Moon Over Miami Boston

Most people aren’t surprised that Miami is suffering through more flooding because of sea level rise. After all, the surrounding land lies very low (there really aren’t any hills in Miami, in fact there are precious few in the whole state of Florida). The sea level at any given moment doesn’t have to rise far above MHHW (Mean Higher High Water) to flood the streets.

Other areas aren’t so vulnerable. Boston, for instance, is on the coast but the region isn’t so low-elevation; there are plenty of hills. And according to Sweet & Marra, for local flooding to occur the sea needs to rise 0.68 m (a bit over two feet) above MHHW. Of course that can happen; when storms hit the storm surge is sometimes considerably greater than that and they sometimes hit at or near high tide. But the threshhold at Boston in higher than in most locations, in fact it’s the 3rd-highest threshhold level in the list of 27 eastern U.S. cities studied by Sweet & Marra.

So — is high tide alone enough to cause flooding in Boston, now that the sea has risen to higher heights?

I retrieved hourly sea level data for Boston from the Joint Archive for Sea Level (JASL) at the Univeristy of Hawaii Sea Level Center (UHSLC). Then I tallied, for each day, the highest value to estimate HHW (Higher High Water). I removed days that didn’t have data for all 24 hours (there were only a few dozen in the nearly 92 years of data). I then computed the mean value during the time span 1960 through 1979, the standard choice for calculating MHHW. Subtracting MHHW from the daily high water values yields a record of daily high water level in Boston above MHHW, which looks like this:

The horizontal red line is the 0.68-meter value, the threshhold for flooding due to high water (flooding can also happen due to torrential rainfall).

Clearly, that has happened more often recently. In fact we can count the number of days on which HHW exceeds 0.68 m above MHHW:

The red line is a lowess smooth, the blue line a fit using Poisson regression. Both suggest, and the data make clear, that flooding is on the increase in Boston. In fact, it’s happening a lot more frequently recently. But that’s not the question at hand: is it possible for such flooding to occur in Boston due to tide alone, without requiring storm surge or precipitation?

To answer that question, one needs to know what part of the ocean height (at HHW) is due to the tides. The tides are multiperiodic, i.e. they are a combination of periodic factors, so first I Fourier-analyzed the data, giving this amplitude spectrum (I’m fond of amplitude spectra rather than power spectra):

There are plenty of spectral peaks, but not all of them are due to independent periods. However, the two strongest ones are, at 13.26 and 24.74 cycles/yr. Their associated periods are 27.55 and 14.77 days.

That first period is the anomalistic month. It’s the time required for the moon to orbit the earth once, then move a little further yet so it returns to perigee, it’s closest approach to Earth. This takes longer than its orbital period because the moon’s orbit itself changes, with perigee advancing a wee bit each orbit. Perigee affects tides because when the moon is closer the tides are stronger, so once each anomalistic month, when we reach perigee, that effect is at its peak.

The second period is one half of the synodic month. It’s the time required for the moon to orbit the earth once, than move a bit further so it returns to alignment with the sun. The sun’s gravity affects the tides just as the moon’s does, and when the two are aligned (either in the same, or opposite, directions) their influences join forces to make very strong tides. When they are out of alignment, they oppose each other and the tides are weak. A strong alignment tide is called a spring tide while a weak out-of-alignment tide is a neap tide.

That period is half the synodic month because we have spring tide twice each cycle, when the sun and moon are in the same direction, and when they’re in opposite directions.

Yet another cyclic component of daily high water is at a frequency of precisely one year, with a period of precisely one year. That’s because the sun also has a stronger influence when we’re closer, and it takes just about 1 year for Earth (in its orbit) to return to perihelion, the point of closest approach to the sun.

I also identified a cycle component with period 18.32 years. Honestly, I haven’t figured out the cause of that.

In addition to the cyclic components, there’s also spectral power at very low frequencies, not due to periodic behavior, but because of the long-term trend. For Boston, it’s well approximated by a cubic polynomial.

In addition to the fundamental frequencies of oscillation, there are harmonics (multiples of the fundamental frequencies) and combinations (sums of multiples of more than one fundamental frequency). In all, I’ve identified three harmonics and seven combinations in the spectrum of daily high water at Boston.

With four fundamental, three harmonic, and seven combination frequencies, that gives us a 14-frequency Fourier fit to model daily high water. Plus a cubic polynomial for the long term trend. The model tells us, with excellent accuracy, what the tidal part of high water is, apart from the impacts of storm surge and precipitation. And it looks like this:

That answers the question. Yes, tide alone is sufficient to cause flooding in Boston, even without storm surge or precipitation.

It didn’t used to be. In fact, it wasn’t this way until 2011. These data end with 2012, but it has continued to be that way, and will continue to be so. In fact it will get worse because sea level rise continues. It may get especially worse for Boston, because at the moment, sea level rise there is happening faster than the global average, by quite a bit.

UPDATE

Interesting story.

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