Tide

• 1. Introduction

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  Tides are the periodic rise and fall of sea level, driven by the gravitational pull of the Moon and the Sun. Yet in 1770, when James Cook's barque HMS Endeavour ran aground on the Great Barrier Reef, it was a tide that trapped the ship and another that set it free. Over seven weeks in the mouth of the Endeavour River, Cook watched the waters rise and fall, and at spring tides he recorded a morning rise of 7 feet and an evening rise of 9 feet. Two tides in a single day, and they were not even the same height. Why? What invisible machinery governs something as ancient and reliable as the sea's breath?

  The answer involves the Moon tugging at water from a quarter million miles away, a force so subtle it shifts the ocean by centimeters yet moves billions of tonnes of seawater. It involves the work of scholars from ancient Seleucia to 18th-century Paris, and a machine built from pulleys that could predict the tides for any port on Earth. And it extends beyond the oceans: the solid ground beneath your feet rises and falls with the tides too, by as much as 55 cm at the Equator. The tidal cycle shapes coastline ecosystems, slows the Earth's rotation, and may be slowly pushing the Moon away from us at about 3.8 cm per year. The story of tides is, in the end, the story of everything held together by gravity.

• 2. Moon, Sun, and the Tidal Force

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  Isaac Newton, born in 1642, was the first person to explain tides as the product of gravitational attraction between astronomical masses. His explanation appeared in the Principia in 1687, and it rested on a key insight: the gravitational force weakens with distance, so the Moon pulls slightly harder on the side of Earth facing it than on the side facing away. That difference in pull, not the pull itself, is what drives the tides. This residual is called the tide-generating force, and it stretches the ocean into two bulges aligned along the Earth-Moon axis.

  The Sun participates too, though its enormous distance dilutes its effect. The solar gravitational force on Earth is on average 179 times stronger than the lunar force, yet because the Sun is on average 389 times farther away, its tidal force is only 46% as large as the Moon's. At spring tide, the Moon contributes 69% of the combined tidal force and the Sun contributes 31%. More precisely, the lunar tidal acceleration along the Moon-Earth axis at Earth's surface is about 1.1 microgals, while the solar tidal acceleration is about 0.52 microgals. The other planets contribute negligible amounts; when Venus is at its closest, its effect is only 0.000113 times the solar effect.

  The theoretical amplitude of ocean tides caused by the Moon alone is about 54 cm at the highest point, and the Sun's theoretical contribution is about 25 cm. At spring tide, the two effects add to a theoretical level of 79 cm. If both the Sun and Moon were at their closest positions simultaneously and aligned at new moon, the theoretical amplitude would reach 93 cm. Real tides depart substantially from these figures because ocean basins have irregular shapes, continents block water movement, and the ocean's natural response time does not match the tidal forcing period.

• 3. Springs, Neaps, and the Lunar Cycle

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  Roughly twice a month, around new moon and full moon, the Sun, Moon, and Earth form a line in a configuration known as syzygy. The tidal forces of Sun and Moon reinforce each other at these moments, producing what is called the spring tide. The word has nothing to do with the season; like the word for a natural spring, it derives from an older meaning of "jump, burst forth, rise." Spring tides bring higher-than-average high waters, lower-than-average low waters, and stronger tidal currents.

  At first quarter and third quarter moon, the Sun and Moon are separated by 90 degrees as seen from Earth, a position called quadrature. The solar tidal force partially cancels the Moon's, and the tidal range shrinks to its minimum. These are neap tides. "Neap" is an Anglo-Saxon word meaning "without the power." There is about a seven-day interval between springs and neaps.

  The changing distance between Earth and Moon adds another layer. At perigee, when the Moon is closest, tidal ranges increase. At apogee, they shrink. Six or eight times a year, perigee coincides with a new or full moon, producing perigean spring tides with the largest tidal range of the year. The difference in tide height between a perigean spring tide and a spring tide when the Moon is at apogee can be as large as a foot at some locations. The Springs and neaps in the North Sea, for example, lag two days behind the new or full moon and the first or third quarter moon, a delay known as the tide's age.

• 4. A History of Understanding

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  Seleucus of Seleucia theorized around 150 BC that tides were caused by the Moon, and according to the geographer Strabo he was the first to link the height of tides to the Moon's position relative to the Sun. He was right about the cause, though he believed the interaction was mediated by a substance called pneuma. The Naturalis Historia of Pliny the Elder collected many tidal observations, noting that spring tides peak a few days after new and full moon and reach their greatest heights around the equinoxes.

