(see later posts here)

[mathjax]Seth Carlo Chandler Jr was an actuary who studied his namesake wobble for thirty years.

ENSO and the Southern Oscillation Index has confounded everyone with its unpredictability.

Could a connection exist between the ENSO and the Chandler Wobble ? [1]

Based on what I have been analyzing with respect to the ENSO data, I am leaning in that direction.  In the first post on the Southern Oscillation Index Model (SOIM), my initial analysis lead to a fundamental Mathieu frequency T of 6.3 years, a value of a = 2.83  and q = 2.72 :

• The Southern Oscillation Index Model

I followed that up with additional checks and analogies to other physical phenomena :

• SOIM and the Paul Trap

That culminated with a trial fit of the SOI with a set of Mathieu parameters. Yet — even though the fit was decent — I was not satisfied with the result as it tended to overfit with respect to the adjustable parameters.  The ideal situation would limit the number of fundamental frequency terms.

Three observations lead me to a much simplified representation.

• The main Mathieu frequency of 6.3 years seemed to vary over the historical record.
• The pressure index of the SOI is essentially a differential measure, and so the derivative of the Mathieu function should be fit to the pressure, e.g. use MathieuCPrime and not MathieuC .
• The connection between the original fit of 6.3 years and the Chandler Wobble beat frequency of 6.39 years (= 1/(1-365.25/433)), and the fact that this measure has been known to vary over the past 100+ years.

↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

Continue reading →