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Tidal EnergyBadarla Sandeep

ContentsArticles

Tide 1Sea level 22Tide table 30Slack water 31Bathymetry 32Lunitidal interval 35Amphidromic point 36Tidal force 37Theory of tides 41Tidal acceleration 46Tidal power 52Intertidal ecology 57Internal tide 63Earth tide 66Galactic tide 70Tidal locking 74Tidal prism 80Tidal range 82Tidal resonance 83Tide pool 84Tideline 88Tidal bore 88Storm surge 94Head of tide 101Tidal stream generator 101Tidal barrage 108Marine energy 113

ReferencesArticle Sources and Contributors 115Image Sources, Licenses and Contributors 118

Article LicensesLicense 120

Tide 1

Tide

High tide, Alma, New Brunswick in the Bay of Fundy Low tide at the same fishing port in Bay of Fundy

Tides (from low-German 'tiet' = 'time') are the rise and fall of sea levels caused by the combined effects of thegravitational forces exerted by the Moon and the Sun and the rotation of the Earth.Most places in the ocean usually experience two high tides and two low tides each day (semi-diurnal tide), but somelocations experience only one high and one low tide each day (diurnal tide). The times and amplitude of the tides atthe coast are influenced by the alignment of the Sun and Moon, by the pattern of tides in the deep ocean and by theshape of the coastline and near-shore bathymetry (see Timing).[1][2][3]

Tides vary on timescales ranging from hours to years due to numerous influences. To make accurate records, tidegauges at fixed stations measure the water level over time. Gauges ignore variations caused by waves with periodsshorter than minutes. These data are compared to the reference (or datum) level usually called mean sea level.[4]

While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forcessuch as wind and barometric pressure changes, resulting in storm surges, especially in shallow seas and near coasts.Tidal phenomena are not limited to the oceans, but can occur in other systems whenever a gravitational field thatvaries in time and space is present. For example, the solid part of the Earth is affected by tides, though this is not aseasily seen as the water tidal movements.

Tide 2

Characteristics

Types of tides

Tide changes proceed via the following stages:•• Sea level rises over several hours, covering the

intertidal zone; flood tide.•• The water rises to its highest level, reaching high

tide.•• Sea level falls over several hours, revealing the

intertidal zone; ebb tide.•• The water stops falling, reaching low tide.Tides produce oscillating currents known as tidalstreams. The moment that the tidal current ceases iscalled slack water or slack tide. The tide thenreverses direction and is said to be turning. Slackwater usually occurs near high water and low water.But there are locations where the moments of slacktide differ significantly from those of high and lowwater.[5]

Tides are most commonly semi-diurnal (two highwaters and two low waters each day), or diurnal(one tidal cycle per day). The two high waters on agiven day are typically not the same height (thedaily inequality); these are the higher high waterand the lower high water in tide tables. Similarly,the two low waters each day are the higher lowwater and the lower low water. The daily inequalityis not consistent and is generally small when the Moon is over the equator.[6]

Tidal constituentsTidal changes are the net result of multiple influences that act over varying periods. These influences are called tidalconstituents. The primary constituents are the Earth's rotation, the positions of the Moon and the Sun relative toEarth, the Moon's altitude (elevation) above the Earth's equator, and bathymetry.Variations with periods of less than half a day are called harmonic constituents. Conversely, cycles of days, months,or years are referred to as long period constituents.The tidal forces affect the entire earth, but the movement of the solid Earth is only centimeters. The atmosphere ismuch more fluid and compressible so its surface moves kilometers, in the sense of the contour level of a particularlow pressure in the outer atmosphere.

Principal lunar semi-diurnal constituentIn most locations, the largest constituent is the "principal lunar semi-diurnal", also known as the M2 (or M2) tidalconstituent. Its period is about 12 hours and 25.2 minutes, exactly half a tidal lunar day, which is the average timeseparating one lunar zenith from the next, and thus is the time required for the Earth to rotate once relative to theMoon. Simple tide clocks track this constituent. The lunar day is longer than the Earth day because the Moon orbitsin the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at12:00 and then again at about 1:05½ (not at 1:00).

Tide 3

The Moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than aday—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it haspassed overhead (culmination) once and underfoot once (at an hour angle of 00:00 and 12:00 respectively), so inmany places the period of strongest tidal forcing is the above mentioned, about 12 hours and 25 minutes. Themoment of highest tide is not necessarily when the Moon is nearest to zenith or nadir, but the period of the forcingstill determines the time between high tides.Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightlystronger force on the side of the Earth facing the Moon than average, and a slightly weaker force on the oppositeside. The Moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earthdeforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularlyhorizontally. As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth'ssurface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catchup" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonethelesscauses rhythmic changes in sea surface height.

Semi-diurnal range differences

When there are two high tides each day with different heights (and two low tides also of different heights), thepattern is called a mixed semi-diurnal tide.[7]

Range variation: springs and neaps

The types of tides

The semi-diurnal range (the difference inheight between high and low waters overabout half a day) varies in a two-week cycle.Approximately twice a month, around newmoon and full moon when the Sun, Moonand Earth form a line (a condition known assyzygy[8]) the tidal force due to the sunreinforces that due to the Moon. The tide'srange is then at its maximum: this is calledthe spring tide, or just springs. It is notnamed after the season but, like that word,derives from the meaning "jump, burst forth,rise", as in a natural spring.

When the Moon is at first quarter or thirdquarter, the sun and Moon are separated by90° when viewed from the Earth, and thesolar tidal force partially cancels the

Moon's. At these points in the lunar cycle, the tide's range is at its minimum: this is called the neap tide, or neaps (aword of uncertain origin).

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 tidalconditions. There is about a seven-day interval between springs and neaps.

Tide 4

Lunar altitude

Negative low tide at Ocean Beach in San Francisco

The changing distance separating the Moon and Earth also affectstide heights. When the Moon is closest, at perigee, the rangeincreases, and when it is at apogee, the range shrinks. Every 7½lunations (the full cycles from full moon to new to full), perigeecoincides with either a new or full moon causing perigean springtides with the largest tidal range. Even at its most powerful thisforce is still weak[9] causing tidal differences of inches atmost.[10]

Bathymetry

The shape of the shoreline and the ocean floor changes the waythat tides propagate, so there is no simple, general rule thatpredicts the time of high water from the Moon's position in thesky. Coastal characteristics such as underwater bathymetry andcoastline shape mean that individual location characteristicsaffect tide forecasting; actual high water time and height may differ from model predictions due to the coastalmorphology's effects on tidal flow. However, for a given location the relationship between lunar altitude and the timeof high or low tide (the lunitidal interval) is relatively constant and predictable, as is the time of high or low tiderelative to other points on the same coast. For example, the high tide at Norfolk, Virginia, predictably occursapproximately two and a half hours before the Moon passes directly overhead.

Land masses and ocean basins act as barriers against water moving freely around the globe, and their varied shapesand sizes affect the size of tidal frequencies. As a result, tidal patterns vary. For example, in the U.S., the East coasthas predominantly semi-diurnal tides, as do Europe's Atlantic coasts, while the West coast predominantly has mixedtides.[11][12][13]

Tide 5

Other constituentsThese include solar gravitational effects, the obliquity (tilt) of the Earth's equator and rotational axis, the inclinationof the plane of the lunar orbit and the elliptical shape of the Earth's orbit of the sun.A compound tide (or overtide) results from the shallow-water interaction of its two parent waves.[14]

Phase and amplitude

The M2 tidal constituent. Amplitude is indicated by color, and the white lines are cotidaldiffering by 1 hour. The curved arcs around the amphidromic points show the direction of

the tides, each indicating a synchronized 6-hour period.[15][16]

Because the M2 tidal constituentdominates in most locations, the stageor phase of a tide, denoted by the timein hours after high water, is a usefulconcept. Tidal stage is also measuredin degrees, with 360° per tidal cycle.Lines of constant tidal phase are calledcotidal lines, which are analogous tocontour lines of constant altitude ontopographical maps. High water isreached simultaneously along thecotidal lines extending from the coastout into the ocean, and cotidal lines(and hence tidal phases) advance alongthe coast. Semi-diurnal and long phaseconstituents are measured from highwater, diurnal from maximum floodtide. This and the discussion that follows is precisely true only for a single tidal constituent.

For an ocean in the shape of a circular basin enclosed by a coastline, the cotidal lines point radially inward and musteventually meet at a common point, the amphidromic point. The amphidromic point is at once cotidal with high andlow waters, which is satisfied by zero tidal motion. (The rare exception occurs when the tide encircles an island, as itdoes around New Zealand, Iceland and Madagascar.) Tidal motion generally lessens moving away from continentalcoasts, so that crossing the cotidal lines are contours of constant amplitude (half the distance between high and lowwater) which decrease to zero at the amphidromic point. For a semi-diurnal tide the amphidromic point can bethought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high watercotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic pointonce every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation isgenerally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused bythe Coriolis effect. The difference of cotidal phase from the phase of a reference tide is the epoch. The reference tideis the hypothetical constituent equilibrium tide on a landless Earth measured at 0° longitude, the Greenwichmeridian.

In the North Atlantic, because the cotidal lines circulate counterclockwise around the amphidromic point, the hightide passes New York Harbor approximately an hour ahead of Norfolk Harbor. South of Cape Hatteras the tidalforces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines.

Tide 6

Physics

History of tidal physicsTidal physics was important in the early development of heliocentrism and celestial mechanics, with the existence oftwo daily tides being explained by the Moon's gravity. Later the daily tides were explained more precisely by theinteraction of the Moon's gravity and the sun's gravity to cause the variation of tides.An early explanation of tides was given by Galileo Galilei in his 1632 Dialogue Concerning the Two Chief WorldSystems, whose working title was Dialogue on the Tides. However, the resulting theory was incorrect – he attributedthe tides to water sloshing due to the Earth's movement around the sun, hoping to provide mechanical proof of theEarth's movement – and the value of the theory is disputed, as discussed there. At the same time Johannes Keplercorrectly suggested that the Moon caused the tides, based upon ancient observation and correlations, an explanationwhich was rejected by Galileo. It was originally mentioned in Ptolemy's Tetrabiblos as being derived from ancientobservation.Isaac Newton (1642–1727) was the first person to explain tides by the gravitational attraction of masses. Hisexplanation of the tides (and many other phenomena) was published in the Principia (1687).[17][18] and used histheory of universal gravitation to account for the tide-generating forces as due to the lunar and solar attractions.[19]

Newton and others before Pierre-Simon Laplace worked with an equilibrium theory, largely concerned with anapproximation that describes the tides that would occur in a non-inertial ocean evenly covering the whole Earth.[17]

The tide-generating force (or its corresponding potential) is still relevant to tidal theory, but as an intermediatequantity rather than as a final result; theory has to consider also the Earth's accumulated dynamic tidal response tothe force, a response that is influenced by bathymetry, Earth's rotation, and other factors.[20]

In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides. DanielBernoulli, Leonhard Euler, Colin Maclaurin and Antoine Cavalleri shared the prize.Maclaurin used Newton’s theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidalforce of a single deforming body is a prolate spheroid (essentially a three dimensional oval) with major axis directedtoward the deforming body. Maclaurin was the first to write about the Earth's rotational effects on motion. Eulerrealized that the tidal force's horizontal component (more than the vertical) drives the tide. In 1744 Jean le Rondd'Alembert studied tidal equations for the atmosphere which did not include rotation.Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to itssurface height, the first major dynamic theory for water tides. The Laplace tidal equations are still in use today.William Thomson, 1st Baron Kelvin, rewrote Laplace's equations in terms of vorticity which allowed for solutionsdescribing tidally driven coastally trapped waves, known as Kelvin waves.[21][22][23]

Others including Kelvin and Henri Poincaré further developed Laplace's theory. Based on these developments andthe lunar theory of E W Brown describing the motions of the Moon, Arthur Thomas Doodson developed andpublished in 1921[24] the first modern development of the tide-generating potential in harmonic form: Doodsondistinguished 388 tidal frequencies.[25] Some of his methods remain in use.[26]

ForcesThe tidal force produced by a massive object (Moon, hereafter) on a small particle located on or in an extensive body (Earth, hereafter) is the vector difference between the gravitational force exerted by the Moon on the particle, and the gravitational force that would be exerted on the particle if it were located at the Earth's center of mass. Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).[27][28] The solar gravitational force on the Earth is on average 179 times stronger than the lunar, but because the sun is on average 389 times farther from the Earth, its field gradient is weaker. The solar tidal force is 46% as large as the lunar.[29] More precisely, the lunar tidal

Tide 7

acceleration (along the moon-Earth axis, at the Earth's surface) is about 1.1 × 10−7 g, while the solar tidalacceleration (along the sun-Earth axis, at the Earth's surface) is about 0.52 × 10−7 g, where g is the gravitationalacceleration at the Earth's surface.[30] Venus has the largest effect of the other planets, at 0.000113 times the solareffect.

The lunar gravity differential field at the Earth'ssurface is known as the tide-generating force.

This is the primary mechanism that drives tidalaction and explains two equipotential tidal

bulges, accounting for two daily high waters.

Tidal forces can also be analysed this way: each point of the Earthexperiences the moon's radially decreasing gravity differently. Only thetidal forces' horizontal components actually tidally accelerate the waterparticles since there is small resistance. The tidal force on a particleequals about one ten millionth that of Earth's gravitational force.

The ocean's surface is closely approximated by an equipotentialsurface, (ignoring ocean currents) commonly referred to as the geoid.Since the gravitational force is equal to the potential's gradient, thereare no tangential forces on such a surface, and the ocean surface is thusin gravitational equilibrium. Now consider the effect of massiveexternal bodies such as the moon and sun. These bodies have stronggravitational fields that diminish with distance in space and which actto alter the shape of an equipotential surface on the Earth. Thisdeformation has a fixed spatial orientation relative to the influencing body. The Earth's rotation relative to this shapecauses the daily tidal cycle. Gravitational forces follow an inverse-square law (force is inversely proportional to thesquare of the distance), but tidal forces are inversely proportional to the cube of the distance. The ocean surfacemoves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, which occurs on thepart of the Earth nearest to and furthest from the moon. When the tidal equipotential changes, the ocean surface is nolonger aligned with it, so that the apparent direction of the vertical shifts. The surface then experiences a down slope,in the direction that the equipotential has risen.

Laplace's tidal equationsOcean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be modelledusing the Laplace tidal equations which incorporate the following features:1. The vertical (or radial) velocity is negligible, and there is no vertical shear—this is a sheet flow.2. The forcing is only horizontal (tangential).3. The Coriolis effect appears as a fictitious lateral forcing proportional to velocity.4.4. The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth.

As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively.The boundary conditions dictate no flow across the coastline and free slip at the bottom.The Coriolis effect steers waves to the right in the northern hemisphere and to the left in the southern allowingcoastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity.[31]

Amplitude and cycle timeThe theoretical amplitude of oceanic tides caused by the moon is about 54 centimetres (unknown operator: u'strong' in) 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 rotating in step with the moon's orbit. The sun similarly causes tides, of which the theoretical amplitude is about 25 centimetres (unknown operator: u'strong' in) (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 centimetres (unknown operator: u'strong' in), while at neap tide the theoretical level is reduced to 29 centimetres (unknown operator: u'strong' in). Since the orbits of the Earth about the sun, and the moon about the

Tide 8

Earth, are elliptical, tidal amplitudes change somewhat as a result of the varying Earth–sun and Earth–moondistances. 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 theoreticalamplitude would reach 93 centimetres (unknown operator: u'strong' in).Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also becausewave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if therewere no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along theequator halfway around the Earth (by comparison, the Earth's lithosphere has a natural period of about 57 minutes).Earth tides, which raise and lower the bottom of the ocean, and the tide's own gravitational self attraction are bothsignificant and further complicate the ocean's response to tidal forces.

DissipationEarth's tidal oscillations introduce dissipation at an average rate of about 3.75 terawatt.[32] About 98% of thisdissipation is by marine tidal movement.[33] Dissipation arises as basin-scale tidal flows drive smaller-scale flowswhich experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angularmomentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earthcorrespondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, atabout 3.8 centimetres (unknown operator: u'strong' in)/year, lengthening the terrestrial day.[34] Day length hasincreased by about 2 hours in the last 600 million years. Assuming (as a crude approximation) that the decelerationrate has been constant, this would imply that 70 million years ago, day length was on the order of 1% shorter withabout 4 more days per year.

Observation and prediction

History

Brouscon's Almanach of 1546: Compass bearingsof high waters in the Bay of Biscay (left) and the

coast from Brittany to Dover (right).

From ancient times, tidal observation and discussion has increased insophistication, first marking the daily recurrence, then tides'relationship to the sun and moon. Pytheas travelled to the British Islesabout 325 BC and seems to be the first to have related spring tides tothe phase of the moon.

In the 2nd century BC, the Babylonian astronomer, Seleucus ofSeleucia, correctly described the phenomenon of tides in order tosupport his heliocentric theory.[35] He correctly theorized that tideswere caused by the moon, although he believed that the interaction wasmediated by the pneuma. He noted that tides varied in time andstrength in different parts of the world. According to Strabo (1.1.9),Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the moon'sposition relative to the sun.[36]

In China, Wang Chong (27–100 AD) correlated tide to the moon's movement in the book entitled Lunheng. He notedthat "tide's rise and fall follow the moon and vary in magnitude."[37]

Tide 9

Brouscon's Almanach of 1546: Tidal diagrams"according to the age of the moon".

The Naturalis Historia of Pliny the Elder collates many tidalobservations, e.g., the spring tides are a few days after (or before) newand full moon and are highest around the equinoxes, though Plinynoted many relationships now regarded as fanciful. In his Geography,Strabo described tides in the Persian Gulf having their greatest rangewhen the moon was furthest from the plane of the equator. All thisdespite the relatively small amplitude of Mediterranean basin tides.(The strong currents through the Euripus Strait and the Strait ofMessina puzzled Aristotle.) Philostratus discussed tides in Book Fiveof The Life of Apollonius of Tyana. Philostratus mentions the moon,but attributes tides to "spirits". In Europe around 730 AD, theVenerable Bede described how the rising tide on one coast of the British Isles coincided with the fall on the otherand described the time progression of high water along the Northumbrian coast.

In the 9th century, the Arabian earth-scientist, Al-Kindi (Alkindus), wrote a treatise entitled Risala fi l-Illa al-Failalil-Madd wa l-Fazr (Treatise on the Efficient Cause of the Flow and Ebb), in which he presents an argument on tideswhich "depends on the changes which take place in bodies owing to the rise and fall of temperature." He describes aprecise laboratory experiment that proved his argument.[38]

The first tide table in China was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore inthe Qiantang River. The first known British tide table is thought to be that of John Wallingford, who died Abbot ofSt. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at the Thamesmouth than upriver at London.William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867. Themain result was the building of a tide-predicting machine using a system of pulleys to add together six harmonic timefunctions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machineswere used until the 1960s.[39]

The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the ThamesEstuary. Many large ports had automatic tide gage stations by 1850.William Whewell first mapped co-tidal lines ending with a nearly global chart in 1836. In order to make these mapsconsistent, he hypothesized the existence of amphidromes where co-tidal lines meet in the mid-ocean. These pointsof no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the NorthSea.[21]

Tide 10

Timing

The same tidal forcing has different results depending on many factors, including coastorientation, continental shelf margin, water body dimensions.

There is a delay between the phases ofthe moon and the effect on the tide.Springs and neaps in the North Sea, forexample, are two days behind thenew/full moon and first/third quartermoon. This is called the tide'sage.[40][41]

The local bathymetry greatlyinfluences the tide's exact time andheight at a particular coastal point.There are some extreme cases: the Bayof Fundy, on the east coast of Canada,features the world's largest

well-documented tidal ranges, 17 metres (unknown operator: u'strong' ft) because of its shape.[42] Some expertsbelieve Ungava Bay in northern Quebec to have even higher tidal ranges, but it is free of pack ice for only about fourmonths every year, while the Bay of Fundy rarely freezes.

Southampton in the United Kingdom has a double high water caused by the interaction between the region's differenttidal harmonics, caused primarily by the east/west orientation of the English Channel and the fact that when it is highwater at Dover it is low water at Land's End (some 300 nautical miles distant) and vice versa. This is contrary to thepopular belief that the flow of water around the Isle of Wight creates two high waters. The Isle of Wight isimportant, however, since it is responsible for the 'Young Flood Stand', which describes the pause of the incomingtide about three hours after low water.[43]

Because the oscillation modes of the Mediterranean Sea and the Baltic Sea do not coincide with any significantastronomical forcing period, the largest tides are close 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. Elsewhere, as alongthe southern coast of Australia, low tides can be due to the presence of a nearby amphidrome.

Analysis

A regular water level chart

Isaac Newton's theory of gravitationfirst enabled an explanation of whythere were generally two tides a day,not one, and offered hope for detailedunderstanding. Although it may seemthat tides could be predicted via asufficiently detailed knowledge of theinstantaneous astronomical forcings,the actual tide at a given location is determined by astronomical forces accumulated over many days. Precise resultsrequire detailed knowledge of the shape of all the ocean basins—their bathymetry and coastline shape.

Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by William Thomson. It is based on the principle that the astronomical theories of the motions of sun and moon determine a large number of component frequencies, and at each frequency there is a component of force tending to produce tidal motion, but that at each place of interest on the Earth, the tides respond at each frequency with an amplitude and phase peculiar to that locality. At each place of interest, the tide heights are therefore measured for a period of time sufficiently long (usually more than a year in the case of a new port not previously studied) to enable the response at

Tide 11

each significant tide-generating frequency to be distinguished by analysis, and to extract the tidal constants for asufficient number of the strongest known components of the astronomical tidal forces to enable practical tideprediction. The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for eachcomponent. Because astronomical frequencies and phases can be calculated with certainty, the tide height at othertimes can then be predicted once the response to the harmonic components of the astronomical tide-generating forceshas been found.The main patterns in the tides are•• the twice-daily variation•• the difference between the first and second tide of a day• the spring–neap cycle•• the annual variationThe Highest Astronomical Tide is the perigean spring tide when both the sun and the moon are closest to the Earth.When confronted by a periodically varying function, the standard approach is to employ Fourier series, a form ofanalysis that uses sinusoidal functions as a basis set, having frequencies that are zero, one, two, three, etc. times thefrequency of a particular fundamental cycle. These multiples are called harmonics of the fundamental frequency, andthe process is termed harmonic analysis. If the basis set of sinusoidal functions suit the behaviour being modelled,relatively few harmonic terms need to be added. Orbital paths are very nearly circular, so sinusoidal variations aresuitable for tides.For the analysis of tide heights, the Fourier series approach has in practice to be made more elaborate than the use ofa single frequency and its harmonics. The tidal patterns are decomposed into many sinusoids having manyfundamental frequencies, corresponding (as in the lunar theory) to many different combinations of the motions of theEarth, the moon, and the angles that define the shape and location of their orbits.For tides, then, harmonic analysis is not limited to harmonics of a single frequency.[44] In other words, theharmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simplerFourier series approach. Their representation as a Fourier series having only one fundamental frequency and its(integer) multiples would require many terms, and would be severely limited in the time-range for which it would bevalid.The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and GeorgeDarwin. A.T. Doodson extended their work, introducing the Doodson Number notation to organise the hundreds ofresulting terms. This approach has been the international standard ever since, and the complications arise as follows:the tide-raising force is notionally given by sums of several terms. Each term is of the form

A·cos(w·t + p)where A is the amplitude, w is the angular frequency usually given in degrees per hour corresponding to t measuredin hours, and p is the phase offset with regard to the astronomical state at time t = 0 . There is one term for the moonand a second term for the sun. The phase p of the first harmonic for the moon term is called the lunitidal interval orhigh water interval. The next step is to accommodate the harmonic terms due to the elliptical shape of the orbits.Accordingly, the value of A is not a constant but also varying with time, slightly, about some average figure. Replaceit then by A(t) where A is another sinusoid, similar to the cycles and epicycles of Ptolemaic theory. Accordingly,

A(t) = A·(1 + Aa·cos(wa·t + pa)) ,which is to say an average value A with a sinusoidal variation about it of magnitude Aa , with frequency wa and phasepa . Thus the simple term is now the product of two cosine factors:

A·[1 + Aa·cos(wa + pa)]·cos(w·t + p)Given that for any x and y

cos(x)·cos(y) = ½·cos( x + y ) + ½·cos( x–y ) ,

Tide 12

it is clear that a compound term involving the product of two cosine terms each with their own frequency is the sameas three simple cosine terms that are to be added at the original frequency and also at frequencies which are the sumand difference of the two frequencies of the product term. (Three, not two terms, since the whole expression is (1 +cos(x))·cos(y) .) Consider further that the tidal force on a location depends also on whether the moon (or the sun) isabove or below the plane of the equator, and that these attributes have their own periods also incommensurable witha day and a month, and it is clear that many combinations result. With a careful choice of the basic astronomicalfrequencies, the Doodson Number annotates the particular additions and differences to form the frequency of eachsimple cosine term.

Tidal prediction summing constituent parts.

Remember that astronomical tides do not includeweather effects. Also, changes to local conditions(sandbank movement, dredging harbour mouths,etc.) away from those prevailing at themeasurement time affect the tide's actual timingand magnitude. Organisations quoting a "highestastronomical tide" for some location mayexaggerate the figure as a safety factor againstanalytical uncertainties, distance from the nearestmeasurement point, changes since the lastobservation time, ground subsidence, etc., to avertliability should an engineering work beovertopped. Special care is needed when assessingthe size of a "weather surge" by subtracting theastronomical tide from the observed tide.

Careful Fourier data analysis over a nineteen-yearperiod (the National Tidal Datum Epoch in theU.S.) uses frequencies called the tidal harmonicconstituents. Nineteen years is preferred becausethe Earth, moon and sun's relative positions repeatalmost exactly in the Metonic cycle of 19 years,which is long enough to include the 18.613 yearlunar nodal tidal constituent. This analysis can be

done using only the knowledge of the forcing period, but without detailed understanding of the mathematicalderivation, which means that useful tidal tables have been constructed for centuries.[45] The resulting amplitudes andphases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours(the semi-diurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer termconstituents are 14 day or fortnightly, monthly, and semiannual. Semi-diurnal tides dominated coastline, but someareas such as the South China Sea and the Gulf of Mexico are primarily diurnal. In the semi-diurnal areas, theprimary constituents M2 (lunar) and S2 (solar) periods differ slightly, so that the relative phases, and thus theamplitude of the combined tide, change fortnightly (14 day period).[46]

In the M2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides inphase with equilibrium at Greenwich. The lines rotate around the amphidromic points counterclockwise in thenorthern hemisphere so that from Baja California Peninsula to Alaska and from France to Ireland the M2 tidepropagates northward. In the southern hemisphere this direction is clockwise. On the other hand M2 tide propagatescounterclockwise around New Zealand, but this is because the islands act as a dam and permit the tides to havedifferent heights on the islands' opposite sides. (The tides do propagate northward on the east side and southward onthe west coast, as predicted by theory.)

Tide 13

The exception is at Cook Strait where the tidal currents periodically link high to low water. This is because cotidallines 180° around the amphidromes are in opposite phase, for example high water across from low water at each endof Cook Strait. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so theM2 patterns cannot be used for other tide components.

Example calculationFurther information: The article on A.T. Doodson has a fully worked example calculation for Bridgeport,Connecticut, U.S.A.

Tides at Bridgeport, Connecticut, U.S.A. during a 50 hour period.

Tides at Bridgeport, Connecticut, U.S.A. during a 30 day period.

Tides at Bridgeport, Connecticut, U.S.A. during a 400 day period.

Because the moon is moving in its orbit around theearth and in the same sense as the Earth's rotation, apoint on the earth must rotate slightly further to catchup so that the time between semidiurnal tides is nottwelve but 12.4206 hours—a bit over twenty-fiveminutes extra. The two peaks are not equal. The twohigh tides a day alternate in maximum heights: lowerhigh (just under three feet), higher high (just over threefeet), and again lower high. Likewise for the low tides.

When the Earth, moon, and sun are in line(sun–Earth–moon, or sun–moon–Earth) the two maininfluences combine to produce spring tides; when thetwo forces are opposing each other as when the anglemoon–Earth–sun is close to ninety degrees, neap tidesresult. As the moon moves around its orbit it changesfrom north of the equator to south of the equator. Thealternation in high tide heights becomes smaller, untilthey are the same (at the lunar equinox, the moon isabove the equator), then redevelop but with the otherpolarity, waxing to a maximum difference and thenwaning again.

Current

The tides' influence on current flow is much moredifficult to analyse, and data is much more difficult tocollect. A tidal height is a simple number which appliesto a wide region simultaneously. A flow has both amagnitude and a direction, both of which can varysubstantially with depth and over short distances due tolocal bathymetry. Also, although a water channel'scenter is the most useful measuring site, marinersobject when current-measuring equipment obstructswaterways. A flow proceeding up a curved channel is the same flow, even though its direction varies continuouslyalong the channel. Surprisingly, flood and ebb flows are often not in opposite directions. Flow

Tide 14

Two spring tides per month vs. one.

direction is determined by the upstream channel'sshape, not the downstream channel's shape. Likewise,eddies may form in only one flow direction.

Nevertheless, current analysis is similar to tidalanalysis: in the simple case, at a given location theflood flow is in mostly one direction, and the ebb flowin another direction. Flood velocities are given positivesign, and ebb velocities negative sign. Analysisproceeds as though these are tide heights.In more complex situations, the main ebb and floodflows do not dominate. Instead, the flow direction andmagnitude trace an ellipse over a tidal cycle (on a polarplot) instead of along the ebb and flood lines. In this case, analysis might proceed along pairs of directions, with theprimary and secondary directions at right angles. An alternative is to treat the tidal flows as complex numbers, aseach value has both a magnitude and a direction.Tide flow information is most commonly seen on nautical charts, presented as a table of flow speeds and bearings athourly intervals, with separate tables for spring and neap tides. The timing is relative to high water at some harbourwhere the tidal behaviour is similar in pattern, though it may be far away.As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weatherconditions, which can completely change the outcome.The tidal flow through Cook Strait between the two main islands of New Zealand is particularly interesting, as thetides on each side of the strait are almost exactly out of phase, so that one side's high water is simultaneous with theother's low water. Strong currents result, with almost zero tidal height change in the strait's center. Yet, although thetidal surge normally flows in one direction for six hours and in the reverse direction for six hours, a particular surgemight last eight or ten hours with the reverse surge enfeebled. In especially boisterous weather conditions, thereverse surge might be entirely overcome so that the flow continues in the same direction through three or moresurge periods.A further complication for Cook Strait's flow pattern is that the tide at the north side (e.g. at Nelson) follows thecommon bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidalpattern has only one cycle per month, as on the east side: Wellington, and Napier.Figure 12 shows separately the high water and low water height and time, through November 2007; these are notmeasured values but instead are calculated from tidal parameters derived from years-old measurements. Cook Strait'snautical chart offers tidal current information. For instance the January 1979 edition for 41°13·9’S 174°29·6’E (northwest of Cape Terawhiti) refers timings to Westport while the January 2004 issue refers to Wellington. Near CapeTerawhiti in the middle of Cook Strait the tidal height variation is almost nil while the tidal current reaches itsmaximum, especially near the notorious Karori Rip. Aside from weather effects, the actual currents through CookStrait are influenced by the tidal height differences between the two ends of the strait and as can be seen, only one ofthe two spring tides at the north end (Nelson) has a counterpart spring tide at the south end (Wellington), so theresulting behaviour follows neither reference harbour.

Tide 15

Power generationTidal energy can be extracted by two means: inserting a water turbine into a tidal current, or building ponds thatrelease/admit water through a turbine. In the first case, the energy amount is entirely determined by the timing andtidal current magnitude. However, the best currents may be unavailable because the turbines would obstruct ships. Inthe second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, shipnavigation is disrupted. However, with multiple ponds, power can be generated at chosen times. So far, there are fewinstalled systems for tidal power generation (most famously, La Rance by Saint Malo, France) which faces manydifficulties. Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineeringchallenges.Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, savefor weather effects. While some generation is possible for most of the tidal cycle, in practice turbines lose efficiencyat lower operating rates. Since the power available from a flow is proportional to the cube of the flow speed, thetimes during which high power generation is possible are brief.

Navigation

Civil and maritime uses of tidal data

Tidal flows are important fornavigation, and significant errors inposition occur if they are notaccommodated. Tidal heights are alsoimportant; for example many riversand harbours have a shallow "bar" atthe entrance which prevents boats withsignificant draft from entering at lowtide.

Until the advent of automatednavigation, competence in calculatingtidal effects was important to navalofficers. The certificate of examinationfor lieutenants in the Royal Navy oncedeclared that the prospective officer

was able to "shift his tides".[47]

Tidal flow timings and velocities appear in tide charts or a tidal stream atlas. Tide charts come in sets. Each chartcovers a single hour between one high water and another (they ignore the leftover 24 minutes) and show the averagetidal flow for that hour. An arrow on the tidal chart indicates the direction and the average flow speed (usually inknots) for spring and neap tides. If a tide chart is not available, most nautical charts have "tidal diamonds" whichrelate specific points on the chart to a table giving tidal flow direction and speed.

The standard procedure to counteract tidal effects on navigation is to (1) calculate a "dead reckoning" position (orDR) from travel distance and direction, (2) mark the chart (with a vertical cross like a plus sign) and (3) draw a linefrom the DR in the tide's direction. The distance the tide moves the boat along this line is computed by the tidalspeed, and this gives an "estimated position" or EP (traditionally marked with a dot in a triangle).

