Paul,

Fine effort applied to the specific lunar contribution to QBO.

Struggling to see whether the convergence seen in the top graph is pure evidence of lunar forcing, or just ongoing smoothing of QBO average over time. Lunar cycles of course start high-Q smooth, and multiple smooth sequences correlate mathematically, if not causally, physically. The bottom graphs are not extremely compelling, as there are so many spurious equivalent peaks compared to supposed hits.

What if historic QBO data is simply still too crude for a reliable measure of correlation? Can we not say that the unspecified causes of noise may represent unidentified forcings that may well be of higher order?

Sensitive systems effectively paint a hologram of their surroundings. QBO statistical "noise" is trying to tell us far more than just tidal information. Its selective attention to focus on the lunar contribution, when complex bulk harmonics and other critical factors remain poorly identified.