Biennial Mode of SST and ENSO

This recent 2016 paper [1] by Kim is supporting consensus to my model of a modulated biennial forcing to ENSO. I had read some of Kim’s earlier papers [2] where he introduced the idea of cyclostationary behavior.

The insight that they and I share is that the strictly biennial oscillation is modulated by longer frequencies such that +/- sideband frequencies are created around the 2-year period.

$sin(pi t) cdot sin(omega_m t) = frac{1}{2} ( cos(pi t - omega_m t) - cos(pi t + omega_m t) )$
$.$

This is not aliasing but essentially a non-aliased frequency modulation of the base cycle. The insight is clarified by Kim with respect to Meehl’s [3] tropospheric biennial oscillation (TBO).

From [1]

That biennial mode locks the base frequency in place to a seasonal cycle, with the modulation creating what looks like a more chaotic pattern. That’s why ENSO has been so stubborn to analysis, in that the number of Fourier frequencies doubles with each modulating term. Yet in reality it’s likely half as complicated as most scientists have been lead to believe.

Seasonal Aliasing of Tidal Forcing in Mean Sea Level Height

I applied the QBO aliased lunar tidal model to another measure that seems pretty obvious — long term monthly time series data of sea-level height (SLH), in this particular case tidal gauge readings in Sydney harbor (I wrote about correlating Sydney data to ENSO before — post 1 and post 2).

The key here is that I used the second-derivative of the tidal data for the multiple regression fit:

Fig 1:  QBO factors over the training interval

This is remarkable as it applies the as-is QBO factors to Sydney training data from 1940 to 1970. That is, the parameters are solely derived from the critical aliased lunisolar periods used to optimize the QBO fit.