Tide 16

Tidal Indicator, Delaware River, Delaware c. 1897. At the time shown in thefigure, the tide is 1¼ feet above mean low water and is still falling, as indicated bypointing of the arrow. Indicator is powered by system of pulleys, cables and a float.

(Report Of The Superintendent Of The Coast & Geodetic Survey Showing TheProgress Of The Work During The Fiscal Year Ending With June 1897 (p. 483))

Nautical charts display the water's "charteddepth" at specific locations with"soundings" and the use of bathymetriccontour lines to depict the submergedsurface's shape. These depths are relative toa "chart datum", which is typically the waterlevel at the lowest possible astronomical tide(although other datums are commonly used,especially historically, and tides may belower or higher for meteorological reasons)and are therefore the minimum possiblewater depth during the tidal cycle. "Dryingheights" may also be shown on the chart,which are the heights of the exposed seabedat the lowest astronomical tide.

Tide tables list each day's high and lowwater heights and times. To calculate theactual water depth, add the charted depth tothe published tide height. Depth for othertimes can be derived from tidal curvespublished for major ports. The rule oftwelfths can suffice if an accurate curve isnot available. This approximation presumesthat the increase in depth in the six hoursbetween low and high water is: first hour — 1/12, second — 2/12, third — 3/12, fourth — 3/12, fifth — 2/12, sixth— 1/12.

Biological aspects

Tide 17

Intertidal ecology

A rock, seen at low water, exhibiting typical intertidalzonation.

Intertidal ecology is the study of intertidal ecosystems, whereorganisms live between the low and high water lines. At lowwater, the intertidal is exposed (or ‘emersed’) whereas at highwater, the intertidal is underwater (or ‘immersed’). Intertidalecologists therefore study the interactions between intertidalorganisms and their environment, as well as among the differentspecies. The most important interactions may vary according tothe type of intertidal community. The broadest classifications arebased on substrates — rocky shore or soft bottom.

Intertidal organisms experience a highly variable and often hostileenvironment, and have adapted to cope with and even exploit theseconditions. One easily visible feature is vertical zonation, in whichthe community divides into distinct horizontal bands of specificspecies at each elevation above low water. A species' ability tocope with desiccation determines its upper limit, whilecompetition with other species sets its lower limit.

Humans use intertidal regions for food and recreation.Overexploitation can damage intertidals directly. Otheranthropogenic actions such as introducing invasive species andclimate change have large negative effects. Marine ProtectedAreas are one option communities can apply to protect these areasand aid scientific research.

Biological rhythmsThe approximately fortnightly tidal cycle has large effects on intertidal organisms. Hence their biological rhythmstend to occur in rough multiples of this period. Many other animals such as the vertebrates, display similar rhythms.Examples include gestation and egg hatching. In humans, the menstrual cycle lasts roughly a lunar month, an evenmultiple of the tidal period. Such parallels at least hint at the common descent of all animals from a marineancestor.[48]

Other tidesWhen oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internalwaves with tidal frequencies. Such waves are called internal tides.Shallow areas in otherwise open water can experience rotary tidal currents, flowing in directions that continuallychange and thus the flow direction (not the flow) completes a full rotation in 12½ hours (for example, the NantucketShoals.[49]

In addition to oceanic tides, large lakes can experience small tides and even planets can experience atmospheric tidesand Earth tides. These are continuum mechanical phenomena. The first two take place in fluids. The third affects theEarth's thin solid crust surrounding its semi-liquid interior (with various modifications).

Tide 18

Lake tidesLarge lakes such as Superior and Erie can experience tides of 1 to 4 cm, but these can be masked bymeteorologically induced phenomena such as seiche.[50] The tide in Lake Michigan is described as 0.5 to 1.5 inches(unknown operator: u'strong' to unknown operator: u'strong' mm)[51] or 1¾ inches.[52]

Atmospheric tidesAtmospheric tides are negligible at ground level and aviation altitudes, masked by weather's much more importanteffects. Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about80–120 kilometres (unknown operator: u'strong'unknown operator: u'strong'unknown operator: u'strong'unknown operator: u'strong') above which the molecular density becomes too low to support fluid behavior.

Earth tidesEarth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquid gyroscope with a verythin crust. The Earth's crust shifts (in/out, east/west, north/south) in response to lunar and solar gravitation, oceantides, and atmospheric loading. While negligible for most human activities, terrestrial tides' semi-diurnal amplitudecan reach about 55 centimetres (unknown operator: u'strong' in) at the equator—15 centimetres (unknownoperator: u'strong' in) due to the sun—which is important in GPS calibration and VLBI measurements. Preciseastronomical angular measurements require knowledge of the Earth's rotation rate and nutation, both of which areinfluenced by Earth tides. The semi-diurnal M2 Earth tides are nearly in phase with the moon with a lag of about twohours.Some particle physics experiments must adjust for terrestrial tides.[53] For instance, at CERN and SLAC, the verylarge particle accelerators account for terrestrial tides. Among the relevant effects are circumference deformation forcircular accelerators and particle beam energy.[54][55] Since tidal forces generate currents in conducting fluids in theEarth's interior, they in turn affect the Earth's magnetic field. Earth tides have also been linked to the triggering ofearthquakes[56] (see also earthquake prediction).

Galactic tidesGalactic tides are the tidal forces exerted by galaxies on stars within them and satellite galaxies orbiting them. Thegalactic tide's effects on the Solar System's Oort cloud are believed to cause 90 percent of long-period comets.[57]

MisapplicationsTsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is given bytheir resemblance to the tide, rather than any actual link to the tide. Other phenomena unrelated to tides but using theword tide are rip tide, storm tide, hurricane tide, and black or red tides.

Tide 19

Notes[1] M. P. M. Reddy, M. Affholder (2002). Descriptive physical oceanography: State of the Art (http:/ / books. google. com/

?id=2NC3JmKI7mYC& pg=PA436& dq=tides+ centrifugal+ "equilibrium+ theory"+ date:2000-2010). Taylor and Francis. p. 249.ISBN 90-5410-706-5. OCLC 223133263 47801346. .

[2] Richard Hubbard (1893). Boater's Bowditch: The Small Craft American Practical Navigator (http:/ / books. google. com/?id=nfWSxRr8VP4C& pg=PA54& dq=centrifugal+ revolution+ and+ rotation+ date:1970-2009). McGraw-Hill Professional. p. 54.ISBN 0-07-136136-7. OCLC 44059064. .

[3] Coastal orientation and geometry affects the phase, direction, and amplitude of amphidromic systems, coastal Kelvin waves as well asresonant seiches in bays. In estuaries seasonal river outflows influence tidal flow.

[4] "Tidal lunar day" (http:/ / www. oceanservice. noaa. gov/ education/ kits/ tides/ media/ supp_tide05. html). NOAA. . Do not confuse with theastronomical lunar day on the Moon. A lunar zenith is the Moon's highest point in the sky.

[5] Mellor, George L. (1996). Introduction to physical oceanography. Springer. p. 169. ISBN 1-56396-210-1.[6] 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 values in the sense that they derive frommean data. "Glossary of Coastal Terminology: H–M" (http:/ / www. ecy. wa. gov/ programs/ sea/ swces/ products/ publications/ glossary/words/ H_M. htm). Washington Department of Ecology, State of Washington. . Retrieved 5 April 2007.

[7] "Types and causes of tidal cycles" (http:/ / oceanservice. noaa. gov/ education/ kits/ tides/ tides07_cycles. html). U S National Oceanic andAtmospheric Administration (NOAA) National Ocean Service (Education section). .

[8] Swerdlow, Noel M.; Neugebauer, Otto (1984). Mathematical astronomy in Copernicus's De revolutionibus, Volume 1 (http:/ / books. google.com/ ?id=4YDvAAAAMAAJ& q=Syzygy& dq=Syzygy& cd=30). Springer-Verlag. p. 76. ISBN 0-387-90939-7, 9780387909394.

[9] Plait, Phil (11 March 2011). "No, the “supermoon” didn’t cause the Japanese earthquake" (http:/ / blogs. discovermagazine. com/badastronomy/ 2011/ 03/ 11/ no-the-supermoon-didnt-cause-the-japanese-earthquake/ ). Discover Magazine. . Retrieved 16 May 2012.

[10] Rice, Tony (4 May 2012). "Super moon looms Saturday" (http:/ / www. wral. com/ weather/ blogpost/ 11061791/ ). WRAL-TV. . Retrieved 5May 2012.

[11] U S National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section), map showing worlddistribution of tide patterns (http:/ / oceanservice. noaa. gov/ education/ kits/ tides/ media/ supp_tide07b. html), semi-diurnal, diurnal andmixed semi-diurnal.

[12] Thurman, H V (1994). Introductory Oceanography (7 ed.). New York, NY: Macmillan. pp. 252–276.ref[13] Ross, D A (1995). Introduction to Oceanography. New York, NY: HarperCollins. pp. 236–242.[14] Le Provost, Christian(1991). Generation of Overtides and compound tides (review). In Bruce B. Parker, ed Tidal Hydrodynamics. John

Wiley and Sons, ISBN 978-0-471-51498-5[15] Y. Accad, C. L. Pekeris (November 28, 1978). "Solution of the Tidal Equations for the M2 and S2 Tides in the World Oceans from a

Knowledge of the Tidal Potential Alone". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and PhysicalSciences 290 (1368): 235–266.

[16] "Tide forecasts" (http:/ / www. niwa. cri. nz/ rc/ prog/ chaz/ news/ coastal#tide). New Zealand: National Institute of Water & AtmosphericResearch. . Retrieved 2008-11-07. Including animations of the M2, S2 and K1 tides for New Zealand.

[17] E Lisitzin (1974). "2 "Periodical sea-level changes: Astronomical tides"". Sea-Level Changes, (Elsevier Oceanography Series). 8. p. 5.[18] "What Causes Tides?" (http:/ / oceanservice. noaa. gov/ education/ kits/ tides/ tides02_cause. html). U S National Oceanic and Atmospheric

Administration (NOAA) National Ocean Service (Education section). .[19] See for example, in the 'Principia' (Book 1) (1729 translation), Corollaries 19 and 20 to Proposition 66, on pages 251–254 (http:/ / books.

google. com/ books?id=Tm0FAAAAQAAJ& pg=PA251), referring back to page 234 et seq.; and in Book 3 Propositions 24, 36 and 37,starting on page 255 (http:/ / books. google. com/ books?id=6EqxPav3vIsC& pg=PA255).

[20] J Wahr (1995). Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1,. pp. 40–46.[21] Yang Zuosheng, K. O. Emery, Xui Yui (July 1989). "Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables".

Limnology and Oceanography 34 (5): 953–957. doi:10.4319/lo.1989.34.5.0953.[22] David E. Cartwright (1999). Tides: A Scientific History. Cambridge, UK: Cambridge University Press.[23] Case, James (March 2000). "Understanding Tides—From Ancient Beliefs to Present-day Solutions to the Laplace Equations". SIAM News

33 (2).[24] A T Doodson (December, 1921). "The Harmonic Development of the Tide-Generating Potential". Proceedings of the Royal Society of

London. Series A 100 (704): 305–329. Bibcode 1921RSPSA.100..305D.[25] S Casotto, F Biscani (April 2004). "A fully analytical approach to the harmonic development of the tide-generating potential accounting for

precession, nutation, and perturbations due to figure and planetary terms". AAS Division on Dynamical Astronomy 36 (2): 67.[26] See e.g. T D Moyer (2003), "Formulation for observed and computed values of Deep Space Network data types for navigation", vol.3 in

Deep-space communications and navigation series, Wiley (2003), e.g. at pp.126–8.[27] NASA (May 4, 2000). "Interplanetary Low Tide" (http:/ / science. nasa. gov/ headlines/ y2000/ ast04may_1m. htm). . Retrieved September

26, 2009.[28] Two points on either side of the Earth sample the imposed gravity at two nearby points, effectively providing a finite difference of the

gravitational force that varies as the inverse square of the distance. The derivative of 1/r2, with r = distance to originating body, varies as the

Tide 20

inverse cube.[29] According to NASA (http:/ / imagine. gsfc. nasa. gov/ docs/ ask_astro/ answers/ 961029b. html) the lunar tidal force is 2.21 times larger than

the solar.[30] See Tidal force – Mathematical treatment and sources cited there.[31][31] Hypothetically, if the ocean were a constant depth, there were no land, and the Earth did not rotate, high water would occur as two bulges in

the oceans' height, one facing the moon and the other facing away from the moon. There would also be smaller, superimposed bulges on thesides facing toward and away from the sun.

[32] Munk, W.; Wunsch, C (1998). "Abyssal recipes II: energetics of tidal and wind mixing". Deep Sea Research Part I OceanographicResearch Papers 45 (12): 1977. Bibcode 1998DSRI...45.1977M. doi:10.1016/S0967-0637(98)00070-3.

[33] Ray, R. D.; Eanes, R. J.; Chao, B. F. (1996). "Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry". Nature 381(6583): 595. Bibcode 1996Natur.381..595R. doi:10.1038/381595a0.

[34] Lecture 2: The Role of Tidal Dissipation and the Laplace Tidal Equations by Myrl Hendershott. GFD Proceedings Volume, 2004, WHOINotes by Yaron Toledo and Marshall Ward.

[35] Flussi e riflussi. Milano: Feltrinelli. 2003. ISBN 88-07-10349-4.[36] "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences (500 (1)): 525–545 [527].

1987.[37] Baike.baidu.com (http:/ / baike. baidu. com/ view/ 135336. htm)[38] Prioreschi, Plinio (2002). "Al-Kindi, A Precursor Of The Scientific Revolution". Journal of the International Society for the History of

Islamic Medicine (2): 17–19 [17].[39] "The Doodson–Légé Tide Predicting Machine" (http:/ / www. pol. ac. uk/ home/ insight/ doodsonmachine. html). Proudman Oceanographic

Laboratory. . Retrieved 2008-10-03.[40] Glossary of Meteorology (http:/ / amsglossary. allenpress. com/ glossary/ search?id=age1) American Meteorological Society.[41] Webster, Thomas (1837). The elements of physics (http:/ / books. google. com/ books?id=dUwEAAAAQAAJ). Printed for Scott, Webster,

and Geary. p. 168. ., Extract of page 168 (http:/ / books. google. com/ books?id=dUwEAAAAQAAJ& pg=PA168)[42] "FAQ" (http:/ / www. waterlevels. gc. ca/ english/ FrequentlyAskedQuestions. shtml#importantes). . Retrieved June 23, 2007.[43] English Channel double tides. Retrieved April 24, 2008. (http:/ / www. bristolnomads. org. uk/ stuff/ double_tides. htm)[44] To demonstrate this Tides Home Page (http:/ / www. arachnoid. com/ tides/ index. html) offers a tidal height pattern converted into an .mp3

sound file, and the rich sound is quite different from a pure tone.[45] Center for Operational Oceanographic Products and Services, National Ocean Service, National Oceanic and Atmospheric Administration

(January 2000). "Tide and Current Glossary" (http:/ / tidesandcurrents. noaa. gov/ publications/ glossary2. pdf). Silver Spring, MD. .[46] Harmonic Constituents (http:/ / tidesandcurrents. noaa. gov/ harmonic_cons_defs. html), NOAA.[47] Society for Nautical Research (1958). The Mariner's Mirror (http:/ / books. google. com/ ?id=lagPAAAAIAAJ& q="shift+ his+ tides"&

dq="shift+ his+ tides"). . Retrieved 2009-04-28.[48] The Descent of Man, and Selection in Relation to Sex. London: John Murray. 1871.[49] Le Lacheur, Embert A. Tidal currents in the open sea: Subsurface tidal currents at Nantucket Shoals Light Vessel (http:/ / www. jstor. org/

pss/ 208104) Geographical Review, April 1924. Accessed: 4 February 2012.[50] "Do the Great Lakes have tides?" (http:/ / www. great-lakes. net/ teach/ chat/ answers/ 100100_tides. html). Great Lakes Information

Network. October 1, 2000. . Retrieved 2010-02-10.[51] "Tides on Lake Michigan" (http:/ / www. newton. dep. anl. gov/ askasci/ phy00/ phy00330. htm). Argonne National Laboratory. . Retrieved

2010-02-10.[52] Duane Dunkerson. "moon and Tides" (http:/ / www. thespaceguy. com/ moontides. htm). Astronomy Briefly. . Retrieved 2010-02-10.[53] "Linac" (http:/ / news-service. stanford. edu/ news/ 2000/ march29/ linac-329. html). Stanford. .[54] "Effects of Tidal Forces on the Beam Energy in LEP" (http:/ / accelconf. web. cern. ch/ accelconf/ e00/ PAPERS/ MOP5A04. pdf). PAC

(IEEE). 1993. .[55] "Long term variation of the circumference of the spring-8 storage ring" (http:/ / accelconf. web. cern. ch/ accelconf/ p93/ PDF/

PAC1993_0044. PDF). Proceedings of EPAC. 2000 Location=Vienna, Austria. .[56] Tanaka, Sachiko (2010). "Tidal triggering of earthquakes precursory to the recent Sumatra megathrust earthquakes of 26 December 2004

(Mw9.0), 28 March 2005 (Mw8.6), and 12 September 2007 (Mw8.5)". Geophys. Res. Lett. 37 (2): L02301. Bibcode 2010GeoRL..3702301T.doi:10.1029/2009GL041581.

[57] 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 (4): 1367–1376. Bibcode 2001MNRAS.327.1367N.doi:10.1046/j.1365-8711.2001.04854.x.

Tide 21

External links• 150 Years of Tides on the Western Coast: The Longest Series of Tidal Observations in the Americas (http:/ /

tidesandcurrents. noaa. gov/ publications/ 150_years_of_tides. pdf) NOAA (2004).• Eugene I. Butikov: A dynamical picture of the ocean tides (http:/ / faculty. ifmo. ru/ butikov/ Projects/ tides1. pdf)• Earth, Atmospheric, and Planetary Sciences MIT Open Courseware; Ch 8 §3 (http:/ / ocw. mit. edu/ NR/

rdonlyres/ Earth--Atmospheric--and-Planetary-Sciences/ 12-090Spring-2007/ LectureNotes/ earthsurface_8. pdf)• Myths about Gravity and Tides (http:/ / www. jal. cc. il. us/ ~mikolajsawicki/ Tides_new2. pdf) by Mikolaj

Sawicki (2005).• Ocean Motion: Open-Ocean Tides (http:/ / www. oceanmotion. org/ html/ background/ tides-ocean. htm)• Oceanography: tides (http:/ / www. seafriends. org. nz/ oceano/ tides. htm) by J. Floor Anthoni (2000).• Our Restless Tides (http:/ / tidesandcurrents. noaa. gov/ restles1. html): NOAA's practical & short introduction to

tides.• Planetary alignment and the tides (NASA) (http:/ / science. nasa. gov/ headlines/ y2000/ ast04may_1m. htm)• Tidal Misconceptions (http:/ / www. lhup. edu/ ~dsimanek/ scenario/ tides. htm) by Donald E. Simanek.• Tides and centrifugal force (http:/ / www. vialattea. net/ maree/ eng/ index. htm): Why the centrifugal force does

not explain the tide's opposite lobe (with nice animations).• O. Toledano et al. (2008): Tides in asynchronous binary systems (http:/ / arxiv. org/ abs/ astro-ph/ 0610563v1)• Gif Animation of TPX06 tide model based on TOPEX/Poseidon (T/P) satellite radar altimetry (http:/ / volkov.

oce. orst. edu/ tides)• Gaylord Johnson "How Moon and Sun Generate the Tides" (http:/ / books. google. com/

books?id=uSgDAAAAMBAJ& pg=PA50& dq=Popular+ Science+ 1932+ plane& hl=en&ei=qXo-TZy2MMP88AaF_NSQCg& sa=X& oi=book_result& ct=result& resnum=1&ved=0CCgQ6AEwADgU#v=onepage& q& f=true) Popular Science, April 1934

• Tide gauge observation reference networks (http:/ / refmar. shom. fr) (French designation REFMAR: Réseaux deréférence des observations marégraphiques)

Tide predictions• NOAA Tide Predictions (http:/ / tidesandcurrents. noaa. gov/ tide_predictions. shtml)• NOAA Tides and Currents information and data (http:/ / tidesandcurrents. noaa. gov/ )• History of tide prediction (http:/ / www. co-ops. nos. noaa. gov/ predhist. html)• Department of Oceanography, Texas A&M University (http:/ / oceanworld. tamu. edu/ resources/ ocng_textbook/

chapter17/ chapter17_04. htm)• Mapped, graphical and tabular tide charts for US displayed as calendar months (http:/ / www. protides. com/ )• Mapped, graphical US tide tables/charts in calendar form from NOAA data (http:/ / tidesite. appspot. com/ )• SHOM Tide Predictions (http:/ / www. shom. fr/ fr_page/ fr_serv_prediction/ ann_marees. htm)• UK Admiralty Easytide (http:/ / easytide. ukho. gov. uk/ EasyTide/ EasyTide/ index. aspx)• UK, South Atlantic, British Overseas Territories and Gibraltar tide times from the UK National Tidal and Sea

Level Facility (http:/ / www. pol. ac. uk/ ntslf/ tidalp. html)• Tide Predictions for Australia, South Pacific & Antarctica (http:/ / www. bom. gov. au/ oceanography/ tides/

index. shtml)• Tide and Current Predictor, for stations around the world (http:/ / tbone. biol. sc. edu/ tide/ index. html)• World Tide Tables (http:/ / www. tides4fishing. com)• Famous Tidal Prediction Pioneers and Notable Contributions (http:/ / www. juliantrubin. com/ schooldirectory/

tide_prediction. html)

Sea level 22

Sea level

This marker indicating the sea level is placed on the path from Jerusalem to theDead Sea.

Mean sea level (MSL) is a measure of theaverage height of the ocean's surface (suchas the halfway point between the mean hightide and the mean low tide); used as astandard in reckoning land elevation.[1]

MSL also plays an extremely important rolein aviation, where standard sea levelpressure is used as the measurement datumof altitude at flight levels.

Measurement

Sea level measurements from 23 long tide gauge records ingeologically stable environments show a rise of around 200

millimetres (unknown operator: u'strong' in) during the 20thcentury (2 mm/year).

To an operator of a tide gauge, MSL means the "stillwater level"—the level of the sea with motions such aswind waves averaged out—averaged over a period oftime such that changes in sea level, e.g., due to thetides, also get averaged out. One measures the values ofMSL in respect to the land. Hence a change in MSLcan result from a real change in sea level, or from achange in the height of the land on which the tidegauge operates.

In the UK, the Ordnance Datum (the 0 metres height onUK maps) is the mean sea level measured at Newlyn inCornwall between 1915 and 1921. Prior to 1921 thedatum was MSL at the Victoria Dock, Liverpool.

In France, the Marégraphe in Marseilles measurescontinuously the sea level since 1883 and offers thelongest collapsed data about the sea level. It is used for a part of continental Europe and main part of Africa asofficial sea level.Satellite altimeters have been making precise measurements of sea level since the launch of TOPEX/Poseidon in1992. A joint mission of NASA and CNES, TOPEX/Poseidon was followed by Jason-1 in 2001 and the OceanSurface Topography Mission on the Jason-2 satellite in 2008.

Sea level 23

Difficulties in utilization

1. Ocean. 2. Reference ellipsoid.3. Local plumb line. 4. Continent. 5. Geoid

To extend this definition far from the seameans comparing the local height of themean sea surface with a "level" referencesurface, or datum, called the geoid. In a stateof rest or absence of external forces, themean sea level would coincide with thisgeoid surface, being an equipotential surfaceof the Earth's gravitational field. In reality,due to currents, air pressure variations,temperature and salinity variations, etc., thisdoes not occur, not even as a long termaverage. The location-dependent, butpersistent in time, separation between mean sea level and the geoid is referred to as (stationary) ocean surfacetopography. It varies globally in a range of ± 2 m.

Traditionally, one had to process sea-level measurements to take into account the effect of the 228-month Metoniccycle and the 223-month eclipse cycle on the tides. Mean sea level is not constant over the surface of the Earth. Forinstance, mean sea level at the Pacific end of the Panama Canal stands 20 cm (unknown operator: u'strong' in)higher than at the Atlantic end.

Sea level and dry land

Sea level sign (2/3 of the way up the cliff face)above Badwater Basin, Death Valley National

Park, USA

Several terms are used to describe the changing relationships betweensea level and dry land. When the term "relative" is used, it meanschange relative to a fixed point in the sediment pile. The term"eustatic" refers to global changes in sea level relative to a fixed point,such as the centre of the earth, for example as a result of meltingice-caps. The term "steric" refers to global changes in sea level due tothermal expansion and salinity variations. The term "isostatic" refers tochanges in the level of the land relative to a fixed point in the earth,possibly due to thermal buoyancy or tectonic effects; it implies nochange in the volume of water in the oceans. The melting of glaciers atthe end of ice ages is one example of eustatic sea level rise. Thesubsidence of land due to the withdrawal of groundwater is an isostaticcause of relative sea level rise. Paleoclimatologists can track sea levelby examining the rocks deposited along coasts that are verytectonically stable, like the east coast of North America. Areas likevolcanic islands are experiencing relative sea level rise as a result ofisostatic cooling of the rock which causes the land to sink.

On other planets that lack a liquid ocean, planetologists can calculate a"mean altitude" by averaging the heights of all points on the surface. This altitude, sometimes referred to as a "sealevel", serves equivalently as a reference for the height of planetary features.

Sea level 24

Sea level change

Local and eustatic sea level

Water cycles between ocean, atmosphere, andglaciers.

Local mean sea level (LMSL) is defined as the height of the sea withrespect to a land benchmark, averaged over a period of time (such as amonth or a year) long enough that fluctuations caused by waves andtides are smoothed out. One must adjust perceived changes in LMSL toaccount for vertical movements of the land, which can be of the sameorder (mm/yr) as sea level changes. Some land movements occurbecause of isostatic adjustment of the mantle to the melting of icesheets at the end of the last ice age. The weight of the ice sheetdepresses the underlying land, and when the ice melts away the landslowly rebounds. Changes in ground-based ice volume also affect localand regional sea levels by the readjustment of the geoid and true polar wander. Atmospheric pressure, ocean currentsand local ocean temperature changes can affect LMSL as well.

Eustatic change (as opposed to local change) results in an alteration to the global sea levels due to changes in eitherthe volume of water in the world oceans or net changes in the volume of the ocean basins.[2]

Short term and periodic changesThere are many factors which can produce short-term (a few minutes to 14 months) changes in sea level.

Periodic sea level changes

Diurnal and semidiurnal astronomical tides 12–24 h P 0.2–10+ m

Long-period tides

Rotational variations (Chandler wobble) 14 month P

Meteorological and oceanographic fluctuations

Atmospheric pressure Hours to months –0.7 to 1.3 m

Winds (storm surges) 1–5 days Up to 5 m

Evaporation and precipitation (may also follow long-term pattern) Days to weeks

Ocean surface topography (changes in water density and currents) Days to weeks Up to 1 m

El Niño/southern oscillation 6 mo every 5–10 yr Up to 0.6 m

Seasonal variations

Seasonal water balance among oceans (Atlantic, Pacific, Indian)

Seasonal variations in slope of water surface

River runoff/floods 2 months 1 m

Seasonal water density changes (temperature and salinity) 6 months 0.2 m

Seiches

Seiches (standing waves) Minutes to hours Up to 2 m

Earthquakes

Tsunamis (generate catastrophic long-period waves) Hours Up to 10 m

Abrupt change in land level Minutes Up to 10 m

Sea level 25

Long term changes

Sea-level changes and relative temperatures

Various factors affect the volume or mass ofthe ocean, leading to long-term changes ineustatic sea level. The primary influence isthat of temperature on seawater density andthe amounts of water in rivers, lakes,glaciers, polar ice caps and sea ice. Overmuch longer geological timescales, changesin the shape of the oceanic basins and inland/sea distribution will also affect sealevel.

Observational and modelling studies ofmass loss from glaciers and ice caps indicatea contribution to sea-level rise of 0.2 to0.4 mm/yr averaged over the 20th century.

Glaciers and ice caps

Each year about 8 mm (0.3 inch) of water from the entire surface of the oceans falls into the Antarctica andGreenland ice sheets as snowfall. If no ice returned to the oceans, sea level would drop 8 mm every year. To a firstapproximation, the same amount of water appeared to return to the ocean in icebergs and from ice melting at theedges. Scientists previously had estimated which is greater, ice going in or coming out, called the mass balance,important because it causes changes in global sea level. High-precision gravimetry from satellites in low-noise flighthas since determined Greenland is losing billions of tons per year, in accordance with loss estimates from groundmeasurement.Ice shelves float on the surface of the sea and, if they melt, to first order they do not change sea level. Likewise, themelting of the northern polar ice cap which is composed of floating pack ice would not significantly contribute torising sea levels. Because they are lower in salinity, however, their melting would cause a very small increase in sealevels, so small that it is generally neglected.• Scientists previously lacked knowledge of changes in terrestrial storage of water. Surveying of water retention by

soil absorption and by reservoirs outright ("impoundment") at just under the volume of Lake Superior agreed witha dam-building peak in the 1930s-1970s timespan. Such impoundment masked tens of millimetres of sea levelrise in that span. ( Impact of Artificial Reservoir Water Impoundment on Global Sea Level. B. F. Chao,* Y. H.Wu, Y. S. Li).

• If small glaciers and polar ice caps on the margins of Greenland and the Antarctic Peninsula melt, the projectedrise in sea level will be around 0.5 m. Melting of the Greenland ice sheet would produce 7.2 m of sea-level rise,and melting of the Antarctic ice sheet would produce 61.1 m of sea level rise.[3] The collapse of the groundedinterior reservoir of the West Antarctic Ice Sheet would raise sea level by 5–6 m.[4]

• The snowline altitude is the altitude of the lowest elevation interval in which minimum annual snow coverexceeds 50%. This ranges from about 5,500 metres above sea-level at the equator down to sea level at about 70°N&S latitude, depending on regional temperature amelioration effects. Permafrost then appears at sea level andextends deeper below sea level polewards.

• As most of the Greenland and Antarctic ice sheets lie above the snowline and/or base of the permafrost zone, theycannot melt in a timeframe much less than several millennia; therefore it is likely that they will not, throughmelting, contribute significantly to sea level rise in the coming century. They can, however, do so throughacceleration in flow and enhanced iceberg calving.

Sea level 26

• Climate changes during the 20th century are estimated from modelling studies to have led to contributions ofbetween –0.2 and 0.0 mm/yr from Antarctica (the results of increasing precipitation) and 0.0 to 0.1 mm/yr fromGreenland (from changes in both precipitation and runoff).

•• Estimates suggest that Greenland and Antarctica have contributed 0.0 to 0.5 mm/yr over the 20th century as aresult of long-term adjustment to the end of the last ice age.

The current rise in sea level observed from tide gauges, of about 1.8 mm/yr, is within the estimate range from thecombination of factors above[5] but active research continues in this field. The terrestrial storage term, thought to behighly uncertain, is no longer positive, and shown to be quite large.

Geological influences

Comparison of two sea level reconstructions during the last 500 Ma. The scale ofchange during the last glacial/interglacial transition is indicated with a black bar.

Note that over most of geologic history, long-term average sea level has beensignificantly higher than today.

At times during Earth's long history, theconfiguration of the continents and seafloorhave changed due to plate tectonics. Thisaffects global sea level by determining thedepths of the ocean basins and howglacial-interglacial cycles distribute iceacross the Earth.

The depth of the ocean basins is a functionof the age of oceanic lithosphere: aslithosphere becomes older, it becomesdenser and sinks. Therefore, a configurationwith many small oceanic plates that rapidlyrecycle lithosphere will produce shallowerocean basins and (all other things beingequal) higher sea levels. A configurationwith fewer plates and more cold, denseoceanic lithosphere, on the other hand, willresult in deeper ocean basins and lower sea levels.

When there were large amounts of continental crust near the poles, the rock record shows unusually low sea levelsduring ice ages, because there was lots of polar land mass upon which snow and ice could accumulate. During timeswhen the land masses clustered around the equator, ice ages had much less effect on sea level.

Over most of geologic time, long-term sea level has been higher than today (see graph above). Only at thePermian-Triassic boundary ~250 million years ago was long-term sea level lower than today. Long term changes insea level are the result of changes in the oceanic crust, with a downward trend expected to continue in the very longterm.[6]

During the glacial/interglacial cycles over the past few million years, sea level has varied by somewhat more than ahundred metres. This is primarily due to the growth and decay of ice sheets (mostly in the northern hemisphere) withwater evaporated from the sea.The Mediterranean Basin's gradual growth as the Neotethys basin, begun in the Jurassic, did not suddenly affectocean levels. While the Mediterranean was forming during the past 100 million years, the average ocean level wasgenerally 200 metres above current levels. However, the largest known example of marine flooding was when theAtlantic breached the Strait of Gibraltar at the end of the Messinian Salinity Crisis about 5.2 million years ago. Thisrestored Mediterranean sea levels at the sudden end of the period when that basin had dried up, apparently due togeologic forces in the area of the Strait.

