Tide
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Tides are the cyclic rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. Tides cause changes in the depth of the marine and estuarine water bodies and produce oscillating currents known as tidal streams, making prediction of tides important for coastal navigation (see Tides and navigation). The strip of seashore that is submerged at high tide and exposed at low tide, the intertidal zone, is an important ecological product of ocean tides (see Intertidal ecology).
The changing tide produced at a given location is the result of the changing positions of the Moon and Sun relative to the Earth coupled with the effects of Earth rotation and the local bathymetry. [1] Sea level measured by coastal tide gauges may also be strongly affected by wind.
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[edit] Introduction and tidal terminology
A tide is a repeated cycle of sea level changes in the following stages:
- over several hours the water rises or advances up a beach in the flood tide.
- the water reaches its highest level and stops at high tide. Because tidal currents cease this is also called slack water or slack tide. The tide reverses direction and is said to be turning.
- The sea level recedes or falls over several hours during the ebb tide.
- The level stops falling at low tide. This point is also described as slack or turning.
Tides may be semidiurnal, with a period of approximately half a day, or diurnal, repeating about once a day. In most locations, there are two tides per day (semidiurnal), but because of the diurnal contribution, the two high tides reach different levels; these are differentiated as the higher high water and the lower high water in tide tables. [2] The difference in height between the two is known as the daily inequality. The daily inequality is generally small when the Moon is over the equator. The two low tides are called the higher low water and the lower low water. Semidiurnal tides occur about 12 hours 24 minutes apart. The time taken to complete two semidurnal tidal cycles, 24 hours 49 mintutes, is the time required for the Earth to rotate once relative to the moon. [3]
Tides vary over days, weeks, months, years, decades, centuries, millenia, etc so to make accurate records tide gauges measure the water level over time at fixed stations which are screened from variations caused by waves shorter than minutes in duration. This data is compared to the average (or reference) level called mean sea level.
The various frequencies of astromical forcing which contribute to tidal variations are called constituents. In most locations, the largest is the "principal lunar semi-diurnal" constituent, also known as the M2 (or M2) tidal constituent, and its period is exactly half a "tidal lunar day", the average time separating one lunar zenith from the next. [4] The M2 constituent is tracked by simple tide clocks. Other constituents arise from factors such as the tilt of the Earth's rotation axis, the inclination of the lunar orbit and the ellipticity of the orbits of the Moon and the Earth. Variations of with periods of less than half a day, such as 8, 6, or 4 hours, are call harmonic constituents. There are also long period constituents with periods of days, ''''months, and years''.''
[edit] Tidal range variation: springs and neaps
The semidiurnal tidal range (the difference in height between high and low tides over about a half day) varies in a two-week or fortnightly cycle. Around new and full moon when the Sun, Moon and Earth form a line (a condition known as syzygy), the tidal forces due to the Sun reinforce those of the Moon. The tide's range is then maximum: this is called the spring tide, or just springs and is derived not from the season of spring but rather from the verb meaning "to jump" or "to leap up". When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the earth, and the forces due to the Sun partially cancel those of the Moon. At these points in the lunar cycle, the tide's range is minimum: this is called the neap tide, or neaps. Spring tides result in high waters that are higher than average, low waters that are lower than average, slack water time that is shorter than average and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven day interval between springs and neaps.
The relative distance of the Moon from the Earth also affects tide heights. When the Moon is at perigee the range is increased and when it is at apogee the range is reduced. Every 7½ lunations, perigee and (alternately) either a new or full moon coincide causing perigean tides wtih largest the tidal range, and if a storm happens to be moving onshore at this time, the consequences (in the form of property damage, etc.) can be especially severe.
[edit] Tidal phase and amplitude
Tides apparently advance along ocean coastlines, with waters directly off shore reaching high and low tide simultaneously, this defines cotidal. Cotidal points lie along a curve called a cotidal line. [6]
If one thinks of ocean as basin enclosed by a coastline (pretend the ocean is circular), the cotidal lines point radially inward and must eventually meet at a common point, the amphidromic point or simply the amphidrome. An amphidrome is at once cotidal with high and low tides, which is satisfied by no tidal motion. (The rare exception occurs if the tide is circling around an island, such as New Zealand.) Indeed tidal motion generally lessens moving away from the continental coasts, so that crossing the cotidal lines, are contours of decreasing common amplitude(half of the distance between high and low tide). For a 12 hour semidiurnal tide the amphidrome behaves roughly like a clock face, [7] with the hour hand pointing in the direction of the high tide cotidal line; the opposite direciton is low tide cotidal line. High tide rotates once every 12 or so hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. The relative position of a cotidal line in this cycle is the phase and is often measured in hours or degrees. The difference of cotidal phase from the phase of a reference tide is the epoch. [8]
The shape of the shoreline and the ocean floor change the way that tides propagate, so there is no simple, general rule for predicting the time of high tide from the position of the Moon in the sky.
