This post was inspired by David Archibald’s post on the SOI on Watts Up With That where his analysis struck me as facile and not particularly instructive.

Here is the Southern Oscillation Index plotted from the same original data:

Southern Oscillation Index 1876-2010

What I decided to do is what I’ve been doing with a lot of climatological data, by looking at the Fourier spectrum to see if there are hidden oscillations in the noise.

And there are some hidden oscillations

SOI Fourier Spectrum

The diagram above is not all the spectrum, but just the interesting ones that rise above the noise.

The obvious peaks are at k=3, k=10, k=15, k=21, k=28, k=36, k=38 and correspond to 45 years, 13.5 years, 6.42 years, 4.82 years, 3.75 years and 3.55 years respectively.

But note also that they are all nearly exact harmonics of k=3. I could argue that there is really one dominant signal – one that corresponds almost exactly to two Hale Solar cycles (which are approximately 22.5 years long).

The best analogy I can give is that its like shaking a bathtub half full of water: there will be modes which reflect the external shaking of the tub, some which reflect the geometry of the tub and some missing harmonics where the two modes cancel each other out.

I’d appreciate some feedback into how to quantify the statistical significance of the powers of the Fourier Spectrum so as to be more specific as to what is signal and what is noise.

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So it’s the Sun stupid! All over again. That is a nice piece of work, thank you.

John,

Good to see you picking up on spectral analysis. Although I have only a passing knowledge of the technique, I think you may want to try cross-spectral analysis (see: http://www.statsoft.com/textbook/time-series-analysis/) with other time series such as the Hale Cycles. I believe there are tests that indicate when the power at particular frequencies is significant. The work I’m familiar with was done in the 1980s comparing deep-core data to orbital parameters – the SPECMAP project.

Thanks Gary

I’ll take a look. I would like to get a much better analysis of these sorts of time series. Fourier is very robust – but only if there are no gaps. For more messy data, then a Lomb-Scargle Periodogram is used (extensively in astrophysics to find pulsars, for example)