I don't think you understand the bad science that NOAA perpetrated by removing the annual signal from the ENSO time-series. It would be OK if they filtered the *A=Annual* portion of the time-series if it was composed as linearly independent factors $$f(t) = A + B$$

Yet, when a non-linear mechanism enters in the picture, such as $$f(t) = (A + B)^2$$

then by removing the *A* term (and its harmonics), it will leave the cross-term *AB* sitting by itself $$f(t) = A^2 + 2AB + B^2$$
but with no way to estimate what the missing causal term was.

No wonder that scientists have had a hard time deconvolving the behavior of time-series such as ENSO when they aren't given a complete starting data picture. When the filtered-out annual term is factored back in, one can easily see I guessed 100% dead-on what the missing deterministic forcing term was. As I said, this is further substantiation that ENSO is not chaotic, but rather non-linear deterministic.

As far solving Laplace's Tidal Equations in analytical terms, which creates the nonlinear but non-chaotic solution, the key *ansatz* that [I applied](https://imagizer.imageshack.com/img923/6538/yRorrd.png) was to create a partial derivative decomposition $$ \frac{d \zeta}{d \phi} = \frac{d \zeta}{dt} \frac{dt}{d \phi} $$
that I then reinserted into the equations, resulting in an elegantly simple final formulation.

BTW, the physical reason that this works is because the greatest tidal force acts horizontally to the surface, and the partial derivative expansion captures that topological mechanism.

>>> ![](https://imagizer.imageshack.com/img924/5656/pgzegj.png)

I have no idea why it took 200+ years for someone like me to come up with such an obvious (in hindsight) ansatz.


> "It is now generally regarded that Laplace's methods on their own, though vital to the development of (orbital mechanics), are not sufficiently precise to demonstrate the stability of the Solar System, and indeed, the Solar System is understood to be chaotic, although it happens to be fairly stable."

... What's your point? It's stable on any time scale we would be interested in.

Keep at it, you may catch up at some point.