Here is an animated view of how the ENSO model is trained.

The general idea is that Laplace's tidal equation solution evolves with wavenumber applied. The initial forcing is from the lunar tidal pattern modulated by an annual impulse. The wavenumber is then increased from a low-value to higher value to better match the standing wave pattern of ENSO, spanning the years 1880 to present.

https://youtu.be/Y466JuI2MPQ

The ENSO model requires three crucial ingredients: (1) An annual impulse (2) A monthly/fortnightly tidal forcing (3) Analytical solution to Laplace's tidal equations. The last one is the non-intuitive master puzzle piece, worked in via a nonlinear fitting procedure which is essentially animated in the video.

This all seems complicated largely because there are these 3 pieces that have to be simultaneously applied. That may be a fact of solving challenging problems:

![](https://imagizer.imageshack.com/img924/3435/NlwY71.png)