QBO

[pukpr]

QBO 50 hPA

Tested at the 1975-1980 cross-validation interval

Cross-validation with training between 1960 and 1980

Underlying long-period tidal forcing

Total : Declination X Perigee

Declination only, obvious 18.6 y nodal envelope, centered at zero with an almost sin instead of cos symmetry, indicative of a stronger diurnal character (not as much bleed-through-to-opposite-side-of-Earth lunar forcing)

Perigee only, 4.4y and a 18.06y cycle indicative of perigee-syzygy maximum, with strong fortnightly as declination and sun impact perigee

This is data
https://gist.github.com/pukpr/2326fba3f5061ed2a8cec58b43db8308?permalink_comment_id=5077144#gistcomment-5077144
https://gist.github.com/pukpr/2326fba3f5061ed2a8cec58b43db8308?permalink_comment_id=5077196#gistcomment-5077196

[pukpr]

Signal processing signatures and pattern matching and ML

Thought I would write up one example that has a connection to symbolic regression ML. The details and charts are at https://geoenergymath.com/2025/04/05/qbo-pattern-recognition-and-signal-processing

The objective here is to determine whether a tidal mechanism is responsible for the QBO reversal, which I published several years ago. The primary signature is that the QBO matches that expected from a non-linear mixing of draconic and annual forcing. However, that's not much to go by as this could be just a fortuitous alignment. So a few other expected signatures may help the confidence with the claim. One is that satellite sub-band frequencies should also appear in addition to the primary mixed signal. I used the now-proprietary symbolic regression tool Eureqa to see if it could find these frequencies -- and after sufficient exploration, it did, determining the primary sideband at 0.42 and then weaker sidebands at 1+0.44 and 2+0.42 of the annual harmonics. These were the strongest 3 of the 4 sinusoids it found at a specific Pareto complexity level. That is strong evidence for a mixed signal origin for the QBO time-series, on par with what one would find via FM or AM spectra, which in fact one can determine via a Fourier transform of the same data. Yet Eureqa only used symbolic regression and not an FFT.

The other signature requires knowing that the draconic cycle is not a pure sinusoid but is modulated by the sun and perihelia distance. I didn't have the exact Fourier series representation for this modulation but gave the fitting algorithm the possible periods and determined whether (1) it would improve the QBO fit, (2) maintain cross-validation, i.e. minimal over-fitting, and (3) match to the qualitative draconic modulation one can find on the lunar eclipse NASA site (after the QBO fitting process completed). All 3 of these checked out, increasing confidence in the model.

There is one other aspect to the fit described in the post related to Laplace's tidal equation modeling, which is routinely found by symbolic algebra, but will skip that here.

In summary, the salient aspects of the QBO time-series is that it is somewhat erratic and although the tidal solution is simple, it does capture much of the erratic nature.

Having published this circa 2018, but revisiting as new data comes in, I will note that a LLM tool such as Google Gemini does a decent job of walking through the formulation, given a minimum prompt.
https://geoenergymath.com/2025/04/05/qbo-pattern-recognition-and-signal-processing/comment-page-1/#comment-4377

[pukpr]

When a behavior of a time series that results in a Fourier series featuring sidebands of a suppressed carrier with the carrier frequency matching that of an external source, it has to be modulation of the external frequency by another signal. That’s basic signal processing deduction, as in what you would infer if you discovered sidebands in a SETI signal.

But in the case I presented above, this sideband behavior is happening in a natural signal, the QBO. Yet, ever since Richard Lindzen published his model of the QBO, the focus has been on some internal resonance defining the cycling, with the typical claim that density and pressure determine the resonant frequency, as in a Brunt–Väisälä frequency, or that it could be some self-organizing behavior determining the periodic overturning. But of course this resonant class of behavior would not display sidebands. Only some externally forced modulation could do that. I offered up tidal forces as a matching frequency, as that had originally been proposed by Lindzen in his early papers, but he could not match the period directly from tidal harmonic.s, so he quickly gave up on that (can find that out in at least two of his papers). Alas, he gave up too soon, because they are sidebands on the annual carrier! He never considered that.

Now, could some form of machine learning deduce this from the info I presented, via a combination of symbolic regression (to find the critical Fourier components) and an LLM to infer relationships? Or does this all have to be nudged along by the physics as I have described?

https://andthentheresphysics.wordpress.com/2025/03/16/reaping-the-whirlwind/