I may do that some day but alas I had my license to the Eureqa engine expire. I can still look at old logs but I can't do any more experiments for the time being.
Let me alternatively propose a premise. Suppose it was 200 years ago and scientists knew about the concept of tides and that they had measured the Draconic and Synodic cycles to values of 27.212 days and 29.531 days, respectively. Say they also knew that a specific month of the year had some maximum interaction with the tidal oscillation. This interaction would dwarf the rest of the year in its impact so that it was ok to just use that value as the yearly data point.
What would the resultant oscillation look like when plotted year-to-year?
One would be cos((2$\pi$/(27.212/365.25)-13x2$\pi$)t+phase) and the other
cos((2*$\pi$/(29.531/365.25)-12x2$\pi$)t+phase) , where t is time in years.
i.e. the tidal frequency folded by N x 2$\pi$ (easy to check this graphically as well)
Now, consider that some scientists wanted to find evidence that this phenomenon was actually happening. With a lot of effort (before the age of computers) they deconstructed some known oscillating time-series data set to see if there were factors which matched these periods. If they had access to the QBO data, they would have been very happy and would have patted themselves on the back for finding the tidal influence.
Given that same premise, turn the clock to today and do the same experiment. Nothing has changed, yet the acceptance of the findings would get questioned. It doesn't matter how close the numbers are or if they can be reproduced with a validation set, as you are suggesting. Somebody is going to say that the premise is invalid, i.e. tides have nothing to do with it, and that will be that ( note caveat below [*] )
Yet, the results of the QBO analysis in [#22](/discussion/comment/14843/#Comment_14843) should not be surprising. The Wikipedia entry says that
> " The precise nature of the waves responsible for this effect was heavily debated; in recent years, however, gravity waves have come to be seen as a major contributor and the QBO is now simulated in a growing number of climate models (Takahashi 1996, Scaife et al. 2000, Giorgetta et al. 2002)"
One form of a gravity wave is the lunar tide.
The other factor is that the medium has a property that it has a maximal impact coinciding with a specific calendar month.
And that is likely the same mechanism for ENSO. The two behaviors, QBO and ENSO just happen to have the same underlying forcing mechanism. However, unless we can first get some buy-in to the physical premise, there may be not a heck of a lot more we can do to change minds.
That's what is fun about doing this. We are trying to topple the apple cart of the scientific establishment's current understanding. What's also sweet about this is that the main target is likely Richard Lindzen (yes that Lindzen, notable AGW denier) who has the original theory of QBO, and which apparently has nothing to do with lunar tides.
[*] the caveat is that there are papers that propose this effect. I wrote about it [here on my blog](http://contextearth.com/2014/08/15/change-of-tide-in-thought/) over a year ago.
Li, G., Zong, H., & Zhang, Q. (2011). 27.3-day and average 13.6-day periodic oscillations in the Earth’s rotation rate and atmospheric pressure fields due to celestial gravitation forcing. Advances in Atmospheric Sciences, 28, 45-58.
Krahenbuhl, D. S., Pace, M. B., Cerveny, R. S., & Balling, R. C. (2011). Monthly lunar declination extremes' influence on tropospheric circulation patterns. Journal of Geophysical Research: Atmospheres (1984–2012), 116(D23).