I looked at old data for length-of-day (LOD) measurements of the earth to get an idea of angular momentum changes in the rotation. I did not use data from the official IERS website because it looks like it gets filtered too aggressively.
The results are [here](http://contextearth.com/2016/06/02/seasonal-aliasing-of-long-period-tides-found-in-length-of-day-data/)
Not hard to believe because it is predictable based on what I inferred with the QBO and ENSO model, but sure enough, the primary angular momentum variations corresponds to a seasonally aliased 27.21 day Draconic lunar cycle.
Via dumb machine learning of over 160 years worth of data, the first experiment resulted in an unaliased value of 27.2121 days, to be compared to the known value of 27.21222 days. The precise value is important as any error of the period will induce a gradual phase change over a long duration, thus destroying any coherence in the effect.
The explanation is basic Newtonian physics in that variations of an orbiting satellite like the moon are going to induce changes in the earth's rotation -- and that this will transitively provide a forcing to induce a sloshing mode in the ocean ala ENSO or in atmospheric winds such as QBO. The short period -- diurnal and semidurnal -- effects have been detected in the LOD measurements before but not these seasonally aliased periodic cycles of 2 to 3 years. Nothing in science is provable but these results certainly substantiate the QBO and ENSO models. In other words, if I didn't find a 27.212 day period and it came out to (for example) 26.98 days instead, the QBO and ENSO models would likely be invalidated, as the seasonally-aliased forcing period would not correlate with the fundamental periods found in the QBO and ENSO data.