Previous comment I wrote:
> "The ENSO fit then has only amplitude and phase unknowns with regard to the 3 lunar monthly cycles, making it conceptually identical to an ocean tidal model fit. "
Here is an example of the detail I can get with the ENSO model.
The ENSO model is able to discern the variation in the length (and phase) of the lunar Draconic month (see here https://eclipse.gsfc.nasa.gov/SEhelp/moonorbit.html#draconic). This is a detailed second-order effect that would only be possible to measure if the model of the first-order effect is correct.
So the AGU-2016 ENSO model is based completely on the long-period lunar tidal cycles reinforced by seasonal cycle impulses. The same numerical techniques used for modeling ocean tides are applied, but with a different concept for seasonal reinforcing. The model therefore has gone from being an explanation of the ENSO behavior to a sensitive [metrology](https://en.wikipedia.org/wiki/Metrology) technique -- specifically for measuring lunar and solar cycles based on the sloshing sensitivity of a layered fluid medium to forcing changes.
That's one way you substantiate a model's veracity -- flip it from a question of over-fitting to one of precisely identifying physical constants. That's one way to get buy-in.