The premise that I am working from is that the response follows from the solution to the wave equation for a largely unknown set of inputs.

This is a hard problem to discern what the inputs may be, but remember that we have two separate sets of measures that we can evaluate against : (1) the ENSO standing wave and (2) the QBO standing wave.

That's like having two different electrical circuits to discriminate against given a common unknown forcing. The additional constraints will narrow the forcing solution possibilities.

And there may be more of these measures available to check against -- for example, tidal gauge data shows a strong indicator for an ENSO signature

http://contextearth.com/2014/09/21/an-enso-predictor-based-on-a-tide-gauge-data-model/

also here on Azimuth

https://forum.azimuthproject.org/discussion/comment/12573/#Comment_12573

That particular tidal gauge dataset is the first I tried since it appeared to be one of the longer time-series available. There lots more of these available.

My feeling is that this is a rich environment for analysis that curiously has not been tapped.