Sea level 27

Long-term causes Range ofeffect

Vertical effect

Change in volume of ocean basins

Plate tectonics and seafloor spreading (plate divergence/convergence) and change in seafloor elevation(mid-ocean volcanism)

Eustatic 0.01 mm/yr

Marine sedimentation Eustatic < 0.01 mm/yr

Change in mass of ocean water

Melting or accumulation of continental ice Eustatic 10 mm/yr

• Climate changes during the 20th century

•• Antarctica (the results of increasing precipitation) Eustatic -0.2 to0.0 mm/yr

•• Greenland (from changes in both precipitation and runoff) Eustatic 0.0 to 0.1 mm/yr

• Long-term adjustment to the end of the last ice age

•• Greenland and Antarctica contribution over 20th century Eustatic 0.0 to 0.5 mm/yr

Release of water from earth's interior Eustatic

Release or accumulation of continental hydrologic reservoirs Eustatic

Uplift or subsidence of Earth's surface (Isostasy)

Thermal-isostasy (temperature/density changes in earth's interior) Local effect

Glacio-isostasy (loading or unloading of ice) Local effect 10 mm/yr

Hydro-isostasy (loading or unloading of water) Local effect

Volcano-isostasy (magmatic extrusions) Local effect

Sediment-isostasy (deposition and erosion of sediments) Local effect < 4 mm/yr

Tectonic uplift/subsidence

Vertical and horizontal motions of crust (in response to fault motions) Local effect 1–3 mm/yr

Sediment compaction

Sediment compression into denser matrix (particularly significant in and near river deltas) Local effect

Loss of interstitial fluids (withdrawal of groundwater or oil) Local effect ≤ 55 mm/yr

Earthquake-induced vibration Local effect

Departure from geoid

Shifts in hydrosphere, aesthenosphere, core-mantle interface Local effect

Shifts in earth's rotation, axis of spin, and precession of equinox Eustatic

External gravitational changes Eustatic

Evaporation and precipitation (if due to a long-term pattern) Local effect

Sea level 28

Changes through geologic time

Comparison of two sea level reconstructions during the last 500 Ma.The scale of change during the last glacial/interglacial transition isindicated with a black bar. Note that over most of geologic history

long-term average sea level has been significantly higher than today.

Sea level change since the end of the last glacial episode. Changesdisplayed in metres.

Sea level has changed over geologic time. As the graphshows, sea level today is very near the lowest level everattained (the lowest level occurred at thePermian-Triassic boundary about 250 million yearsago).

During the most recent ice age (at its maximum about20,000 years ago) the world's sea level was about130 m lower than today, due to the large amount of seawater that had evaporated and been deposited as snowand ice, mostly in the Laurentide ice sheet. Themajority of this had melted by about 10,000 years ago.

Hundreds of similar glacial cycles have occurredthroughout the Earth's history. Geologists who studythe positions of coastal sediment deposits through timehave noted dozens of similar basinward shifts ofshorelines associated with a later recovery. This resultsin sedimentary cycles which in some cases can becorrelated around the world with great confidence. Thisrelatively new branch of geological science linkingeustatic sea level to sedimentary deposits is calledsequence stratigraphy.

The most up-to-date chronology of sea level changeduring the Phanerozoic shows the following long termtrends:[7]

• Gradually rising sea level through the Cambrian• Relatively stable sea level in the Ordovician, with a

large drop associated with the end-Ordovicianglaciation

• Relative stability at the lower level during the Silurian• A gradual fall through the Devonian, continuing through the Mississippian to long-term low at the

Mississippian/Pennsylvanian boundary• A gradual rise until the start of the Permian, followed by a gentle decrease lasting until the Mesozoic.

Recent changesFor at least the last 100 years, sea level has been rising at an average rate of about 1.8 mm per year.[8] The majorityof this rise can be attributed to the increase in temperature of the sea and a slight resulting thermal expansion of theupper 500m of sea water. Additional contributions, as much as one-fourth of the total, come from water sources onland such as melting snow and glaciers and extraction of groundwater for irrigation and other agricultural and humanneeds. (see global warming).[9]

Sea level 29

AviationUsing pressure to measure altitude results in two other types of altitude. Distance above true or MSL (mean sea level)is the next best measurement to absolute. MSL altitude is the distance above where sea level would be if there wereno land. If one knows the elevation of terrain, the distance above the ground is calculated by a simple subtraction.An MSL altitude—called pressure altitude by pilots—is useful for predicting physiological responses inunpressurized aircraft (see hypoxia). It also correlates with engine, propeller, and wing performance, which alldecrease in thinner air.Pilots can estimate height above terrain with an altimeter set to a defined barometric pressure. Generally, thepressure used to set the altimeter is the barometric pressure that would exist at MSL in the region being flown over.This pressure is referred to as either QNH or "altimeter" and is transmitted to the pilot by radio from air trafficcontrol (ATC) or an Automatic Terminal Information Service (ATIS). Since the terrain elevation is also referencedto MSL, the pilot can estimate height above ground by subtracting the terrain altitude from the altimeter reading.Aviation charts are divided into boxes and the maximum terrain altitude from MSL in each box is clearly indicated.Once above the transition altitude (see below), the altimeter is set to the international standard atmosphere (ISA)pressure at MSL which is 1013.2 HPa or 29.92 inHg.[10]

Flight levelMSL is useful for aircraft to avoid terrain, but at high enough altitudes, there is no terrain to avoid. Above that level,pilots are primarily interested in avoiding each other, so they adjust their altimeter to standard temperature andpressure conditions (average sea level pressure and temperature) and disregard actual barometric pressure—untildescending below transition level. To distinguish from MSL, such altitudes are called flight levels. Standard pilotshorthand is to express flight level as hundreds of feet, so FL 240 is 24000 feet (unknown operator: u'strong' m).Pilots use the international standard pressure setting of 1013.25 hPa (29.92 inHg) when referring to Flight Levels.The altitude at which aircraft are mandated to set their altimeter to flight levels is called "transition altitude". It variesfrom country to country. For example in the U.S. it is 18,000 feet, in many European countries it is 3,000 or 5,000feet.

Notes[1] What is "Mean Sea Level"? (http:/ / www. straightdope. com/ columns/ read/ 148/ what-is-sea-level#1) Proudman Oceanographic Laboratory[2] "Eustatic sea level" (http:/ / www. glossary. oilfield. slb. com/ Display. cfm?Term=eustatic sea level). Oilfield Glossary. Schlumberger

Limited. . Retrieved 10 June 2011.[3] "Some physical characteristics of ice on Earth" (http:/ / www. grida. no/ climate/ ipcc_tar/ wg1/ 412. htm#tab113). Climate Change 2001:

The Scientific Basis. .[4] Geologic Contral on Fast Ice Flow - West Antarctic Ice Sheet (http:/ / www. ldeo. columbia. edu/ ~mstuding/ wais. html). by Michael

Studinger, Lamont-Doherty Earth Observatory[5] GRID-Arendal. "Climate Change 2001: The Scientific Basis" (http:/ / www. grida. no/ climate/ ipcc_tar/ wg1/ 428. htm). . Retrieved

2005-12-19.[6] Müller, R. Dietmar; et al. (2008-03-07). "Long-Term Sea-Level Fluctuations Driven by Ocean Basin Dynamics". Science 319 (5868):

1357–1362. doi:10.1126/science.1151540. PMID 18323446.[7] Haq, B. U.; Schutter, SR (2008). "A Chronology of Paleozoic Sea-Level Changes" (http:/ / www. sciencemag. org/ cgi/ content/ full/ 322/

5898/ 64). Science 322 (5898): 64–8. doi:10.1126/science.1161648. PMID 18832639. .[8] Bruce C. Douglas (1997). "Global Sea Rise: A Redetermination". Surveys in Geophysics 18 (2/3): 279–292. doi:10.1023/A:1006544227856.[9] Bindoff, N.L.; Willebrand, J.; Artale, V.; Cazenave, A.; Gregory, J.; Gulev, S.; Hanawa, K.; Le Quéré, C. et al (2007). "Observations:

Oceanic Climate Change and Sea Level" (http:/ / www. ipcc. ch/ pdf/ assessment-report/ ar4/ wg1/ ar4-wg1-chapter5. pdf). In Solomon, S.;Qin, D.; Manning, M. et al. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth AssessmentReport of the Intergovernmental Panel on Climate Change. Cambridge University Press. .

[10] US Federal Aviation Administration, Code of Federal Regulations Sec. 91.121 (http:/ / rgl. faa. gov/ Regulatory_and_Guidance_Library/rgFar. nsf/ 3276afbe72d00920852566c700670189/ da37f1d83828491d852566cf00615210!OpenDocument)

Sea level 30

External links• Sea Level Rise:Understanding the past - Improving projections for the future (http:/ / www. cmar. csiro. au/

sealevel)• Permanent Service for Mean Sea Level (http:/ / www. pol. ac. uk/ psmsl/ )• Global sea level change: Determination and interpretation (http:/ / www. agu. org/ revgeophys/ dougla01/

dougla01. html)• Environment Protection Agency Sea level rise reports (http:/ / yosemite. epa. gov/ oar/ globalwarming. nsf/

content/ ResourceCenterPublicationsSeaLevelRiseIndex. html)• Properties of isostasy and eustasy (http:/ / www. homepage. montana. edu/ ~geol445/ hyperglac/ sealevel2/ index.

htm)• Measuring Sea Level from Space (http:/ / sealevel. jpl. nasa. gov/ )• Rising Tide Video: Scripps Institution of Oceanography (http:/ / www. scivee. tv/ node/ 8324)• Sea Levels Online: National Ocean Service (CO-OPS) (http:/ / tidesandcurrents. noaa. gov/ sltrends/ sltrends.

shtml)• Système d'Observation du Niveau des Eaux Littorales (SONEL) (http:/ / www. sonel. org/ )• Sea level rise - How much and how fast will sea level rise over the coming centuries? (http:/ / ice. tsu. ru/ index.

php?option=com_content& view=category& layout=blog& id=1& Itemid=138)

Tide table

A tide table for Monterey Bay Aquarium

A tide table, sometimes called a tide chart, is used for tidal predictionand shows the daily times and height of high water and low water for aparticular location. Tide heights at intermediate times (between highand low water) can be approximately calculated using the rule oftwelfths or more accurately by using a published tidal curve for thelocation.

Tide tables are published as small booklets in their own right, as part ofnautical almanacs, on the Internet, in some newspapers (generallythose serving readers in coastal regions or having maritime interests)and as the output of tidal prediction software.

Tide tables are only calculated and published for major commercialports called standard ports. The tides for nearby minor ports can beestimated by time and height differences between a "standard" port andthese minor ports.

The dates of spring tides and neap tides, approximately seven daysapart, can be determined by the heights of the tides on the tide table: asmall range indicates neaps and large indicates springs.

On the Atlantic coast of northwest Europe, the interval between each low and high tide averages about 6 hours and10 minutes, giving two high tides and two low tides each day.

Tide prediction was long beset by the problem of laborious calculations; and in earlier times, before the use of digitalcomputers, official tide tables were often generated by the use of a special-purpose calculating machine, thetide-predicting machine.

Tide table 31

External links• Canadian tide tables (http:/ / www. waterlevels. gc. ca/ english/ Canada. shtml)• Dutch tide tables (http:/ / www. getij. nl/ )• German Bight tide tables (http:/ / www. bsh. de/ de/ Meeresdaten/ Vorhersagen/ Gezeiten/ index. jsp)• UK tide tables (http:/ / www. bbc. co. uk/ weather/ coast/ tides/ )• US tide tables (NOAA) (http:/ / tidesandcurrents. noaa. gov/ )• XTide tide prediction software (http:/ / www. flaterco. com/ xtide/ )• Free Tides Tables, Charts and Scripts for NOAA Coasts and Harbors (http:/ / www. freetidetables. com/ )• Mapped, graphical US tide tables/charts in calendar form from NOAA data (http:/ / tidesite. appspot. com/ )• Tide tables, graphs and maps for US and Canada using XTide (http:/ / gofishingforum. net/ tide_stations. pl)• Tide Wizard - Windows based tide prediction and tide tables software (http:/ / www. smartcomsoftware. com/

tidewizard. html)• Tidely - Tide table web app (http:/ / www. tidely. com)

Slack waterSlack water, which used to be known as 'The stand of the tide', is a short period in a body of tidal water either sideof high water or low water essentially when the water is completely unstressed, and therefore with no rise or fall ofthe tide and no movement either way in the tidal stream, and which occurs before the direction of the tidal streamreverses.[1] Slack water can be estimated using a tide table, a tidal atlas or the tidal diamond information on anautical chart.[2] Tide tables, which tabulate the time of high and low water, are generally only published forStandard Ports. To determine the time of slack water at less important locations, the time difference (or TidalConstant) between the time of high water at the Standard Port and at that location also needs to be known.For scuba divers, the absence of a flow means that less effort is required to swim, and there is less likelihood ofdrifting away from a vessel or shore. Slack water can reduce underwater visibility, as there is no flow to removedebris such as sand or mud. In areas with potentially dangerous tides and currents, it is standard practice for divers toplan a dive at slack times.For any vessel, a favourable flow will improve the vessel's speed over the bottom for a given speed in the water.Difficult channels are also more safely navigated during slack water, as any flow may set a vessel out of a channeland into danger.In many locations, in addition to the tidal streams there is also a current causing the tidal stream in the one directionto be stronger than, and last for longer than the stream in the opposite direction six hours later. Variations in thestrength of that current will also vary the time when the stream reverses, thus altering the time and duration of slackwater. Variations in wind stress also reflect directly on the height of the tide, and the inverse relationship between theheight of the tide and atmospheric pressure is well understood (1 cm change in sea level for each 1 mb change inpressure) while the duration of slack water at a given location is inversely related to the height of the tide at thatlocation.Slack water is a much misused term, often used to describe a period of equilibrium between two opposing streams when the water is anything but slack, but highly stressed. Although there may be no flow in either direction there may be many eddies, and since this so-called slack water occurs before high water while the tide is still rising, the tide may continue to rise even after the direction of the stream has reversed. Conversely, since it occurs after low water while the tide is rising, the tide may also continue to rise during this so-called low water slack period. Such conditions typically occur at river mouths, or in straits open at both ends where their entrances have markedly different physical characteristics. Examples include The Rip between Point Nepean and Point Lonsdale at the entrance to Port Philip Bay, Victoria, Australia; the Menai Strait [3] between Anglesey and Wales; or the Strait of

Slack water 32

Gibraltar at the entrance to the Mediterranean Sea.Slack water may also be misused to refer to a process in caves. This occurs when a stream cave, or fluviokarst, iscompletely filled with water during flooding.

Dodge tidesSome localities have unusual tidal characteristics, such as Gulf St Vincent, South Australia, where the amplitudes ofthe main semi-diurnal tide constituents are almost identical. At neap tides the semi-diurnal tide is virtually absent,resulting in the phenomenon known as a "dodge tide"—a day-long period of slack water—occurring twice a month;this effect is accentuated near the equinoxes when the diurnal component also vanishes, resulting in a period of 2-3days of slack water.[4][5][6]

References[1] The American Practical Navigator, Chapter 9:Tides and Tidal Currents (http:/ / msi. nga. mil/ MSISiteContent/ StaticFiles/ NAV_PUBS/

APN/ Chapt-09. pdf), page 139. Accessed 3 September 2011.[2][2] Sport Diving, British Sub Aqua Club, ISBN 0-09-163831-3, page 167[3] www.lodestoneman.com (http:/ / www. lodestoneman. com/ 2Bdge/ Two_Bridges_Too_Far/ narative/ p_1. htm): Two Bridges Too Far.

Accessed 2 September 2011.[4] Bye, J.A.T. (1976): Physical oceanography of Gulf St Vincent and Investigator Strait. In: Twidale, C.R., Tyler, M.J. & Webb, B.P. (Eds.),

Natural history of the Adelaide Region. Royal Society of SA Inc, Adelaide.[5] Bye, J.A.T. & Kämpf, J. (2008): Physical oceanography. In: Shepherd, S.A., Bryars, S., Kirkegaard, I.R., Harbison, P. & Jennings, J.T.

(Eds.): Natural history of Gulf St Vincent. Royal Society of South Australia Inc, Adelaide.[6] The American Practical Navigator, Chapter 9:Tides and Tidal Currents (http:/ / msi. nga. mil/ MSISiteContent/ StaticFiles/ NAV_PUBS/

APN/ Chapt-09. pdf), pages 134-5. Accessed 3 September 2011.

Bathymetry

Present day Earth bathymetry (and altimetry).Data from the National Geophysical Data

Center's TerrainBase Digital Terrain Model [1].

Bathymetry is the study of underwater depth of lake or ocean floors.In other words, bathymetry is the underwater equivalent to hypsometryor topography. The name comes from Greek βαθύς (bathus), "deep",[2]

and μέτρον (metron), "measure".[3] Bathymetric (or hydrographic)charts are typically produced to support safety of surface or sub-surfacenavigation, and usually show seafloor relief or terrain as contour lines(called depth contours or isobaths) and selected depths (soundings),and typically also provide surface navigational information.Bathymetric maps (a more general term where navigational safety isnot a concern) may also use a Digital Terrain Model and artificialillumination techniques to illustrate the depths being portrayed.Paleobathymetry is the study of past underwater depths.

Bathymetry 33

Measurement

First printed map of oceanic bathymetry, produced with data fromUSS Dolphin (1836)

Originally, bathymetry involved the measurement ofocean depth through depth sounding. Early techniquesused pre-measured heavy rope or cable lowered over aship's side.This technique measures the depth only asingle point at a time, and so is inefficient. It is alsosubject to movements of the ship and currents movingthe line out of true and therefore is inaccurate.

The data used to make bathymetric maps todaytypically comes from an echosounder (sonar) mountedbeneath or over the side of a boat, "pinging" a beam ofsound downward at the seafloor or from remote sensingLIDAR or LADAR systems.[4] The amount of time ittakes for the sound or light to travel through the water,bounce off the seafloor, and return to the sounder tellsthe equipment what the distance to the seafloor is. LIDAR/LADAR surveys are usually conducted by airbornesystems.

The seafloor topography near the Puerto Rico Trench

Starting in the early 1930s, single-beam sounders wereused to make bathymetry maps. Today, multibeamechosounders (MBES) are typically used, which usehundreds of very narrow adjacent beams arranged in afan-like swath of typically 90 to 170 degrees across.The tightly packed array of narrow individual beamsprovides very high angular resolution and accuracy. Ingeneral a wide swath, which is depth dependent, allowsa boat to map more seafloor in less time than asingle-beam echosounder by making fewer passes. Thebeams update many times per second (typically 0.1-50Hz depending on water depth), allowing faster boatspeed while maintaining 100% coverage of theseafloor. Attitude sensors allow for the correction of the boat's roll, pitch and yaw on the ocean surface, and agyrocompass provides accurate heading information to correct for vessel yaw. (Most modern MBES systems use anintegrated motion-sensor and position system that measures yaw as well as the other dynamics and position.) Aboat-mounted Global Positioning System (GPS) (or other Global Navigation Satellite System (GNSS)) positions thesoundings with respect to the surface of the earth. Sound speed profiles (speed of sound in water as a function ofdepth) of the water column correct for refraction or "ray-bending" of the sound waves owing to non-uniform watercolumn characteristics such as temperature, conductivity, and pressure. A computer system processes all the data,correcting for all of the above factors as well as for the angle of each individual beam. The resulting soundingmeasurements are then processed either manually, semi-automatically or automatically (in limited circumstances) toproduce a map of the area. As of 2010 a number of different outputs are generated, including a sub-set of the originalmeasurements that satisfy some conditions (e.g., most representative likely soundings, shallowest in a region, etc.) orintegrated Digital Terrain Models (DTM) (e.g., a regular or irregular grid of points connected into a surface).Historically, selection of measurements was more common in hydrographic applications while DTM constructionwas used for engineering surveys, geology, flow modeling, etc. Since ca. 2003-2005, DTMs have become moreaccepted in hydrographic practice.

Bathymetry 34

Satellites are also used to measure bathymetry. Satellite radar maps deep-sea topography by detecting the subtlevariations in sea level caused by the gravitational pull of undersea mountains, ridges, and other masses. On average,sea level is higher over mountains and ridges than over abyssal plains and trenches.[5]

In the United States the United States Army Corps of Engineers performs or commissions most surveys of navigableinland waterways, while the National Oceanic and Atmospheric Administration (NOAA) performs the same role forocean waterways. Coastal bathymetry data is available from NOAA's National Geophysical Data Center (NGDC)[6].[7] Bathymetric data is usually referenced to tidal vertical datums.[8] For deep-water bathymetry, this is typicallyMean Sea Level (MSL), but most data used for nautical charting is referenced to Mean Lower Low Water (MLLW)in American surveys, and Lowest Astronomical Tide (LAT) in other countries. Many other datums are used inpractice, depending on the locality and tidal regime.Occupations or careers related to bathymetry include the study of oceans and rocks and minerals on the ocean floor,and the study of underwater earthquakes or volcanoes. The taking and analysis of bathymetric measurements is oneof the core areas of modern hydrography, and a fundamental component in ensuring the safe transport of goodsworldwide.

References[1] http:/ / www. ngdc. noaa. gov/ seg/ fliers/ se-1104. shtml[2] βαθύς (http:/ / www. perseus. tufts. edu/ hopper/ text?doc=Perseus:text:1999. 04. 0057:entry=baqu/ s), Henry George Liddell, Robert Scott, A

Greek-English Lexicon, on Perseus[3] μέτρον (http:/ / www. perseus. tufts. edu/ hopper/ text?doc=Perseus:text:1999. 04. 0057:entry=me/ tron), Henry George Liddell, Robert Scott,

A Greek-English Lexicon, on Perseus[4] Olsen, R. C. (2007), Remote Sensing from Air and Space, SPIE, ISBN 978-0-8194-6235-0[5] Thurman, H. V. (1997), Introductory Oceanography, New Jersey, USA: Prentice Hall College, ISBN 0-13-262072-3[6] http:/ / www. ngdc. noaa. gov[7] NGDC-Bathymetry, Topography, & Relief (http:/ / www. ngdc. noaa. gov/ mgg/ bathymetry/ relief. html)[8] NGDC/WDC MGG, Boulder-Coastal relief model development (http:/ / www. ngdc. noaa. gov/ mgg/ coastal/ model. html)

External links• Overview for underwater terrain, data formats, etc. (http:/ / www. vterrain. org/ Elevation/ Bathy/ ) (vterrain.org)• High resolution bathymetry for the Great Barrier Reef and Coral Sea (http:/ / e-atlas. org. au/ content/

gbr_jcu_bathymetry-3dgbr)• A.PO.MA.B.-Academy of Positioning Marine and Bathymetry (http:/ / apomabdoc. altervista. org/ index. html)

Lunitidal interval 35

Lunitidal intervalThe lunitidal interval,[1] measures the time lag from the moon passing overhead, to the next high or low tide. It isalso called the high water interval (HWI)/[2][3]

Tides are known to be mainly caused by the moon's gravity. Theoretically, peak tidal forces at a given location occurwhen the moon is at the meridian, but there is usually a delay before high tide that depends largely on the shape ofthe coastline, and the sea floor, therefore, the lunitidal interval varies from place to place. The lunitidal intervalfurther varies within about +/- 30 minutes according to the lunar phase.The approximate lunitidal interval can be calculated if the moon-rise, moon-set and high tide times are known for alocation. In the northern hemisphere, the moon is at its highest point when it is southernmost in the sky. Lunar dataare available from printed tables and online [4]. Tide tables tell the time of the next high water [5] [6]. The differencebetween these two times is the lunitidal interval. This value can be used to calibrate certain clocks and wristwatchesto allow for simple but crude tidal predictions.

References[1] Australian Hydrographic Service definition (http:/ / www. hydro. gov. au/ prodserv/ tides/ lunitidal-intervals. htm)[2] NOAA HWI definition (http:/ / tidesandcurrents. noaa. gov/ datum_options. html)[3] Proudman Oceanographic laboratory definition (http:/ / www. pol. ac. uk/ ntslf/ sharing_knowledge. php)[4] Time And Date (http:/ / www. timeanddate. com)[5] UK Tidal Predictions (http:/ / www. pol. ac. uk/ ntslf/ tidalp. html)[6] NOAA Tides & Currents (http:/ / tidesandcurrents. noaa. gov/ tide_predictions. shtml)

External links• HWI Datum table for locations in the US (http:/ / co-ops. nos. noaa. gov/ station_retrieve. shtml?type=Datums&

sort=A. STATION_ID& state=& id1=)• HWI table for UK (http:/ / www. pol. ac. uk/ ntslf/ sharing_knowledge. php)• HWI map for france (http:/ / www. shom. fr/ fr_page/ fr_act_oceano/ img/ etablissement_moyen. jpg)• Table of values for Australia (http:/ / www. hydro. gov. au/ prodserv/ tides/ lunitidal-intervals. htm)• Values for the Netherlands (http:/ / live. waternormalen. nl/ waternormalen_waterstanden. cfm?taal=en)

Amphidromic point 36

Amphidromic pointAn amphidromic point is a point of zero amplitude of one harmonic constituent of the tide.[1] The tidal range (theamplitude, or height difference between high tide and low tide) for that harmonic constituent increases with distancefrom this point.[2] These points are sometimes called tidal nodes.The term amphidromic point derives from the Greek words amphi (around) and dromos (running), referring to therotary tides running around them.[3]

The M2 tidal constituent, the amplitude indicated by color. The white lines are cotidallines spaced at phase intervals of 30° (a bit over 1 hr).[4] The amphidromic points are the

dark blue areas where the lines come together.

Amphidromic points occur because ofthe Coriolis effect and interferencewithin oceanic basins, seas and bayscreating a wave pattern — called anamphidromic system — which rotatesaround the amphidromic point.[5][6] Atthe amphidromic points of thedominant tidal constituent, there isalmost no vertical movement fromtidal action. There can be tidal currentsas the water levels on either side of theamphidromic point are not the same. Aseparate amphidromic system iscreated by each periodic tidalcomponent.[7]

In most locations M2 is the largest(semidiurnal) tidal constituent, with an amplitude of roughly half of the full tidal range. Cotidal points means theyreach high tide at the same time and low tide at the same time. In the accompanying figure, the low tide lags or leadsby 1 hr 2 min from its neighboring lines. Where the lines meet are amphidromes and the tide rotates around them; forexample: along the Chilean coast, and from southern Mexico to Peru the tide propagates southward, while from BajaCalifornia to Alaska the tide propagates northward.

Amphidromic points in the M2 tidal constituentBased on the accompanying figure, the set of clockwise amphidromic points includes:• north of the Seychelles• near Enderby Land• off Perth• east of New Guinea• south of Easter Island• west of the Galapagos Islands• north of Queen Maud LandCounterclockwise amphidromic points include:• near Sri Lanka• north of New Guinea• at Tahiti• between Mexico and Hawaii• near the Leeward Islands

Amphidromic point 37

• east of Newfoundland• midway between Rio de Janeiro and Angola• east of IcelandThe islands of Madagascar and New Zealand are amphidromic points in the sense that the tide goes around them(counterclockwise in both cases) in about 12 and a half hours, but the amplitude of the tides on their coasts is insome places large.Note that the rotational direction of tides around an amphidromic point bears no relationship to its location relative tothe equator.

References and notes[1] http:/ / journals. hil. unb. ca/ index. php/ ag/ article/ view/ 729/ 1081[2] https:/ / www. e-education. psu. edu/ earth540/ content/ c6_p1. html[3] Cartwright, David Edgar (2000). Tides: A Scientific History. Cambridge University Press. p. 243. ISBN 978-0-521-79746-7.[4] Picture credit: R. Ray, TOPEX/Poseidon: Revealing Hidden Tidal Energy (http:/ / svs. gsfc. nasa. gov/ stories/ topex/ tides. html) GSFC,

NASA. Redistribute with credit to R. Ray, as well as NASA-GSFC, NASA-JPL, Scientific Visualization Studio, and Television ProductionNASA-TV/GSFC

[5] https:/ / www. e-education. psu. edu/ earth540/ content/ c6_p1. html[6] http:/ / www. salemstate. edu/ ~lhanson/ gls214/ gls214_tides. html[7] http:/ / ffden-2. phys. uaf. edu/ 645fall2003_web. dir/ ellie_boyce/ amphidromic. htm

Tidal force

Figure 1: Comet Shoemaker-Levy 9 in 1994 after breaking up under the influenceof Jupiter's tidal forces during a previous pass in 1992.

The tidal force is a secondary effect of theforce of gravity and is responsible for thetides. It arises because the gravitationalforce per unit mass exerted on one body bya second body is not constant across itsdiameter, the side nearest to the secondbeing more attracted by it than the sidefarther away. Stated differently, the tidalforce is a differential force. Consider threethings being pulled by the moon: the oceansnearest the moon, the solid earth, and the oceans farthest from the moon. The moon pulls on the solid earth, but itpulls harder on the near oceans, so they approach the moon more causing a high tide; and the moon pulls least of allon the far oceans (on the other side of the planet), so they stay behind more, causing another high tide at the sametime. If we imagine looking at the Earth from space, we see that the whole Earth was pulled, but the near oceansmore and the far oceans less; the far oceans stayed behind since they are pulled less (since they are farther away).

In a more general usage in celestial mechanics, the expression 'tidal force' can refer to a situation in which a body ormaterial (for example, tidal water, or the Moon) is mainly under the gravitational influence of a second body (forexample, the Earth), but is also perturbed by the gravitational effects of a third body (for example, by the Moon inthe case of tidal water, or by the Sun in the case of the Moon). The perturbing force is sometimes in such cases calleda tidal force[1] (for example, the perturbing force on the Moon): it is the difference between the force exerted by thethird body on the second and the force exerted by the third body on the first.[2]

Tidal force 38

Explanation

Figure 2: The Moon's gravity differential field at the surface of theEarth is known (along with another and weaker differential effect due tothe Sun) as the Tide Generating Force. This is the primary mechanism

driving tidal action, explaining two tidal equipotential bulges, andaccounting for two high tides per day. In this figure, the Moon is either

on the right side or on the left side of the Earth (at center). The outwarddirection of the arrows on the right and left indicates that where theMoon is overhead (or at the nadir) its perturbing force opposes andweakens the Earth's net attraction; and the inward direction of the

arrows at top and bottom indicates that where the Moon is 90 degreesaway from overhead, its perturbing effect reinforces and strengthens the

Earth's net attraction.

When a body (body 1) is acted on by the gravity ofanother body (body 2), the field can varysignificantly on body 1 between the side of the bodyfacing body 2 and the side facing away from body 2.Figure 2 shows the differential force of gravity on aspherical body (body 1) exerted by another body(body 2). These so called tidal forces cause strains onboth bodies and may distort them or even, in extremecases, break one or the other apart.[3] The Roche limitis the distance from a planet at which tidal effectswould cause an object to disintegrate because thedifferential force of gravity from the planetovercomes the attraction of the parts of the object forone another.[4] These strains would not occur if thegravitational field were uniform, because a uniformfield only causes the entire body to acceleratetogether in the same direction and at the same rate.

Effects of tidal forces

Figure 3: Saturn's rings are inside the orbits of its largest moons. Tidal forcesoppose the material in the rings from coalescing gravitationally to form moons.[5]

In the case of an infinitesimally small elasticsphere, the effect of a tidal force is to distortthe shape of the body without any change involume. The sphere becomes an ellipsoidwith two bulges, pointing towards and awayfrom the other body. Larger objects distortinto an ovoid, and are slightly compressed,which is what happens to the Earth's oceansunder the action of the Moon. The Earth andMoon rotate about their common center ofmass or barycenter, and their gravitationalattraction provides the centripetal forcenecessary to maintain this motion. To anobserver on the Earth, very close to thisbarycenter, the situation is one of the Earthas body 1 acted upon by the gravity of theMoon as body 2. All parts of the Earth aresubject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sidesnear the Moon and far from the Moon.[6]

Tidal force 39

When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotationalkinetic energy as heat. If the body is close enough to its primary, this can result in a rotation which is tidally lockedto the orbital motion, as in the case of the Earth's moon. Tidal heating produces dramatic volcanic effects on Jupiter'smoon Io. Stresses caused by tidal forces also cause a regular monthly pattern of moonquakes on Earth's Moon.Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy towardthe poles. It has been suggested that in addition to other factors, harmonic beat variations in tidal forcing maycontribute to climate changes.[7]

Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes,where they are responsible for the "spaghettification" of infalling matter. Tidal forces create the oceanic tide ofEarth's oceans, where the attracting bodies are the Moon and, to a lesser extent, the Sun.Tidal forces are also responsible for tidal locking and tidal acceleration.

Mathematical treatmentFor a given (externally-generated) gravitational field, the tidal acceleration at a point with respect to a body isobtained by vectorially subtracting the gravitational acceleration at the center of the body (due to the givenexternally-generated field) from the gravitational acceleration (due to the same field) at the given point.Correspondingly, the term tidal force is used to describe the forces due to tidal acceleration. Note that for thesepurposes the only gravitational field considered is the external one; the gravitational field of the body (as shown inthe graphic) is not relevant. (In other words the comparison is with the conditions at the given point as they would beif there were no externally-generated field acting unequally at the given point and at the center of the reference body.The externally-generated field is usually that produced by a perturbing third body, often the Sun or the Moon in thefrequent example-cases of points on or above the Earth's surface in a geocentric reference frame.).

