>"What data did you use to create your visualizations?"

Daniel, I don't have any visualizations of the sloshing behavior per se. I assume that whatever is there is a standing wave that has been stationary over time.

So in one dimension, I am assuming the standing wave is separable:

$ f(x,t) = g(x) \cdot h(t) $

All I am looking at is h(t).

The question on whether the ENSO time series are stationary is discussed [here [1]](http://www.stat.pitt.edu/stoffer/dss_files/adaptSPECjasa.pdf)

>"The estimated posterior probabilities that the time series are stationary, that is,Pr(m=1|x) are 0.95, 0.93, and 0.99 for the SOI, Nĩno3.4, and DSLPA indices, respectively. These results confirm the findings of Rosen, Wood, and Stoffer (2009), Solow(2006), and Nicholls (2008).
>One explanation for the difference between these findings and the earlier study of Trenberth and Hoar (1996) is that Trenberth and Hoar (1996) tested explicitly if there had been a change in
frequency from 1981 onward. "

The current unresolved issue is if something changed at around 1981. I believe the behavior did change, best seen in a wavelet scalogram with the transition centered around 1200 months = 100 years after 1980.


The question is does the top scalogram look as if it has a tilt to it thus creating a continuous transition? Or is it 2 pieces as in the lower model?

There was a significant self-organized critical behavior that occurred in 1982 -- the massive El Chichon eruption. This was large enough that it did change the amount of solar insolation that the ocean received for several years.


If I were to do something with 2D sloshing visualization it would be something like this

[1] Rosen, Ori, Sally Wood, and David S Stoffer. “AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series.” Journal of the American Statistical Association 107, no. 500 (2012): 1575–89.