[edit] Tidal physics
- See also: Tidal force
The first well-documented mathematical explanation of tidal forces was given in 1687 by Isaac Newton in the Philosophiae Naturalis Principia Mathematica. In spite of the British practical interests in tides, it was the Académie Royale des Sciences in Paris that offered a prize for the best theoretical essay on tides. Daniel Bernoulli, Antoine Cavalleri, Leonhard Euler, and Colin Maclaurin shared the prize in 1840. Maclaurin used Newton’s theory to show that a smooth sphere covered by a suffiently deep ocean under the tidal force of a single deforming body is a prolate spheroid with major axis directed toward the deforming body. Maclaurin was also the first to write about the Earth's rotational effects on motion. Euler realized that the horizontal component of the tidal force (not the vertical) which drives the tide. In 1744 D'Alembert studied tidal equations for atmosphere which do not include rotation. The first major theoretical formulation for water tides was made by Marquis de Laplace, who formulated a system of partial differential equations relating the horizontal flow to the surface height of the ocean. The Laplace tidal equations are still in use today. William Thomson rewrote Laplaces equations for vorticity which allowed for solutions describing tidal motion along the coast line, in what are now called Kelvin waves.
Though the gravitational force exerted on the Earth by the Sun is almost 200 times stronger than that exerted on the Earth by the Moon, the tidal force produced by the Moon is about twice as strong as that produced by the Sun. This is because the tidal force is related not to the strength of a gravitational field but to its gradient. If the ocean were a constant depth and there were no land, high water would occur as two bulges in the height of the oceans, one facing the Moon and the other on the opposite side of the earth, facing away from the Moon. There would also be smaller, superimposed bulges on the sides facing toward and away from the Sun. The field gradient decreases with distance from the source more rapidly than does the field strength; as the Sun is about 400 times further from the Earth than is the Moon, the gradient of the Sun's field, and thus the tidal force produced by the Sun, is weaker.
Ignoring complications arising from ocean currents, the ocean's surface is closely approximated by an equipotential surface, which is commonly referred to as the geoid. Since the gravitational force is equal to the gradient of the potential, there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium. Now consider the effect of external, massive bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance in space and which act to alter the shape of an equipotential surface on the Earth. This deformation of the geoid has a fixed orientation in space relative to the influencing body, and it is the rotation of the Earth relative to this shape that causes the daily tidal cycle. Gravitational forces follow an inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube of the distance. While the Sun's gravitational pull on Earth is on average 179 times as great as the Moon's, the Sun is on average 389 times as far away as the Moon, making the Sun's tidal effect only 46% as large as the Moon's.
For simplicity, consider the tidal influence caused by the Moon: it should be understood that the same description applies to the Sun as well. At the point right "under" the Moon (the sub-lunar point), the water is closer than the solid Earth; so it is pulled more and rises. On the opposite side of the Earth, facing away from the Moon (the antipodal point), the water is farther from the moon than the solid earth, so it is pulled less and effectively moves away from Earth (i.e. the Earth moves more toward the Moon than the water does), rising as well. On the lateral sides, the water is pulled in a slightly different direction than at the centre. The vectorial difference with the force at the centre points almost straight inwards to Earth. It can be shown that the forces at the sub-lunar and antipodal points are approximately equal and that the inward forces at the sides are about half that size. Somewhere in between (at 55° from the orbital plane) there is a point where the tidal force is parallel to the Earth's surface. Those parallel components actually contribute most to the formation of tides, since the water particles are free to follow. The actual force on a particle is only about a ten millionth of the force caused by the Earth's gravity.
[edit] Tidal amplitude and cycle time
The theoretical amplitude of oceanic tides due to the Moon is about 54 cm at the highest point, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were not rotating. The Sun similarly causes tides, of which the theoretical amplitude is about 25 cm (46% of that of the Moon) with a cycle time of 12 hours. At spring tide the two effects add to each other to a theoretical level of 79 cm, while at neap tide the theoretical level is reduced to 29 cm. Since the orbit of the Earth about the Sun, and the Moon about the Earth, are elliptical, the amplitudes of the tides change somewhat as a result of the varying Earth-Sun and Earth-Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 cm.