Figure 4: Graphic of tidal forces; the gravity fieldis generated by a body to the right. The top

picture shows the gravitational forces; the bottomshows their residual once the field of the sphere issubtracted; this is the tidal force. See Figure 2 for

a more exact version

Tidal acceleration does not require rotation or orbiting bodies; forexample, the body may be freefalling in a straight line under theinfluence of a gravitational field while still being influenced by(changing) tidal acceleration.

By Newton's law of universal gravitation and laws of motion, a body ofmass m a distance R from the center of a sphere of mass M feels a force

equivalent to an acceleration , where:

. . . , and . . . . . . ,

where is a unit vector pointing from the body M to the body m (here,acceleration from m towards M has negative sign).

Consider now the acceleration due to the sphere of mass Mexperienced by a particle in the vicinity of the body of mass m. With Ras the distance from the center of M to the center of m, let ∆r be the(relatively small) distance of the particle from the center of the body ofmass m. For simplicity, distances are first considered only in thedirection pointing towards or away from the sphere of mass M. If thebody of mass m is itself a sphere of radius ∆r, then the new particle considered may be located on its surface, at adistance (R ± ∆r) from the centre of the sphere of mass M, and ∆r may be taken as positive where the particle'sdistance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by theparticle towards m on account of m's own mass, we have the acceleration on the particle due to gravitational forcetowards M as:

Tidal force 40

Pulling out the R2 term from the denominator gives:

The Maclaurin series of 1/(1 + x)2 is 1 – 2x + 3x2 – ..., which gives a series expansion of:

The first term is the gravitational acceleration due to M at the center of the reference body , i.e. at the pointwhere is zero. This term does not affect the observed acceleration of particles on the surface of m because withrespect to M, m (and everything on its surface) is in free fall. When the force on the far particle is subtracted from theforce on the near particle, this first term cancels, as do all other even-order terms. The remaining (residual) termsrepresent the difference mentioned above and are tidal force (acceleration) terms. When ∆r is small compared to R,the terms after the first residual term are very small and can be neglected, giving the approximate tidal acceleration

(axial) for the distances ∆r considered, along the axis joining the centers of m and M:

(axial)

When calculated in this way for the case where ∆r is a distance along the axis joining the centers of m and M, isdirected outwards from to the center of m (where ∆r is zero).Tidal accelerations can also be calculated away from the axis connecting the bodies m and M, requiring a vectorcalculation. In the plane perpendicular to that axis, the tidal acceleration is directed inwards (towards the centerwhere ∆r is zero), and its magnitude is (axial) in linear approximation as in Figure 2.The tidal accelerations at the surface of planets in the Solar System are generally very small. For example, the lunartidal acceleration at the Earth's surface along the Moon-Earth axis is about 1.1 × 10−7 g, while the solar tidalacceleration at the Earth's surface along the Sun-Earth axis is about 0.52 × 10−7 g, where g is the gravitationalacceleration at the Earth's surface. Modern estimates put the size of the tide-raising force (acceleration) due to theSun at about 45% of that due to the Moon.[8] The solar tidal acceleration at the Earth's surface was first given byNewton in the 'Principia'[9]

Relation with centrifugal forceIf a secondary body orbits a primary body, the forces that could tear the second body apart if its strength and internalgravity are not enough, are the tidal force and the "centrifugal force" associated with any rotation of the secondarybody about its axis.

References[1] "On the tidal force" (http:/ / adsabs. harvard. edu/ full/ 1977SvAL. . . . 3. . . 96A), I N Avsiuk, in "Soviet Astronomy Letters", vol.3 (1977),

pp.96-99[2] See p.509 in "Astronomy: a physical perspective" (http:/ / books. google. com/ books?id=2QVmiMW0O0MC& pg=PA509& lpg=PA509&

dq="tidal+ force"+ perturb& source=bl& ots=46yDoQd9k7& sig=bep2Wi1UfMQhsfmHAd1N2VfWTso& hl=en&ei=J1GYSvTeDIKNjAe8lvm_BQ& sa=X& oi=book_result& ct=result& resnum=10#v=onepage& q="tidal force" perturb& f=false), M LKutner (2003).

[3] R Penrose (1999). The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (http:/ / books. google. com/books?id=oI0grArWHUMC& pg=PA264& vq=tidal& dq=tidal+ force). Oxford University Press. p. 264. ISBN 0-19-286198-0. .

[4] Thérèse Encrenaz, J -P Bibring, M Blanc (2003). The Solar System (http:/ / books. google. com/ books?id=Je61Y7UbqWgC& pg=PA16&vq=tide& dq=tidal+ force#PPA16,M1). Springer. p. 16. ISBN 3-540-00241-3. .

[5] R. S. MacKay, J. D. Meiss (1987). Hamiltonian Dynamical Systems: A Reprint Selection (http:/ / books. google. com/books?id=uTeqNsyj86QC& pg=PA36& dq=tidal+ force). CRC Press. p. 36. ISBN 0-85274-205-3. .

Tidal force 41

[6] Rollin A Harris (1920). The Encyclopedia Americana: A Library of Universal Knowledge (http:/ / books. google. com/books?id=r8BPAAAAMAAJ& pg=PA612& dq=tidal+ force#PPA612,M1) (Vol. 26 ed.). Encyclopedia Americana Corp.. pp. 611–617. .

[7] "Millennial Climate Variability: Is There a Tidal Connection?" (http:/ / ams. allenpress. com/ archive/ 1520-0442/ 15/ 4/ pdf/i1520-0442-15-4-370. pdf). .

[8] Gran Bretaña (1987). Admiralty manual of navigation, Volume 1 (http:/ / books. google. com/ books?id=GCgXCxG4VLcC). The StationeryOffice. p. 277. ISBN 0-11-772880-2. ., Chapter 11, p. 277 (http:/ / books. google. com/ books?id=GCgXCxG4VLcC& pg=PA277)

[9] Newton, Isaac (1729). The mathematical principles of natural philosophy, Volume 2 (http:/ / books. google. com/ books?id=6EqxPav3vIsC).p. 307. ISBN 0-11-772880-2. ., Book 3, Proposition 36, Page 307 (http:/ / books. google. com/ books?id=6EqxPav3vIsC& pg=PA307)Newton put the force to depress the sea at places 90 degrees distant from the Sun at "1 to 38604600" (in terms of g), and wrote that the forceto raise the sea along the Sun-Earth axis is "twice as great", i.e. 2 to 38604600, which comes to about 0.52 × 10-7 g as expressed in the text.

External links• Gravitational Tides (http:/ / burro. astr. cwru. edu/ Academics/ Astr221/ Gravity/ tides. html) by J. Christopher

Mihos of Case Western Reserve University• Audio: Cain/Gay - Astronomy Cast (http:/ / www. astronomycast. com/ solar-system/ episode-47-tidal-forces/ )

Tidal Forces - July 2007.

Theory of tidesThe theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations ofplanetary and satellite bodies and their atmospheres and oceans, under the gravitational loading of anotherastronomical body or bodies. It commonly refers to the fluid dynamic motions for the Earth's oceans.

Origin of theoryIn 1616, Galileo Galilei wrote Discourse on the Tides (in Italian: Discorso del flusso e reflusso del mare),[1] a paperin which he tried to explain the occurrence of the tides as the result of the Earth's rotation around the Sun. However,Galileo's theory was, in the later Newtonian terms, an error.[1] Later analysis over the centuries had led to the currenttidal physics.

Tidal physics

Tidal forcing

A. Lunar gravitational potential: thisdepicts the Moon directly over 30° N (or30° S) viewed from above the Northern

Hemisphere.

B. This view shows same potential from180° from view A. Viewed from abovethe Northern Hemisphere. Red up, blue

down.

Theory of tides 42

The forces discussed here apply to body (Earth tides), oceanic and atmospheric tides. Atmospheric tides on Earth,however, tend to be dominated by forcing due to solar heating.On the planet (or satellite) experiencing tidal motion consider a point at latitude and longitude at distance from the center of mass, then this point can be written in cartesian coordinates as where

Let be the declination and be the right ascension of the deforming body, the Moon for example, then thevector direction is

and be the orbital distance between the center of masses and the mass of the body. Then the force on thepoint is

where For a circular orbit the angular momentum centripetal acceleration balances gravity at the planetary center ofmass

where is the distance between the center of mass for the orbit and planet and is the planetary mass.Consider the point in the reference fixed without rotation, but translating at a fixed translation with respect to thecenter of mass of the planet. The body's centripetal force acts on the point so that the total force is

Substituting for center of mass acceleration, and reordering

In ocean tidal forcing, the radial force is not significant, the next step is to rewrite the coefficient. Let

then

where is the inner product determining the angle z of the deforming body or Moon from thezenith. This means that

if ε is small. If particle is on the surface of the planet then the local gravity is and set .

which is a small fraction of . Note also that force is attractive toward the Moon when the and repulsivewhen .This can also be used to derive a tidal potential.

Theory of tides 43

Laplace's tidal equationsin 1776, Pierre-Simon Laplace formulated a single set of linear partial differential equations, for tidal flow describedas a barotropic two-dimensional sheet flow. Coriolis effects are introduced as well as lateral forcing by gravity.Laplace obtained these equations by simplifying the fluid dynamic equations. But they can also be derived fromenergy integrals via Lagrange's equation.For a fluid sheet of average thickness D, the vertical tidal elevation ς, as well as the horizontal velocity components uand v (in the latitude φ and longitude λ directions, respectively) satisfy Laplace's tidal equations[2][3]:

where Ω is the angular frequency of the planet's rotation, g is the planet's gravitational acceleration at the mean oceansurface, and U is the external gravitational tidal-forcing potential.William Thomson (Lord Kelvin) rewrote Laplace's momentum terms using the curl to find an equation for vorticity.Under certain conditions this can be further rewritten as a conservation of vorticity.

Tidal analysis and prediction

Harmonic analysisLaplace's improvements in theory were substantial, but they still left prediction in an approximate state. This positionchanged in the 1860s when the local circumstances of tidal phenomena were more fully brought into account byWilliam Thomson's application of Fourier analysis to the tidal motions. Thomson's work in this field was thenfurther developed and extended by George Darwin: Darwin's work was based on the lunar theory current in his time.His symbols for the tidal harmonic constituents are still used. Darwin's harmonic developments of thetide-generating forces were later brought up to date with modern developments by A T Doodson whose developmentof the tide generating potential (TGP) in harmonic form was carried out and published in 1921:[4] Doodsondistinguished 388 tidal frequencies.[5] Doodson's analysis of 1921 was based on the then-latest lunar theory of E WBrown.[6]

Doodson devised a practical system for specifying the different harmonic components of the tide-generatingpotential, the Doodson Numbers, a system still in use.[7]

Since the mid-twentieth century further analysis has generated many more terms than Doodson's 388. About 62constituents are of sufficient size to be considered for possible use in marine tide prediction, but sometimes manyless even than that can predict tides to useful accuracy. The calculations of tide predictions using the harmonicconstituents are laborious, and from the 1870s to about the 1960s they were carried out using a mechanicaltide-predicting machine, a special-purpose form of analog computer now superseded in this work by digitalelectronic computers that can be programmed to carry out the same computations.

Theory of tides 44

Tidal constituentsTidal constituents combine to give an endlessly-varying aggregate because of their different and incommensurablefrequencies: the effect is visualized in an animation of the American Mathematical Society [8] illustrating the way inwhich the components used to be mechanically combined in the tide-predicting machine. Amplitudes of tidalconstituents are given below for the following example locations:

ME Eastport,MS Biloxi,PR San Juan,AK Kodiak,CA San Francisco, andHI Hilo.

Higher harmonics Darwin Period Phase Doodson coefs Doodson Amplitude at example location(cm)

NOAA

Species Symbol (hr) rate(°/hr) n1

(L)n2(m)

n3(y)

n4(mp)

number ME MS PR AK CA HI order

Shallow waterovertides of principallunar

M4 6.210300601 57.9682084 4 455.555 6.0 0.6 0.9 2.3 5

Shallow waterovertides of principallunar

M6 4.140200401 86.9523127 6 655.555 5.1 0.1 1.0 7

Shallow waterterdiurnal

MK3 8.177140247 44.0251729 3 1 365.555 0.5 1.9 8

Shallow waterovertides of principalsolar

S4 6 60 4 4 -4 491.555 0.1 9

Shallow water quarterdiurnal

MN4 6.269173724 57.4238337 4 -1 1 445.655 2.3 0.3 0.9 10

Shallow water overtidesof principal solar

S6 4 90 6 6 -6 * 0.1 12

Lunar terdiurnal M3 8.280400802 43.4761563 3 355.555 0.5 32

Shallow waterterdiurnal

2"MK3 8.38630265 42.9271398 3 -1 345.555 0.5 0.5 1.4 34

Shallow water eighthdiurnal

M8 3.105150301 115.9364166 8 855.555 0.5 0.1 36

Shallow water quarterdiurnal

MS4 6.103339275 58.9841042 4 2 -2 473.555 1.8 0.6 1.0 37

Semi-diurnal Darwin Period Phase Doodson coefs Doodson Amplitude at example location(cm)

NOAA

Species Symbol (hr) (°/hr) n1(L)

n2(m)

n3(y)

n4(mp)

number ME MS PR AK CA HI order

Principal lunarsemidiurnal

M2 12.4206012 28.9841042 2 255.555 268.7 3.9 15.9 97.3 58.0 23.0 1

Principal solarsemidiurnal

S2 12 30 2 2 -2 273.555 42.0 3.3 2.1 32.5 13.7 9.2 2

Theory of tides 45

Larger lunar ellipticsemidiurnal

N2 12.65834751 28.4397295 2 -1 1 245.655 54.3 1.1 3.7 20.1 12.3 4.4 3

Larger lunar evectional ν2 12.62600509 28.5125831 2 -1 2 -1 247.455 12.6 0.2 0.8 3.9 2.6 0.9 11

Variational MU2 12.8717576 27.9682084 2 -2 2 237.555 2.0 0.1 0.5 2.2 0.7 0.8 13

Lunar ellipticalsemidiurnalsecond-order

2"N2 12.90537297 27.8953548 2 -2 2 235.755 6.5 0.1 0.5 2.4 1.4 0.6 14

Smaller lunar evectional λ2 12.22177348 29.4556253 2 1 -2 1 263.655 5.3 0.1 0.7 0.6 0.2 16

Larger solar elliptic T2 12.01644934 29.9589333 2 2 -3 272.555 3.7 0.2 0.1 1.9 0.9 0.6 27

Smaller solar elliptic R2 11.98359564 30.0410667 2 2 -1 274.555 0.9 0.2 0.1 0.1 28

Shallow watersemidiurnal

2SM2 11.60695157 31.0158958 2 4 -4 291.555 0.5 31

Smaller lunar ellipticsemidiurnal

L2 12.19162085 29.5284789 2 1 -1 265.455 13.5 0.1 0.5 2.4 1.6 0.5 33

Lunisolar semidiurnal K2 11.96723606 30.0821373 2 2 275.555 11.6 0.9 0.6 9.0 4.0 2.8 35

Diurnal Darwin Period Phase Doodson coefs Doodson Amplitude at example location(cm)

NOAA

Species Symbol (hr) (°/hr) n1

(L)n2(m)

n3(y)

n4(mp)

number ME MS PR AK CA HI order

Lunar diurnal K1 23.93447213 15.0410686 1 1 165.555 15.6 16.2 9.0 39.8 36.8 16.7 '4

Lunar diurnal O1 25.81933871 13.9430356 1 -1 145.555 11.9 16.9 7.7 25.9 23.0 9.2 6

Lunar diurnal OO1 22.30608083 16.1391017 1 3 185.555 0.5 0.7 0.4 1.2 1.1 0.7 15

Solar diurnal S1 24 15 1 1 -1 164.555 1.0 0.5 1.2 0.7 0.3 17

Smaller lunar ellipticdiurnal

M1 24.84120241 14.4920521 1 155.555 0.6 1.2 0.5 1.4 1.1 0.5 18

Smaller lunar ellipticdiurnal

J1 23.09848146 15.5854433 1 2 -1 175.455 0.9 1.3 0.6 2.3 1.9 1.1 19

Larger lunar evectionaldiurnal

ρ 26.72305326 13.4715145 1 -2 2 -1 137.455 0.3 0.6 0.3 0.9 0.9 0.3 25

Larger lunar ellipticdiurnal

Q1 26.868350 13.3986609 1 -2 1 135.655 2.0 3.3 1.4 4.7 4.0 1.6 26

Larger elliptic diurnal 2Q1 28.00621204 12.8542862 1 -3 2 125.755 0.3 0.4 0.2 0.7 0.4 0.2 29

Solar diurnal P1 24.06588766 14.9589314 1 1 -2 163.555 5.2 5.4 2.9 12.6 11.6 5.1 30

Long period Darwin Period Phase Doodson coefs Doodson Amplitude at example location(cm)

NOAA

Species Symbol (hr) (°/hr) n1(L)

n2(m)

n3(y)

n4(mp)

number ME MS PR AK CA HI order

Lunar monthly Mm 661.3111655 0.5443747 0 1 -1 65.455 0.7 1.9 20

Solar semiannual Ssa 4383.076325 0.0821373 0 2 57.555 1.6 2.1 1.5 3.9 21

Solar annual Sa 8766.15265 0.0410686 0 1 56.555 5.5 7.8 3.8 4.3 22

Lunisolar synodicfortnightly

Msf 354.3670666 1.0158958 0 2 -2 73.555 1.5 23

Lunisolar fortnightly Mf 327.8599387 1.0980331 0 2 75.555 1.4 2.0 0.7 24

Theory of tides 46

References[1] Rice University - Galileo's Theory of the Tides (http:/ / galileo. rice. edu/ sci/ observations/ tides. html) - by Rossella Gigli, retrieved 10

March 2010[2] http:/ / kiwi. atmos. colostate. edu/ group/ dave/ pdf/ LTE. frame. pdf[3] http:/ / siam. org/ pdf/ news/ 621. pdf[4][4] A T Doodson (1921), "The Harmonic Development of the Tide-Generating Potential", Proceedings of the Royal Society of London. Series A,

Vol. 100, No. 704 (Dec. 1, 1921), pp. 305-329.[5][5] S Casotto, F Biscani, "A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession,

nutation, and perturbations due to figure and planetary terms", AAS Division on Dynamical Astronomy, April 2004, vol.36(2), 67.[6] D E Cartwright, "Tides: a scientific history", Cambridge University Press 2001, at pages 163-4 (http:/ / books. google. com/

books?id=sSesNjG96JYC& pg=PA163).[7][7] See e.g. T D Moyer (2003), "Formulation for observed and computed values of Deep Space Network data types for navigation", vol.3 in

Deep-space communications and navigation series, Wiley (2003), e.g. at pp.126-8.[8] http:/ / www. ams. org/ featurecolumn/ archive/ tidesIII3. html

Tidal acceleration

A picture of the Earth and the Moon from Mars. Thepresence of the moon (which has about 1/81 the mass

of the Earth), is slowing Earth's rotation andlengthening the day by about 2 ms every one hundred

years.

Tidal acceleration is an effect of the tidal forces between anorbiting natural satellite (e.g. the Moon), and the primary planetthat it orbits (e.g. the Earth). The acceleration is usually negative,as it causes a gradual slowing and recession of a satellite in aprograde orbit away from the primary, and a correspondingslowdown of the primary's rotation. The process eventually leadsto tidal locking of first the smaller, and later the larger body. TheEarth-Moon system is the best studied case.

The similar process of tidal deceleration occurs for satellites thathave an orbital period that is shorter than the primary's rotationalperiod, or that orbit in a retrograde direction.

Earth-Moon system

Discovery history of the secular acceleration

Edmond Halley was the first to suggest, in 1695,[1] that the meanmotion of the Moon was apparently getting faster, by comparison with ancient eclipse observations, but he gave nodata. (It was not yet known in Halley's time that what is actually occurring includes a slowing-down of the Earth'srate of rotation: see also Ephemeris time - History. When measured as a function of mean solar time rather thanuniform time, the effect appears as a positive acceleration.) In 1749 Richard Dunthorne confirmed Halley's suspicionafter re-examining ancient records, and produced the first quantitative estimate for the size of this apparent effect:[2]

a centurial rate of +10" (arcseconds) in lunar longitude (a surprisingly good result for its time, not far different fromvalues assessed later, e.g. in 1786 by de Lalande,[3] and to compare with values from about 10" to nearly 13" beingderived about century later.)[4][5]

Pierre-Simon Laplace produced in 1786 a theoretical analysis giving a basis on which the Moon's mean motionshould accelerate in response to perturbational changes in the eccentricity of the orbit of the Earth around the Sun.Laplace's initial computation accounted for the whole effect, thus seeming to tie up the theory neatly with bothmodern and ancient observations.

Tidal acceleration 47

However, in 1854, J C Adams caused the question to be re-opened by finding an error in Laplace's computations: itturned out that only about half of the Moon's apparent acceleration could be accounted for on Laplace's basis by thechange in the Earth's orbital eccentricity.[6] Adams' finding provoked a sharp astronomical controversy that lastedsome years, but the correctness of his result, agreed by other mathematical astronomers including C E Delaunay, waseventually accepted.[7] The question depended on correct analysis of the lunar motions, and received a furthercomplication with another discovery, around the same time, that another significant long-term perturbation that hadbeen calculated for the Moon (supposedly due to the action of Venus) was also in error, was found onre-examination to be almost negligible, and practically had to disappear from the theory. A part of the answer wassuggested independently in the 1860s by Delaunay and by William Ferrel: tidal retardation of the Earth's rotation ratewas lengthening the unit of time and causing a lunar acceleration that was only apparent.It took some time for the astronomical community to accept the reality and the scale of tidal effects. But eventually itbecame clear that three effects are involved, when measured in terms of mean solar time. Beside the effects ofperturbational changes in the Earth's orbital eccentricity, as found by Laplace and corrected by Adams, there are twotidal effects (a combination first suggested by Emmanuel Liais). First there is a real retardation of the Moon's angularrate of orbital motion, due to tidal exchange of angular momentum between the Earth and Moon. This increases theMoon's angular momentum around the Earth (and moves the Moon to a higher orbit with a slower period). Secondlythere is an apparent increase in the Moon's angular rate of orbital motion (when measured in terms of mean solartime). This arises from the Earth's loss of angular momentum and the consequent increase in length of day.[8]

A diagram of the Earth-Moon system showinghow the tidal bulge is pushed ahead by the Earth'srotation. This offset bulge exerts a net torque onthe Moon, boosting it while slowing the Earth's

rotation.

Effects of Moon's gravity

Because the Moon's mass is a considerable fraction of that of the Earth(about 1:81), the two bodies can be regarded as a double planet system,rather than as a planet with a satellite. The plane of the Moon's orbitaround the Earth lies close to the plane of the Earth's orbit around theSun (the ecliptic), rather than in the plane perpendicular to the axis ofrotation of the Earth (the equator) as is usually the case with planetarysatellites. The mass of the Moon is sufficiently large, and it issufficiently close, to raise tides in the matter of the Earth. In particular,the water of the oceans bulges out along both ends of an axis passingthrough the centers of the Earth and Moon. The average tidal bulgeclosely follows the Moon in its orbit, and the Earth rotates under thistidal bulge in just over a day. However, the rotation drags the positionof the tidal bulge ahead of the position directly under the Moon. As aconsequence, there exists a substantial amount of mass in the bulgethat is offset from the line through the centers of the Earth and Moon.Because of this offset, a portion of the gravitational pull betweenEarth's tidal bulges and the Moon is perpendicular to the Earth-Moonline, i.e. there exists a torque between the Earth and the Moon. Thisboosts the Moon in its orbit, and decelerates the rotation of the Earth.

As a result of this process, the mean solar day, which is nominally 86400 seconds long, is actually getting longerwhen measured in SI seconds with stable atomic clocks. (The SI second, when adopted, was already a little shorterthan the current value of the second of mean solar time.[9]) The small difference accumulates every day, which leadsto an increasing difference between our clock time (Universal Time) on the one hand, and Atomic Time andEphemeris Time on the other hand: see ΔT. This makes it necessary to insert a leap second at irregular intervals.In addition to the effect of the ocean tides, there is also a tidal acceleration due to flexing of the earth's crust, but thisaccounts for only about 4% of the total effect when expressed in terms of heat dissipation.[10]

Tidal acceleration 48

If other effects were ignored, tidal acceleration would continue until the rotational period of the Earth matched theorbital period of the Moon. At that time, the Moon would always be overhead of a single fixed place on Earth. Sucha situation already exists in the Pluto-Charon system. However, the slowdown of the Earth's rotation is not occurringfast enough for the rotation to lengthen to a month before other effects make this irrelevant: About 2.1 billion yearsfrom now, the continual increase of the Sun's radiation will cause the Earth's oceans to vaporize, removing the bulkof the tidal friction and acceleration. Even without this, the slowdown to a month-long day would still not have beencompleted by 4.5 billion years from now when the Sun will evolve into a red giant and likely destroy both the Earthand Moon.Tidal acceleration is one of the few examples in the dynamics of the Solar System of a so-called secularperturbation of an orbit, i.e. a perturbation that continuously increases with time and is not periodic. Up to a highorder of approximation, mutual gravitational perturbations between major or minor planets only cause periodicvariations in their orbits, that is, parameters oscillate between maximum and minimum values. The tidal effect givesrise to a quadratic term in the equations, which leads to unbounded growth. In the mathematical theories of theplanetary orbits that form the basis of ephemerides, quadratic and higher order secular terms do occur, but these aremostly Taylor expansions of very long time periodic terms. The reason that tidal effects are different is that unlikedistant gravitational perturbations, friction is an essential part of tidal acceleration, and leads to permanent loss ofenergy from the dynamical system in the form of heat. In other words, we do not have a Hamiltonian system here.

Angular momentum and energyThe gravitational torque between the Moon and the tidal bulge of the Earth causes the Moon to be promoted in itsorbit, and the Earth to be decelerated in its rotation. As in any physical process within an isolated system, totalenergy and angular momentum are conserved. Effectively, energy and angular momentum are transferred from therotation of the Earth to the orbital motion of the Moon (however, most of the energy lost by the Earth is converted toheat, and only about one 30th is transferred to the Moon). The Moon moves farther away from the Earth, so itspotential energy (in the Earth's gravity well) increases. It stays in orbit, and from Kepler's 3rd law it follows that itsvelocity actually decreases, so the tidal action on the Moon actually causes a deceleration of its motion across thecelestial sphere. Although its kinetic energy decreases, its potential energy increases by a larger amount. The tidalforce has a component in the direction of the Moon's motion, and therefore increases its energy, but the non-tidal partof the Earth's gravity pulls (on average) slightly backwards on the Moon (which on average has a slight outwardvelocity), so the net result is that the Moon slows down. The Moon's orbital angular momentum increases.The rotational angular momentum of the Earth decreases and consequently the length of the day increases. The nettide raised on Earth by the Moon is dragged ahead of the Moon by Earth's much faster rotation. Tidal friction isrequired to drag and maintain the bulge ahead of the Moon, and it dissipates the excess energy of the exchange ofrotational and orbital energy between the Earth and Moon as heat. If the friction and heat dissipation were notpresent, the Moon's gravitational force on the tidal bulge would rapidly (within two days) bring the tide back intosynchronization with the Moon, and the Moon would no longer recede. Most of the dissipation occurs in a turbulentbottom boundary layer in shallow seas such as the European shelf around the British Isles, the Patagonian shelf offArgentina, and the Bering Sea.[11]

The dissipation of energy by tidal friction averages about 3.75 terawatts, of which 2.5 terawatts are from theprincipal M2 lunar component and the remainder from other components, both lunar and solar.[12]

An equilibrium tidal bulge does not really exist on Earth because the continents do not allow this mathematical solution to take place. Oceanic tides actually rotate around the oceans basin as vast gyres around several amphidromic points where no tide exists. The Moon pulls on each individual undulation as Earth rotates—some undulations are ahead of the Moon, others are behind it, while still others are on either side. The "bulges" that actually do exist for the Moon to pull on (and which pull on the Moon) are the net result of integrating the actual undulations over all the world's oceans. Earth's net (or equivalent) equilibrium tide has an amplitude of only 3.23 cm,

Tidal acceleration 49

which is totally swamped by oceanic tides that can exceed one metre.

Historical evidenceThis mechanism has been working for 4.5 billion years, since oceans first formed on the Earth. There is geologicaland paleontological evidence that the Earth rotated faster and that the Moon was closer to the Earth in the remotepast. Tidal rhythmites are alternating layers of sand and silt laid down offshore from estuaries having great tidalflows. Daily, monthly and seasonal cycles can be found in the deposits. This geological record is consistent withthese conditions 620 million years ago: the day was 21.9±0.4 hours, and there were 13.1±0.1 synodic months/yearand 400±7 solar days/year. The length of the year has remained virtually unchanged during this period because noevidence exists that the constant of gravitation has changed. The average recession rate of the Moon between thenand now has been 2.17±0.31 cm/year, which is about half the present rate.[13]

Quantitative description of the Earth-Moon caseThe motion of the Moon can be followed with an accuracy of a few centimeters by lunar laser ranging (LLR). Laserpulses are bounced off mirrors on the surface of the moon, emplaced during the Apollo missions of 1969 to 1972 andby Lunokhod 2 in 1973.[14][15] Measuring the return time of the pulse yields a very accurate measure of the distance.These measurements are fitted to the equations of motion. This yields numerical values for the Moon's secularacceleration in longitude and the rate of change of the semimajor axis of the Earth-Moon ellipse. From the period1970–2007, the results are:

−25.85"/cy² in ecliptic longitude[16]

(cy is centuries, here taken to the square)+38.14 mm/yr in the mean Earth-Moon distance[16]

This is consistent with results from satellite laser ranging (SLR), a similar technique applied to artificial satellitesorbiting the Earth, which yields a model for the gravitational field of the Earth, including that of the tides. The modelaccurately predicts the changes in the motion of the Moon.Finally, ancient observations of solar eclipses give fairly accurate positions for the Moon at those moments. Studiesof these observations give results consistent with the value quoted above.[17]

The other consequence of tidal acceleration is the deceleration of the rotation of the Earth. The rotation of the Earthis somewhat erratic on all time scales (from hours to centuries) due to various causes.[18] The small tidal effectcannot be observed in a short period, but the cumulative effect on the Earth's rotation as measured with a stable clock(ephemeris time, atomic time) of a shortfall of even a few milliseconds every day becomes readily noticeable in afew centuries. Since some event in the remote past, more days and hours have passed (as measured in full rotationsof the Earth) (Universal Time) than as measured with stable clocks calibrated to the present, longer length of the day(ephemeris time). This is known as ΔT. Recent values can be obtained from the International Earth Rotation andReference Systems Service (IERS).[19] A table of the actual length of the day in the past few centuries is alsoavailable.[20]

From the observed change in the Moon's orbit, the corresponding change in the length of the day can be computed:+2.3 ms/cy(cy is centuries).

However, from historical records over the past 2700 years the following average value is found:+1.70 ± 0.05 ms/cy[21][22]

The corresponding cumulative value is a parabola having a coefficient of T² (time in centuries squared) of:ΔT = +31 s/cy²

Tidal acceleration 50

Opposing the tidal deceleration of the Earth is a mechanism that is in fact accelerating the rotation. The Earth is not asphere, but rather an ellipsoid that is flattened at the poles. SLR has shown that this flattening is decreasing. Theexplanation is, that during the ice age large masses of ice collected at the poles, and depressed the underlying rocks.The ice mass started disappearing over 10000 years ago, but the Earth's crust is still not in hydrostatic equilibriumand is still rebounding (the relaxation time is estimated to be about 4000 years). As a consequence, the polardiameter of the Earth increases, and since the mass and density remain the same, the volume remains the same;therefore the equatorial diameter is decreasing. As a consequence, mass moves closer to the rotation axis of theEarth. This means that its moment of inertia is decreasing. Because its total angular momentum remains the sameduring this process, the rotation rate increases. This is the well-known phenomenon of a spinning figure skater whospins ever faster as she retracts her arms. From the observed change in the moment of inertia the acceleration ofrotation can be computed: the average value over the historical period must have been about −0.6 ms/cy. This largelyexplains the historical observations.

Other cases of tidal accelerationMost natural satellites of the planets undergo tidal acceleration to some degree (usually small), except for the twoclasses of tidally decelerated bodies. In most cases, however, the effect is small enough that even after billions ofyears most satellites will not actually be lost. The effect is probably most pronounced for Mars' second moonDeimos, which may become an Earth-crossing asteroid after it leaks out of Mars' grip . The effect also arisesbetween different components in a binary star.[23]

Tidal decelerationThis comes in two varieties:1. Fast satellites: Some inner moons of the gas giant planets and Phobos orbit within the synchronous orbit radius

so that their orbital period is shorter than their planet's rotation. In this case the tidal bulges raised by the moon ontheir planet lag behind the moon, and act to decelerate it in its orbit. The net effect is a decay of that moon's orbitas it gradually spirals towards the planet. The planet's rotation also speeds up slightly in the process. In the distantfuture these moons will impact the planet or cross within their Roche limit and be tidally disrupted into fragments.However, all such moons in the Solar System are very small bodies and the tidal bulges raised by them on theplanet are also small, so the effect is usually weak and the orbit decays slowly. The moons affected are:• Around Mars: Phobos• Around Jupiter: Metis and Adrastea• Around Saturn: none, except for the ring particles (like Jupiter, Saturn is a very rapid rotator but has no

satellites close enough)• Around Uranus: Cordelia, Ophelia, Bianca, Cressida, Desdemona, Juliet, Portia, Rosalind, Cupid, Belinda, and

Perdita• Around Neptune: Naiad, Thalassa, Despina, Galatea and Larissa

2. Retrograde satellites: All retrograde satellites experience tidal deceleration to some degree because the moon'sorbital motion and the planet's rotation are in opposite directions, causing restoring forces from their tidal bulges.A difference to the previous "fast satellite" case here is that the planet's rotation is also slowed down rather thansped up (angular momentum is still conserved because in such a case the values for the planet's rotation and themoon's revolution have opposite signs). The only satellite in the Solar System for which this effect isnon-negligible is Neptune's moon Triton. All the other retrograde satellites are on distant orbits and tidal forcesbetween them and the planet are negligible.

