Sea Level on the U.S. East Coast

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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9 responses to “Sea Level on the U.S. East Coast

  1. You might take an experimental look at a circumAntarctic ring of tide stations to see if there’s an ENSO driven oscillation of similar frequency

  2. This kind of analysis is important, but, to get good results, the method is important to do correctly.

    So, first questions I have are, given the series is finite, what kind of windowing did you assume? What kind of sampling rate did you assume? And did you do anything to control spectral leakage?

    Second, I don’t know how, precisely, this was done, but constructing spectra from observational data is such a common and perilous operation, that people have developed techniques, like the multi-taper method, which offers some improvements over conventional Fourier analysis. I recommend the psd package in R.

    To see how alternative techniques can be usefully applied in a different context, check out the ENSO predictions done by Paul Pukite.

  3. Very interesting. Learned a few things here (including the term ‘nutation’) both directly and by following up on the reference to the ‘Chandler wobble.’ I’ll eagerly await the continuation–here in the ‘Mid-South’.

  4. I learned several new things. Thank you!

  5. This suggests hot spots of sea level on the US east coast, including the current rapid rise in Florida, may be tied ENSO and NAO.

    It the 12.8 year period you found related to these or is it something else?

    [Response: I’m inclined to think the recent upturn n Florida and the southern mid-Atlantic may be more due to the slowdown of the Gulf Stream system.]

  6. David B. Benson

    Well done.

  7. Dutch Sea Level analysis seem to be routinely filtered from the 18.6 year lunar node cycle. See for instance the Zeespiegelmonitor (Sea level monitor) from Deltares, which is used to assess the need for upgrading the sea defences:
    It is in Dutch, but formula (2) on page 7 should be clear enough.

    An English laguage reference could be:
    Baart, F., P.H.A.J.M.Van Gelder, J. De Ronde, M. Van Koningsveld en B. Wouters (2012). The effect of the 18.6-year lunar nodal cycle on regional sea-level rise estimates. Journal of Coastal Research, 28(2), 511–516. West Palm Beach (Florida), ISSN 0749-0208

    From the abstract:
    “Here, we show how failing to account for the nodal cycle resulted in an overestimation of Dutch sea-level rise. The nodal cycle is present across the globe with a varying phase and a median amplitude of 2.2 cm. Accounting for the nodal cycle increases the probability of detecting acceleration in the rate of sea-level rise.”

    So how is the 18.6yr cycle missing? Perhaps from the combination of several stations?