  In 725, the English scholar Bede set down something genuinely systematic in his De temporum ratione, known in English as The Reckoning of Time. Bede noted that tides rise and fall 4/5 of an hour later each day, just as the Moon rises 4/5 of an hour later. He calculated that in two lunar months of 59 days the Moon circles Earth 57 times and there are 114 tides. He named the swelling tides malinae and the diminishing tides ledones, and he recorded that tides at locations north of his own monastery at Monkwearmouth arrived earlier than his own, while tides to the south arrived later.

  Medieval European understanding was then shaped largely by Muslim scholars. Abu Ma'shar al-Balkhi, who died around 886, taught in his Introductorium in astronomiam that ebb and flood were caused by the Moon and discussed the effects of wind and lunar phases on tidal strength. In 1608, Simon Stevin explicitly argued in De spiegheling der Ebbenvloet that the Moon's attraction caused the tides and called for further research. In 1609, Johannes Kepler independently reached the same conclusion. Galileo Galilei rejected both, dismissing lunar attraction as occult and proposing instead that tides resulted from the combined motions of Earth's rotation and revolution. His 1632 Dialogue Concerning the Two Chief World Systems originally bore the working title Dialogue on the Tides.

  After Newton's breakthrough in 1687, the Academie Royale des Sciences in Paris offered a prize in 1740 for the best theoretical essay on tides. Daniel Bernoulli, Leonhard Euler, Colin Maclaurin, and Antoine Cavalleri shared it. Maclaurin used Newton's theory to show that a sphere covered by a deep ocean under tidal force takes the shape of a prolate spheroid. Euler demonstrated that the horizontal component of tidal force drives the tides more than the vertical component. Pierre-Simon Laplace then formulated a system of partial differential equations relating horizontal ocean flow to surface height, and those equations remain in use today.

• 5. Prediction and the Art of Harmonic Analysis

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  William Thomson, later known as Lord Kelvin, led the first systematic harmonic analysis of tidal records starting in 1867. Tidal prediction rests on a simple principle: the Moon and Sun generate oscillating forces at many specific frequencies, and any given location on Earth responds to each frequency with a fixed amplitude and phase delay. Measure the tides at that location for long enough, usually more than a year for a new port, and you can extract those local constants. Then you can predict tides indefinitely into the future.

  The main tidal constituent in most locations is the M2, the principal lunar semi-diurnal, with a period of about 12 hours and 25.2 minutes, exactly half of the average time between successive lunar overheads. Simple tide clocks track only this constituent. About 62 constituents in total are large enough to matter for practical marine prediction, including effects from the elliptical shape of Earth's orbit and the tilt of the lunar orbital plane.

  Thomson turned this mathematics into hardware. His tide-predicting machine used a system of pulleys to add together six harmonic time functions simultaneously. It was programmed by resetting gears and chains to adjust the phasing and amplitudes for a particular port. Similar machines remained in use until the 1960s. Arthur Thomas Doodson extended Laplace's and Kelvin's work, publishing in 1921 the first comprehensive development of the tide-generating potential in harmonic form. Doodson distinguished 388 tidal frequencies and introduced the Doodson Number notation to organize them. Some of his methods remain standard today.

  Careful Fourier analysis over a 19-year period, known as the National Tidal Datum Epoch in the United States, is preferred because the Earth, Moon, and Sun's relative positions nearly repeat in the Metonic cycle of 19 years, long enough to capture the 18.613-year lunar nodal constituent. The first known British tide table was compiled by John Wallingford, who died as Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day. The first tide table in China dates to 1056 AD, produced primarily for visitors who wanted to witness the famous tidal bore on the Qiantang River.

• 6. Extreme Tides and Unusual Places

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  The Bay of Fundy, on the east coast of Canada, is often cited as the location of the world's highest tides. Measurements made in November 1998 at Burntcoat Head recorded a maximum tidal range of 16.3 m and a highest predicted extreme of 17 m. Measurements made in March 2002 at Leaf Basin in Ungava Bay, in northern Quebec, gave similar values: a maximum range of 16.2 m and a highest predicted extreme of 16.8 m. Ungava Bay and the Bay of Fundy lie at similar distances from the continental shelf edge, but Ungava Bay is free of pack ice for only about four months each year.