The planet Venus is believed to have no satellites chiefly because any hypothetical satellites would have suffereddeceleration long ago, from either cause; Venus has a very slow and retrograde rotation.

Tidal acceleration 51

References[1] E Halley (1695), "Some Account of the Ancient State of the City of Palmyra, with Short Remarks upon the Inscriptions Found there" (http:/ /

rstl. royalsocietypublishing. org/ content/ 19/ 215-235/ 160. full. pdf), Phil. Trans., vol.19 (1695-1697), pages 160-175; esp. at pages 174-175.[2] Richard Dunthorne (1749), "A Letter from the Rev. Mr. Richard Dunthorne to the Reverend Mr. Richard Mason F. R. S. and Keeper of the

Wood-Wardian Museum at Cambridge, concerning the Acceleration of the Moon" (http:/ / rstl. royalsocietypublishing. org/ content/ 46/491-496/ 162. full. pdf), Philosophical Transactions (1683-1775), Vol. 46 (1749 - 1750) #492, pp.162-172; also given in PhilosophicalTransactions (abridgements) (1809), vol.9 (for 1744-49), p669-675 (http:/ / www. archive. org/ stream/ philosophicaltra09royarich#page/ 669/mode/ 2up) as "On the Acceleration of the Moon, by the Rev. Richard Dunthorne".

[3] J de Lalande (1786): "Sur les equations seculaires du soleil et de la lune" (http:/ / www. academie-sciences. fr/ membres/ in_memoriam/Lalande/ Lalande_pdf/ Mem1786_p390. pdf), Memoires de l'Academie Royale des Sciences, pp.390-397, at page 395.

[4] J D North (2008), "Cosmos: an illustrated history of astronomy and cosmology", (University of Chicago Press, 2008), chapter 14, at page 454(http:/ / books. google. com/ books?id=qq8Luhs7rTUC& pg=PA454).

[5] See also P Puiseux (1879), "Sur l'acceleration seculaire du mouvement de la Lune" (http:/ / archive. numdam. org/ article/ASENS_1879_2_8__361_0. pdf), Annales Scientifiques de l'Ecole Normale Superieure, 2nd series vol.8 (1879), pp.361-444, at pages 361-5.

[6] Adams, J C (1853). "On the Secular Variation of the Moon's Mean Motion" (http:/ / rstl. royalsocietypublishing. org/ content/ 143/ 397. full.pdf) (PDF). Phil. Trans. R. Soc. Lond. 143: 397–406. doi:10.1098/rstl.1853.0017. .

[7] D E Cartwright (2001), "Tides: a scientific history" (http:/ / books. google. com/ books?id=78bE5U7TVuIC& pg=PA144), (CambridgeUniversity Press 2001), chapter 10, section: "Lunar acceleration, earth retardation and tidal friction" at pages 144-146.

[8] F R Stephenson (2002), "Harold Jeffreys Lecture 2002: Historical eclipses and Earth's rotation" (http:/ / articles. adsabs. harvard. edu/ full/2003A& G. . . . 44b. . 22S), in Astronomy & Geophysics, vol.44 (2002), pp. 2.22-2.27.

[9] :(1) In "The Physical Basis of the Leap Second", by D D McCarthy, C Hackman and R A Nelson, in Astronomical Journal, vol.136 (2008),pages 1906-1908, it is stated (page 1908), that "the SI second is equivalent to an older measure of the second of UT1, which was too small tostart with and further, as the duration of the UT1 second increases, the discrepancy widens." :(2) In the late 1950s, the cesium standard wasused to measure both the current mean length of the second of mean solar time (UT2) (result: 9192631830 cycles) and also the second ofephemeris time (ET) (result:9192631770 +/-20 cycles), see "Time Scales", by L. Essen (http:/ / www. leapsecond. com/ history/1968-Metrologia-v4-n4-Essen. pdf), in Metrologia, vol.4 (1968), pp.161-165, on p.162. As is well known, the 9192631770 figure was chosenfor the SI second. L Essen in the same 1968 article (p.162) stated that this "seemed reasonable in view of the variations in UT2".

[10] Munk, Progress in Oceanography 40 (1997) 7; http:/ / www. sciencedirect. com/ science/ article/ pii/ S0079661197000219[11] Munk, Walter (1997). "Once again: once again—tidal friction". Progress in Oceanography 40 (1–4): 7–35. Bibcode 1997PrOce..40....7M.

doi:10.1016/S0079-6611(97)00021-9.[12] Munk, W.; Wunsch, C (1998). "Abyssal recipes II: energetics of tidal and wind mixing". Deep Sea Research Part I Oceanographic

Research Papers 45 (12): 1977. Bibcode 1998DSRI...45.1977M. doi:10.1016/S0967-0637(98)00070-3[13] Williams, George E. (2000). "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". Reviews of

Geophysics 38 (1): 37–60. Bibcode 2000RvGeo..38...37W. doi:10.1029/1999RG900016.[14][14] Most laser pulses, 78%, are to the Apollo 15 site. See Williams, et al. (2008), p. 5.[15] Another reflector emplaced by Lunokhod 1 in 1970 is no longer functioning. See Lunar Lost & Found: The Search for Old Spacecraft by

Leonard David (http:/ / www. space. com/ scienceastronomy/ 060327_mystery_monday. html)[16] J. G. Williams, D. H. Boggs and W. M. Folkner (2008). DE421 Lunar orbit, physical librations, and surface coordinates (http:/ / naif. jpl.

nasa. gov/ pub/ naif/ generic_kernels/ spk/ planets/ de421_lunar_ephemeris_and_orientation. pdf) p. 7. "These derived values depend on atheory which is not accurate to the number of digits given."

[17] F.R. Stephenson, L.V. Morrison (1995): " Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990 (http:/ / rsta.royalsocietypublishing. org/ content/ 351/ 1695/ 165. full. pdf)". Philosophical Transactions of the Royal Society of London Series A,pp.165–202. doi:10.1098/rsta.1995.0028

[18] Jean O. Dickey (1995): "Earth Rotation Variations from Hours to Centuries". In: I. Appenzeller (ed.): Highlights of Astronomy. Vol. 10pp.17..44.

[19] http:/ / www. iers. org/ nn_10910/ IERS/ EN/ Science/ EarthRotation/ UT1-TAI. html[20] LOD (http:/ / www. iers. org/ iers/ earth/ rotation/ ut1lod/ table3. html)[21] Dickey, Jean O.; Bender, PL; Faller, JE; Newhall, XX; Ricklefs, RL; Ries, JG; Shelus, PJ; Veillet, C et al (1994). "Lunar Laser ranging: a

continuing legacy of the Apollo program" (http:/ / www. physics. ucsd. edu/ ~tmurphy/ apollo/ doc/ Dickey. pdf). Science 265 (5171):482–90. Bibcode 1994Sci...265..482D. doi:10.1126/science.265.5171.482. PMID 17781305. .

[22] F.R. Stephenson (1997): Historical Eclipses and Earth's Rotation (http:/ / books. google. com/ books?id=DTb4DDuJNa4C). CambridgeUniv.Press.

[23] Zahn, J.-P. (1977). "Tidal Friction in Close Binary Stars". Astron. Astrophys. 57: 383–394. Bibcode 1977A&A....57..383Z.

Tidal acceleration 52

External links• The Recession of the Moon and the Age of the Earth-Moon System (http:/ / www. talkorigins. org/ faqs/ moonrec.

html)• Tidal Heating as Described by University of Washington Professor Toby Smith (http:/ / www. astro. washington.

edu/ users/ smith/ Astro150/ Tutorials/ TidalHeat/ TidalHeat. html)

Tidal powerTidal power, also called tidal energy, is a form of hydropower that converts the energy of tides into useful forms ofpower - mainly electricity.Although not yet widely used, tidal power has potential for future electricity generation. Tides are more predictablethan wind energy and solar power. Among sources of renewable energy, tidal power has traditionally suffered fromrelatively high cost and limited availability of sites with sufficiently high tidal ranges or flow velocities, thusconstricting its total availability. However, many recent technological developments and improvements, both indesign (e.g. dynamic tidal power, tidal lagoons) and turbine technology (e.g. new axial turbines, cross flow turbines),indicate that the total availability of tidal power may be much higher than previously assumed, and that economicand environmental costs may be brought down to competitive levels.Historically, tide mills have been used, both in Europe and on the Atlantic coast of North America. The incomingwater was contained in large storage ponds, and as the tide went out, it turned waterwheels that used the mechanicalpower it produced to mill grain. [1] The earliest occurrences date from the Middle Ages, or even from Romantimes.[2][3] It was only in the 19th century that the process of using falling water and spinning turbines to createelectricity was introduced in the U.S. and Europe. [4]

The world's first large-scale tidal power plant (the Rance Tidal Power Station) became operational in 1966.

Tidal power 53

Generation of tidal energy

Variation of tides over a day

Tidal power is extracted from the Earth's oceanic tides;tidal forces are periodic variations in gravitationalattraction exerted by celestial bodies. These forcescreate corresponding motions or currents in the world'soceans. Due to the strong attraction to the oceans, abulge in the water level is created, causing a temporaryincrease in sea level. When the sea level is raised, waterfrom the middle of the ocean is forced to move towardthe shorelines, creating a tide. This occurrence takesplace in an unfailing manner, due to the consistentpattern of the moon’s orbit around the earth. [5] Themagnitude and character of this motion reflects thechanging positions of the Moon and Sun relative to theEarth, the effects of Earth's rotation, and localgeography of the sea floor and coastlines.

Tidal power is the only technology that draws onenergy inherent in the orbital characteristics of theEarth–Moon system, and to a lesser extent in theEarth–Sun system. Other natural energies exploited byhuman technology originate directly or indirectly withthe Sun, including fossil fuel, conventionalhydroelectric, wind, biofuel, wave and solar energy.Nuclear energy makes use of Earth's mineral depositsof fissionable elements, while geothermal power taps the Earth's internal heat, which comes from a combination ofresidual heat from planetary accretion (about 20%) and heat produced through radioactive decay (80%).[6]

A tidal generator converts the energy of tidal flows into electricity. Greater tidal variation and higher tidal currentvelocities can dramatically increase the potential of a site for tidal electricity generation.Because the Earth's tides are ultimately due to gravitational interaction with the Moon and Sun and the Earth'srotation, tidal power is practically inexhaustible and classified as a renewable energy resource. Movement of tidescauses a loss of mechanical energy in the Earth–Moon system: this is a result of pumping of water through naturalrestrictions around coastlines and consequent viscous dissipation at the seabed and in turbulence. This loss of energyhas caused the rotation of the Earth to slow in the 4.5 billion years since its formation. During the last 620 millionyears the period of rotation of the earth (length of a day) has increased from 21.9 hours to 24 hours;[7] in this periodthe Earth has lost 17% of its rotational energy. While tidal power may take additional energy from the system, theeffect is negligible and would only be noticed over millions of years.

Tidal power 54

Generating methods

The world's first commercial-scale andgrid-connected tidal stream generator – SeaGen –in Strangford Lough.[8] The strong wake shows

the power in the tidal current.

Top-down view of a DTP dam. Blue and dark redcolors indicate low and high tides, respectively.

Tidal power can be classified into three generating methods:

Tidal stream generator

Tidal stream generators (or TSGs) make use of the kinetic energy ofmoving water to power turbines, in a similar way to wind turbines thatuse wind to power turbines. Some tidal generators can be built into thestructures of existing bridges, involving virtually no aestheticproblems. Likewise, “tidal bridging” is a relatively new advancementthat is gaining recognition as a more practical and beneficial way togenerate tidal power. Blue Energy Canada is a company that is focusedon building bridges to match today's demands. [9]

Tidal barrage

Tidal barrages make use of the potential energy in the difference inheight (or head) between high and low tides. When using tidal barragesto generate power, the potential energy from a tide is seized throughstrategic placement of specialized dams. When the sea level rises andthe tide beings to come in, the temporary increase in tidal power ischanneled into a large basin behind the dam, holding a large amount ofpotential energy. With the receding tide, this energy is then convertedinto mechanical energy as the water is released through large turbinesthat create electrical power though the use of generators. [10] Barragesare essentially dams across the full width of a tidal estuary.

Dynamic tidal power

Dynamic tidal power (or DTP) is a theoretical generation technology that would exploit an interaction betweenpotential and kinetic energies in tidal flows. It proposes that very long dams (for example: 30–50 km length) be builtfrom coasts straight out into the sea or ocean, without enclosing an area. Tidal phase differences are introducedacross the dam, leading to a significant water-level differential in shallow coastal seas – featuring strongcoast-parallel oscillating tidal currents such as found in the UK, China and Korea.

US and Canadian studies in the twentieth centuryThe first study of large scale tidal power plants was by the US Federal Power Commission in 1924 which wouldhave been located if built in the northern border area of the US state of Maine and the south eastern border area ofthe Canadian province of New Brunswick, with various dams, powerhouses and ship locks enclosing the Bay ofFundy and Passamaquoddy Bay (note: see map in reference). Nothing came of the study and it is unknown whetherCanada had been approached about the study by the US Federal Power Commission.[11]

There was also a report on the international commission in April 1961 entitled " Investigation of the InternationalPassamaquoddy Tidal Power Project" produced by both the US and Canadian Federal Governments. According tobenefit to costs ratios, the project was beneficial to the US but not to Canada. A highway system along the top of thedams was envisioned as well.A study was commissioned by the Canadian, Nova Scotian and New Brunswick Governments (Reassessment of Fundy Tidal Power) to determine the potential for tidal barrages at Chignecto Bay and Minas Basin – at the end of

Tidal power 55

the Fundy Bay estuary. There were three sites determined to be financially feasible: Shepody Bay (1550 MW),Cumberline Basin (1085 MW) and Cobequid Bay (3800 MW). These were never built despite their apparentfeasibility in 1977.[12]

Current and future tidal power schemes• The first tidal power station was the Rance tidal power plant built over a period of 6 years from 1960 to 1966 at

La Rance, France.[13] It has 240 MW installed capacity.• 254 MW Sihwa Lake Tidal Power Plant in South Korea is the largest tidal power installation in the world.

Construction was completed in 2011.[14][15]

• The first tidal power site in North America is the Annapolis Royal Generating Station, Annapolis Royal, NovaScotia, which opened in 1984 on an inlet of the Bay of Fundy.[16] It has 20 MW installed capacity.

• The Jiangxia Tidal Power Station, south of Hangzhou in China has been operational since 1985, with currentinstalled capacity of 3.2 MW. More tidal power is planned near the mouth of the Yalu River.[17]

• The first in-stream tidal current generator in North America (Race Rocks Tidal Power Demonstration Project)was installed at Race Rocks on southern Vancouver Island in September 2006.[18][19] The next phase in thedevelopment of this tidal current generator will be in Nova Scotia.[20]

• A small project was built by the Soviet Union at Kislaya Guba on the Barents Sea. It has 0.4 MW installedcapacity. In 2006 it was upgraded with a 1.2MW experimental advanced orthogonal turbine.

• Jindo Uldolmok Tidal Power Plant in South Korea is a tidal stream generation scheme planned to be expandedprogressively to 90 MW of capacity by 2013. The first 1 MW was installed in May 2009.[21]

• A 1.2 MW SeaGen system became operational in late 2008 on Strangford Lough in Northern Ireland.[22]

• The contract for an 812 MW tidal barrage near Ganghwa Island north-west of Incheon has been signed byDaewoo. Completion is planned for 2015.[14]

• A 1,320 MW barrage built around islands west of Incheon is proposed by the Korean government, with projectedconstruction start in 2017.[23]

• Other South Korean projects include barrages planned for Garorim Bay, Ansanman, and Swaseongho, and tidalgeneration associated with the Saemangeum reclamation project. The barrages are all in the multiple-hundredmegawatts range.[24]

• The Scottish Government has approved plans for a 10MW array of tidal stream generators near Islay, Scotland,costing 40 million pounds, and consisting of 10 turbines – enough to power over 5,000 homes. The first turbine isexpected to be in operation by 2013.[25]

• The Indian state of Gujarat is planning to host South Asia's first commercial-scale tidal power station. Thecompany Atlantis Resources is to install a 50MW tidal farm in the Gulf of Kutch on India's west coast, withconstruction starting early in 2012.[26]

• In New York City, 30 tidal turbines will be installed in the East River by 2015 with a capacity of 1,050kilowatts.[27]

Notes• Baker, A. C. 1991, Tidal power, Peter Peregrinus Ltd., London.• Baker, G. C., Wilson E. M., Miller, H., Gibson, R. A. & Ball, M., 1980. "The Annapolis tidal power pilot

project", in Waterpower '79 Proceedings, ed. Anon, U.S. Government Printing Office, Washington, pp 550–559.• Hammons, T. J. 1993, "Tidal power", Proceedings of the IEEE, [Online], v81, n3, pp 419–433. Available from:

IEEE/IEEE Xplore. [July 26, 2004].• Lecomber, R. 1979, "The evaluation of tidal power projects", in Tidal Power and Estuary Management, eds.

Severn, R. T., Dineley, D. L. & Hawker, L. E., Henry Ling Ltd., Dorchester, pp 31–39.

Tidal power 56

References[1] Ocean Energy Council (2011). "Tidal Energy: Pros for Wave and Tidal Power" (http:/ / www. oceanenergycouncil. com/ index. php/

Tidal-Energy/ Tidal-Energy. html). .[2] "Microsoft Word - RS01j.doc" (http:/ / www. kentarchaeology. ac/ authors/ 005. pdf) (PDF). . Retrieved 2011-04-05.[3] Minchinton, W. E. (October 1979). "Early Tide Mills: Some Problems". Technology and Culture (Society for the History of Technology) 20

(4): 777–786. doi:10.2307/3103639. JSTOR 3103639.[4] Dorf, Richard (1981). The Energy Factbook. New York: McGraw-Hill.[5] DiCerto, JJ (1976). The Electric Wishing Well: The Solution to the Energy Crisis. New York: Macmillan.[6] Turcotte, D. L.; Schubert, G. (2002). "4". Geodynamics (2 ed.). Cambridge, England, UK: Cambridge University Press. pp. 136–137.

ISBN 978-0-521-66624-4.[7] George E. Williams (2000). "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit". Reviews of

Geophysics 38 (1): 37–60. Bibcode 2000RvGeo..38...37W. doi:10.1029/1999RG900016.[8] Douglas, C. A.; Harrison, G. P.; Chick, J. P. (2008). "Life cycle assessment of the Seagen marine current turbine". Proceedings of the

Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment 222 (1): 1–12.doi:10.1243/14750902JEME94.

[9] Blue Energy Canada (2010). "Tidal Power: Blue Energy" (http:/ / www. bluenergy. com/ technology_method_tidal_bridge. html). .[10] Evans, Robert (2007). Fueling Our Future: An Introduction to Sustainable Energy. New York: Cambridge University Press.[11] "Niagra's Power From The Tides" (http:/ / books. google. com/ books?id=zigDAAAAMBAJ& pg=PA29& dq=Popular+ Science+ 1933+

plane+ "Popular+ Science"& hl=en& ei=MIb5TZaFEajx0gGxtaHPAw& sa=X& oi=book_result& ct=result& resnum=4&ved=0CDUQ6AEwAzhQ#v=onepage& q& f=true) May 1924 Popular Science Monthly

[12] Chang, Jen (2008), Hydrodynamic Modeling and Feasibility Study of Harnessing Tidal Power at the Bay of Fundy (http:/ / digitallibrary.usc. edu/ assetserver/ controller/ item/ etd-Chang-20080312. pdf) (PhD thesis), Los Angeles: University of Southern California, , retrieved2011-09-27

[13] L'Usine marémotrice de la Rance (http:/ / membres. lycos. fr/ chezalex/ projets/ rance/ sommaire_rance. htm)[14] "Hunt for African Projects" (http:/ / www. newsworld. co. kr/ cont/ article2009/ 0909-52. htm). Newsworld.co.kr. . Retrieved 2011-04-05.[15] Tidal power plant nears completion (http:/ / engsales. yonhapnews. co. kr/ YNA/ ContentsSales/ EngSales/ YISW_PopupPhotoPreview.

aspx?CID=PYH20110411088100341)[16] "Nova Scotia Power - Environment - Green Power- Tidal" (http:/ / www. nspower. ca/ en/ home/ environment/ renewableenergy/ tidal/

annapolis. aspx). Nspower.ca. . Retrieved 2011-04-05.[17] "China Endorses 300 MW Ocean Energy Project" (http:/ / www. renewableenergyworld. com/ rea/ news/ article/ 2004/ 11/

china-endorses-300-mw-ocean-energy-project-17685). Renewableenergyworld.com. . Retrieved 2011-04-05.[18] "Race Rocks Demonstration Project" (http:/ / www. cleancurrent. com/ technology/ rrproject. htm). Cleancurrent.com. . Retrieved

2011-04-05.[19] "Tidal Energy, Ocean Energy" (http:/ / www. racerocks. com/ racerock/ energy/ tidalenergy/ tidalenergy2. htm). Racerocks.com. . Retrieved

2011-04-05.[20] "Information for media inquiries" (http:/ / www. cleancurrent. com/ media/ index. htm). Cleancurrent.com. 2009-11-13. . Retrieved

2011-04-05.[21] Korea's first tidal power plant built in Uldolmok, Jindo (http:/ / www. korea. net/ news/ News/ newsView. asp?serial_no=20090518009&

part=101& SearchDay=2009. 05. 18& page=1)[22] "Tidal energy system on full power" (http:/ / news. bbc. co. uk/ 2/ hi/ uk_news/ northern_ireland/ 7790494. stm). BBC News. December 18,

2008. . Retrieved March 26, 2010.[23] $ 3-B tidal power plant proposed near Korean islands (http:/ / ecoseed. org/ en/ general-green-news/ green-politics/ green-policies/

asia-pacific/ 3457)[24] "Microsoft PowerPoint - presentation_t4_1_kim" (http:/ / pemsea. org/ eascongress/ international-conference/ presentation_t4-1_kim. pdf)

(PDF). . Retrieved 2011-04-05.[25] "Islay to get major tidal power scheme" (http:/ / www. bbc. co. uk/ news/ uk-scotland-glasgow-west-12767211). BBC. March 17, 2011. .

Retrieved 2011-03-19.[26] "India plans Asian tidal power first" (http:/ / www. bbc. co. uk/ news/ science-environment-12215065). BBC News. January 18, 2011. .[27] "Turbines Off NYC East River Will Create Enough Energy to Power 9,500 Homes" (http:/ / energy. gov/ articles/

turbines-nyc-east-river-will-create-enough-energy-power-9500-homes). U.S. Department of Energy. . Retrieved 13 February 2012.

Tidal power 57

External links• Enhanced tidal lagoon with pumped storage and constant output (http:/ / www. inference. phy. cam. ac. uk/

sustainable/ book/ tex/ Lagoons. pdf) as proposed by David J.C. MacKay, Cavendish Laboratory, University ofCambridge, UK.

• Marine and Hydrokinetic Technology Database (http:/ / www1. eere. energy. gov/ windandhydro/ hydrokinetic/default. aspx) The U.S. Department of Energy's Marine and Hydrokinetic Technology Database providesup-to-date information on marine and hydrokinetic renewable energy, both in the U.S. and around the world.

• Severn Estuary Partnership: Tidal Power Resource Page (http:/ / www. severnestuary. net/ sep/ resource. html)• Location of Potential Tidal Stream Power sites in the UK (http:/ / maps. google. co. uk/ maps/ ms?hl=en& q=&

ie=UTF8& msa=0& msid=107402675945400268346. 0000011377c9bc61b8af9& ll=54. 977614,-5. 800781&spn=11. 389793,29. 179688& z=5& om=1)

• University of Strathclyde ESRU (http:/ / www. esru. strath. ac. uk/ EandE/ Web_sites/ 05-06/ marine_renewables/home/ 1st_page. htm)-- Detailed analysis of marine energy resource, current energy capture technology appraisaland environmental impact outline

• Coastal Research - Foreland Point Tidal Turbine and warnings on proposed Severn Barrage (http:/ / www.coastalresearch. co. uk/ index. html)

• Sustainable Development Commission (http:/ / www. sd-commission. org. uk/ publications. php?id=607) - Reportlooking at 'Tidal Power in the UK', including proposals for a Severn barrage

• World Energy Council (http:/ / www. worldenergy. org/ publications/ survey_of_energy_resources_2007/tidal_energy/ 754. asp) - Report on Tidal Energy

• European Marine Energy Centre (http:/ / www. emec. org. uk/ tidal_developers. asp) - Listing of Tidal EnergyDevelopers -retrieved 1 July 2011

• Resources on Tidal Energy (http:/ / www. environmentportal. in/ category/ thesaurus/ tidal-energy)

Intertidal ecology

Anjajavy Forest on Tsingy rocks jutting into the Indian Ocean

Intertidal ecology is the study of intertidal ecosystems,where organisms live between the low and high tidelines. At low tide, the intertidal is exposed whereas athigh tide, the intertidal is underwater. Intertidalecologists therefore study the interactions betweenintertidal organisms and their environment, as well asbetween different species of intertidal organisms withina particular intertidal community. The most importantenvironmental and species interactions may vary basedon the type of intertidal community being studied, thebroadest of classifications being based on substrates -rocky shore and soft bottom communities.

Organisms living in this zone have a highly variableand 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 distinctvertical bands of specific species going up the shore. Species ability to cope with abiotic factors associated withemersion stress, such as desiccation determines their upper limits, while biotic interactions e.g.competition withother species sets their lower limits.

Intertidal ecology 58

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 intertidalcommunities. In some places Marine Protected Areas have been established to protect these areas and aid inscientific research.

Types of intertidal communitiesIntertidal habitats can be characterized as having either hard or soft bottoms substrates. Rocky intertidal communitiesoccur on rocky shores, such as headlands, cobble beaches, or human-made jetties. Their degree of exposure may becalculated using the Ballantine Scale. Soft-sediment habitats include sandy beaches, and intertidal wetlands (e.g.,mudflats, and salt marshes). These habitats differ in levels of abiotic, or non-living, environmental factors. Rockyshores tend to have higher wave action, requiring adaptations allowing the inhabitants to cling tightly to the rocks.Soft-bottom habitats are generally protected from large waves but tend to have more variable salinity levels. Theyalso offer a third habitable dimension—depth—thus, many soft-sediment inhabitants are adapted for burrowing.

Environment

A rock, seen at low tide, exhibiting typicalintertidal zonation.

Because intertidal organisms endure regular periods of immersion andemersion, they essentially live both underwater and on land and mustbe adapted to a large range of climatic conditions. The intensity ofclimate stressors varies with relative tide height because organismsliving in areas with higher tide heights are emersed for longer periodsthan those living in areas with lower tide heights. This gradient ofclimate with tide height leads to patterns of intertidal zonation, withhigh intertidal species being more adapted to emersion stresses thanlow intertidal species. These adaptations may be behavioral (i.e.movements or actions), morphological (i.e. characteristics of externalbody structure), or physiological (i.e. internal functions of cells andorgans).[1] In addition, such adaptations generally cost the organism interms of energy (e.g. to move or to grow certain structures), leading totrade-offs (i.e. spending more energy on deterring predators leaves lessenergy for other functions like reproduction).

Intertidal organisms, especially those in the high intertidal, must copewith a large range of temperatures. While they are underwater,temperatures may only vary by a few degrees over the year. However,at low tide, temperatures may dip to below freezing or may becomescaldingly hot, leading to a temperature range that may approach 30 °C

(86 °F) during a period of a few hours. Many mobile organisms, such as snails and crabs, avoid temperaturefluctuations by crawling around and searching for food at high tide and hiding in cool, moist refuges (crevices orburrows) at low tide.[2] Besides simply living at lower tide heights, non-motile organisms may be more dependent oncoping mechanisms. For example, high intertidal organisms have a stronger stress response, a physiological responseof making proteins that help recovery from temperature stress just as the immune response aids in the recovery frominfection.

Intertidal organisms are also especially prone to desiccation during periods of emersion. Again, mobile organisms avoid desiccation in the same way as they avoid extreme temperatures: by hunkering down in mild and moist refuges. Many intertidal organisms, including Littorina snails, prevent water loss by having waterproof outer surfaces, pulling completely into their shells, and sealing shut their shell opening. Limpets (Patella) do not use such

Intertidal ecology 59

a sealing plate but occupy a home-scar to which they seal the lower edge of their flattened conical shell using agrinding action. They return to this home-scar after each grazing excursion, typically just before emersion. On softrocks, these scars are quite obvious. Still other organisms, such as the algae Ulva and Porphyra, are able to rehydrateand recover after periods of severe desiccation.The level of salinity can also be quite variable. Low salinities can be caused by rainwater or river inputs offreshwater. Estuarine species must be especially euryhaline, or able to tolerate a wide range of salinities. Highsalinities occur in locations with high evaporation rates, such as in salt marshes and high intertidal pools. Shading byplants, especially in the salt marsh, can slow evaporation and thus ameliorate salinity stress. In addition, salt marshplants tolerate high salinities by several physiological mechanisms, including excreting salt through salt glands andpreventing salt uptake into the roots.In addition to these exposure stresses (temperature, desiccation, and salinity), intertidal organisms experience strongmechanical stresses, especially in locations of high wave action. There are myriad ways in which the organismsprevent dislodgement due to waves. Morphologically, many mollusks (such as limpets and chitons) have low-profile,hydrodynamic shells. Types of substrate attachments include mussels’ tethering byssal threads and glues, sea stars’thousands of suctioning tube feet, and isopods’ hook-like appendages that help them hold onto intertidal kelps.Higher profile organisms, such as kelps, must also avoid breaking in high flow locations, and they do so with theirstrength and flexibility. Finally, organisms can also avoid high flow environments, such as by seeking out low flowmicrohabitats. Additional forms of mechanical stresses include ice and sand scour, as well as dislodgment bywater-borne rocks, logs, etc.For each of these climate stresses, species exist that are adapted to and thrive in the most stressful of locations. Forexample, the tiny crustacean copepod Tigriopus thrives in very salty, high intertidal tidepools, and many filterfeeders find more to eat in wavier and higher flow locations. Adapting to such challenging environments gives thesespecies competitive edges in such locations.

Food web structure

Semibalanus balanoides

During tidal immersion, the food supply to intertidal organisms issubsidized by materials carried in seawater, includingphotosynthesizing phytoplankton and consumer zooplankton. Theseplankton are eaten by numerous forms of filter feeders—mussels,clams, barnacles, sea squirts, and polychaete worms—which filterseawater in their search for planktonic food sources. The adjacentocean is also a primary source of nutrients for autotrophs,photosynthesizing producers ranging in size from microscopic algae(e.g. benthic diatoms) to huge kelps and other seaweeds. Theseintertidal producers are eaten by herbivorous grazers, such as limpetsthat scrape rocks clean of their diatom layer and kelp crabs that creepalong blades of the feather boa kelp Egregia eating the tiny leaf-shaped bladelets. Crabs are eaten by GoliathGrouper, which are then eaten by sharks. Higher up the food web, predatory consumers—especially voraciousstarfish—eat other grazers (e.g. snails) and filter feeders (e.g. mussels). Finally, scavengers, including crabs and sandfleas, eat dead organic material, including dead producers and consumers.

Intertidal ecology 60

Species interactions

Tide pools with sea stars and sea anemone in Santa Cruz

In addition to being shaped by aspects ofclimate, intertidal habitats—especiallyintertidal zonation patterns—are stronglyinfluenced by species interactions, such aspredation, competition, facilitation, andindirect interactions. Ultimately, theseinteractions feed into the food web structure,described above. Intertidal habitats havebeen a model system for many classicecological studies, including thoseintroduced below, because the residentcommunities are particularly amenable toexperimentation.

One dogma of intertidal ecology—supportedby such classic studies—is that species’ lower tide height limits are set by species interactions whereas their upperlimits are set by climate variables. Classic studies by Robert Paine[3][4] established that when sea star predators areremoved, mussel beds extend to lower tide heights, smothering resident seaweeds. Thus, mussels’ lower limits are setby sea star predation. Conversely, in the presence of sea stars, mussels’ lower limits occur at a tide height at whichsea stars are unable to tolerate climate conditions.

