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Originally posted by shunyadragon
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[ATTACH]18190[/ATTACH]. Anomalies are calculated as a departure from a designated baseline. For measuring things like the global warming trend, we pick some baseline (say, 1940-1970) and then mean anomalies as a departure from the mean over that base period. For ONI, they are going to have new baseline 30 year period defined every 5 years, and ONI values will be given with respect to the baseline period in which they are most centralized. That is:
A curious numeric consequence of this is that recent ONI values have to be defined with respect to the most recent baseline period, and every 5 years they going to recalculated for the new normal, until they get to the one in which they are most central. That's unfortunate... but I can guess at why they might want to do that. Using a centralized baseline means El Nino and La Nina are both roughly matching magnitudes and opposite sign. If using baseline periods in the past, then the steady warming trends mean ONI values will bias positive, and give bigger values for El Nino than for La Nina; as an artifact of the definition as not as a real indication of the relative magnitudes of El Nino and La Nina.
A consequence of all this is that the numeric values of the index are going to bias slightly positive as you approach the most recent value. And that will of course tend to give an increased variance as well.
On top of all that, the definitions are really crude. This is okay for a heuristic guide. But it does mean it's really unsafe to read anything much into fine analysis of the raw numbers. They are given to only one figure of accuracy, which is appropriate. More than that would be pretty meaningless, I think.
So... with all that in mind. I've calculated the mean and standard deviation of ONI values for the first and the last 30 year period available on that page.
Over the first period (about 1950-1980) we have mean 0.01 and stddev 0.73
Over the last period (about 1986-2016) we have mean 0.07 and stddev 0.83
So: yes, the variance over recent times is greater, but only slightly. And the mean is also greater, which is what I would expect from how ONI is defined, given the global warming trend going on under our feet. Most of the apparent increase in magnitude is probably not a real increase in the magnitude of ENSO itself, but an artifact of how the index is defined. It's not that warming drives a strong ENSO cycle. (It might, it might not; I don't know.) But we cannot sensibly use these numbers as evidence for or against that hypothesis, IMO.
Also: on the "cycle". This is pretty obviously not a regular cycle. Being defined in terms of departures from a mean, it must of necessity be sometimes positive and sometimes negative. But to be genuinely "cyclic" there needs to be some consistency in how changes occur. To look at this properly I should do some Fourier analysis. But I've never learned to do that properly and so I haven't added it to my spreadsheet. Instead, I ran the data through a conventional lowpass butterworth digital filter. (This is one of the basic tools I have in my spreadsheet to help look at what any time series is doing. Basically, I filter out all the high frequency noise, and retain any low frequency signal.) I've used a filter with a cut off at 5 year cycles. Such filters are a convenient way to "smooth" data. (The cutoff is not sharp; basically a signal which cycles every 5 years gets reduced by half in this filter, and so marks a kind of mid point. High frequencies get reduced much more, lower frequencies are reduced less.)
Technical note... filtering like this has a problem with maintaining sensible behaviour at the tail of a series. I pad with linear data based on regression lines, using upper and lower bounds at 95% confidence. This means that at the end of the series, the filter diverges into a high part and low part; I think this is a good way to illustrate the uncertainty we have when smoothing data with an unknown future.
Here's the smoothed data:
[ATTACH]18188[/ATTACH]
And here it is again, with a smooth cut off at 2 year cycles:
[ATTACH]18189[/ATTACH]
Basically, it looks to me that the ONI tends to cycle over shorter periods than 9 to 15 years; it is more like 2 to 7 years. You'd need a fourier analysis to get precise about that, however. You get the longer periods not by looking at the way it cycles, but by roughly how often you get a "big" event. And that has more to do with variance than with periodicity in the data, I suggest. The ONI index is a long way from being "cyclic"; unless everything that goes up and down could by called cyclic; which rather dilutes the meaning of the term.
Anyhoo... I've been looking for an excuse to try out the spreadsheet I've been working on the last few days and this was a nice bit of data to try with it!
Cheers -- Sylas
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