Lately I’ve been looking closely at sea level time series from the east coast of the U.S. Available stations are marked here with red dots:
A pair of Canadian stations (off the Maine coast) are included. I (arbitrarily) divided the area into four sub-regions, New England (from Boston north), the mid-north Atlantic, the mid-south Atlantic, and Florida.
First I aligned all the station records to form a composite, an estimate of sea level for the entire U.S. east coast region. That gave me this time series, to which I’ve added a lowess smooth (on a 20-year time scale) in red:
Just curious, I Fourier transformed the residuals from that smooth fit and got this:
The dashed colored lines are estimates of “statistical significance” which take into account both autocorrelation and multiple testing. Of course that is a very inexact procedure — but it generally gets us at least in the ballpark. In this case, it suggests that the frequency at 0.0783 cycles per year (period about 12.8 years) is really there, at least maybe.
I’m not given to declaring periodic or even pseudo-periodic behavior without some real evidence of it. In fact, when it comes to the idea I tend toward the most severe skepticism, having often shown just how feeble is the evidence supporting many such claims.
Yet in this case, not only does the given frequency reach “significance” statistically (although I’m skeptical of that too), the spectrum also shows signs of harmonics. I fit three harmonics to model this short-time scale (12.8 years is pretty short in this context) cycle and it fit surprisingly well. Of course I then looked at the spectrum of the residuals from that and added another frequency to my model, in this case 0.843 cycles/year (period 433 days). Here’s the spectrum I get from combining the best fit to the selected frequencies (which are highlighted in red) with the Fourier amplitude spectrum of the residuals:
I can’t emphasize strongly enough how foolish it is to go about fitting periodic functions to data with a Fourier series, based on what you think you’ve found that is periodic, then declaring it the truth when it’s really just your wishful (and often naive) thinking.
But here I am saying that the case is very strong the 12.8-year period is real. I wouldn’t say it is for global sea level, in fact it probably isn’t, but it’s a feature of the U.S. east coast region. Because there are three harmonic components to the 12.8-year period, its full amplitude is an impressively large 57 mm (2.2 in.), a nontrivial fraction of the total rise of about 317 mm (12.5 in.) during the observed time span. As for the 433-day period, it’s the Chandler wobble and shows up surprisingly often in sea level time series.
Identifying these periodic components enables us to remove them (at least, an estimate) leaving “adjusted” values that better reflect the trend — the changes that are not periodic. Here is the adjusted time series:
A most interesting feature is that the 12.8-year period (or thereabouts) shows up in the sub-regions too. It’s strongest in the mid-south region, weakest in Florida, but it (and the Chandler wobble) is persistently there:
We can of course define adjusted data (removing the periodic components) for the subregions too:
I’ll have more to say about these, but for now I’ll mention that both Florida and the mid-south coast show a large uptick in just the last 10 years.
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