Competition, especially for space, is another dominant interaction structuring intertidal communities. Spacecompetition is especially fierce in rocky intertidal habitats, where habitable space is limited compared tosoft-sediment habitats in which three-dimensional space is available. As seen with the previous sea star example,mussels are competitively dominant when they are not kept in check by sea star predation. Joseph Connell's researchon two types of high intertidal barnacles, Balanus balanoides, now Semibalanus balanoides, and a Chthamalusstellatus, showed that zonation patterns could also be set by competition between closely related organisms.[5] In thisexample, Balanus outcompetes Chthamalus at lower tide heights but is unable to survive at higher tide heights. Thus,Balanus conforms to the intertidal ecology dogma introduced above: its lower tide height limit is set by a predatorysnail and its higher tide height limit is set by climate. Similarly, Chthamalus, which occurs in a refuge fromcompetition (similar to the temperature refuges discussed above), has a lower tide height limit set by competitionwith Balanus and a higher tide height limit is set by climate.

Intertidal ecology 61

Hermit Crabs and live Tegula snails on a dead Gumboot chiton, Cryptochitonstelleri, in a tide pool at low tide in central California

Although intertidal ecology has traditionallyfocused on these negative interactions(predation and competition), there isemerging evidence that positive interactionsare also important.[6] Facilitation refers toone organism helping another withoutharming itself. For example, salt marsh plantspecies of Juncus and Iva are unable totolerate the high soil salinities whenevaporation rates are high, thus they dependon neighboring plants to shade the sediment,slow evaporation, and help maintaintolerable salinity levels.[7] In similarexamples, many intertidal organismsprovide physical structures that are used asrefuges by other organisms. Mussels,although they are tough competitors with

certain species, are also good facilitators as mussel beds provide a three-dimensional habitat to species of snails,worms, and crustaceans.

All of the examples given so far are of direct interactions: Species A eat Species B or Species B eats Species C. Alsoimportant are indirect interactions[8] where, using the previous example, Species A eats so much of Species B thatpredation on Species C decreases and Species C increases in number. Thus, Species A indirectly benefits Species C.Pathways of indirect interactions can include all other forms of species interactions. To follow the sea star-musselrelationship, sea stars have an indirect negative effect on the diverse community that lives in the mussel bed because,by preying on mussels and decreasing mussel bed structure, those species that are facilitated by mussels are lefthomeless. Additional important species interactions include mutualism, which is seen in symbioses between seaanemones and their internal symbiotic algae, and parasitism, which is prevalent but is only beginning to beappreciated for its effects on community structure.

Current topicsHumans are highly dependent on intertidal habitats for food and raw materials[9], and over 50% of humans livewithin 100 km of the coast. Therefore, intertidal habitats are greatly influenced by human impacts to both ocean andland habitats. Some of the conservation issues associated with intertidal habitats and at the head of the agendas ofmanagers and intertidal ecologists are:1. Climate change: Intertidal species are challenged by several of the effects of global climate change, includingincreased temperatures, sea level rise, and increased storminess. Ultimately, it has been predicted that thedistributions and numbers of species will shift depending on their abilities to adapt (quickly!) to these newenvironmental conditions.[9] Due to the global scale of this issue, scientists are mainly working to understand andpredict possible changes to intertidal habitats.2. Invasive species: Invasive species are especially prevalent in intertidal areas with high volumes of shippingtraffic, such as large estuaries, because of the transport of non-native species in ballast water.[10] San Francisco Bay,in which an invasive Spartina cordgrass from the east coast is currently transforming mudflat communities intoSpartina meadows, is among the most invaded estuaries in the world. Conservation efforts are focused on trying toeradicate some species (like Spartina) in their non-native habitats as well as preventing further species introductions(e.g. by controlling methods of ballast water uptake and release).

Intertidal ecology 62

3. Marine protected areas: Many intertidal areas are lightly to heavily exploited by humans for food gathering (e.g.clam digging in soft-sediment habitats and snail, mussel, and algal collecting in rocky intertidal habitats). In somelocations, marine protected areas have been established where no collecting is permitted. The benefits of protectedareas may spill over to positively impact adjacent unprotected areas. For example, a greater number of larger eggcapsules of the edible snail Concholepus in protected vs. non-protected areas in Chile indicates that these protectedareas may help replenish snail stocks in areas open to harvesting.[11] The degree to which collecting is regulated bylaw differs with the species and habitat.

References

Cited[1] Somero, G. N. 2002. Thermal physiology and vertical zonation of intertidal animals: optima, limits, and cost of living. Integrative and

Comparative Biology 42:780-789.[2] Burnaford, J. L. 2004. Habitat modification and refuge from sublethal stress drive a marine plant-herbivore association. Ecology

85:2837-2849.[3] Paine, R. T. 1966. Food web complexity and species diversity. American Naturalist 100:65-75.[4] Paine, R. T. 1974. Intertidal community structure: experimental studies on the relationship between a dominant competitor and its principal

predator. Oecologia 15:93-120.[5] Connell, J. H. 1961. The influence of interspecific competition and other factors on the distribution of the barnacle Chthamalus stellatus.

Ecology 42:710-723.[6] Bruno, J. F., J. J. Stachowicz, and M. D. Bertness. 2003. Inclusion of facilitation into ecological theory. Trends in Ecology and Evolution

18:119-125.[7] Bertness, M. D., and S. D. Hacker. 1994. Physical stress and positive associations among marsh plants. American Naturalist 144:363-372.[8] Menge, B. A. 1995. Indirect effects in marine rocky intertidal interaction webs: patterns and importance. Ecological Monographs 65:21-74.[9] Harley, C. D. G., A. R. Hughes, K. M. Hultgren, B. G. Miner, C. J. B. Sorte, C. S. Thornber, L. F. Rodriguez, L. Tomanek, and S. L.

Williams. 2006. The impacts of climate change in coastal marine systems. Ecology Letters 9:228-241.[10] Cohen, A. N., and J. T. Carlton. 1998. Accelerating invasion rate in a highly invaded estuary. Science 279:555-558.[11] Manriquez, P. H., and J. C. Castilla. 2001. Significance of marine protected areas in central Chile as seeding grounds for the gastropod

Concholepus concholepus. Marine Ecology Progress Series 215:201-211.

General• Bertness MD, SD Gaines, and ME Hay (2001) Marine community ecology. Sinauer Associates, Inc.• Kozloff EN (1973) Seashore life of the northern Pacific coast. University of Washington Press.• Ricketts EF, J Calvin and JW Hedgpeth (1939) Between Pacific Tides (5th Ed.) Stanford University Press.

External links• Rocky intertidal species, Australia (http:/ / www. rockyshores. auz. info/ back_info04. htm#)

Internal tide 63

Internal tideInternal tides are generated as the surface tides move stratified water up and down sloping topography, whichproduces a wave in the ocean interior. So internal tides are internal waves at a tidal frequency. The other majorsource of internal waves is the wind which produces internal waves near the inertial frequency. When a small waterparcel is displaced from its equilibrium position, it will return either downwards due to gravity or upwards due tobuoyancy. The water parcel will overshoot its original equilibrium position and this disturbance will set off aninternal gravity wave. Munk (1981) notes, "Gravity waves in the ocean's interior are as common as waves at the seasurface-perhaps even more so, for no one has ever reported an interior calm." [1]

Simple explanation

Figure 1: Water parcels in the whole watercolumn move together with the surface tide (top),while shallow and deep waters move in opposite

directions in an internal tide (bottom). Thesurface displacement and interface displacementare the same for a surface wave (top), while foran internal wave the surface displacements are

very small, while the interface displacements arelarge (bottom). This figure is a modified version

of one appearing in Gill (1982). [2]

The surface tide propagates as a wave, in which water parcels in thewhole water column oscillate in the same direction at a given phase(i.e., in the trough or at the crest, Fig. 1, top). At the simplest level, aninternal wave can be thought of as an interfacial wave (Fig. 1, bottom).If there are two levels in the ocean, such as a warm surface layer andcold deep layer separated by a thermocline,then motions on theinterface are possible. The interface movement is large compared tosurface movement. The restoring force for internal waves and tides isstill gravity but its effect is reduced because the densities of the 2layers are relatively similar compared to the large density difference atthe air-sea interface. Thus larger displacements are possible inside theocean than at the sea surface.Tides occur mainly at diurnal and semidiurnal periods. The principallunar semidiurnal constituent is known as M2 and generally has thelargest amplitudes. (See external links for more information.)

Location

The largest internal tides are generated at steep, midocean topography such as the Hawaiian Ridge, Tahiti, theMacquarie Ridge, and submarine ridges in the Luzon Strait. [3] Continental slopes such as the Australian North WestShelf also generate large internal tides. [4] These internal tide may propagate onshore and dissipate much like surfacewaves. Or internal tides may propagate away from the topography into the open ocean. For tall, steep, midoceantopography, such as the Hawaiian Ridge, it is estimated that about 85% of the energy in the internal tide propagatesaway into the deep ocean with about 15% of its energy being lost within about 50 km of the generation site. The lostenergy contributes to turbulence and mixing near the generation sites. [5] [6] It is not clear where the energy thatleaves the generation site is dissipated, but there are 3 possible processes: 1) the internal tides scatter and/or break atdistant midocean topography, 2) interactions with other internal waves remove energy from the internal tide, or 3)the internal tides shoal and break on continental shelves.

Internal tide 64

Propagation and dissipation

Figure 2: The internal tide sea surface elevationthat is in phase with the surface tide (i.e., crestsoccur in a certain spot at a certain time that are

both the same relative to the surface tide) can bedetected by satellite (top). (The satellite track isrepeated about every 10 days and so M2 tidal

signals are shifted to longer periods due toaliasing.) The longest internal tide wavelengths

are about 150 km near Hawaii and the nextlongest waves are about 75 km long. The surfacedisplacements due to the internal tide are plotted

as wiggly red lines with amplitudes plottedperpendicular to the satellite groundtracks (black

lines). Figure is adapted from Johnston et al.(2003).

Briscoe (1975)noted that “We cannot yet answer satisfactorily thequestions: ‘where does the internal wave energy come from, wheredoes it go, and what happens to it along the way?’” [7] Althoughtechnological advances in instrumentation and modeling haveproduced greater knowledge of internal tide and near-inertial wavegeneration, Garrett and Kunze (2007) observed 33 years later that “Thefate of the radiated [large-scale internal tides] is still uncertain. Theymay scatter into [smaller scale waves] on further encounter withislands[8] [9] or the rough seafloor [10] , or transfer their energy tosmaller-scale internal waves in the ocean interior [11] ” or “break ondistant continental slopes [12]”. [13] It is now known that most of theinternal tide energy generated at tall, steep midocean topographyradiates away as large-scale internal waves. This radiated internal tideenergy is one of the main sources of energy into the deep ocean,roughly half of the wind energy input .[14] Broader interest in internaltides is spurred by their impact on the magnitude and spatialinhomogeneity of mixing, which in turn has first order effect on themeridional overturning circulation [3] [14] .[15]

The internal tidal energy in one tidal period going through an areaperpendicular to the direction of propagation is called the energy fluxand is measured in Watts/m . The energy flux at one point can besummed over depth- this is the depth-integrated energy flux and ismeasured in Watts/m. The Hawaiian Ridge produces depth-integratedenergy fluxes as large as 10 kW/m. The longest wavelength waves arethe fastest and thus carry most of the energy flux. Near Hawaii, thetypical wavelength of the longest internal tide is about 150 km whilethe next longest is about 75 km. These waves are called mode 1 andmode 2, respectively. Although Fig. 1 shows there is no sea surfaceexpression of the internal tide, there actually is a displacement of a fewcentimeters. These sea surface expressions of the internal tide atdifferent wavelengths can be detected with the Topex/Poseidon orJason-1 satellites (Fig. 2). [9] Near 15 N, 175 W on the Line IslandsRidge, the mode-1 internal tides scatter off the topography, possiblycreating turbulence and mixing, and producing smaller wavelength mode 2 internal tides. [9]

The inescapable conclusion is that energy is lost from the surface tide to the internal tide at midocean topographyand continental shelves, but the energy in the internal tide is not necessarily lost in the same place. Internal tides maypropagate thousands of kilometers or more before breaking and mixing the abyssal ocean.

Abyssal mixing and meridional overturning circulationThe importance of internal tides and internal waves in general relates to their breaking, energy dissipation, and mixing of the deep ocean. If there were no mixing in the ocean, the deep ocean would be a cold stagnant pool with a thin warm surface layer. [16] While the meridional overturning circulation (also referred to as the thermohaline circulation) redistributes about 2 PW of heat from the tropics to polar regions, the energy source for this flow is the interior mixing which is comparatively much smaller- about 2 TW. [14] Sandstrom (1908) showed a fluid which is

Internal tide 65

both heated and cooled at its surface cannot develop a deep overturning circulation. [17] Most global models haveincorporated uniform mixing throughout the ocean because they do not include or resolve internal tidal flows.However, models are now beginning to include spatially variable mixing related to internal tides and the roughtopography where they are generated and distant topography where they may break. Wunsch and Ferrari (2004)describe the global impact of spatially inhomogeneous mixing near midocean topography: “A number of lines ofevidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost whollygoverned by the forcing of the wind field and secondarily by deep water tides... The now inescapable conclusion thatover most of the ocean significant ‘vertical’ mixing is confined to topographically complex boundary areas implies apotentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulationmodels... neither explicitly accounting for the energy input into the system nor providing for spatial variability in themixing, have any physical relevance under changed climate conditions is at issue.” There is a limited understandingof “the sources controlling the internal wave energy in the ocean and the rate at which it is dissipated” and are onlynow developing some “parameterizations of the mixing generated by the interaction of internal waves, mesoscaleeddies, high-frequency barotropic fluctuations, and other motions over sloping topography.”

Internal tides at the beach

Figure 3: The internal tide produces large verticaldifferences in temperature at the research pier at

the Scripps Institution of Oceanography. Theblack line shows the surface tide elevationrelative to mean lower low water (MLLW).

Figure provided by Eric Terrill, ScrippsInstitution of Oceanography with funding from

the U.S. Office of Naval Research

Internal tides may also dissipate on continental slopes and shelves [12]

or even reach within 100 m of the beach (Fig. 3). Internal tides bringpulses of cold water shoreward and produce large vertical temperaturedifferences. When surface waves break, the cold water is mixedupwards, making the water cold for surfers, swimmers, and otherbeachgoers. Surface waters in the surf zone can change by about 10 °Cin about an hour.

References[1] Munk, W. (1981). B. A. Warren and C. Wunsch. ed. "Internal Waves and

Small-Scale Processes". Evolution of Physical Oceanography (MIT Press): 264–291.[2] Gill, A. E. (1982). Atmosphere-ocean dynamics. Academic. pp. 662.

ISBN 0-12-283522-0.[3] Simmons, H. L., R. W. Hallberg, and B. K. Arbic (2004). "Internal wave generation

in a global baroclinic tide model". Deep-Sea Res. II 51 (25–26): 3043–3068.doi:10.1016/j.dsr2.2004.09.015.

[4] Holloway, P. E. (2001). "A regional model of the semidiurnal tide on the AustralianNorth West Shelf". J. Geophys. Res.. 106 (C9): 19,625–19,638.

[5] Carter, G. S., M. A. Merrifield, J. M. Becker, K. Katsumata, M. C. Gregg, D. S. Luther, M. D. Levine, T. J. Boyd, and Y. L. Firing (2008)."Energetics of M2 Barotropic-to-Baroclinic Tidal Conversion at the Hawaiian Islands". J. Phys. Oceanogr. 38 (10): 2205–2223.doi:10.1175/2008JPO3860.1.

[6] Klymak, J. M., J. N. Moum, J. D. Nash, E. Kunze, J. B. Girton, G. S. Carter, C. M. Lee, T. B. Sanford, and M. C. Gregg (2006). "An Estimateof Tidal Energy Lost to Turbulence at the Hawaiian Ridge". J. Phys. Oceanogr. 36 (6): 1148–1164. doi:10.1175/JPO2885.1.

[7] Briscoe, M. (1975). "Introduction to a collection of papers on oceanographic internal waves". J. Geophys. Res. 80 (3): 289–290.Bibcode 1975JGR....80..289B. doi:10.1029/JC080i003p00289.

[8] Johnston, T. M. S., and M. A. Merrifield (2003). "Internal tide scattering at seamounts, ridges and islands". J. Geophys. Res.. 108 (C6) 3126(C6): 3180. Bibcode 2003JGRC..108.3180J. doi:10.1029/2002JC001528.

[9] Johnston, T. M. S., M. A. Merrifield, and P. E. Holloway (2003). "Internal tide scattering at the Line Islands Ridge". J. Geophys. Res.. 108(C11) 3365 (C11): 3365. Bibcode 2003JGRC..108.3365J. doi:10.1029/2003JC001844.

[10] St. Laurent, L. C., and C. Garrett (2002). "The Role of Internal Tides in Mixing the Deep Ocean". J. Phys. Oceanogr. 32 (10): 2882–2899.doi:10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2. ISSN 1520-0485.

[11] MacKinnon, J. A., and K. B. Winters (2005). "Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.9 degrees". Geophys.Res. Lett.. 32 L15605 (15): L15605. Bibcode 2005GeoRL..3215605M. doi:10.1029/2005GL023376.

Internal tide 66

[12] Nash, J. D., E. Kunze, J.M. Toole, and R.W. Schmitt (2004). "Internal tide reflection and turbulent mixing on the continental slope". J. Phys.Oceanogr. 34 (5): 1117–1134. doi:10.1175/1520-0485(2004)034<1117:ITRATM>2.0.CO;2. ISSN 1520-0485.

[13] Garrett, C., and E. Kunze (2007). "Internal tide generation in the deep ocean". Annu. Rev. Fluid Mech. 39 (1): 57–87.doi:10.1146/annurev.fluid.39.050905.110227.

[14] Wunsch, C., and R. Ferrari (2004). "Vertical mixing, energy, and the general circulation of the ocean". Annu. Rev. Fluid Mech. 36 (1):281–314. doi:10.1146/annurev.fluid.36.050802.122121.

[15] Munk, W., and Wunsch, C. (1998). "Abyssal recipes II: Energetics of tidal and wind mixing". Deep-Sea Res. 45 (12): 1977–2010.Bibcode 1998DSRI...45.1977M. doi:10.1016/S0967-0637(98)00070-3.

[16] Munk, W. (1966). "Abyssal recipes". Deep-Sea Res. 13: 707–730.[17] Sandstrom, J. W. (1908). "Dynamische Versuche mit Meerwasser". Ann. Hydrodyn. Marine Meteorology: 6.

External links• (http:/ / sio. ucsd. edu) Scripps Institution of Oceanography• (http:/ / www. sccoos. org/ ) Southern California Coastal Ocean Observing System• (http:/ / www. arsc. edu/ challenges/ 2004/ oceans. html) Internal Tides of the Oceans, Harper Simmons, by Jenn

Wagaman of Arctic Region Supercomputing Center• (http:/ / oceanworld. tamu. edu/ resources/ ocng_textbook/ chapter17/ chapter17_04. htm) Principal tidal

constituents in Physical oceanography textbook, Bob Stewart of Texas A&M University• (http:/ / web. uvic. ca/ ~kunze) Eric Kunze's work on internal waves, internal tides, mixing, and more

Earth tideEarth tide or body tide is the sub-meter motion of the Earth surface at periods of about 12 hours and longer. Themotion is caused by the gravity of the Moon and Sun. The largest body tide constituents are semidiurnal, but thereare also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational forcing causingearth tides and ocean tides is the same, the responses are quite different.

Tidal forcing

A. Lunar tidal forcing: this depicts theMoon directly over 30° N (or 30° S)

viewed from above the NorthernHemisphere.

B. This view shows same forcing from180° from view A. Viewed from abovethe Northern Hemisphere. Red up, blue

down.

The larger of the periodic gravitational forcings is from the Moon but that of the Sun is also important. The images here show lunar tidal forcing when the Moon appears directly over 30° N (or 30° S). This pattern remains fixed with the red area directed toward (or directly away from) the Moon. Red indicates upward pull, blue downward. If, for example the Moon is directly over 90° W (or 90° E), the center of the red areas are centered on the western northern

Earth tide 67

hemisphere, on upper right. Red up, blue down. If for example the Moon is directly over 90° W (90° E), the center ofthe red area is 30° N, 90° W and 30° S, 90° E, and the center of the bluish band follows the great circle equidistantfrom those points. At 30° latitude a strong peak occurs once per lunar day, giving significant diurnal forcing at thatlatitude. Along the equator two equally sized peaks (and depressions) are equally sized, giving semi-diurnal forcingthere.

Body tide

Vertical displacements of sectorialmovement. Red up, blue down.

East-west displacements of sectorialmovement. Red east, blue west.

North-south displacements of sectorialmovement. Red north, blue south.

Vertical displacements of tessearalmovement. Red up, blue down.

East-West displacements of tessearalmovement. Red east, blue west.

North-South displacements of tessearalmovement. Red north, blue south.

Vertical displacements of zonalmovement. Red up, blue down.

The Earth tide encompasses the entire body of the Earth and is unhindered bythe thin crust and land masses of the surface, on scales that make the rigidityof rock irrelevant. Ocean tides are a consequence of the resonance of the samedriving forces with water movement periods in ocean basins accumulatedover many days, so that their amplitude and timing are quite different andvary over short distances of just a few hundred kilometres. The oscillationperiods of the earth as a whole are not near the astronomical periods, so itsflexing is due to the forces of the moment.

The tide components with a period near twelve hours have a lunar amplitude(earth bulge/depression distances) that are a little more than twice the heightof the solar amplitudes, as tabulated below. At new and full moon, the Sun

Earth tide 68

and the Moon are aligned, and the lunar and the solar tidal maxima and minima (bulges and depressions) addtogether for the greatest tidal range at particular latitudes. At first- and third-quarter phases of the moon, lunar andsolar tides are in opposition, and the tidal range is at a minimum. The semi-diurnal tides go through one full cycle (ahigh and low tide) about once every 12 hours and one full cycle of maximum height (a spring and neap tide) aboutonce every 14 days.The classical theory of Earth tides first became established in 1905,[1] primarily to explain nutations, but are alsoused in Earth rotation predictions. The semi-diurnal tide (one maximum every 12 or so hours) is primarily lunar(only S2 is purely solar) and gives rise to sectorial deformations which rise and fall at the same time along the samelongitude.[2] Sectorial variations of vertical and east-west displacements are maximum at the equator and vanish atthe poles. There are two cycles along each latitude, the bulges opposite one another, and the depressions similarlyopposed. The diurnal tide is lunisolar, and gives rise to tesseral deformations. The vertical and east-west movementis maximum at 45° latitude and is zero on the equator and at the poles. Tesseral variation have one cycle per latitude,one bulge and one depression; the bulges are opposed (antipodal), that is to say the western part of the northernhemisphere and the eastern part of the southern hemisphere, for example, and similarly the depressions are opposed,the eastern part of the northern hemisphere and the western part of the southern hemisphere, in this case. Finally,fortnightly and semi-annual tides have 'zonal' deformations (constant along a circle of latitude), as the Moon or Sungravitation is directed alternately away from the northern and southern hemispheres due to tilt. There is zero verticaldisplacement at 35°16' latitude.Since these displacements affect the vertical direction east-west and north-south variations are often tabulated inmilliarc seconds for astronomical use. The vertical displacement is frequent tabulated in μgal, since the gradient ofgravity is location dependent so that the distance conversion is only approximately 3 μgal per cm

Other Earth tide contributorsIn coastal areas because the ocean tide is quite out of step with the earth tide, at high ocean tide there is an excess (orat low tide a deficit) of water about what would be the gravitational equilibrium level and the adjacent ground falls(or rises) in response to the resulting differences in weight. Displacements caused by ocean tidal loading can exceedthe displacements due to the earth body tide. Sensitive instruments far inland often have to make similar corrections.Atmospheric loading and storm events may also be measurable, though the masses in movement are less weighty.

Tidal constituentsPrincipal body tide constituents. The amplitudes may vary from those listed within several per cent.[3][4]

Semi-diurnalTidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)

M2 12.421 hr 384.83 53.84

S2 (solar semi-diurnal) 12.000 hr 179.05 25.05

N2 12.658 hr 73.69 10.31

K2 11.967 hr 48.72 6.82

DiurnalTidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)

K1 23.934 hr 191.78 32.01

O1 25.819 hr 158.11 22.05

P1 24.066 hr 70.88 10.36

φ1 23.804 hr 3.44 0.43

Earth tide 69

ψ1 23.869 hr 2.72 0.21

S1 (solar diurnal) 24.000 hr 1.65 0.25

Long termTidal constituent Period Vertical amplitude (mm) Horizontal amplitude (mm)

Mf 13.661 days 40.36 5.59

Mm (moon monthly) 27.555 days 21.33 2.96

Ssa (solar semi-annual) 0.50000 yr 18.79 2.60

Lunar node 18.613 yr 16.92 2.34

Sa (solar annual) 1.0000 yr 2.97 0.41

Earth tide effectsVolcanologists use the regular, predictable Earth tide movements to calibrate and test sensitive volcano deformationmonitoring instruments. The tides may also trigger volcanic events. [5] Seismologists have determined thatmicroseismic events are correlated to tidal variations in Central Asia (north of the Himalayas). [6] The semidiurnalamplitude of terrestrial tides can reach about 55 cm at the equator which is important in GPS calibration and VLBImeasurements. Also to make precise astronomical angular measurements requires knowledge of the Earth's rate ofrotation and nutation, both of which are influenced by earth tides. Terrestrial tides also need to be taken in account inthe case of some particle physics experiments. [7] For instance, at the CERN or SLAC, the very large particleaccelerators were designed while taking terrestrial tides into account for proper operation. Among the effects thatneed to be taken into account are circumference deformation for circular accelerators and particle beam energy. [8]

Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth'smagnetic field itself.

Notes[1] A.E.H. Love, Proc. Roy. Soc. London, 82, 1905[2] Paul Melchior, "Earth Tides", Surveys in Geophysics, 1, pp. 275-303, March, 1974.[3] John Wahr, "Earth Tides", Global Earth Physics, A Handbook of Physical Constants, AGU Reference Shelf, 1, pp. 40-46, 1995.[4] Michael R. House, "Orbital forcing timescales: an introduction", Geological Society, London, Special Publications; 1995; v. 85; p. 1-18.

http:/ / sp. lyellcollection. org/ cgi/ content/ abstract/ 85/ 1/ 1[5][5] Sottili G., Martino S., Palladino D.M., Paciello A., Bozzano F. (2007), Effects of tidal stresses on volcanic activity at Mount Etna, Italy,

Geophys. Res. Lett., 34, L01311, doi:10.1029/2006GL028190, 2007.[6] Volcano watch (http:/ / hvo. wr. usgs. gov/ volcanowatch/ 1998/ 98_05_28. html), USGS.[7] Accelerator on the move, but scientists compensate for tidal effects (http:/ / news-service. stanford. edu/ news/ 2000/ march29/ linac-329.

html), Stanford online.[8] CERN circumference deformation (http:/ / accelconf. web. cern. ch/ accelconf/ e00/ PAPERS/ MOP5A04. pdf); CERN particle beam energy

(http:/ / accelconf. web. cern. ch/ accelconf/ p93/ PDF/ PAC1993_0044. PDF) affects.

References• Paul Melchior, Earth Tides, Pergamon Press, Oxford, 1983.

Galactic tide 70

Galactic tide

The Mice Galaxies NGC 4676

A galactic tide is a tidal force experiencedby objects subject to the gravitational fieldof a galaxy such as the Milky Way.Particular areas of interest concerninggalactic tides include galactic collisions, thedisruption of dwarf or satellite galaxies, andthe Milky Way's tidal effect on thehypothesized Oort Cloud of our own solarsystem.

Origin

A body in proximity to a larger mass becomes stretched out by tidalforces

When one body (like the blue object in the diagrams atleft) is in the gravitational field of a large mass (theyellow object), it becomes tidally distorted.

Gravitational attraction increases with decreasingdistance; the closer any object A is to another object B,the more intensely A is affected by the object B'sgravity, according to Newton's law of universalgravitation. This is also true of the different parts of anobject; The surface of object A feels a strongerattraction to object B than the core of object A. Whenthe other object's gravity is particularly strong, thiscauses the smaller object's surface to pull away fromthe core, and the object to distend and flatten in thedirection of the larger object. The large body feels asimilar but far weaker distortion caused in the sameway by the gravitational field of the small body. Intechnical terms, the equilibrium shape of the small

body is the one that minimizes its gravitational potential energy. In empty space, this would be a sphere. However, inthe proximity of the large body, the lowest potential energy shape is an ovoid stretched along the axis connecting thetwo bodies.

For example, the tides on Earth are caused by the distortion that the Moon and the Sun cause to the Earth'sgravitational field. In this case, the Earth's rotation is slow enough that the Earth is able to reshape itself so that thedistortions remain oriented approximately in the direction of the Moon and the Sun. From the point of view of aperson on the surface, we pass over the long axes of the distortions approximately twice a day for each, at whichpoints high tide are experienced. Since the relative positions of the Earth, Sun and Moon are constantly changing, thetidal effects reinforce or counteract each other to various degrees. (see Spring tide and Neap tide).Galactic tides demonstrate the same processes on a far grander scale. Tidally interacting galaxies will be stretchedtowards each other. They may eventually flatten out and distend towards the galaxy's centre, or suffer perturbationsto their orbits. Furthermore, if the galaxies are rapidly rotating, their sections may not be able to keep up with the

Galactic tide 71

distortion like the Earth, and long tails of stars and other highly distorted regions can be formed, as seen in thediagrams in this article.

Effects on external galaxies

Galaxy collisions

The lengthy tidal tails of the colliding antennaegalaxies

Tidal forces are dependent on the gradient of a gravitational field,rather than its strength, and so tidal effects are usually limited tothe immediate surroundings of a galaxy. Two large galaxiesundergoing collisions or passing nearby each other will besubjected to very large tidal forces, often producing the mostvisually striking demonstrations of galactic tides in action.Two interacting galaxies will not always collide head-on (if at all),and the tidal forces will distort each galaxy along an axis pointingroughly towards and away from its perturber. As the two galaxiesbriefly orbit each other, these distorted regions, pulled away fromthe main body of each galaxy, will be sheared by the galaxy'sdifferential rotation and flung off into intergalactic space, formingtidal tails. Such tails are typically strongly curved; where a tailappears straight, it is probably being viewed edge-on. The starsand gas that comprise the tails will have been pulled from theeasily distorted galactic discs (or other extremities) of one or bothbodies, rather than the gravitationally bound galactic centres.[1]

Two very prominent examples of collisions producing tidal tailsare the Mice Galaxies and the Antennae Galaxies.

Just as the Moon raises two water tides on opposite sides of the Earth, so a galactic tide produces two arms in itsgalactic companion. While a large tail is formed if the perturbed galaxy is equal to or less massive than its partner, ifit is significantly more massive than the perturbing galaxy, then the trailing arm will be relatively minor, and theleading arm, sometimes called a bridge, will be more prominent.[1] Tidal bridges are typically harder to distinguishthan tidal tails: in the first instance, the bridge may be absorbed by the passing galaxy or the resulting mergedgalaxy, making it visible for a shorter duration than a typical large tail. Secondly, if one of the two galaxies is in theforeground, then the second galaxy — and the bridge between them — may be partially obscured. Together, theseeffects can make it hard to see where one galaxy ends and the next begins. Tidal loops, where a tail joins with itsparent galaxy at both ends, are rarer still.[2]

Galactic tide 72

Satellite interactions

The Andromeda Galaxy. Note its satellite galaxy M32 (top left), whose outer armshave been stripped away by Andromeda's tidal forces.

Because tidal effects are strongest in theimmediate vicinity of a galaxy, satellitegalaxies are particularly likely to beaffected. Such an external force upon asatellite can produce ordered motions withinit, leading to large-scale observable effects:the interior structure and motions of a dwarfsatellite galaxy may be severely affected bya galactic tide, inducing rotation (as with thetides of the Earth's oceans) or an anomalousmass-to-luminosity ratio.[3] Satellitegalaxies can also be subjected to the sametidal stripping that occurs in galacticcollisions, where stars and gas are torn fromthe extremities of a galaxy, possibly to beabsorbed by its companion. The dwarf

galaxy M32, a satellite galaxy of Andromeda, may have lost its spiral arms to tidal stripping, while a high starformation rate in the remaining core may be the result of tidally-induced motions of the remaining molecularclouds[4] (Because tidal forces can knead and compress the interstellar gas clouds inside galaxies, they induce largeamounts of star formation in small satellites. The process is somewhat similar to making something hotter bysqueezing it).

The stripping mechanism is the same as between two comparable galaxies, although its comparatively weakgravitational field ensures that only the satellite, not the host galaxy, is affected. If the satellite is very smallcompared to the host, the tidal debris tails produced are likely to be symmetric, and follow a very similar orbit,effectively tracing the satellite's path.[5] However, if the satellite is reasonably large—typically over one tenthousandth the mass of its host—then the satellite's own gravity may affect the tails, breaking the symmetry andaccelerating the tails in different directions. The resulting structure is dependent on both the mass and orbit of thesatellite, and the mass and structure of the conjectured galactic halo around the host, and may provide a means ofprobing the dark matter potential of a galaxy such as the Milky Way.[6]

Over many orbits of its parent galaxy, or if the orbit passes too close to it, a dwarf satellite may eventually becompletely disrupted, to form a tidal stream of stars and gas wrapping around the larger body. It has been suggestedthat the extended discs of gas and stars around some galaxies, such as Andromeda, may be the result of the completetidal disruption (and subsequent merger with the parent galaxy) of a dwarf satellite galaxy.[7]

Effects on bodies within a galaxyTidal effects are also present within a galaxy, where their gradients are likely to be steepest. This can haveconsequences for the formation of stars and planetary systems. Typically a star's gravity will dominate within its ownsystem, with only the passage of other stars substantially affecting dynamics. However, at the outer reaches of thesystem, the star's gravity is weak and galactic tides may be significant. In our own solar system, the hypotheticalOort cloud, believed to be the source of long-period comets, lies in this transitional region.

