A phase-reversal is a phase-shift of 180 degrees. The polar motion phase-reversal is not artificial; it is real. (It has been observed.) It is evidence of nonstationarity, a concept which you (seem to) repeatedly ignore despite cautions from John S. & I, which should alert you of the need to pursue other methods of power spectrum estimation (besides just basic FFT). [I'm not suggesting John S.'s comments were addressed specifically towards you; nonetheless, we can all benefit from heeding the wise advice he occasionally shares.]

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bill (06:23:54) “It is not as shown in the references you gave which show a rapid phase change of 180 deg. – one figure before 1930 and 180 degrees offset after 1930″

You must be looking at figure 11 in Vondrak (1999) without reading the associated text. The empirical view is at the top of the top panel of figure 10 (as I’ve indicated above). (You will note that figure 11 relates to a simulation Dr. Vondrak ran. See Vondrak (2005) for more details, if interested.)

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bill (06:23:54) “no hint that it is cyclical.”

No claim has been made of cyclicity. (Note that only one phase-reversal occurs in the entire polar motion record (to-date).)

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bill (06:23:54) “There is no associated change in wobble direction”

No claim has been made of a change in wobble direction. (Perhaps you misread “phase reversal” as “rotation reversal” and developed a very serious misunderstanding early-on?)

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bill (06:23:54) “How can this effect climate?”

It is well-established that things that happen in the oceans & atmosphere (& other parts of Earth) affect EOP.

My impression is that your impression of what is being claimed is largely imagination-driven.

I encourage you to:
a) read comments carefully, judiciously, & literally.
b) orient yourself relative to the EOP literature.
c) learn a method of power spectrum estimation that affords time-localization (so as to better cope with nonstationarity).

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Questions:
1) Do you now see that the monthly CDIAC CO2 stats differ from the monthly NOAA CO2 data?
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2) Do you acknowledge that CDIAC fit the raw data to a curve? (as they have acknowledged publicly in writing via their webpages)

Regards,
Paul.

What on earth has this artificial, mathematically produced, phase change got to do with anything?

The phase shift is a methematical artefact.
It is not as shown in the references you gave which show a rapid phase change of 180 deg. – one figure before 1930 and 180 degrees offset after 1930, no hint that it is cyclical.
It is a smooth change in PERIOD from 1.17 to 1.19 year
There is no associated change in wobble direction
It is a natural effect of many driving frequencies on the wobble – can you explain the physical effects of this?
How can this effect climate?
Seems to me that this is the non-event of the earths history!

The lights go on. Like I said: It’s simple.

Case closed.

The simple FFT obviously does not show this. I initially assumed that the peaks at 1.18 years were in reality just a bit of FM on the fundamental. However, the BP filter shows 2 discrete frequencies. Reducing the bw of the bp filter to just include the 1.15 year period shows an amplitude of 0.3 relative. the 1.19 year wobble shows an amplitude of 1.2 relative. The 365.25 period has an amplitude of 1.0 relative during the 1930s

The amplitudr of the 1.15 year wobble may be modulate with a 162 year wave.

2) How do you interpret the bulge around them (in your power spectrum plot)?

A with any plot like this more resolution could show individual frequencies however with the data available it shows as noise or perhaps occassional frequency excursions of the main wobbles (there are a few other discrete frequencies in this area.)

3) Have you ever used windowed-FFT?
The built in excel funcion does not have windowing function. However, I often have, as part ogf my work, used such functions on real-time FFTs on DSOs. I do understand that the window type will affect the shape of the spectrum (but not the frequency of the peaks).

In order to see a phase reversal, one has to first decide, “relative to what?” If you look relative-to-a-stationary-wave, you will see (even without doing any calculations) that the polar motion group-wave (the envelope) is in ~anti-phase with a stationary wave with a period of ~6.4a before ~1931 and in-phase after (if you phase-align the latter part of the record).

1. What is the physical manefestation of yourhyperthetical stationary wave vs group wave phase reversal?
2. If I chose 6 years then the phase is continuously changing. before and after the 30s the main wobble is 1.19 years during the 30s the main chandler wobble is 1.15 years. The chandler wobble beats with the 365.25 day annual wobble to create a 6.4y wave. It is obvious that the wave will be longer with 1.15 y (during the 1930s) and shorter (outside the 30s) This will cause a phase shift!

3.In one post to claim that artificial constraints have been applied to CO2 data from CDIAC on on other posts you impose an artificial FIXED period of 6.4 years to get your phase shift. This is inconsistent?

4. There are other frequencies that filtering picks up
~1.2years reasonably constant amplitude over the period of the data.
~1.225 years reasonably constant amplitude over the period of the data.

