Get a load of this detail:
The first chart above is a model of the QBO that uses the same principal lunar potential frequencies applied in tidal harmonic analysis, but aliased to one year boundaries. Note the richness in the detail of the QBO that the model is matching. The key here is not to filter the QBO data at all -- much of the sub-year detail is captured by the higher harmonics of the one-year aliased fundamental.
The second is a back extrapolation, which shows the 18.6 year beat frequency in the lunar nodes.
Richard Ray of NASA Goddard published the following table of rotation rate coefficients last year. What commodity tide matching algorithms do is pick the strongest gravitational coefficients from the table to get a good first-order match to measured tidal gauge data. They apparently don't blink an eye over what looks like complexity in a model fit. All they have to claim is that (1) this is the known physics of the orbit of the moon wrt the earth and the earth/moon wrt the sun and (2) the rest is essentially fill-in-the-blanks on what the magnitude of the individual factors are. So I follow their basic recipe and apply a multiple linear regression of the strongest factors ( ) to get the fit above.
This is an interim result, as I am not sure where the signal in the QBO stops and the underlying noise (measuring? statistical sampling? random?) in the data takes over. I have a feeling that some further refinement will get the model even closer to the data, since it locks in so closely after just a few aliased lunar cycles are included in the fit.
Frustratingly, I have no idea why this kind of analysis was not performed over the last few decades in which this data has been available. Remember that Richard Lindzen has been studying the QBO for over 50 years, and he even said this in 1974 -- "Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential."
Nice that he wrote this, as any critical response to these new findings really have to be prefaced with Lindzen's own words. Blame it all on him if this mechanism sounds too outlandish.
This is a longer passage by Lindzen:
It may be that Lindzen never found this direct connection between lunar tidal gravitation effects and the QBO because he thought it was too weak. He may also never have thought about the impact of physical aliasing, which is second nature and routine to the engineering side of the sciences. Lindzen's papers are filled with impressive looking sets f partial differential equations, but that is irrelevant if he is unable to come up with a simple first-order physics explanation for an underlying mechanism -- like what I am doing here.
On the other hand, stalwart climate scientists such as Kevin Trenberth have always thought there is something more significant to the QBO. In this paper , Trenberth is discussing the link of stratospheric QBO to the tropospheric climate .
The paper further discusses the concept of aliasing and periodic elements in the data. This was published in 1980 but Trenberth's ideas were not followed through by others, as far as I can trace the citation trail.
If that isn't enough, the model of ENSO that I have been working on uses these same factors relating to changes in the angular momentum of the earth's rotation, but weighted to longer periods as the natural response of the ocean damps out faster cycles. Trenberth, with his link of QBO to the tropospheric climate hinted at a periodic connection and I think the lunar/angular momentum idea will become the core mechanism behind ENSO forcing.
The lesson learned is that one has to know who to trust. Do you trust someone like Lindzen, who is a AGW skeptic forced to retract statements and been known to produce ideas such as the debunked Iris theory of cloud feedback? Or do you trust a careful scientist such as Kevin Trenberth to point you in a good direction? This is a tricky landscape to navigate unless you understand the agendas of the scientists involved. Personally, I do not trust a contrarian such as Lindzen -- and the science may be agreeing with that assessment.
 K. F. Trenberth, “Atmospheric quasi-biennial oscillations,” Monthly Weather Review, vol. 108, no. 9, pp. 1370–1377, 1980. http://www.gps.caltech.edu/~kl/research/reading/Trenberth_MWR_1980.pdf