Galactic tide 73

Diagram of the Oort cloud.

The Oort cloud is believed to be a vast shellsurrounding our solar system, possibly over a light-yearin radius. Across such a vast distance, the gradient ofthe Milky Way's gravitational field plays a far morenoticeable role. Because of this gradient, galactic tidesmay then deform an otherwise spherical Oort cloud,stretching the cloud in the direction of the galacticcentre and compressing it along the other two axes, justas the Earth distends in response to the gravity of theMoon.

The Sun's gravity is sufficiently weak at such a distancethat these small galactic perturbations may be enoughto dislodge some planetesimals from such distantorbits, sending them towards the Sun and planets bysignificantly reducing their perihelion.[8] Such a body,being composed of a rock and ice mixture, would become a comet when subjected to the increased solar radiationpresent in the inner solar system.

It has been suggested that the galactic tide may also contribute to the formation of an Oort cloud, by increasing theperihelion of planetesimals with large aphelion.[9] This shows that the effects of the galactic tide are quite complex,and depend heavily on the behaviour of individual objects within a planetary system. Cumulatively the effect can bequite significant, however; up to 90% of all comets originating from an Oort cloud may be the result of the galactictide.[10]

References[1] Toomre A. & Toomre J. (1972). "Galactic Bridges and Tails". The Astrophysical Journal 178: 623–666. Bibcode 1972ApJ...178..623T.

doi:10.1086/151823.[2] Wehner E.H. et al. (2006). "NGC 3310 and its tidal debris: remnants of galaxy evolution". Monthly Notices of the Royal Astronomical Society

371 (3): 1047–1056. arXiv:astro-ph/0607088. Bibcode 2006MNRAS.371.1047W. doi:10.1111/j.1365-2966.2006.10757.x.[3] Piatek S. & Pryor C. (1993). "Can Galactic Tides Inflate the Apparent M/L's of Dwarf Galaxies?". Bulletin of the American Astronomical

Society 25: 1383. Bibcode 1993AAS...183.5701P.[4] Bekki, Kenji; Couch, Warrick J.; Drinkwater, Michael J.; Gregg, Michael D. (2001). "A New Formation Model for M32: A Threshed

Early-Type Spiral Galaxy?". The Astrophysical Journal 557 (1): Issue 1, pp. L39–L42. arXiv:astro-ph/0107117.Bibcode 2001ApJ...557L..39B. doi:10.1086/323075.

[5] Johnston, K.V.; Hernquist, L. & Bolte, M. (1996). "Fossil Signatures of Ancient Accretion Events in the Halo". The Astrophysical Journal465: 278. arXiv:astro-ph/9602060. Bibcode 1996ApJ...465..278J. doi:10.1086/177418.

[6] Choi, J.-H.; Weinberg, M.D.; Katz, N. (2007). "The dynamics of tidal tails from massive satellites". Monthly Notices of the RoyalAstronomical Society 381 (3): 987–1000. arXiv:astro-ph/0702353. Bibcode 2007MNRAS.381..987C. doi:10.1111/j.1365-2966.2007.12313.x.

[7] Peñarrubia J., McConnachie A. & Babul A. (2006). "On the Formation of Extended Galactic Disks by Tidally Disrupted Dwarf Galaxies".The Astrophysical Journal 650 (1): L33–L36. arXiv:astro-ph/0606101. Bibcode 2006ApJ...650L..33P. doi:10.1086/508656.

[8] Fouchard M. et al. (2006). "Long-term effects of the Galactic tide on cometary dynamics". Celestial Mechanics and Dynamical Astronomy 95(1–4): 299–326. Bibcode 2006CeMDA..95..299F. doi:10.1007/s10569-006-9027-8.

[9] Higuchi A., Kokubo E. & Mukai, T. (2005). "Orbital Evolution of Planetesimals by the Galactic Tide". Bulletin of the American AstronomicalSociety 37: 521. Bibcode 2005DDA....36.0205H.

[10] 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 (4): 1367–1376. Bibcode 2001MNRAS.327.1367N.doi:10.1046/j.1365-8711.2001.04854.x.

Tidal locking 74

Tidal lockingTidal locking (or captured rotation) occurs when the gravitational gradient makes one side of an astronomicalbody always face another; for example, the same side of the Earth's Moon always faces the Earth. A tidally lockedbody takes just as long to rotate around its own axis as it does to revolve around its partner. This synchronousrotation causes one hemisphere constantly to face the partner body. Usually, at any given time only the satellite istidally locked around the larger body, but if the difference in mass between the two bodies and their physicalseparation is small, each may be tidally locked to the other, as is the case between Pluto and Charon. This effect isemployed to stabilize some artificial satellites.

MechanismThe change in rotation rate necessary to tidally lock a body B to a larger body A is caused by the torque applied byA's gravity on bulges it has induced on B by tidal forces.

Tidal bulgesA's gravity produces a tidal force on B which distorts its gravitational equilibrium shape slightly so that it becomeselongated along the axis oriented toward A, and conversely, is slightly reduced in dimension in directionsperpendicular to this axis. These distortions are known as tidal bulges. When B is not yet tidally locked, the bulgestravel over its surface, with one of the two "high" tidal bulges traveling close to the point where body A is overhead.For large astronomical bodies which are near-spherical due to self-gravitation, the tidal distortion produces a slightlyprolate spheroid - i.e., an axially symmetric ellipsoid that is elongated along its major axis. Smaller bodies alsoexperience distortion, but this distortion is less regular.

Bulge draggingThe material of B exerts resistance to this periodic reshaping caused by the tidal force. In effect, some time isrequired to reshape B to the gravitational equilibrium shape, by which time the forming bulges have already beencarried some distance away from the A-B axis by B's rotation. Seen from a vantage point in space, the points ofmaximum bulge extension are displaced from the axis oriented towards A. If B's rotation period is shorter than itsorbital period, the bulges are carried forward of the axis oriented towards A in the direction of rotation, whereas ifB's rotation period is longer the bulges lag behind instead.

Resulting torqueSince the bulges are now displaced from the A-B axis, A's gravitational pull on the mass in them exerts a torque onB. The torque on the A-facing bulge acts to bring B's rotation in line with its orbital period, while the "back" bulgewhich faces away from A acts in the opposite sense. However, the bulge on the A-facing side is closer to A than theback bulge by a distance of approximately B's diameter, and so experiences a slightly stronger gravitational forceand torque. The net resulting torque from both bulges, then, is always in the direction which acts to synchronize B'srotation with its orbital period, leading eventually to tidal locking.

Tidal locking 75

Orbital changes

If rotational frequency is larger than orbitalfrequency, a small torque counteracting the

rotation arises, eventually locking the frequencies(situation depicted in green)

The angular momentum of the whole A-B system is conserved in thisprocess, so that when B slows down and loses rotational angularmomentum, its orbital angular momentum is boosted by a similaramount (there are also some smaller effects on A's rotation). Thisresults in a raising of B's orbit about A in tandem with its rotationalslowdown. For the other case where B starts off rotating too slowly,tidal locking both speeds up its rotation, and lowers its orbit.

Locking of the larger body

The tidal locking effect is also experienced by the more massive bodyA, but at a slower rate because B's gravitational effect is weaker due toB's lower mass. For example, the Earth's rotation is gradually slowing down because of the Moon, by an amount thatbecomes noticeable over geological time in some fossils.[1] For bodies of similar mass the effect may be ofcomparable size for both, and both may become tidally locked to each other. The dwarf planet Pluto and its satelliteCharon are good examples of this—Charon is only visible from one hemisphere of Pluto and vice versa.

Rotation–orbit resonanceFinally, in some cases where the orbit is eccentric and the tidal effect is relatively weak, the smaller body may endup in an orbital resonance, rather than tidally locked. Here the ratio of rotation period to orbital period is somewell-defined fraction different from 1:1. A well known case is the rotation of Mercury—locked to its orbit aroundthe Sun in a 3:2 resonance.

Occurrence

Moons

Due to tidal locking, the inhabitants of the centralbody will never be able to see its side marked

with green.

Most significant moons in the Solar System are tidally locked withtheir primaries, since they orbit very closely and tidal force increasesrapidly (as a cubic) with decreasing distance. Notable exceptions arethe irregular outer satellites of the gas giant planets, which orbit muchfarther away than the large well-known moons.

Pluto and Charon are an extreme example of a tidal lock. Charon is arelatively large moon in comparison to its primary and also has a veryclose orbit. This has made Pluto also tidally locked to Charon. Ineffect, these two celestial bodies revolve around each other (theirbarycenter lies outside of Pluto) as if joined with a rod connecting twoopposite points on their surfaces.

The tidal locking situation for asteroid moons is largely unknown, butclosely orbiting binaries are expected to be tidally locked, as well ascontact binaries.

Tidal locking 76

Earth's Moon

Since the Moon is 1:1 tidally locked, only oneside is visible from Earth.

The Moon's rotation and orbital periods are both just under four weeks,so no matter when the Moon is observed from the Earth the samehemisphere of the Moon is always seen. The far side of the Moon wasnot seen in its entirety until 1959, when photographs were transmittedfrom the Soviet spacecraft Luna 3.

Despite the Moon's rotational and orbital periods being exactly locked,about 59% of the moon's total surface may be seen with repeatedobservations from earth due to the phenomena of librations andparallax. Librations are primarily caused by the Moon's varying orbitalspeed due to the eccentricity of its orbit: this allows earthlings to see upto about 6° more along its perimeter. Parallax is a geometric effect: atthe surface of the Earth we are offset from the line through the centersof Earth and Moon, and because of this we can observe a bit (about 1°)more around the side of the Moon when it is on our local horizon.

Planets

Until radar observations in 1965 proved otherwise, it was thought that Mercury was tidally locked with the Sun.Instead, it turned out that Mercury has a 3:2 spin–orbit resonance, rotating three times for every two revolutionsaround the Sun; the eccentricity of Mercury's orbit makes this resonance stable. Astronomers originally thoughtMercury was tidally locked because whenever it was best placed for observation it was at the same point in its 3:2resonance, showing the same face, just as it would appear if it were tidally locked.

Venus' 583.92-day interval between successive close approaches to the Earth is almost exactly equal to 5 Venusiansolar days (precisely, 5.001444 of these), making approximately the same face visible from Earth at each closeapproach. Whether this relationship arose by chance or is the result of some kind of tidal locking with the Earth isunknown.[2]

StarsClose binary stars throughout the universe are expected to be tidally locked with each other, and extrasolar planetsthat have been found to orbit their primaries extremely closely are also thought to be tidally locked to them. Anunusual example, confirmed by MOST, is Tau Boötis, a star tidally locked by a planet. The tidal locking is almostcertainly mutual.[3]

TimescaleAn estimate of the time for a body of mass to become tidally locked can be obtained using the followingformula: [4]

where• is the initial spin rate (radians per second)• is the semi-major axis of the motion of the satellite around the primary• is the moment of inertia of the satellite• is the dissipation function of the satellite.• is the gravitational constant

Tidal locking 77

• is the mass of the primary• is the tidal Love number of the satellite• is the radius of the satellite.

Q and are generally very poorly known except for the Earth's Moon which has . However, fora really rough estimate one can take Q≈100 (perhaps conservatively, giving overestimated locking times), and

where• is the density of the satellite• is the surface gravity of the satellite• is rigidity of the satellite. This can be roughly taken as 3×1010 Nm−2 for rocky objects and 4×109 Nm−2 for icy

ones.As can be seen, even knowing the size and density of the satellite leaves many parameters that must be estimated(especially w, Q, and ), so that any calculated locking times obtained are expected to be inaccurate, to evenfactors of ten. Further, during the tidal locking phase the orbital radius a may have been significantly different fromthat observed nowadays due to subsequent tidal acceleration, and the locking time is extremely sensitive to thisvalue.Since the uncertainty is so high, the above formulas can be simplified to give a somewhat less cumbersome one. Byassuming that the satellite is spherical, , Q = 100, and it is sensible to guess one revolution every 12 hoursin the initial non-locked state (most asteroids have rotational periods between about 2 hours and about 2 days)

with masses in kg, distances in meters, and μ in Nm−2.As before, note the extremely strong dependence on orbital radius a.For the locking of a primary body to its satellite as in the case of Pluto to Charon, satellite and primary bodyparameters can be interchanged.One conclusion is that other things being equal (such as Q and μ), a large satellite will lock faster than a smallersatellite at the same orbital radius from the primary body because grows much faster with satellite radius than

. A possible example of this is in the Saturn system, where Hyperion is not tidally locked, while the largerIapetus, which orbits at a greater distance, is. It must be noted, however, that this is not clear cut because Hyperionalso experiences strong driving from the nearby Titan, which forces its rotation to be chaotic.

List of known tidally locked bodies

Solar SystemLocked to the Sun

• Mercury (in a 3:2 rotation:orbit resonance)Locked to the Earth

•• MoonLocked to Mars

•• Phobos•• DeimosLocked to Jupiter

Tidal locking 78

•• Metis•• Adrastea•• Amalthea•• Thebe•• Io•• Europa•• Ganymede•• CallistoLocked to Saturn

•• Pan•• Atlas•• Prometheus•• Pandora•• Epimetheus•• Janus•• Mimas•• Enceladus•• Telesto•• Tethys•• Calypso•• Dione•• Rhea•• Titan•• IapetusLocked to Uranus

•• Miranda•• Ariel•• Umbriel•• Titania•• OberonLocked to Neptune

•• Proteus•• TritonLocked to Pluto

• Charon (Pluto is itself locked to Charon)

Tidal locking 79

Extra-solar• Tau Boötis is known to be locked to the close-orbiting giant planet Tau Boötis b.[3]

Bodies likely to be locked

Solar SystemBased on comparison between the likely time needed to lock a body to its primary, and the time it has been in itspresent orbit (comparable with the age of the Solar System for most planetary moons), a number of moons arethought to be locked. However their rotations are not known or not known enough. These are:Probably locked to Saturn

•• Daphnis•• Methone•• Pallene•• Helene•• PolydeucesProbably locked to Uranus

•• Cordelia•• Ophelia•• Bianca•• Cressida•• Desdemona•• Juliet•• Portia•• Rosalind•• Cupid•• Belinda•• Perdita•• Puck•• Mab•• OberonProbably locked to Neptune

•• Naiad•• Thalassa•• Despina•• Galatea•• Larissa

Tidal locking 80

Extra-solar• Gliese 581 c may be tidally locked to its parent star Gliese 581.[5]

• If it exists, Gliese 581 g is probably tidally locked to its parent star Gliese 581.[6] [7]

• Gliese 581 b, Gliese 581 d, and Gliese 581 e may be tidally locked to their parent star Gliese 581.• 55 Cancri e is tidally locked to its parent star 55 Cancri. [8]

References[1] de Pater, Imke (2001). Planetary Sciences. Cambridge. p. 34. ISBN 0-521-48219-4.[2] Gold T., Soter S. (1969), Atmospheric tides and the resonant rotation of Venus, Icarus, v. 11, p 356-366[3] SPACE.com - Role Reversal: Planet Controls a Star (http:/ / www. space. com/ scienceastronomy/ 050523_star_tide. html)[4] B. Gladman et al. (1996). "Synchronous Locking of Tidally Evolving Satellites". Icarus 122: 166. Bibcode 1996Icar..122..166G.

doi:10.1006/icar.1996.0117. (See pages 169-170 of this article. Formula (9) is quoted here, which comes from S.J. Peale, Rotation histories ofthe natural satellites, in J.A. Burns, ed. (1977). Planetary Satellites. Tucson: University of Arizona Press. pp. 87–112.)

[5] Vergano, Dan (2007-04-25). "Out of our world: Earthlike planet" (http:/ / www. usatoday. com/ printedition/ news/ 20070425/1a_bottomstrip25_dom. art. htm). USA Today. . Retrieved 2010-05-25.

[6] "Astronomers Find Most Earth-like Planet to Date" (http:/ / news. sciencemag. org/ sciencenow/ 2010/ 09/ astronomers-find-most-earth-like.html). Science, USA. September 29, 2010. . Retrieved September 30, 2010.

[7] "Gliese 581g the most Earth like planet yet discovered" (http:/ / www. telegraph. co. uk/ science/ space/ 8033124/Gliese-581g-the-most-Earth-like-planet-yet-discovered. html). The Daily Telegraph, UK. September 30, 2010. . Retrieved September 30,2010.

[8] "NASA Space Telescope Sees the Light from an Alien Super-Earth" (http:/ / science. nasa. gov/ science-news/ science-at-nasa/ 2012/08may_superearth/ ). NASA. 2012-05-08. . Retrieved 2012-05-10.

Tidal prismA tidal prism is the volume of water in an estuary or inlet between mean high tide and mean low tide.[1] or thevolume of water leaving an estuary at ebb tide.[2]

The inter-tidal prism volume can be expressed by the relationship: P=H A , where H is the average tidal range and Ais the average surface area of the basin.[3] It can also be thought of as the volume of the incoming tide plus the riverdischarge.[4] Simple tidal prism models stated the relationship of river discharge and inflowing ocean water asPrism=Volume of ocean water coming into an estuary on the flood tide + Volume of river discharge mixing with thatocean water; however, there is some controversy as to whether traditional prism models are accurate.[1] The size ofan estuary’s tidal prism is dependent on the basin of that estuary, the tidal range and other frictional forces.

Applications of Tidal PrismCalculations of tidal prism are useful in determining the residence time of water (and pollutants) in an estuary. If it isknown how much water is exported compared to how much of the estuarine water remains, it can be determined howlong pollutants reside in that estuary. If the tidal prism forms a large proportion of the water in an estuary at hightide, then when the tide ebbs, it will take with it the majority of the water (this occurs in shallow estuaries) and anypollutants or sediments suspended in that water. This means that the estuary has a good flushing time, or that theresidence time of water in that estuary is low.[4] On the contrary, in deeper estuaries, the amount of water that isinfluenced by the tides forms a smaller proportion of the total water. The difference between high tide and low tide isnot as great as in shallower estuaries creating a smaller tidal prism and a longer residence time.The size of an inlet or estuary is determined, according to O’Brien[5] by tidal prism. Tidal prism magnitude can be calculated by multiplying the area of the estuary by the tidal range of that estuary.[6] During spring or fall tides, when sea level is relatively high and floods backbarrier areas that are normally above tidal inundation, the cross sectional area at the entrance of the estuary increases as tidal prism increases.[5] Since tidal prism is largely a function of area of open water and tidal range, it can be changed by alterations of the basin area of estuaries and inlets as in dredging;

Tidal prism 81

however, if the estuary or inlet is dredged, or the size changed, the channel will fill in with sediment until it hasreturned to tidal prism equilibrium.[6]

Sand TransportAdditionally, there are correlations between tidal prism and amount of sediment deposited and exported in an estuaryor inlet. The Walton and Adams[7] relationship shows a strong relationship between the magnitude of the tidal prismand the volume of sand in ebb dominated deltas. The larger the tidal prism, the larger the amount of sand that isdeposited in deltas in ebb-dominated estuaries.[7] Inlets with small tidal prisms have too little power to remove sanddeposited from adjacent shores. Inlets with large tidal prisms can erode sand and deposit it in ebb-tidal deltas indeeper waters (National Research Council). The size of ebb tidal deltas is proportional to tidal prism.[7] If tidal prismincreases, there is an increase in deltas and shoals formed by sand transport during ebb tide.[8]

Tidal Prism Models and AssumptionsThere are assumptions that go along with tidal prism models. The first is that they are applied to smaller estuaries(less than a few kilometers wide) and secondly, that the estuaries are internally well mixed.[3] Additionally, it isassumed that the water entering the estuary is of oceanic salinity mixing with the fresh river discharge, and that themixed water will be exported on the ebb tide. Officer[9] provides a model for simple tidal prism theory where theestuary is represented by a box with the inflow as the volume of river discharge at a salinity of 0, within the estuary,the river discharge mixes with the volume of the tide flooding in (Vp) from the ocean at oceanic salinity (So) and themixed VR + VP) water flows out at ebb tide.

References[1][1] Luketina, D. 1998. Simple tidal prism models revisited. Estuarine, Coastal and Shelf Science; Vol. 46. pp. 77-84.[2][2] Davis, R., D.M. Fitzgerald. 2004. Beaches and Coasts. Blackwell Science Ltd. Malden, MA.[3][3] Lakhan, V.C. (ed). 2003. Advances in Coastal Modelling. Amsterdam, The Netherlands; Elsevier B.V. pp.[4][4] Hume, T.M. 2005. Tidal Prism. Encyclopedia of Coastal Science. Springer Netherlands. M.L. Schwartz, editor. pp. 981. Accessed via

Springerlink database October 13, 2009.[5] O’Brien, M.P. 1931. Estuary tidal prisms related to entrance areas. Civil Engineer; Vol. 1. pp. 738-739.[6][6] Davis, R., D.M. Fitzgerald. 2004. Beaches and Coasts. Blackwell Science Ltd. Malden, MA[7][7] Walton, T.L., W.D. Adams. 1976. Capacity of inlet outer bars to store sand. In Proceedings of the 15th Coastal Engineering Conference,

Honolulu, HI: ASCE, pp. 1919-37.[8][8] National Research Council (U.S.). Committee on Engineerings Implications of Changes in Relative Mean Sea Level. 1987. Responding to

changes in sea level. Washington DC, United States. National Academy Press.[9][9] Officer, C. B. 1976. Physical Oceanography of Estuaries (and Associated Coastal Waters). Wiley, London.

Tidal range 82

Tidal range

The tidal range is difference between the high tide and the low tide.

The tidal range is the verticaldifference between the high tide andthe succeeding low tide. Tides are therise and fall of sea levels caused by thecombined effects of the gravitationalforces exerted by the Moon and theSun and the rotation of the Earth. Thetidal range is not constant, but changesdepending on where the sun and themoon are.

The most extreme tidal range occursaround the time of the full or new moons, when the gravitational forces of both the Sun and Moon are in phasereinforcing each other in the same direction (new moon), or are exactly the opposite phase (full). This type of tide isknown as a spring tide. During neap tides, when the Moon and Sun's gravitational force vectors act in quadrature(making a right angle to the Earth's orbit), the difference between high and low tides is smaller. Neap tides occurduring the first and last quarters of the moon's phases. The largest annual tidal range can be expected around the timeof the Equinox, if coincidental with a spring tide.

Tidal data for coastal areas is published by the National Hydrographic service of the country concerned[1] Tidal datais based on astronomical phenomena and is predictable. Storm force winds blowing from a steady direction for aprolonged time interval combined with low barometric pressure can increase the tidal range particularly in narrowbays. Such weather related effects on the tide, which can cause ranges in excess of predicted values and can causelocalized flooding are not calculable in advance.

GeographyThe typical tidal range in the open ocean is about 0.6 metres (2 feet). Closer to the coast, this range is much greater.Coastal tidal ranges vary globally and can differ anywhere from near zero to over 11 metres (38 feet).[2] The exactrange depends on the volume of water adjacent to the coast, and the geography of the basin the water sits in. Largerbodies of water have higher ranges, and the geography can act as a funnel amplifying or dispersing the tide.[3] Theworld's largest tidal range of 11.7 metres (38.4 feet) occurs at Burntcoat Head in the Bay of Fundy, EasternCanada.[2] The Bristol Channel, between England and Wales, regularly experiences tidal ranges of up to 9 metres.The top 50 locations with the largest tidal ranges world-wide are listed by the National Oceanic and AtmosphericAdministration of the United States.[2]

Some of the smallest tidal ranges occur in the Mediterranean, Baltic, and Caribbean Seas. A point within a tidalsystem where the tidal range is almost zero is called an amphidromic point.

Tidal range 83

ClassificationThe tidal range has been classified[4] as:• Micromareal, when the tidal range is lower than 2 meters.• Mesomareal, when the tidal range is between 2 meters and 4 meters.• Macromareal, when the tidal range is higher than 4 meters.

References[1] Hydrographic and Oceanographic Agencies (http:/ / co-ops. nos. noaa. gov/ faq3. html)[2] NOAA. "FAQ2 Where are the highest tides?" (http:/ / www. co-ops. nos. noaa. gov/ faq2. html#26). . Retrieved 27 Jan 2011.[3] NOAA. "It appears that the range of the tides gets larger the further the location from the equator. What causes this??" (http:/ / www. co-ops.

nos. noaa. gov/ faq2. html#27). . Retrieved 27 Jan 2011.[4] Masselink, G.; Short, A. D. (1993). "The effect of tidal range on beach morphodynamics and morphology: a conceptual beach model".

Journal of Coastal Research 9 (3): 785–800. ISSN 0749-0208.

Tidal resonance

High and low tides at Portishead Docks in the BristolChannel. Such extreme tidal ranges (13 m) are almostcertainly due to a resonant tidal wave trapped between

the coast and the edge of the continental shelf.

In oceanography, a tidal resonance occurs when the tide excitesone of the resonant modes of the ocean .[1] The effect is moststriking when a continental shelf is about a quarter wavelengthwide. Then an incident tidal wave can be reinforced by reflectionsbetween the coast and the shelf edge, the result producing a muchhigher tidal range at the coast.

Famous examples of this effect are found in the Bay of Fundy,where the world's highest tides are reportedly found, and in theBristol Channel. Large tides due to resonances are also found onthe Patagonian Shelf [2] and on the N.W. Australian continentalshelf.

The speed of long waves in the ocean is given, to a goodapproximation, by , where g is the acceleration of gravityand h is the depth of the ocean [3] [4] .[5] For a typical continentalshelf with a depth of 100 m, the speed is approximately 30 m/s. Soif the tidal period is 12 hours, a quarter wavelength shelf will havea width of about 300 km.With a narrower shelf, there is still a resonance but it has lesseffect at tidal frequencies. However the effect is still enough topartly explain why tides along a coast lying behind a continentalshelf are often higher than at offshore islands in the deep ocean.The strong tidal currents associated with resonances also mean thatthe resonant regions are the areas where most tidal energy isdissipated.In the deep ocean, where the depth is typically 4000 m, the speed of long waves increases to approximately 200 m/s.The difference in speed, when compared to the shelf, is responsible for the reflections at the continental shelf edge.Away from resonance this can stop tidal energy moving onto the shelf. However near a resonant frequency the phaserelationships between the wave on the shelf and in the deep ocean can have the effect of drawing energy onto theshelf.

Tidal resonance 84

The increased speed of long waves in the deep ocean means that the tidal wavelength there is of order 10,000 km. Asthe ocean basins have a similar size, they also have the potential of being resonant [6] .[7] In practice deep oceanresonances are difficult to observe, probably because the deep ocean loses tidal energy too rapidly to the resonantshelves.

Tidal lockingThe above concept of tidal resonance differs from another sort of resonance resulting from tides, called tidal locking,which causes a moon's rotational period to coincide with the period of its revolution around the planet that it orbits,so that one side of the moon always faces the planet.

References[1] Platzman, G.W. (1991), "Tidal Evidence for Ocean Normal Modes", in Parker, B.P., Tidal Hydrodynamics, New York: John Wiley & Sons,

pp. 883[2] Webb, D.J. (1976). "A Model of Continental-shelf Resonances". Deep-Sea Research 25: 1–15.[3] Segar, D.A. (2007). Introduction to Ocean Science. New York: W.W. Norton. pp. 581+.[4] Knauss, J.A. (1997). Introduction to Physical Oceanography. Long Grove, USA: Waveland Press. pp. 309.[5] Defant, A. (1961). Introduction to Physical Oceanography, Vol. II. Oxford: Pergamon Press. pp. 598.[6] Platzman, G.W.; Curtis, G.A., Hansen, K.S., Slater, R.D. (1981). "Normal Modes of the World ocean. Part II: Description of Modes in the

Period Range 8 to 80 Hours". Journal of Physical Oceanography 11 (5): 579–603. Bibcode 1981JPO....11..579P.doi:10.1175/1520-0485(1981)011<0579:NMOTWO>2.0.CO;2.

[7] Webb, D.J. (1973). "Tidal Resonance in the Coral Sea". Nature 243 (5409): 511. Bibcode 1973Natur.243..511W. doi:10.1038/243511a0.

Tide pool

The side of a tide pool showing sea stars (Dermasterias), sea anemones(Anthopleura) and sea sponges in Santa Cruz, California.

Tide pools are rocky pools by oceans thatare filled with seawater. Many of thesepools exist as separate entities only at lowtide.

Tide pools are habitats of uniquelyadaptable animals that have engaged thespecial attention of naturalists and marinebiologists, as well as philosophical essayists:John Steinbeck wrote in The Log from theSea of Cortez, "It is advisable to look fromthe tide pool to the stars and then back to thetide pool again."[1]

Tide pool 85

A tide pool in Porto Covo, west coast of Portugal

Zones from shallow to deep

Tide pools in Santa Cruz, California from spray/splash zone to low tide zone

Tidal pools exist in the intertidal zones.These zones receives spray from waveaction during high tides and storms. Atother times the rocks experience otherextreme conditions, baking in the sunor exposed to cold winds. Feworganisms can survive such harshconditions. Lichens and barnacles livein this region.[1] In this zone, differentbarnacle species live at very tightlyconstrained elevations. Tidalconditions precisely determine theexact height of an assemblage relativeto sea level.

The intertidal zone is periodically exposed to sun and wind, so it desiccates barnacles which need to be well adaptedto water loss. Their calcite shells are impermeable, and they possess two plates which they slide across their mouthopening when not feeding. These plates also protect against predation.

Tide pool 86

High tide zoneThe high tide zone is flooded during each high tide. Organisms must survive wave action, currents, and exposure tothe sun. This zone is inhabited by sea anemones, seastars, chitons, crabs, green algae, and mussels. Marine algaeprovide shelter for nudibranchs and hermit crabs. The same waves and currents that make the life in the high tidezone so difficult bring food to filter feeders and other intertidal animals.

Low tide zone in a tide pool

Low tide zone

This subregion is mostly submerged, and is exposed only during lowtide. It teems with life and has much more marine vegetation,especially seaweeds. There is also greater biodiversity. Organisms inthis zone do not have to be as well adapted to drying out andtemperature extremes. Low tide zone organisms include abalone,anemones, brown seaweed, chitons, crabs, green algae, hydroids,isopods, limpets, mussels, nudibranchs, sculpin, sea cucumber, sealettuce, sea palms, sea stars, sea urchins, shrimp, snails, sponges, surfgrass, tube worms, and whelks.

These creatures can grow to larger sizes because there is more available energy and better water coverage: The wateris shallow enough to allow more light for photosynthetic activity, and the salinity is at almost normal levels. Thisarea is also relatively protected from large predators because of the wave action and shallow water.

Life in the tide poolTide pools provide a home for hardy organisms such as sea stars, mussels and clams. Inhabitants must be able tocope with a constantly changing environment — fluctuations in water temperature, salinity, and oxygen content.Huge waves, strong currents, exposure to midday sun and predators are only a few of the hazards that tide pools'animals must endure to survive.Waves can dislodge mussels and draw them out to sea. Gulls pick up and drop sea urchins to break them open.Starfish prey on mussels and are eaten by gulls themselves. Even black bears sometimes feast on intertidal creaturesat low tide.[2] Although tide pool organisms must avoid getting washed away into the ocean, drying up in the sun, orgetting eaten, they depend on the tide pool's constant changes for food.[1]

FaunaThe sea anemone Anthopleura elegantissima produces clones of itself in order to reproduce through a process calledlongitudinal fission, in which the animal splits into two parts along its length.[3] The sea anemone Anthopleura solaoften engages in territorial fights. The white tentacles (acrorhagi), which contain stinging cells, are for fighting. Thesea anemones sting each other repeatedly until one moves.[4]

Some species of starfish have the ability to regenerate lost arms. Most species must retain an intact central part of thebody to be able to regenerate, but a few can regrow from a single ray. The regeneration of these stars is possiblebecause the vital organs are in the arms.[5]

Tide pool 87

FloraSea palms look very much as palm trees do. They live in the middle to upper intertidal zones in areas with greaterwave action. High wave action may increase nutrient availability and moves the blades of the thallus, allowing moresunlight to reach the organism so that it can photosynthesize. In addition, the constant wave action removescompetitors, such as the mussel species Mytilus californianus.Recent studies have shown that Postelsia grows in greater numbers when such competition exists — a control groupwith no competition produced fewer offspring than an experimental group with mussels; from this it is thought thatthe mussels provide protection for the developing gametophytes.[6] Alternatively, the mussels may prevent thegrowth of competing algae such as Corallina or Halosaccion, allowing Postelsia to grow freely after wave actionremoves the mussels.[7]

A large sea anemoneAnthopleura sola consuming a"by-the-wind-sailor" Velella

velella a blue hydrozoan

Postelsia palmaeformis at lowtide in a tide pool

Sea star, Pisaster ochraceusconsuming a mussel in tide pools

Sea anemones, Anthopleura solaengaged in a battle for territory

References[1] "NPCA Tide pools" (http:/ / www. npca. org/ marine_and_coastal/ beaches/ tide_pools. html). npca.org. September 5, 2008. . Retrieved

2008-09-06.[2] "Botanical Beach Tide Pools" (http:/ / www. juandefucamarinetrail. com/ botanical_beach. html). juandefucamarinetrail.com. September 5,

2008. . Retrieved 2008-09-06.[3] "Sea Anemones" (http:/ / homepages. ed. ac. uk/ evah01/ anemone. htm). homepages.ed.ac.uk. September 5, 2008. . Retrieved 2008-09-06.[4] "Snakelocks Anemone" (http:/ / www. glaucus. org. uk/ Snakelok. htm). British Marine Life Study Society. September 5, 2008. . Retrieved

2008-09-06.[5] "Biology:Regeneration" (http:/ / en. allexperts. com/ q/ Biology-664/ Regeneration. htm). Dana Krempels, Ph.D.. September 5, 2008. .