Real amplitudes differ considerably, not only because of variations in ocean depth, and the obstacles to flow caused by the continents, but also because the natural period of wave propagation is of the same order of magnitude as the rotation period: about 30 hours. If there were no land masses, it would take about 30 hours for a long wavelength ocean surface wave to propagate along the equator halfway around the Earth (by comparison, the natural period of the Earth's lithosphere is about 57 minutes).
[edit] Tidal lag
- See also: Tidal acceleration
Because the Moon's tidal forces drive the oceans with a period of about 12.42 hours, which is considerably less than the natural period of the oceans, complex resonance phenomena take place. This, as well as the effects of friction, gives rise to an average lag time of 12 minutes between the occurrence of high tide and lunar zenith. This tidal lag time corresponds to an angle of about 3 degrees between the position of the Moon, the center of the Earth, and the location of the global average high tide. This tidal lag gives rise to a gravitational torque on the Moon that results in the gradual transfer of angular momentum to its orbit, and a gradual increase in the Earth-Moon separation. As a result of the principle of conservation of angular momentum, the rotational velocity of the Earth is correspondingly slowed. Thus, over geologic time, the Moon recedes from the Earth and the length of the terrestrial day increases. See tidal acceleration for further details.
[edit] Tidal observation and analysis
Tides had been observed and discussed with increasing sophistication, first noting the daily recurrence, then its relationship to the Sun and Moon. Eventually the first tide table in China was recorded in 1056 A.D. primarily for the benefit of visitors to see the famous tidal bore in the Qiantang River. In Europe the first known tide-table is thought to be that of John, Abbott of Wallingford (d. 1213), based on high water occurring 48 minutes later each day, and three hours later at London than at the mouth of the Thames. William Thomson led the first systematic harmonic analysis to tidal records starting in 1867. The main result was the building of a tide-predicting machine (TPM) on using a system of pulleys to add together six harmonic functions of time. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s.
The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary, and many large ports had automatic tide gages stations by 1850.
William Whewell first mapped co-tidal lines ending with a nearly global chart in 1836. In order make these maps consistent, he hypothesized the existence of amphidromes where co-tidal lines meet in the mid-ocean. These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea. [9]
[edit] Timing
In most places there is a delay between the phases of the Moon and the effect on the tide. Springs and neaps in the North Sea, for example, are two days behind the new/full Moon and first/third quarter. This is because the tide originates in the southern oceans, the only place on the globe where a circumventing wave (as caused by the tidal force of the Moon) can travel unimpeded by land.
The resulting effect on the amplitude, or height, of the tide travels across the oceans. It travels as a single broad wave pulse northwards over the Atlantic. This causes relatively low tidal ranges in some locations (nodes) and high ones in others. This is not to be confused with tidal ranges caused by local geography, as can be found in Nova Scotia, the Bristol Channel, the Channel Islands and the English Channel. In these places tidal ranges can be over 10 metres. The Atlantic tidal wave arrives after approximately a day in the English Channel area of the European coast and needs another day to go around the British Isles in order to have an effect in the North Sea. Highs and lows of the Channel wave and North Sea wave meet in the Strait of Dover at about the same time but generally favour a current in the direction of the North Sea.
The exact time and height of the tide at a particular coastal point is also greatly influenced by the local bathymetry. There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the largest well-documented tidal ranges in the world, 16 metres (53 ft), because of the shape of the bay. Southampton in the United Kingdom has a double high tide caused by the interaction between the different tidal harmonics within the region. This is contary to the popular belief that the flow of water around the Isle of Wight creates two high waters. The Isle of Wight is important, however, as it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water. Ungava Bay in Northern Quebec, north eastern Canada, is believed by some experts to have higher tidal ranges than the Bay of Fundy (about 17 metres or 56 ft), but it is free of pack ice for only about four months every year, whereas the Bay of Fundy rarely freezes.
There are only very slight tides in the Mediterranean Sea and the Baltic Sea owing to their narrow connections with the Atlantic Ocean. Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan. On the southern coast of Australia, because the coast is extremely straight (partly due to the tiny quantities of runoff flowing from rivers), tidal ranges are equally small.