Note the imposed annual structure for CDIAC. This is important for anyone modeling seasonal fluxes (such as ecosystem carbon modelers I know).

The results for Alert are even more dramatic (as has been discussed previously).

This is the page you need to compare monthly values:
ftp://ftp.cmdl.noaa.gov/ccg/co2/in-situ/brw/brw_01C0_mm.co2

Difference both series and study the annual structure comparatively (across years & series). I look forward to hearing what you find.

Also, you are looking at Barrow, Alaska, USA. Recall that I was looking at Alert, Nunavut, Canada when I found the problem.

As previously indicated: There isn’t a problem if you are only interested in the undifferenced trend at super-annual timescales. (I want to make sure there are no misunderstandings.)

I will run the analysis for Barrow now (to make sure there are not further misunderstandings).

Feel welcome to ask any follow-up questions.

This suggests misunderstandings bill.

To probe them, I will ask 3 questions:
1) Do you think the 2 frequencies you mention are both continuously operating across the record?
2) How do you interpret the bulge around them (in your power spectrum plot)?
3) Have you ever used windowed-FFT?

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bill (07:37:27)
“however in physical terms all that happens is a slowing down of chandler period during the 30s.”

That’s part of it.

In order to see a phase reversal, one has to first decide, “relative to what?” If you look relative-to-a-stationary-wave, you will see (even without doing any calculations) that the polar motion group-wave (the envelope) is in ~anti-phase with a stationary wave with a period of ~6.4a before ~1931 and in-phase after (if you phase-align the latter part of the record).

This is equivalent to what Vondrak (& others) showed.
Figure 10 – top of top panel:
http://www.yspu.yar.ru/astronomy/lib/Rotation.pdf

It’s not complicated. I suppose if it is confusing (&/or has confused) people it might have something to do with the nature of the time series (2-dimensional vector with a beat-envelope – i.e. not the type of series (all) folks around these forums are normally used to handling – e.g. temperature time series, sunspot curves, etc.)

It is interesting to note that the (absolute) power falls during the ~20 year phase reversal interval. (This suggests other wavelet transforms – for example timescale-normalized. (The one I presented was time-normalized.)) …So at the time of the Chandler slow down / polar motion envelope phase-shift, the annual wobble played a (relatively) stronger role.

If you now go back through my earlier comments (in earlier threads) you will probably easily see why I took differences & used them to calculate a vector magnitude (makes things simpler). If you go through that exercise & plot the results on a grid with 6.4a (horizontal) spacing, the phase reversal is plain-as-day. [As I said upthread: I only (generally) bother with a wavelet transform if I can already envision that it will provide a concise summary of something I already see. However, unfortunately: Many of the academics I deal with dismiss the wavelet transforms on the grounds that they do not know enough about wavelet transforms to assess them. This certainly creates an "interesting" challenge.]

It is interesting to note that the simple FFT so despised by Paul Vaughan, shows two distinct chandler frequencies. Using a bandpass filter pulls each frequency out of the mix 1 year, 1.15 years and 1.19 years. This seems to be an amazing band pass algorithm for excel. I will have to check it out on some other manufactured data and check for phase accuracy etc.
The same web site has a useful smoothing algorithm (hodrick prescott) which seems to produce a level of filering similar to a moving average with little phase/amplitude distortion compared to the moving average.
http://www.web-reg.de/

However,there seem to be 2 chandler frequencies 1.15 and 1.19 years as shown in these two plots.
during the 30s the 1.15 slowly displaces the 1.19. I would therefore expect a phase change between the 6.4 fixed period (because that is what you have done) and the mixed chandler frequencies of 1.15+1.19.

however in physical terms all that happens is a slowing down of chandler period during the 30s. I was expecting a phase shift between x and y (i.e. reversal of direction).

Can you confirm that this is your “phase shift”
1.19ish period chandler wobble
http://img411.imageshack.us/img411/576/chandlerwobble119.jpg
1.15ish period chandler wobble
http://img151.imageshack.us/img151/5341/chandlerwobble115.jpg

Keep in mind the Nasa PR machine (especially when results that leave new questions are publicized as final answers to age-old mysteries).

Keep in mind that SBA & SBO would like to survive & flourish.

Suggested:
Read papers by other authors that give a different treatment (bearing in mind the concept of shared-variance).

And this is telling:
In reviewing Gross’ work (including his 2007 overview in Treatise on Geophysics), pay scrutinizing attention to his treatment of r^2.

bill, I think you will find this a very distracting tangent [if you pursue it now] (but a very interesting one when you have time).

For now, I suggest wrapping up our misunderstanding expeditiously. It has nothing to do with Gross’ 2000 findings (which are limited by the short length of the employed series) and you can manage a basic conceptual understanding without learning wavelet methods – (that can come later, on your own time).