(update here)

The idea is as described earlier : Find the lunar forcing on the earth and then alias the forcing to a seasonal (yearly) period. This becomes the forcing for the QBO. The rationale is that the faster lunar cycles will not cause the stratospheric winds to change direction, but if these cycles are provoked with a seasonal peak in energy, then a longer-term multiyear period will emerge. This is a well-known mechanism that occurs in many different natural phenomena.

There are two steps to the model. (1) Determine the lunar gravitational potential as a function of time, and (2) plot the potential in units of 1 month or 1 year. The last part is critical, as that emulates the aliasing required to remove the sub-monthly cycles in the lunar forcing.

If one then matches this plot against the QBO time-series, you will find a high correlation coefficient. If the lunar potential is tweaked away from its stationary set of parameters, the fit degrades rapidly. So it becomes essentially a binary match. If it didn't fit, then the lunar gravitational potential hypothesis would be invalidated. But since it does fit precisely, then it remains a highly plausible model.

**Figure 1** shows the mean-square potential of the lunar gravitational pull, also known as the tidal generating potential (applied in the context of predicting tides). On the left, the scale is expanded.

**Fig. 1** : Mean-square potential of the lunar gravitational pull (from [1]). On the left, the scale is expanded.

As background, I originally discovered the connection of QBO to the lunar potential via

machine learning (Eureqa), see

**Figure 2**.

**Fig 2**: The original connection from QBO to a tide generating potential was discovered by machine learning -- upper right, panel A. The fitted signal was unaliased, squared and shown to align in panel B. Panel C shows the details with the fully unaliased signal at a finer scale.

This fit worked remarkably well considering that it is very difficult to dig out the aliased periods. Letting the machine learning run for a day helped considerably.

Yet it is also useful to reverse the direction of the fitting process. Instead of deducing the model from a sinusoidal decomposition, let us estimate the tidal generating potential as shown in **Figure 1** and described by Ray [1]. We then inductively proceed forward and see how well it fits to the QBO time-series.

**Fig 3 **: Empirical fit to the tidal generating potential of **Figure 1**.

This empirical fit uses only three factors -- the lunar cycles corresponding to the Draconic month, the Anomalistic month, and the Tropical month. Those are known to a high precision, along with a value for the Tropical year. The composition of these factors is then squared to generate the empirical model of the potential.

If we lay the empirical model on top of Ray's diagram, it looks like **Figure 4**.

**Fig 4** : Alignment of empirical model with Ray chart. Note the long-term 18.6 year (diurnal) beat period and the shorter 4.425 year (semidiurnal) beat period. Also a rapid bi-annual component.

On the expanded scale, the sub-monthly periods appear, as shown in **Figure 5**.

**Fig 5** : Expanded scale showing the sub-monthly variations in the tidal generating potential.

These higher frequency components disappear when the alias is introduced.

I did not do a complete ephemeris-based empirical model for the tidal generating potential as Ray did, since the basic pattern is fairly easy to deduce from the three lunar cycles.

The final step is to un-square and then alias the tidal generating potential and compare to the QBO time-series. This is shown in **Figure 6**.

**Fig 6**: Fit of the unaliased tidal generating potential to the QBO

There is nothing at all complicated about the recipe for fitting the tidal generating potential to the QBO. It is a mechanical process since none of the lunar cycles parameters can be changed.

As a next step I will submit this finding to Physical Review Letters. From what I have seen in the literature search, there is no consideration of applying a straightforward forcing of the lunar gravitational pull to model QBO. It appears that most QBO models derive from what Richard Lindzen originally proposed some 40+ years ago -- but since many mainstream climate scientists do not consider Lindzen (an AGW denier) very trustworthy or even competent (e.g. a trail of retracted papers and debunked theories), it's likely that his original model was simply wrong, or at best, incomplete. What the new model does is provide a concise recipe and a highly plausible geophysical context for understanding the origin of QBO.

The further significance of all this is that the same lunar forcing that applies to QBO also likely applies to the phenomena of El Nino and modeling the ENSO time-series, see the ENSO sloshing paper and some more recent work.

## References

[1] R. D. Ray, “Decadal climate variability: Is there a tidal connection?,” Journal of climate, vol. 20, no. 14, pp. 3542–3560, 2007.