Supertides are real!

The highest high tides occur once every 18 years, and can lead to surprising floods. Here’s the science behind them.

“But less intelligible still was the flood that was caused by forty days’ rain, and forty nights’. For here on the moors there were some years when it rained for two hundred days and two hundred nights, almost without fairing; but there was never any Flood.” –Halldór Laxness

There’s a mystery afoot: a famous French Abbey — Mount Saint-Michel — floods and becomes an island once every 18 years.

In fact, it happened just a few days ago, and won’t happen again until 2033. The culprit? Believe it or not, it’s simply the tides. Well, a supertide!

Twice a day, the rotation of the Earth causes us to pass through a region of high and low waters, as the oceans bulge out due to the position of the Sun and the Moon. Think about the fact that the gravitational pull from any mass on a sphere — not just a point, but a solid sphere — will cause that body to distort, as some points are closer to the mass while others are farther away, and still others are off-axis.

These forces are exerted at every point on our world, and are known as tidal forces. While our Earth is a nearly perfect, solid sphere, the oceans — a liquid — change their shape much more easily, and bulge out due to the gravitational effects of the masses in our Solar System pulling on them.

As time passes, the tides come in and out, causing sea levels to rise and fall. In some cases, such as in bays, inlets and other coastal locations, the differences can be dramatic.

But as spectacular as this is, you can come back at other times of the month — just a few days later, in this case — and see an even grander change in the water levels!

The difference between these two videos? The relative position of the Sun and the Moon as seen from Earth. Along with the rotating Earth, these two bodies — the Sun and Moon — are the only two masses in our Solar System with the right properties, the right combinations of distances and masses, to have an impact on our tides.

Although the Sun is some 400 times larger (in diameter) than the Moon, it’s also, on average, about 400 times farther away. This explains why they appear about the same angular size from Earth. But the Sun is only about 27 million times as massive as the Moon.

Why in the world would I say “only” there? Because it would have to be about (400)^3 times the mass of the Moon, or 64 million times its mass, in order to have the same effect on Earth’s tides as our small, lunar neighbor. As it stands, tides from the Sun are only about 40% as strong as tides from the Moon. When the Sun and Moon line up in either the “new” or “full” Moon phases, we get spring tides, 140% as large as a typical tide, and when they’re at right angles, we get neap tides, only 60% as strong as a standard tide.

So, you might think, tides go in a cycle:

• they start out with two very high and low tides, daily, during new moons,
• then they get weaker, approaching a minimum when the Moon’s half full,
• then they reach a maximum again during full moons,
• then they get minimally weak again during the last quarter,
• and then they approach maximum as the Moon becomes new again.

This is right! Well, it’s kind of right.

I mean, this would be perfectly right if the Moon made a nice, circular orbit around our planet. And it kind of does, but the Moon is noticeably elliptical in its orbit around Earth, meaning that at some points in its orbit, it’s farther away from us, producing weaker tides, and at some points it’s closer to our world, producing stronger tides.

If you only look at one month’s worth of data, you’re only going to see what you anticipated: spring tides and neap tides, in a (roughly) one-month cycle.

But if you look over the course of an entire year, you’ll see that some of these spring tides are higher than others, while even some neap tides result in higher high tides and lower low tides than average.

Take a look at this 400-day high-and-low tidal graph from the same location as above.

What causes this? The tides on Earth are strongest not only when the Moon and Sun are aligned — either during a new or full moon — but also when the Moon is closest to Earth, since tidal forces fall off as the inverse of the distance cubed, meaning that when the Moon is just 10% closer to Earth, its tides can be a full 33% stronger!

Sure, the Earth’s orbit around the Sun is elliptical, too, but the effect is much smaller. For comparison, the closest perigee Moon is 13-to-14% closer than the farthest apogee Moon, while the Sun is only 3.3% closer when Earth is nearest to it versus at its farthest. What does this mean for the tides?

It means it’s not just eclipses that are either likely or unlikely as the Moon orbits the Earth while both are orbiting the Sun, but that when a perigee Moon coincides with either a new or full phase, we’re likely to see the biggest tides of all!

What’s even more interesting about this? The effect of the tidal bulges is maximized when the Moon-and-Sun are aligned with Earth’s equator, something that happens during the equinoxes!

So in an ordinary year, the highest high tides and lowest low tides occur during spring tides near the equinoxes. But every once in a while — in particular, once every 18 years — you not only get spring tides right at one of the equinoxes, you get it coincident with a perigee Moon, and hence you get the maximum of all possible tidal effects: a supertide!

And that’s when tidal flooding is most likely, and when this one French Abbey — Mount Saint-Michel — will flood like we just saw. Of course, the flipside of this is that in addition to the highest high tides, we also get the lowest low tides, and that’s spectacular in its own right!

Thanks to Scientific American for bringing this phenomenon to my attention, and to Alex Berezow of RealClearScience for encouraging me to explore it a little deeper. Hope you enjoyed it!

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