19 January 2016

The Pacemaker of the Chandler Wobble

Abstract: The Chandler Wobble is one of the largest circumannual periodic or quasi-periodic variations in the earth's orientation.  After over a century of searching for its forcing, it was found to be caused by atmospheric circulation and induced ocean circulation and pressure.  The question of why there should be such forcing from the atmosphere has remained open. I suggest that variations in earth-sun distance cause this forcing to the atmosphere and thence the ocean.  Analysis of earth-sun distance, earth's orientation, and atmospheric winds shows a coherent relationship between the atmosphere and earth orientation at just those periods expected from earth-sun distance variation.  As this is a general mechanism, it can be used in examining regular climatic variations on a wide range of periods and for climate parameters other than the earth's orientation.

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That is the abstract for the paper I link to below.  It's not a peer-reviewed paper in the sense of being in a peer-reviewed journal.   But it has been reviewed by an expert in the field (William P. O'Connor), who was quite favorable.

I am posting the idea and paper here.  Long past time for the ideas to be discussed.  If they're shredded in the blogosphere, so be it.  I have quite a bit more than what I've put in the document. Over the next few days and weeks, I'll post more of those additional materials as well.

The Pacemaker of the Chandler Wobble, Grumbine 2014


William Beeson said...

If I understand correctly, variations in TSI cause variations in wind/pressure, etc.

You calculate the effect of the moon's orbit (or, more accurately, the earth's orbit around the earth/moon common center of gravity) to have the largest amplitude after the yearly variations.

My question is this:

Do you account for the additional variation in TSI due to the waxing and waning of the moon's reflection, which is most intense at full moon, when the Earth is also closest to the Sun?

Kevin O'Neill said...

Paul Pukite at contextEarth has some interesting machine learning (Eureka) equations concerning the Chandler wobble, ENSO, the QBO, and the SOI. Back in 2014 he had one specifically on the Chandler wobble and the SOI.

@whut said...

Kevin gave me a nod
"Back in 2014 he had one specifically on the Chandler wobble and the SOI."

Lots to chew on, that's for certain. I have made some interesting progress since that post, especially with regards to QBO, which has periodic sub-yearly content that may be physically aliasing the lunar with the solar cycles. The issue with ENSO measures such as SOI is that the sub-yearly data is very noisy.

Curious, what happened with Claire Perigaud at NASA? She wrote a proposal suggesting that scientists look closer at the luni-solar connections to climate via assorted geoscience measures, but it never got funded. So she went off on her own ... see the MoonClimate org web site.

Robert Grumbine said...

The lunar period, around 1 month, is too fast to drive the Chandler Wobble around 14 months. It's in the table because it is indeed something which changes the earth-sun distance. The moon is 14 magnitudes (astronomical magnitudes) fainter than the sun, which makes for the moon being about 2.5 ppm of the solar constant. That's equivalent to a distance variation of about 1.25 micro-AU. So it's quite a bit smaller than the main variation (about 31 micro-AU), but would have to be considered if we were doing a thorough job examining the effects of the moon since it's larger than the next drivers in the earth-sun distance due to the moon (about 0.5 micro-AU).

The introduction of Mathieu functions looks unmotivated in that page alone. But looks like more reading is worthwhile (maybe a better explanation in one of the links).

SOI (et al.) affecting the earth's orientation and rate of rotation is not fundamentally surprising. They affect the winds and pressure fields, which then mean effects on the atmospheric angular momentum and mass.

Robert Grumbine said...

Don't know about Perigaud. Will have to follow up the link.

Doing the work from the side of observation first is fraught with difficulty. It is appallingly easy to find harmonic relations between given a handful of base frequencies and a target frequency. No matter what the target frequency, you can always find a combination of the base frequencies that will beat or alias to it (or somewhere close).

That's why I started from something physical that couldn't mislead me that way. Earth-sun distance dictates a very specific set of frequencies. The seasonal cycle and its harmonics has many possible sources. So the atmospheric and oceanic circulation can show seasonal effects for many reasons. But if they're doing something at 399 or 584 days ... well, those are quite peculiar and not pushed by the internals the climate system.

@whut said...

"The introduction of Mathieu functions looks unmotivated in that page alone. But looks like more reading is worthwhile (maybe a better explanation in one of the links)."

The application of a Mathieu DiffEq formulation was motivated by the physics of sloshing of liquids in a tank. A recent review article is here:

[1]R. A. Ibrahim, “Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems,” Journal of Fluids Engineering, vol. 137, no. 9, p. 090801, 2015.

It's essentially a perturbation of the wave equation, the latter which is what the ENSO scientists such as Allan Clarke at FSU are advocating. Solving a Mathieu equation can be either chaotic or quasi-periodic or periodic depending on the strength of the perturbation.

I spent time early on with the Mathieu formulation thinking that something obvious might pop out because the SOI waveform is so erratic and has similarities to the sloshing solutions I have worked with. Some machine learning experiments suggested that the effect might be there, but its still elusive. Now I am leaning towards the idea that complicated forcing might be more at work, based on what one can find with the QBO.

The QBO is amazing in terms of being constructed from the lunar periods. Lots of this is being worked out at John Carlos Baez's mathematical physics forum AzimuthProject (the forum, not the blog).

@whut said...

"It is appallingly easy to find harmonic relations between given a handful of base frequencies and a target frequency."

That really is true ... until you find the actual combination that works. Consider that there are hundreds of Fourier terms in the model for tidal predictions. Yet no one blinks an eye to whether that is considered overfitting. Check NASA's Richard Ray's latest table which contains ~80 terms:
Ray, Richard D., and Svetlana Y. Erofeeva. "Long‐period tidal variations in the length of day." Journal of Geophysical Research: Solid Earth 119.2 (2014): 1498-1509.

The other aspect to this is the strict application in separating training and validation intervals. Given the fact that historical coral proxy data is available for ENSO that spans hundreds of years, there is lots of room to validate harmonic models.

So the question is whether the behavior of ENSO is periodic and whether there has been enough effort to deduce any of the quite peculiar (as you call them) base frequencies in the time series. Negative results are usually not published, so I may be beating a dead horse, but I figured it is worth pursuing this approach.