Tides come in three daily types (semidiurnal, with two roughly equal highs and lows each lunar day of about 24 hours 50 minutes; diurnal, with one high and one low; and mixed, with two highs and lows of unequal height) and two monthly types: spring tides with the largest range around new and full moon, and neap tides with the smallest around the quarter moons. Perigean spring tides, often called king tides, are the extra-large spring tides that come when the Moon is also at its closest to Earth.
The Moon, the Sun and the Two Bulges
The Moon's gravity pulls harder on the ocean facing it than on Earth's centre, and harder on Earth's centre than on the ocean on the far side. The difference between those pulls, the tide-generating force, stretches the oceans into two bulges: one under the Moon and one opposite it. Earth turns beneath both, so a typical coast passes through two high and two low waters. Because the Moon moves along its orbit in the same direction Earth spins, a point on Earth needs about 24 hours 50 minutes to come back under the Moon. That is the lunar day, and it is why high tide arrives roughly 50 minutes later each day.
The Sun raises its own pair of bulges. Its pull on Earth is about 178 times stronger than the Moon's, but tidal force depends on the difference in pull across Earth's diameter, which falls off with the cube of distance. The Sun is about 390 times farther away than the Moon (see how big the Moon is compared to Earth), so its tide-raising effect is roughly 46% of the Moon's.
Real oceans cannot keep pace with bulges sweeping around the planet, and continents block the way, so the actual tide is each basin's response to this forcing. Scientists split the forcing into constituents with fixed periods. The four that matter most are M2, the principal lunar semidiurnal tide (12.42 hours); S2, the solar semidiurnal tide (12.00 hours); and the diurnal K1 (23.93 hours) and O1 (25.82 hours). How strongly a coast responds to each one decides its type of tide.
Semidiurnal, Diurnal and Mixed: Three Daily Rhythms
Oceanographers sort coasts with a form factor: the amplitudes of K1 + O1 divided by M2 + S2. Below about 0.25 the tide is semidiurnal; between 0.25 and 3 it is mixed; above 3 it is diurnal.
Semidiurnal tides
Two high and two low waters each lunar day, the highs of nearly equal height and about 12 hours 25 minutes apart. This is the standard pattern around the North Atlantic: the British Isles, the Atlantic coast of France, and the US East Coast.
Diurnal tides
One high and one low water a day, found where a basin damps the semidiurnal constituents but responds to the diurnal ones. The northern Gulf of Mexico is the classic North American case: at Pensacola or Mobile the tide rises and falls once a day, by only about half a metre. In Southeast Asia, the Gulf of Tonkin off northern Vietnam and parts of the Java Sea are diurnal. These tides peak when the Moon is farthest north or south of the equator and weaken when it crosses the equator, about every 13.7 days.
Mixed tides
Two highs and two lows a day, but of clearly unequal heights. The US Pacific coast is the standard example: San Francisco and Seattle each see a higher high and a lower high water, then a higher low and a lower low. The inequality comes from the Moon's tilt: when it is well north or south of the equator, an observer passes through the thick part of one bulge and the thin edge of the other.
Spring Tides and Neap Tides Across the Lunar Month
The second classification follows the 29.5-day cycle of lunar phases. At new and full moon, the Sun, Moon and Earth line up and the solar bulges stack on the lunar ones. The result is a spring tide: higher highs, lower lows and the largest range of the fortnight. The name comes from the old sense of water "springing up" and has nothing to do with the season; spring tides happen twice a month, all year.
At first and third quarter, the Sun and Moon sit at right angles as seen from Earth. The Sun's bulges then partly fill the Moon's lows and shave its highs, producing a neap tide with the smallest range. With the Sun at 46% of the Moon's effect, theory gives spring and neap ranges of about 1.46 and 0.54, nearly three to one. The biggest tides tend to arrive a day or two after new or full moon, a lag called the age of the tide.