[edit] Tidal analysis
Careful Fourier and data analysis over a 19 year period ( the National Tidal Datum Epoch in the US) uses carefully selected frequencies called the tidal harmonic constituents. This analysis can be done using only the knowledge of the period of forcing, but without detailed understanding of the physical mathematics, which means that useful tidal tables have been constructed for well over a century. [10] The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day or fortnightly, monthly, and semiannual. Most coastline is dominated by semidiurnal tides, but some areas such as the [[South China Sea] and the Gulf of Mexico are primarily diurnal. In the semidiurnal areas, the primary constituents M2(lunar) and S2(solar) periods differ slightly so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period). [11]
In the M2 plot above each cotidal line differs by 1 hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich. The lines rotate around the amphidromic points counterclockwise in the northern hemisphere so that from Baja California to Alaska and from France to Ireland the M2 tide propagates northward. In the southern hemspere this direction is clockwise. On the other hand M2 tide propagates counterclockwise around New Zealand, but this because the islands act as dam and permit the tides to have different heights on opposite sides of the islands. But the tides do propagate northward on the eastside and southward on the west coast, as predicted by theory. The exception is the Cook Strait where the tidal currents periodically link high to low tide. This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high tide across from low tide. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M2 patterns cannot be used for other tides.
[edit] Tides and navigation
Tidal flows are of profound importance in navigation and very significant errors in position will occur if they are not taken into account. Tidal heights are also very important; for example many rivers and harbours have a shallow "bar" at the entrance which will prevent boats with significant draft from entering at certain states of the tide.
The timings and velocities of tidal flow can be found by looking at a tidal chart or tidal stream atlas for the area of interest. Tidal charts come in sets, with each diagram of the set covering a single hour between one high tide and another (they ignore the extra 24 minutes) and give the average tidal flow for that one hour. An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots) for spring and neap tides. If a tidal chart is not available, most nautical charts have "tidal diamonds" which relate specific points on the chart to a table of data giving direction and speed of tidal flow.
Standard procedure to counteract the effects of tides on navigation is to (1) calculate a "dead reckoning" position (or DR) from distance and direction of travel, (2) mark this on the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the direction of the tide. The distance the tide will have moved the boat along this line is computed by the tidal speed, and this gives an "estimated position" or EP (traditionally marked with a dot in a triangle).
Nautical charts display the "charted depth" of the water at specific locations with "soundings" and the use of bathymetric contour lines to depict the shape of the submerged surface. These depths are relative to a "chart datum", which is typically the level of water at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum water depth possible during the tidal cycle. "Drying heights" may also be shown on the chart, which are the heights of the exposed seabed at the lowest astronomical tide.
Heights and times of low and high tide on each day are published in tide tables. The actual depth of water at the given points at high or low water can easily be calculated by adding the charted depth to the published height of the tide. The water depth for times other than high or low water can be derived from tidal curves published for major ports. If an accurate curve is not available, the rule of twelfths can be used. This approximation works on the basis that the increase in depth in the six hours between low and high tide will follow this simple rule: first hour - 1/12, second - 2/12, third - 3/12, fourth - 3/12, fifth - 2/12, sixth - 1/12.
[edit] Intertidal ecology
Intertidal ecology is the study of intertidal ecosystems, where organisms live between the low and high tide lines. At low tide, the intertidal is exposed (or ‘emersed’) whereas at high tide, the intertidal is underwater (or ‘immersed’). Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, as well as between different species of intertidal organisms within a particular intertidal community. The most important environmental and species interactions may vary based on the type of intertidal community being studied, the broadest of classifications being based on substrates - rocky shore and soft bottom communities.
Organisms living in this zone have a highly variable and often hostile environment, and have evolved various adaptations to cope with and even exploit these conditions. One easily visible feature of intertidal communities is vertical zonation, where the community is divided into distinct vertical bands of specific species going up the shore. Species ability to cope with dessication determines their upper limits, while competition with other species sets their lower limits.
Intertidal regions are utilized by humans for food and recreation, but anthropogenic actions also have major impacts, with overexploitation, invasive species and climate change being among the problems faced by intertidal communities. In some places Marine Protected Areas have been established to protect these areas and aid in scientific research.
[edit] Other tides
In addition to oceanic tides, there are atmospheric tides as well as terrestrial tides. All of these are continuum mechanical phenomena, the first two being fluids and the third solid (with various modifications).
Atmospheric tides are negligible from ground level and aviation altitudes, drowned by the much more important effects of weather. Atmospheric tides are both gravitational and thermal in origin, and are the dominant dynamics from about 80 km to 120 km where the molecular density becomes too small to be considered fluid.
