one (fruitful) way to go if you decide to pursue this.

There are other ways to access the details of the wiggles, as I have indicated on WUWT (indirectly). (You may recall I suggested looking at higher derivatives.)

Awareness of the wiggles is nothing new, but certainly sites like yours (drawing attention to graphs like Carl’s) go a LONG way towards spreading the awareness to a LARGER population.

[Landscheidt's work is out there (i.e. easily-accessible on the net), but it is not going to be clear to everyone in his audience what he was doing with his 'moving variances', windowed-integrals of derivatives, etc.]

-
Length of Day (LOD) time series can be obtained as follows:

Annual – RGO – 1623+:
http://hpiers.obspm.fr/eop-pc/earthor/ut1lod/lod-1623.html

Annual – Nasa JPL – 1832-1997:
http://hpiers.obspm.fr/eoppc/series/longterm/jpl_c.eop

Daily – IERS – 1962+:
http://www.iers.org/products/177/11221/orig/eopc04_IAU2000.62-now

More generally:
Earth Orientation Parameters (EOP) series can be obtained via:
http://hpiers.obspm.fr/eop-pc/

Important Note:
Measurement methods improved dramatically around 1960.

Strongly Recommended:
Plot the error estimates before working with the earlier data.

If you need help converting the daily data to monthly, feel free to request Excel tips.

REPLY: Landscheidt and Jose were looking at different wiggles, but were close. If they had Carl’s graph all those years ago we would know so much more by now, it has been put on ice for 40 years. I would be interested to see if you can gain any extra detail out of Carl’s work, I am suspicious there might be a chance of some solar reduction around 2045. Thanks for the links, do you know if any of the links are supplying corrected data ie allowances made for the normal tidal affects.

Thank you for shining some light on the “misunderstanding” (to use a polite term) Carsten & Geoff seem to be having. You illustrate the source of the confounding:

The different variables being addressed are RELATED BY DEFINITION.

I’ve pointed this out in a related discussion on WUWT (indirectly, by suggesting graphing exercises designed to lead investigators to independent insight).

It seems to me that many researchers overlook one of Jose’s (1965) most basic points.

Jose suggested investigating a VARIETY of these related variables; however, many have (for over 4 decades now) limited the search (mainly) to variables Jose graphed. (Could this (at least in part) explain the stall in progress?…)

Jose STRESSED (rather subtly, I admit) that his listed & graphed variables were EXAMPLES, encouraging BROADER investigation. [There are an INFINITE number of functions to investigate (but, of course, not all of them are physically meaningful...)]

-
See – owe to Rich [post #17] said, “There is also the theory and data suggesting that solar maxima are timed according to JEV syzygies, [...] , though I am a bit less convinced by that as I don’t understand how the filtering is done on that.”

You can read all of the details – the whole story – here:

http://pagesperso-orange.fr/jpdesm/sunspots/
“Sunspot cycles are they caused by Venus, Earth and Jupiter syzygies?”
by Jean-Pierre Desmoulins (1988, with later updates)

I’ve reproduced the basic pattern he finds by a different method. (For clarity: I’m not drawing any conclusions.)

I recommend reading every branch of Desmoulins’ website in full detail – he is very careful with both methods & communication.

-
Geoff, you’ve made an interesting suggestion that there might be confounding (in the statistical sense) interfering with efforts to understand seasonal variations in LOD.

(For clarity: I’m not suggesting I agree with you, but certainly efforts to consider & investigate potential confounding are to be applauded.)

I see that your graphs all show seasonal variation. Have you extended your investigation to interannual timescales? (This would be one way to probe your musings further…)

Even if you don’t want to get bogged down with the computational details of wavelet analysis, there are some really simple treatments you can give the (monthly, I assume) data – for example:
1) Difference the series.
In Excel, if the time series is in column A:
In cell B2 enter “+A2-A1″.
Copy/paste B2 down column B.
2) Then apply a 12month moving-average.
In cell C8 enter “=+average(B3:B13,average(B2,B14))”.
Copy/paste C8 down column C – and then delete the last 6 column-C cells (i.e. check that the formula in the last (undeleted) column-C cell does NOT refer to any cell below the last cell in column B).
3) Make some simple timeplots & scatterplots.

This will take no more than 1 minute – (feel free to ask for clarification).

-
Re: Adolfo Giurfa [post #36]

It seems you are aware that the sun’s motion relative to the SSB was retrograde around 1990. Other interesting events in 1989:
1) Power grid failure on Earth:
http://en.wikipedia.org/wiki/March_1989_geomagnetic_storm
http://www.agu.org/sci_soc/eiskappenman.html
2) ‘Unusual’ solar flares – including ‘unusual’ activity in the fall (…according to what I have read – but I lack expertise in this area — maybe someone else has details…)

(For clarity: I’m not drawing any conclusions – just pointing out interesting ‘coincidences’ that may be worthy of attention.)

REPLY: Jose was the man in my books, and Carl discovered the missing link from his work. I am sure if Jose or Landscheidt were around today they would have made much of his graph. The Desmoulins site is excellent and it will be interesting to see if the 2 phases come back together during SC24. Hopefully he will update his work. I dont have access to the LOD data, but if I get my hands on it I will try your exercise.

REPLY: I wouldnt expect any solar changes around 1989 going on angular momentum records other than a gradual decrease in solar activity overall. 1989 had the Sun almost dead centre of the solar system which gives an AM reading of near zero which means reasonably good strength for solar activity. Very high AND very low AM have the same effect on solar activity. The inner loop that 1989 is part of is the standard trefoil pattern, very different to the inner loop we are in today.

REPLY: I will definitely look at that….you also gave me another idea, what if the acceleration lines up with the Jupiter perihelion modulation, guess what it does. Check out the “what point do the Jovians Orbit” article.