Elsewhere, I made a comment that essentially states that the model I am using for ENSO is so obvious that others would have to first prove that it can't occur. The essential idea is that a volume of water has to slosh if it is subject to changes in angular momentum such as those caused by known periodic factors such as QBO, the Chandler Wobble, and diurnal lunar tides.
Take a look at the elegance of the two model fits below. The first is a differential expansion of the SOI model
$ LHS(t) \leftarrow f''(t) + \omega_0^2 f(t) = A \cdot qbo(t) +B \cdot cw(t) + C \cdot tide(t)\rightarrow RHS(t) $
where the LHS is the wave equation transformed ENSO data (observe the noise in the signal), and the RHS is an empirical model of the known forcing factors.
The second figure is the differential equation solution, where the f(t) is compared to the actual SOI over a 100 year time span.