Perigean Spring Tides and King Tides
The Moon's orbit is an ellipse. At perigee it comes within about 356,500 to 370,000 km of Earth; at apogee it is about 404,000 to 406,700 km away. Because tidal force varies with the inverse cube of distance, the Moon raises larger tides near perigee. Perigee repeats every 27.55 days, out of step with the 29.53-day phase cycle, so a few times a year it falls close to a new or full moon. The result is a perigean spring tide.
"King tide" is the informal name, used in Australia, New Zealand, the Pacific Islands and on US coasts, for these highest tides of the year. The extra height over an ordinary spring tide is usually a few centimetres to a few tens of centimetres. That is enough to flood low streets in Miami Beach, Norfolk (Virginia) or the atolls of Tuvalu and Kiribati on a calm, sunny day.
Where Tides Are Huge and Where They Barely Exist
The open-ocean tide is under a metre almost everywhere. Giant ranges happen where basin shape amplifies it, mainly through resonance. If a bay's natural sloshing period is close to the 12.42-hour M2 tide, each push adds to the last. The Bay of Fundy and Gulf of Maine have a natural period of about 13 hours, which drives spring ranges of about 16 m in the Minas Basin of Nova Scotia. The Bay of Fundy is usually cited as the world record, with Leaf Basin in Ungava Bay, northern Quebec, close enough that some measurements call it a tie.
Funnel-shaped estuaries add a second effect, squeezing the incoming tide into a narrowing, shallowing channel so the water rises higher. The Severn Estuary between England and Wales reaches spring ranges of about 14 to 15 m, the Gulf of Saint-Malo around Mont-Saint-Michel about 13 to 14 m, and Cook Inlet in Alaska about 12 m at Turnagain Arm.
The Mediterranean sits at the other extreme. It connects to the Atlantic only through the 14 km Strait of Gibraltar, which admits little tidal energy, and its basins do not resonate with the semidiurnal period. Most of its coasts see a few tens of centimetres; Venice gets close to a metre at springs and the shallow Gulf of Gabès in Tunisia around 2 m.
The open sea also has dead spots. Each constituent rotates around amphidromic points, places with almost no range, where high water circles like the hand of a clock once per tidal cycle and the range grows with distance from the centre. The North Sea has three M2 amphidromic points, with the tide running anticlockwise around each. Part of the reason the Gulf of Mexico has such a weak semidiurnal tide is that it lies near a semidiurnal amphidrome, leaving the diurnal constituents in control.
Tidal Bores: When the Tide Runs Upriver
In a few rivers with a big tidal range and a shallow, funnel-shaped mouth, the rising tide arrives as a single wall of water, a tidal bore, travelling upstream against the current. Bores are strongest on spring tides, especially near the equinoxes.
The Qiantang River in Zhejiang, China, has the world's largest bore. It enters through the sharply funnelled Hangzhou Bay, its front can stand several metres high, and crowds have watched it for well over a thousand years, traditionally around the 18th day of the eighth lunar month. The Severn Bore in England reaches about 2 m on the biggest tides and is ridden by surfers between Newnham and Gloucester. Near the mouth of the Amazon, the pororoca pushes up the river's northern channels and the Araguari River at heights of up to about 4 m.
Tides vs Waves vs Storm Surge
- Tides are waves too, but with crests half a planet apart, arriving on a schedule that astronomy can predict centuries ahead.
- Wind waves have periods of a few seconds up to about 20 seconds for long swell, and ride on top of the tide. A tsunami, triggered by an earthquake or landslide, has a period of minutes to an hour; calling it a "tidal wave" is a misnomer.
- Storm surge is a weather-driven rise in sea level. Onshore winds pile water against the coast, and low pressure lets the sea bulge by about 1 cm for each hectopascal of drop. Hurricane Katrina in 2005 pushed a surge of about 8.5 m onto the Mississippi coast. Surge plus tide is the storm tide.
The worst floods come when these coincide. The North Sea flood of 31 January to 1 February 1953, which killed more than 1,800 people in the Netherlands and over 300 in England, was a severe surge arriving near a spring high tide. For the places where range peaks and how people use them, see the ranked list of the highest tides in the world.