Since I had a few days left on my evaluation copy of Mathematica, here are a few wavelet transform comparisons of ENSO model and data.

Result :
![result](https://imagizer.imageshack.com/img923/2553/Ixx65T.png)

The wavelet scalogram doesn't show much order yet the model fits well.

The model forcing for the daily time-series fit shows more of a periodic order:

![dailyforce](https://imagizer.imageshack.com/img921/3852/E1bL7Y.png)

Arcsin of data (see [comment #265](#Comment_21110) above) compared to model forcing on the 130 year monthly time-series is shown below:

![arcsin](https://imagizer.imageshack.com/img923/778/4XgJ5d.png)

That is a beautiful scalogram showing a biennial period in the center and more clearly stratified harmonics. This again demonstrates how order emerges from chaos with the arcsin adjoint applied

---

And this is what *sin(k sin(wt))* looks like on a scalogram for increasing values of k

![sinsin](https://imagizer.imageshack.com/img923/6501/2ZF6ap.png)

Applying an arcsin on any one of these will result in a clearly delineated horizontal line. But in general, with multiple sinusoidal factors involved, the the transform will reduce the amount of harmonic structure.