Terrestrial tides or Earth tides that affect the entire mass of the Earth. The Earth's crust shifts (up/down, east/west, north/south) in response to the Moon's and Sun's gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, the semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator (15 cm is due to the Sun) which is important in GPS calibration and VLBI measurements. Also to make precise astronomical angular measurements requires knowledge of the earth's rate of rotation and nutation, both of which are influenced by earth tides. The semi-diurnal M2 Earth tides are nearly in phase with the Moon with tidal lag of about two hours. Terrestrial tides also need to be taken in account in the case of some particle physics experiments (Stanford online). For instance, at the CERN or SLAC, the very large particle accelerators were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are circumference deformation for circular accelerators and particle beam energy.
Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth's magnetic field itself.
The galactic tide is the tidal force exerted by galaxies on stars within them and satellite galaxies orbiting them. The effects of the galactic tide on the Solar System's Oort cloud are believed to be the cause of 90 percent of all observed long-period comets. [12]
[edit] Misapplications
Tsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is due to their resemblence to the tide, rather than any actual link to the tide itself. Other phenomena unrelated to tides but using the word tide are rip tide, storm tide, hurricane tide, and red tide. The term tidal wave appears to be disappearing from popular usage.
[edit] See also
 Wikimedia Commons has media related to:
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[edit] External links
- Oceanography: tides by J. Floor Anthoni (2000).
- Myths about Gravity and Tides by Mikolaj Sawicki (2005).
- Tidal Misconceptions by Donald E. Simanek.
- Our Restless Tides: NOAA's practical & short introduction to tides.
- Tides and centrifugal force: Why the centrifugal force does not explain the tide's opposite lobe (with nice animations).
[edit] Tide predictions
- National Oceanic and Atmospheric Administration (NOAA)
- WWW Tide and Current Predictor
- XTide Tide Prediction Server
- Earth tides calculator
- Tides: Why They Happen -- Beaufort County Library
- Department of Oceanography, Texas A&M University
[edit] References
- ^ The orientation and geometry of the coast affects the phase, direction, and amplitude of coastal Kelvin waves as well as resonant seiches in bays. In estuaries seasonal river outflows influence tidal flow.
- ^ Tide tables usually list mean lower low water (mllw, the 19 year average of mean lower low waters), mean higher low water (mhlw), mean lower high water (mlhw), mean higher high water (mhhw), as well as perigean tides. These are mean in the sense that they are predicted from mean data. Glossary of Coastal Terminology: H – M, Washington Department of Ecology, State of Washington (checked 5 Apr 2007).
- ^ The Moon orbits in the same direction the Earth spins. Compare this to the minute hand crossing the hour hand at 12:00 and then again at about 1:05 (not at 1:00).
- ^ Tidal lunar day, [[NOAA]. Do not confuse with the astronomical lunar day on the Moon. A lunar zenith is the Moon's highest point in the sky.
- ^ "Solution of the Tidal Equations for the M2 and S2 Tides in the World Oceans from a Knowledge of the Tidal Potential Alone", Y. Accad, C. L. Pekeris Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 290, No. 1368 (Nov. 28, 1978), pp. 235-266. Also Primary M2 Tide for New Zealand, animation (checked 4/4/2007).
- ^ This and the discussion that follows is only precisely true for a single tidal constituent.
- ^ Genrally clockwise in the southern hemisphere, and counterclockwise in the northern hemisphere
- ^ The reference tide is the hypothetical constituent equilibrium tide on a landless earth that would be measured at 0° longitude, the Greenwich meridian.
- ^ "Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables," Yang Zuosheng, K. O. Emery, Xui Yui, Limnology and Oceanography, Vol. 34, No. 5 (Jul., 1989), pp. 953-957. Tides: A Scientific History, David E. Cartwright, Cambridge University Press, Cambridge, UK, 1999. reviewed in "Understanding Tides—From Ancient Beliefs to Present-day Solutions to the Laplace Equations," James Case, SIAM News, Volume 33, Number 2 March 2000.
- ^ Tide and Current Glossary, Center for Operational Oceanographic Products and Services, National Ocean Service, National Oceanic and Atmospheric Administration, Silver Spring, MD, January 2000.
- ^ Harmonic Constituents, NOAA.
- ^ Nurmi P., Valtonen M.J. & Zheng J.Q. (2001). "Periodic variation of Oort Cloud flux and cometary impacts on the Earth and Jupiter". Monthly Notices of the Royal Astronomical Society 327: 1367-1376.
