In [comment #81](, I used the historical ENSO coral proxy data as a validation test against an ENSO model fit of post-1880 direct measurements.

The fit was reasonable but it went out-of-phase over one interval. I used a QBO period of 2.333 years for that model.

I have since tried again and this time used a QBO period of 2.366 years. Again the training period is restricted to post-1880 and the correlation coefficient for the entire span is a little over 0.42. The yellow areas show the divergence and it looks slightly worse the farther back it goes but it never shows a negative CC over any interval.


What is interesting about this value for the QBO period is that once I noticed where it was headed I set it exactly to twice the value of the Chandler wobble period of 432.2 days.

2*432.2/365.25 = 2.366 years

The CW period beats against the yearly cycle and produces approximately a 6.5 year angular momentum change cycle, which is the other forcing factor in the model. (There is also a period of 50 years to model multi-decadal changes, and a few non-forcing factors such as TSI fitting the non-ENSO residual).

I think there may be something inherent in the relation between the QBO period and the CW period. The QBO reflects the oscillation of the upper atmosphere, while the Chandler wobble could possibly be an angular momentum response of the Earth's mantle and ocean. How the period doubling (or frequency doubling -- depending on the causal direction) arises is a mystery, making it potentially nothing more than a coincidence.

Azimuth has more than its share of people interested in topological puzzles, so perhaps someone has ideas outside of the chaotic-bifurcation explanation. Yet even that may yield some insight.