  Southampton in the United Kingdom has a double high water, caused by the interaction between the M2 and M4 tidal constituents. Portland, also in the UK, experiences double low waters for the same reason. The M4 tide runs along the full south coast, but its effect is most pronounced between the Isle of Wight and Portland because the M2 tide is weakest in that stretch.

  Cook Strait, between the two main islands of New Zealand, presents a particularly striking case. The tides on each side of the strait are almost exactly out of phase: one side's high water coincides with the other's low water. Strong currents result, with almost zero tidal height change in the strait's center. Although the tidal surge normally flows one way for six hours and reverses for six hours, a particular surge can last eight or ten hours, with the reverse surge diminished. In especially stormy weather, the reverse surge can be entirely overwhelmed, and flow continues in the same direction through three or more surge periods. The amphidromic point for the New Zealand region is one of the rare exceptions to the standard model: the tide encircles the islands rather than rotating around a central nodal point, as it also does around Iceland and Madagascar.

• 7. Tides Beyond the Ocean

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  Earth tides, also called terrestrial tides, affect not the ocean but the solid ground. The Earth's crust shifts inward and outward, east and west, north and south, in response to lunar and solar gravity, ocean loading, and atmospheric pressure. While the effect is negligible for most practical purposes, the semi-diurnal amplitude of terrestrial tides can reach about 55 cm at the Equator, with 15 cm attributable to the Sun alone. These deformations matter significantly for GPS calibration and for Very Long Baseline Interferometry measurements. The solid tide dissipates at least 110 gigawatts of tidal power, about 5% of what the ocean tides dissipate.

  The energy cost of all Earth's tidal oscillations averages about 3.75 terawatts, and roughly 98% of that comes from marine tidal movement. This dissipation creates a torque on the Moon that gradually transfers angular momentum to its orbit, slowly increasing the Earth-Moon separation at about 3.8 cm per year. The corresponding torque on Earth gradually slows its rotation. Day length has increased by about 2 hours over the last 600 million years, implying that roughly 70 million years ago there were about 4 more days per year.

  Atmospheric tides are negligible at ground level and at aviation altitudes, drowned out by weather. But between about 80 and 120 km altitude, in the mesosphere and lower thermosphere, atmospheric tides are the dominant dynamics, driven by both gravitational forcing and solar heating. Galactic tides also operate, exerted by the mass of the Milky Way on stars and satellite galaxies; their effects on the Solar System's Oort cloud are believed to cause 90 percent of all long-period comets.

• 8. Life, Navigation, and the Tidal Inheritance

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  Intertidal organisms occupy a zone that is exposed at low water and submerged at high water, and that alternation shapes them profoundly. Species in these communities arrange themselves into distinct horizontal bands at different elevations above low water, a pattern called vertical zonation. A species' ability to tolerate desiccation sets its upper limit; competition with neighbors sets its lower limit. The approximately 12-hour and fortnightly tidal cycle leaves its mark on animal biology well beyond the shoreline: many vertebrates display circatidal rhythms in gestation and hatching, and in humans the menstrual cycle lasts roughly one lunar month, an even multiple of the tidal period.

  For sailors, tides have been a matter of survival. The certificate of examination for lieutenants in the Royal Navy once declared that the prospective officer was able to "shift his tides," meaning calculate and account for tidal effects. Tidal current information is displayed on nautical charts via tidal diamonds, which link chart positions to tables giving flow direction and speed for both spring and neap conditions. The rule of twelfths offers navigators a quick approximation: in the six hours between low and high water, depth increases by 1/12 in the first hour, 2/12 in the second, 3/12 in the third and fourth, 2/12 in the fifth, and 1/12 in the sixth.

  Tidal power plants extract energy in two ways: by placing turbines in tidal currents, or by impounding water in ponds and releasing it through turbines at controlled times. La Rance at Saint Malo in France is among the most well-known examples. Tidal power is more predictable than wind energy, but turbine efficiency drops at low flow velocity, and because power output scales with the cube of velocity, peak generation is brief. One practical advantage of multi-pond systems is that power can be generated at chosen times rather than at the mercy of the tidal cycle alone. The first systematic sea-level record of an entire spring-neap cycle was made in 1831 on the Navy Dock in the Thames Estuary, a baseline that eventually helped large ports around the world install automatic tide gauge stations by 1850.