The lunisolar gravitational forces control the variation in the earth's rotation speed (dLOD) as a direct solid body inertial response. With the correct accounting of the tidal factor strengths it makes perfect sense assuming a linear transfer function.

OTOH, that same force applied to a stratified liquid will cause that liquid to slosh with a nonlinear response. The only nonlinear response that seems to work is the one that I mathematically derived from analytically solving Laplace's Tidal Equations along the equator.

In the figure below, the lower panel shows the model fit to dLOD using the known tidal factors, while the upper panel shows an ENSO fit applying the LTE transfer function to the same dLOD forcing, i.e. a scaled linear to nonlinear mapping.


(note the difference in the time-series range, thus requiring an extrapolation of the modeled LOD forcing to all dates prior to 1962)

This is all one needs to validate the ENSO model, as it is statistically impossible to match each of the peaks and valleys in the data, while being tightly constrained by a stationary cyclic tidal forcing. There is very little noise in the data because the inertial response of that large a mass will filter out everything but the strongest forcing -- which just happens to be the tidal forces.

Conclusion: If one doesn’t know how to solve the geophysical fluid dynamics problem, one will never be able to fit ENSO to a known forcing.

BTW, as a challenge, there is no need for me to provide any more validation than this as a starting point -- what is needed next is someone to either debunk this model (perhaps by finding a flaw in the fitting algorithm) or having someone devise a better model in terms of fit, [plausibility, and parsimony](

This group apparently claims a decent ENSO model fit using a machine learning training algorithm written in **R**.

Their prediction extends to the next time step

> ![](
> "However, we need to keep in mind that we’re predicting just a single time step ahead. We probably should not overestimate the results."

So, which is a better ENSO model? Mine or this ML version?