I have been concentrating on modeling the quasi-biennial oscillation (QBO) recently because the results I am getting are a sure bet in my opinion, and the ENSO model will mature and follow in due time.
There are no adjustable parameters in my QBO model, as it relies completely on the known lunar tidal periods. So it’s actually conceptually difficult to do a real sensitivity analysis. Those are set in stone, so moving them from their nominal values is artificially changing the physical foundation for the model. Still it would be useful to consider how to move the periods in unison away from the nominal values, so that the artificiality is minimized.
One clever way of doing this is to change a common factor used in the aliasing calculation for each of these periods. Obviously the best candidate is the solar year. To get the correct aliasing with respect to each of the periods, the value of the year in days must be set ( see this article ). And because of the aliased signal’s period sensitivity to the mixing frequency, any change in the year value will magnify the error in a fit. So if the theoretically predicted aliased lunar months form an optimal fit, then any change in the solar year away from the nominal value will degrade this fit. And it should degrade it rapidly, because of the sensitivity of the aliasing calculation.
In the following chart, the nominal value for the solar year is 365.242 days, and the x-axis shows what happens when the value is modified away from this value, based on the multiple linear regression fit. The upper-right inset is a magnified region about 365 days, and the yellow highlighting points to the most highly correlated regions.
The best fit is 365.23 and is close enough to 365.242 in my book. Both are also right on the plateau of maximum correlation, indicating that this may be within the sampling error.
After some prodding on my part, I got this tweet from a climate science gatekeeper
— mtobis (@mtobis) November 20, 2015
It’s straightforward to argue that Richard Lindzen’s model  is wrong by an exclusionary principle. If Lindzen neglected to include the gravitational forcing due to the moon’s orbit, yet an absolutely trivial model shows a nearly unity correlation with a precise alignment, then Lindzen must be over-fitting. So by excluding lunar forcing, what Lindzen came up with is not the real physics but more likely a biased fit, based on the unlimited number of adjustable factors he could draw from. I would suggest that his “tour de force” paper will need to be completely reconsidered from scratch.
So the most plausible and parsimonious explanation is a model not much different than that used to predict the ocean’s tides.
From the NASA site:
“The Ocean Motion website provides resources developed for inquiring minds both in and outside the classroom, for reading level grades 9-12 (Flesch-Kincaid).”
“Observing the changing water levels caused by astronomical tides is relatively simple and has long been important for major ports.”
Although simple, this is real science — no free parameters and nearly perfect agreement with the empirical data.
R. S. Lindzen and J. R. Holton, “A theory of the quasi-biennial oscillation,” Journal of the Atmospheric Sciences, vol. 25, no. 6, pp. 1095–1107, 1968.