Retrieved 2008-09-06.[6] Blanchette, Carol Anne (1995.). "Seasonal patterns of disturbance influence recruitment of the sea palm, Postelsia palmaeformis" (http:/ /

www. ingentaconnect. com/ els/ 00220981/ 1996/ 00000197/ 00000001/ art00141). Department of Zoology, Oregon State University.. .Retrieved 13 July 2007.

[7] Paine, R.T. (1998). "Habitat Suitability and Local Population Persistence of the Sea Palm Postelsia palmaeformis". Ecology 69 (6):1787–1794. doi:10.2307/1941157. JSTOR 1941157.

External links• Tidal swimming pools in Britain (http:/ / homepage. ntlworld. com/ oliver. merrington/ lidos/ lidos4. htm)

Tideline 88

TidelineA tideline refers to where two currents in the ocean converge. Driftwood, floating seaweed, foam, and other floatingdebris may accumulate, forming sinuous lines called tidelines (even though they generally have nothing to do withthe tide.)There are four mechanisms that can cause tidelines to form:1.1. Where one body of water is sinking beneath or riding over top of the surface layer of another body of water

(somewhat similar in mechanics to subduction of the earth plates at continental margins). These types of tidelinesare often found where rivers enter the ocean.

2.2. Along the margins of back-eddies.3. Convergence zones associated with internal gravity waves.4.4. Along adjacent cells formed by wind currents.

References• Thomson, R.E. 1981. Oceanography of the British Columbia Coast. Department of Fisheries and Oceans.

Canadian Special Publication of Fisheries and Aquatic Sciences 56. Ottawa. 291.

Tidal bore

The tidal bore in Upper Cook Inlet, Alaska

A tidal bore (or simply bore in context, oralso aegir, eagre, or eygre) is a tidalphenomenon in which the leading edge ofthe incoming tide forms a wave (or waves)of water that travels up a river or narrow bayagainst the direction of the river or bay'scurrent. As such, it is a true tidal wave andnot to be confused with a tsunami, which isa large ocean wave traveling primarily onthe open ocean.

Bore phenomenon

Bores occur in relatively few locations worldwide, usually in areas with a large tidal range (typically more than 6metres (unknown operator: u'strong' ft) between high and low water) and where incoming tides are funneled into ashallow, narrowing river or lake via a broad bay.[1] The funnel-like shape not only increases the tidal range, but itcan also decrease the duration of the flood tide, down to a point where the flood appears as a sudden increase in thewater level. A tidal bore takes place during the flood tide and never during the ebb tide.

Tidal bore 89

Undular bore and whelps near the mouth of Araguari River in north-eastern Brazil.View is oblique toward mouth from airplane at approximately 100 ft (unknown

operator: u'strong' m) altitude.[2]

A tidal bore may take on various forms,ranging from a single breaking wavefrontwith a roller — somewhat like a hydraulicjump[3] — to "undular bores", comprising asmooth wavefront followed by a train ofsecondary waves (whelps).[4] Large borescan be particularly unsafe for shipping butalso present opportunities for riversurfing.[4]

Two key features of a tidal bore are theintense turbulence and turbulent mixinggenerated during the bore propagation, aswell as its rumbling noise. The visualobservations of tidal bores highlight theturbulent nature of the surging waters. Thetidal bore induces a strong turbulent mixingin the estuarine zone, and the effects may be felt along considerable distances. The velocity observations indicate arapid deceleration of the flow associated with the passage of the bore as well as large velocity fluctuations.[5][6] Atidal bore creates a powerful roar that combines the sounds caused by the turbulence in the bore front and whelps,entrained air bubbles in the bore roller, sediment erosion beneath the bore front and of the banks, scouring of shoalsand bars, and impacts on obstacles. The bore rumble is heard far away because its low frequencies can travel overlong distances. The low-frequency sound is a characteristic feature of the advancing roller in which the air bubblesentrapped in the large-scale eddies are acoustically active and play the dominant role in the rumble-soundgeneration.[7]

The word bore derives through Old English from the Old Norse word bára, meaning "wave" or "swell".

Rivers with tidal boresRivers that have been known to exhibit bores include those listed below.[1] [8]

Asia• Ganges–Brahmaputra, India and Bangladesh• Indus River, Pakistan• Sittaung River, Burma• Qiantang River, China, which has the world's largest bore, up to 9 metres (unknown operator: u'strong' ft) high,

traveling at up to 40 kilometres (unknown operator: u'strong' mi) per hour• Batang Lupar or Lupar River, near Sri Aman, Malaysia. The tidal bore is locally known as benak.[4]

• Bono, Kampar River, Indonesia. The phenomenon is feared by the locals to sink ships. It is reported to break upto 130 kilometres (unknown operator: u'strong' mi) inland.

Tidal bore 90

Australia• Styx River, Queensland• Daly River, Northern Territory

Europe

United Kingdom

The Trent Aegir seen from West Stockwith,Nottinghamshire, 20 September 2005

The Trent Aegir at Gainsborough, Lincolnshire,20 September 2005

• River Dee, Wales and England•• River Mersey• The Severn bore on the River Severn, Wales and England, up to 2

metres (unknown operator: u'strong' ft) high• The Trent Aegir on the River Trent, England, up to 1.5 metres

(unknown operator: u'strong' ft) high. Also other tributaries ofthe Humber Estuary.

•• River Parrett•• River Welland• The Arnside Bore on the River Kent•• River Great Ouse• River Ouse, Yorkshire. Like the Trent bore, this is also known as

"the Aegir".•• River Eden•• River Esk•• River Nith• River Lune, Lancashire• River Ribble, Lancashire

Tidal bore on the River Ribble

France

The phenomenon is generally named un mascaret in French.[9] butsome other local names are preferred.[8]

• Seine, locally named la barre, had a significant bore until the 1960s.Since then, it has been practically eliminated by dredging and rivertraining.[8]

• Baie du Mont Saint Michel including Couesnon, Sélune, and Sée[8]

• Arguenon[8]

• Baie de la Frênaye[8]

• Vire[8]

• Sienne[8]

• Vilaine, locally named le mascarin• Dordogne[8]

• Garonne[8]

Tidal bore 91

North America

United States

Tidal bore on the Petitcodiac River

• The Turnagain arm of Cook Inlet, Alaska. Up to 2 metres(unknown operator: u'strong' ft) and 20 km/h.

• The Savannah River up to 10 miles inland.

Canada

Most rivers draining into the upper Bay of Fundy between Nova Scotiaand New Brunswick have tidal bores. Notable ones include:

• The Petitcodiac River. Formerly the highest bore in North Americaat over 2 metres (unknown operator: u'strong' ft); however,causeway construction and extensive silting reduced it to little morethan a ripple, until the causeway gates were opened on April 14, 2010, as part of the Petitcodiac River Restorationproject and the tidal bore began to grow again.[10]

• The Shubenacadie River, also off the Bay of Fundy in Nova Scotia. When the tidal bore approaches, completelydrained riverbeds are filled. It has claimed the lives of several tourists who were in the riverbeds when the borecame in. Tour boat operators offer rafting excursions in the summer.

• The bore is fastest and highest on some of the smaller rivers that connect to the bay including the River Hebertand Maccan River on the Cumberland Basin, the St. Croix, Herbert and Kennetcook Rivers in the Minas Basin,and the Salmon River in Truro.

Mexico

There is a tidal bore on the Sea of Cortez in Mexico at the entrance of the Colorado River. It forms in the estuaryabout Montague Island and propagates upstream. Once very strong, later diversions of the river for irrigation haveweakened the flow of the river to the point the tidal bore has nearly disappeared.

South America• Amazon River in Brazil and Orinoco River in Venezuela, up to 4 metres (unknown operator: u'strong' ft) high,

running at up to 13 miles per hour (unknown operator: u'strong' km/h). It is known locally as the pororoca.[11]

• Mearim River in Brazil• Araguari River in Brazil

Lakes with tidal boresLakes with an ocean inlet can also exhibit tidal bores.

North America• Nitinat Lake on Vancouver Island has a sometimes dangerous tidal bore at Nitinat Narrows where the lake meets

the Pacific Ocean. The lake is popular with windsurfers due to its consistent winds.

Impact of tidal boresThe tidal bores may be dangerous and some bores have had a sinister reputation: the Seine River (France); the Petitcodiac River (Canada); and the Colorado River (Mexico), to name a few. In China, despite warning signs erected along the Qiantang River banks, a number of tragic accidents happen each year.[1] The tidal bores affect the shipping and navigation in the estuarine zone, for example, in Papua New Guinea (Fly and Bamu Rivers), Malaysia

Tidal bore 92

(Benak at Batang Lupar), and India (Hoogly bore).On the other hand, the tidal-bore affected estuaries are the rich feeding zones and breeding grounds of several formsof wildlife.[1] The estuarine zones are the spawning and breeding grounds of several native fish species, while theaeration induced by the tidal bore contribute to the abundant growth of many species of fish and shrimps (forexample in the Rokan River).

Scientific studies of tidal boresScientific measurements in tidal bores are challenging because of the force of the tidal bore flow. This is evidencedby a number of field work incidents in the Dee River, Rio Mearim, Daly River and Sélune River: "during this […]deployment, the [ADCP] instrument was repeatedly buried in sediment after the 1st tidal cycle and had to be dug outof the sediment, with considerable difficulty, at the time of recovery" (Dee River);[12] "About 20 min after thepassage of the bore the two aluminium frames at site C were toppled. […] A 3-min-duration patch ofmacroturbulence was observed. […] This unsteady motion was sufficiently energetic to topple moorings that hadsurvived much higher, quasi-steady currents of 1.8 m/s" (Daly River);[13] "the field study experienced a number ofproblems and failures. About 40 s after the passage of the bore, the metallic frame started to move. The ADV supportfailed completely 10 minutes after the tidal bore." (Sélune River).[14]

Field studies in United Kingdom• Dee River[12]

Field studies in France• Garonne River[15][16][17]

• Sélune River[14]

Field studies in Australia• Daly River[13]

References[1] Chanson, H. (2011). Tidal Bores, Aegir, Eagre, Mascaret, Pororoca. Theory and Observations (http:/ / www. worldscibooks. com/

engineering/ 8035. html). World Scientific, Singapore. ISBN 978-981-4335-41-6. .[2] Figure 5 in: Susan Bartsch-Winkler; David K. Lynch (1988), Catalog of worldwide tidal bore occurrences and characteristics (http:/ / pubs.

er. usgs. gov/ #search:advance/ page=1/ page_size=100/ advance=undefined/ series_cd=CIR/ report_number=1022:0) (Circular 1022), U. S.Geological Survey,

[3] Chanson, H. (2009). Current Knowledge In Hydraulic Jumps And Related Phenomena. A Survey of Experimental Results (http:/ / espace.library. uq. edu. au/ view/ UQ:162239). European Journal of Mechanics B/Fluids, Vol. 28, No. 2, pp. 191-210 (DOI:10.1016/j.euromechflu.2008.06.004 ) (ISSN 0997-7546). .

[4] Chanson, H. (2009). Environmental, Ecological and Cultural Impacts of Tidal Bores, Benaks, Bonos and Burros (http:/ / espace. library. uq.edu. au/ view/ UQ:185349). Proc. International Workshop on Environmental Hydraulics IWEH09, Theoretical, Experimental andComputational Solutions, Valencia, Spain, 29-30 Oct., Editor P.A. Lopez-Jimenez et al., Invited keynote lecture, 20 pages (CD-ROM). .

[5] Koch, C. and Chanson, H. (2008). Turbulent Mixing beneath an Undular Bore Front (http:/ / espace. library. uq. edu. au/ view/ UQ:151916).Journal of Coastal Research, Vol. 24, No. 4, pp. 999-1007 (DOI: 10.2112/06-0688.1). .

[6] Koch, C. and Chanson, H. (2009). Turbulence Measurements in Positive Surges and Bores (http:/ / espace. library. uq. edu. au/ view/UQ:164015). Journal of Hydraulic Research, IAHR, Vol. 47, No. 1, pp. 29-40 (DOI: 10.3826/jhr.2009.2954). .

[7] Chanson, H. (2009). The Rumble Sound Generated by a Tidal Bore Event in the Baie du Mont Saint Michel (http:/ / espace. library. uq. edu.au/ view/ UQ:178445). Journal of Acoustical Society of America, Vol. 125, No. 6, pp. 3561-3568 (DOI: 10.1121/1.3124781). .

[8] Chanson, H. (2008). Photographic Observations of Tidal Bores (Mascarets) in France (http:/ / espace. library. uq. edu. au/ eserv/UQ:158867). Hydraulic Model Report No. CH71/08, Univ. of Queensland, Australia, 104 pages. ISBN 978-1-86499-930-3. .

[9] (French) definition of mascaret (http:/ / www. cnrtl. fr/ lexicographie/ mascaret)[10] Petitcodiac River changing faster than expected (http:/ / www. cbc. ca/ canada/ new-brunswick/ story/ 2010/ 06/ 07/

nb-petitcodiac-river-changes-619. html)

Tidal bore 93

[11] (English) Pororoca: surfing the Amazon indicates that "The record that we could find for surfing the longest distance on the Pororoca wasset by Picuruta Salazar, a brazilian surfer who, in 2003, managed to ride the wave for 37 minutes and travel 12.5 kilometers." (http:/ /fogonazos. blogspot. com/ 2007/ 03/ pororoca-surfing-amazon. html)

[12] Simpson, J.H., Fisher, N.R., and Wiles, P. (2004). Reynolds Stress and TKE Production in an Estuary with a Tidal Bore. Estuarine, Coastaland Shelf Science, Vol. 60, No. 4, pp. 619-627.

[13] Wolanski, E., Williams, D., Spagnol, S., and Chanson, H. (2004). Undular Tidal Bore Dynamics in the Daly Estuary, Northern Australia(http:/ / espace. library. uq. edu. au/ view/ UQ:74059). Estuarine, Coastal and Shelf Science, Vol. 60, No. 4, pp. 629-636 (DOI:10.1016/j.ecss.2004.03.001). .

[14] Mouazé, D., Chanson, H., and Simon, B. (2010). Field Measurements in the Tidal Bore of the Sélune River in the Bay of Mont Saint Michel(September 2010) (http:/ / espace. library. uq. edu. au/ view/ UQ:226153). Hydraulic Model Report No. CH81/10, School of CivilEngineering, The University of Queensland, Brisbane, Australia, 72 pages. ISBN 978-1-74272-021-0. .

[15] Chanson, H., Lubin, P., Simon, B., and Reungoat, D. (2010). Turbulence and Sediment Processes in the Tidal Bore of the Garonne River:First Observations (http:/ / espace. library. uq. edu. au/ view/ UQ:219711). Hydraulic Model Report No. CH79/10, School of CivilEngineering, The University of Queensland, Brisbane, Australia, 97 pages. ISBN 978-1-74272-010-4. .

[16] Simon, B., Lubin, P., Reungoat, D., Chanson, H. (2011). Turbulence Measurements in the Garonne River Tidal Bore: First Observations(http:/ / espace. library. uq. edu. au/ view/ UQ:243200). Proc. 34th IAHR World Congress, Brisbane, Australia, 26 June-1 July, EngineersAustralia Publication, Eric Valentine, Colin Apelt, James Ball, Hubert Chanson, Ron Cox, Rob Ettema, George Kuczera, Martin Lambert,Bruce Melville and Jane Sargison Editors, pp. 1141-1148. ISBN 978-0-85825-868-6. .

[17] Chanson, H., Reungoat, D., Simon, B., Lubin, P. (2012). High-Frequency Turbulence and Suspended Sediment ConcentrationMeasurements in the Garonne River Tidal Bore (http:/ / espace. library. uq. edu. au/ view/ UQ:261649). Estuarine Coastal and Shelf Science(DOI: 10.1016/j.ecss.2011.09.012). ISSN 0272-7714.

External links• Amateur video of the "Wiggenhall Wave" tidal bore (http:/ / www. youtube. com/ watch?v=Cx89Dstc6v0)• link to Proudman Inst. page (http:/ / www. pol. ac. uk/ home/ insight/ riverbores. html)• Mascaret, Aegir, Pororoca, Tidal Bore. Quid ? Où? Quand? Comment? Pourquoi ? (http:/ / espace. library. uq.

edu. au/ view. php?pid=UQ:9447) in Journal La Houille Blanche, No. 3, pp. 103–114• Turbulent Mixing beneath an Undular Bore Front (http:/ / espace. library. uq. edu. au/ view/ UQ:151916) in

Journal of Coastal Research, Vol. 24, No. 4, pp. 999–1007 (DOI: 10.2112/06-0688.1)

Storm surge 94

Storm surge

Impact of a storm surge

A storm surge is an offshore rise of waterassociated with a low pressure weathersystem, typically tropical cyclones andstrong extratropical cyclones. Storm surgesare caused primarily by high winds pushingon the ocean's surface. The wind causes thewater to pile up higher than the ordinary sealevel. Low pressure at the center of aweather system also has a small secondaryeffect, as can the bathymetry of the body of water. It is this combined effect of low pressure and persistent wind overa shallow water body which is the most common cause of storm surge flooding problems. The term "storm surge" incasual (non-scientific) use is storm tide; that is, it refers to the rise of water associated with the storm, plus tide,wave run-up, and freshwater flooding. When referencing storm surge height, it is important to clarify the usage, aswell as the reference point. National Hurricane Center reference storm surge as water height above predictedastronomical tide level, and storm tide as water height above NGVD-29. Most casualties during a tropical cycloneoccur during the storm surge.

In areas where there is a significant difference between low tide and high tide, storm surges are particularlydamaging when they occur at the time of a high tide. In these cases, this increases the difficulty of predicting themagnitude of a storm surge since it requires weather forecasts to be accurate to within a few hours. Storm surges canbe produced by extratropical cyclones, such as the Night of the Big Wind of 1839 and the Storm of the Century(1993), but the most extreme storm surge events typically occur as a result of tropical cyclones. Factors thatdetermine the surge heights for landfalling tropical cyclones include the speed, intensity, size of the radius ofmaximum winds (RMW), radius of the wind fields, angle of the track relative to the coastline, the physicalcharacteristics of the coastline and the bathymetry of the water offshore. The SLOSH (Sea, Lake, and OverlandSurges from Hurricanes) model is used to simulate surge from tropical cyclones.[1] Additionally, there is anextratropical storm surge model that is used to predict those effects.[2]

The Galveston Hurricane of 1900, a Category 4 hurricane that struck Galveston, Texas, drove a devastating surgeashore; between 6,000 and 12,000 lives were lost, making it the deadliest natural disaster ever to strike the UnitedStates.[3] The deadliest storm surge caused by an extratropical cyclone in the twentieth century was the North Seaflood of 1953, which killed a total of over 2,000 people in the UK and the Netherlands

Mechanics

Schematic diagram of processes that generatestorm surge.

At least five processes can be involved in altering tide levels duringstorms: the pressure effect, the direct wind effect, the effect of theEarth's rotation, the effect of waves, and the rainfall effect.[4] Thepressure effects of a tropical cyclone will cause the water level in theopen ocean to rise in regions of low atmospheric pressure and fall inregions of high atmospheric pressure. The rising water level willcounteract the low atmospheric pressure such that the total pressure atsome plane beneath the water surface remains constant. This effect is estimated at a 10 mm (unknown operator:u'strong' in) increase in sea level for every millibar drop in atmospheric pressure.[4]

Strong surface winds cause surface currents perpendicular to the wind direction, by an effect known as the Ekman Spiral. Wind stresses cause a phenomenon referred to as "wind set-up", which is the tendency for water levels to

Storm surge 95

increase at the downwind shore, and to decrease at the upwind shore. Intuitively, this is caused by the storm simplyblowing the water towards one side of the basin in the direction of its winds. Because the Ekman Spiral effectsspread vertically through the water, the effect is inversely proportional to depth. The pressure effect and the windset-up on an open coast will be driven into bays in the same way as the astronomical tide.[4]

The Earth's rotation causes the Coriolis effect, which bends currents to the right in the Northern Hemisphere and tothe left in the Southern Hemisphere. When this bend brings the currents into more perpendicular contact with theshore it can amplify the surge, and when it bends the current away from the shore it has the effect of lessening thesurge.[4]

The effect of waves, while directly powered by the wind, is distinct from a storm's wind-powered currents. Powerfulwind whips up large, strong waves in the direction of its movement.[4] Although these surface waves are responsiblefor very little water transport in open water, they may be responsible for significant transport near the shore. Whenwaves are breaking on a line more or less parallel to the beach they carry considerable water shoreward. As theybreak, the water particles moving toward the shore have considerable momentum and may run up a sloping beach toan elevation above the mean water line which may exceed twice the wave height before breaking.[5]

The rainfall effect is experienced predominantly in estuaries. Hurricanes may dump as much as 12 in (unknownoperator: u'strong' mm) of rainfall in 24 hours over large areas, and higher rainfall densities in localized areas. As aresult, watersheds can quickly surge water into the rivers that drain them. This can increase the water level near thehead of tidal estuaries as storm-driven waters surging in from the ocean meet rainfall flowing from the estuary.[4]

Surge and wave heights on shore are affected by the configuration and bathymetry of the ocean bottom. A narrowshelf, or one that has a steep drop from the shoreline and subsequently produces deep water in close proximity to theshoreline tends to produce a lower surge, but a higher and more powerful wave. This situation well exemplified bythe southeast coast of Florida. The edge of the Floridian Plateau, where the water depths reach 91 metres (unknownoperator: u'strong' ft), lies just 3000 m (unknown operator: u'strong' ft) offshore of Palm Beach, Florida; just7000 m (unknown operator: u'strong' ft) offshore, the depth increases to over 180 m (unknown operator:u'strong' ft).[6] The 180 m (unknown operator: u'strong' ft) depth contour followed southward from Palm BeachCounty lies more than 30000 m (unknown operator: u'strong' ft) to the east of the upper Keys.Conversely, coastlines along North America such as those along the Gulf of Mexico coast from Texas to Florida, andAsia such as the Bay of Bengal, have long, gently sloping shelves and shallow water depths. On the Gulf side ofFlorida, the edge of the Floridian Plateau lies more than 160 kilometres (unknown operator: u'strong' mi) offshoreof Marco Island in Collier County. Florida Bay, lying between the Florida Keys and the mainland, is also veryshallow; depths typically vary between 0.3 m (unknown operator: u'strong' ft) and 2 m (unknown operator:u'strong' ft).[7] These areas are subject to higher storm surges, but smaller waves. This difference is because indeeper water, a surge can be dispersed down and away from the hurricane. However, upon entering a shallow, gentlysloping shelf, the surge can not be dispersed away, but is driven ashore by the wind stresses of the hurricane.Topography of the land surface is another important element in storm surge extent. Areas where the land lies lessthan a few meters above sea level are at particular risk from storm surge inundation.[4]

For a given topography and bathymetry the surge height is not solely affected by peak wind speed; the size of thestorm also affects the peak surge. With any storm the piled up water has an exit path to the sides and this escapemechanism is reduced in proportion to the surge force (for the same peak wind speed) as the storm covers more area.In the Asian region, Metro Manila or Manila is one of the most affected by storm surges of typhoons. Since thePhilippines serves as a welcome mat for typhoons before entering Japan, Taiwan, China, Vietnam, and Cambodia.The damage and casualties is expected. Even though these occurrences is normal, loss of life is inevitable especiallyglobal warming also affects the typhoon formation, strength, intensity and speed.

Storm surge 96

Measuring surgeSurge can be measured directly at coastal tidal stations as the difference between the forecast tide and the observedrise of water.[8] Another method of measuring surge is by the deployment of pressure transducers along the coastlinejust ahead of an approaching tropical cyclone. This was first tested for Hurricane Rita in 2005.[9] These types ofsensors can be placed in locations that will be submerged, and can accurately measure the height of water abovethem.[10]

After surge from a cyclone has receded, teams of surveyors map high water marks (HWM) on land, in a rigorous anddetailed process that includes photos and written descriptions of the marks. HWM denote the location and elevationof flood waters from a storm event. When HWM are analyzed, if the various components of the water height can bebroken out so that the portion attributable to surge can be identified, then that mark can be classified as storm surge.Otherwise, it is classified as storm tide. HWM on land are referenced to a vertical datum (a reference coordinatesystem). During evaluation, HWM are divided into four categories based on the confidence in the mark; only HWMevaluated as "excellent" are used by NHC in post storm analysis of the surge.[11]

Two different measures are used for storm tide and storm surge measurements. Storm tide is measured using ageodetic vertical datum (NGVD 29 or NAVD 88). Since storm surge is defined as the rise of water beyond whatwould be expected by the normal movement due to tides, storm surge is measured using tidal predictions, with theassumption that the tide prediction is well-known and only slowly varying in the region subject to the surge. Sincetides are a localized phenomenon, storm surge can only be measured in relationship to a nearby tidal station. Tidalbench mark information at a station provides a translation from the geodetic vertical datum to mean sea level (MSL)at that location, then subtracting the tidal prediction yields a surge height above the normal water height.[8][11]

RecordsThe highest storm tide noted in historical accounts was produced by the 1899 Cyclone Mahina, estimated at 43 ft(13 meters) at Bathurst Bay, Australia, but research published in 2000 noted the majority of this was likely waverun-up, due to the steep coastal topography.[12] In the United States, one of the greatest recorded storm surges wasgenerated by 2005's Hurricane Katrina, which produced a maximum storm surge of more than 25 ft (8 meters) in thecommunities of Waveland, Bay St. Louis, Diamondhead, and Pass Christian in Mississippi, with a storm surgeheight of 27.8 ft (8.5 m) in Pass Christian.[13][14][15] Another record storm surge occurred in this same area fromHurricane Camille in August 1969, with the highest storm tide of record noted from a HWM as 24.6 ft (7.5 m), alsofound in Pass Christian.[16] The worst storm surge, in terms of loss of life, was the 1970 Bhola cyclone and ingeneral the Bay of Bengal is vulnerable to storm surge.[17]

Storm surge 97

SLOSH

Example of a SLOSH run

The National Hurricane Center in the US, forecasts storm surge usingthe SLOSH model, which stands for Sea, Lake and Overland Surgesfrom Hurricanes. The model is accurate to within 20 percent.[18]

SLOSH inputs include the central pressure of a tropical cyclone, stormsize, the cyclone's forward motion, its track, and maximum sustainedwinds. Local topography, bay and river orientation, depth of the seabottom, astronomical tides, as well as other physical features are takeninto account, in a predefined grid referred to as a SLOSH basin.Overlapping SLOSH basins are defined for the southern and easterncoastline of the continental U.S.[19] Some storm simulations use morethan one SLOSH basin; for instance, Katrina SLOSH model runs usedboth the Lake Ponchartrain / New Orleans basin, and the MississippiSound basin, for the northern Gulf of Mexico landfall. The final outputfrom the model run will display the maximum envelope of water, or MEOW, that occurred at each location. Toallow for track or forecast uncertainties, usually several model runs with varying input parameters are generated tocreate a map of MOMs, or Maximum of Maximums.[20] And for hurricane evacuation studies, a family of stormswith representative tracks for the region, and varying intensity, eye diameter, and speed, are modeled to produceworst-case water heights for any tropical cyclone occurrence. The results of these studies are typically generatedfrom several thousand SLOSH runs. These studies have been completed by USACE, under contract to the FederalEmergency Management Agency, for several states and are available on their Hurricane Evacuation Studies (HES)website.[21] They include coastal county maps, shaded to identify the minimum SSHS category of hurricane that willresult in flooding, in each area of the county.[22]

MitigationAlthough meteorological surveys alert about hurricanes or severe storms, in the areas where the risk of coastalflooding is particularly high, there are specific storm surge warnings. These have been implemented, for instance, inthe Netherlands,[23] Spain,[24][25] the United States,[26][27] and the United Kingdom.[28]

A prophylactic method introduced after the North Sea Flood of 1953 is the construction of dams and floodgates(storm surge barriers). They are open and allow free passage but close when the land is under threat of a storm surge.Major storm surge barriers are the Oosterscheldekering and Maeslantkering in the Netherlands which are part of theDelta Works project, and the Thames Barrier protecting London.Another modern development (in use in the Netherlands) is the creation of housing communities at the edges ofwetlands with floating structures, restrained in position by vertical pylons.[29] Such wetlands can then be used toaccommodate runoff and surges without causing damage to the structures while also protecting conventionalstructures at somewhat higher low-lying elevations, provided that dikes prevent major surge intrusion.For mainland areas, storm surge is more of a threat when the storm strikes land from seaward, rather thanapproaching from landwards.[30]

Storm surge 98

Notes[1] National Hurricane Center (2005-02-07). "The Deadliest Atlantic Tropical Cyclones, 1492-1996" (http:/ / www. nhc. noaa. gov/ pastdeadly3.

shtml?). National Oceanic and Atmospheric Administration. . Retrieved 2008-08-11.[2] National Weather Service (2009-11-27). "Extratropical Storm Surge" (http:/ / www. nws. noaa. gov/ mdl/ etsurge/ ). Meteorological

Development Laboratory. .[3][3] Hebert, 1983[4][4] Harris 1963[5][5] Granthem 1953[6][6] Lane 1980[7][7] Lane 1981[8] John Boon (2007). "Ernesto: Anatomy of a Storm Tide" (http:/ / www. vims. edu/ physical/ research/ ernesto. pdf) (PDF). Virginia Institute of

Marine Science, College of William and Mary. . Retrieved 2008-08-11.[9] U.S. Geological Survey (2006-10-11). "Hurricane Rita Surge Data, Southwestern Louisiana and Southeastern Texas, September to November

2005" (http:/ / pubs. usgs. gov/ ds/ 2006/ 220/ ). U.S. Department of the Interior. . Retrieved 2008-08-11.[10] Automated (2008). "U20-001-01-Ti: HOBO Water Level Logger Specification" (http:/ / www. onsetcomp. com/ products/ data-loggers/

u20-001-01-ti#tabs1-2). Onset Corp. . Retrieved 2008-08-10.[11] URS Group, Inc. (2006-04-03). "High Water Mark Collection for Hurricane Katrina in Alabama" (http:/ / www. fema. gov/ pdf/ hazard/

flood/ recoverydata/ katrina/ katrina_al_hwm_public. pdf) (PDF). Federal Emergency Management Agency (FEMA). . Retrieved 2008-08-10.[12] Jonathan Nott and Matthew Hayne (2000). "How high was the storm surge from Tropical Cyclone Mahina? North Queensland, 1899" (http:/

/ web. archive. org/ web/ 20080625203948/ http:/ / www. ema. gov. au/ agd/ EMA/ rwpattach. nsf/ viewasattachmentpersonal/(C86520E41F5EA5C8AAB6E66B851038D8)~How_high_was_the_storm_surge_from_Tropical_Cyclone_Mahina. pdf/ $file/How_high_was_the_storm_surge_from_Tropical_Cyclone_Mahina. pdf) (PDF). Emergency Management Australia. Archived from theoriginal (http:/ / www. ema. gov. au/ agd/ EMA/ rwpattach. nsf/ viewasattachmentpersonal/(C86520E41F5EA5C8AAB6E66B851038D8)~How_high_was_the_storm_surge_from_Tropical_Cyclone_Mahina. pdf/ $file/How_high_was_the_storm_surge_from_Tropical_Cyclone_Mahina. pdf) on June 25, 2008. . Retrieved 2008-08-11.

[13] FEMA (2005-11-01). "Mississippi Hurricane Katrina Surge Inundation and Advisory Base Flood Elevation Map Panel Overview" (http:/ /www. fema. gov/ pdf/ hazard/ flood/ recoverydata/ katrina/ ms_overview. pdf) (PDF). Federal Emergency Management Agency (FEMA). .Retrieved 2008-08-11.

[14] FEMA (2006-05-30). "Hurricane Katrina Flood Recovery (Mississippi)" (http:/ / www. fema. gov/ hazard/ flood/ recoverydata/ katrina/katrina_ms_methods. shtm). Federal Emergency Management Agency (FEMA). . Retrieved 2008-08-11.

[15] Knabb, Richard D; Rhome, Jamie R.; Brown, Daniel P (2005-12-20; updated 2006-08-10). "Tropical Cyclone Report: Hurricane Katrina:23–30 August 2005" (http:/ / www. nhc. noaa. gov/ pdf/ TCR-AL122005_Katrina. pdf) (PDF). National Hurricane Center. . Retrieved2008-10-11.

[16][16] Simpson, 1969[17] "Solar System Exploration: Science & Technology: Science Features: Remembering Katrina - Learning and Predicting the Future" (http:/ /

solarsystem. nasa. gov/ scitech/ display. cfm?ST_ID=1350). Solarsystem.nasa.gov. . