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:
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.
The second derivative allows us to fit against a wave equation model.
I don't know why I didn't try this earlier, since it's kind of obvious that whatever lunisolar forces may drive the QBO will certainly drive the sea-level height. Yet I can see why this has been overlooked in the past, since the precise seasonal aliasing of the lunar periods is something that is not intuitively obvious.
Here is another screenshot with an additional low-pass filter applied:
Remember, this is not the fast diurnal tidal changes as seen to the right, but what is averaged over the course of a month. Clearly some aliasing will occur simply due to the math of artificial aliasing (i.e. a lunar month is shorter than a calendar month), but this still has vast implications for how the data needs to be modeled.
And I think it will help fill in the details for an ENSO model, as the tidal gauge data also shows a hidden correlation to the SOI measure:
What the 2-year differencing does is apply an inexpensive filter to the SLH readings, which is enough to remove most of the quasi-biennial time-series content from the SLH. Thus it reveals the remaining fluctuations in the SLH content, which largely consists of the inverted barometer effect of the standing wave ENSO!
So if we add this ENSO factor to the multiple regression fit of QBO, the correlation will improve even more significantly than shown in Figure 1.
See comments for updates.