Here is another fascinating Eureqa search result. Recall that we found a 2.671 rad/year periodicity in the RHS forcing for the model of ENSO Proxy data displayed in comment #23 above. You can also see that the 2.671 frequency has a slight modulation in it that is also sinusoidal over time. That is, it looks like:

$ sin(wt + k sin(vt ... $

The base value for w also matches the 28-month periodicity of QBO. The following Eureqa result decomposes the QBO into that same period.


But notice also how Eureqa is decomposing the period into several layers of modulation.

That is, it results in

$ sin(2.67 \cdot t + sin(0.389 \cdot t + 1.77 sin(0.16 \cdot t + ... $

There is also an enclosing sin modulation that is capturing the form of the peaks, where they appear to be more rounded at the top.

This is a very important result IMO and it is potentially pointing out a significant forcing for the ENSO. The modulation appears in both waveforms and I will next try to see if the particular QBO decomposition improves the ENSO fit.

The QBO data only goes back to the early 1950's but the ENSO Proxy results go back to 1650, so if this fit improves the model correlation significantly it may have some implications for making El Nino predictions.