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 :

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:


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


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


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.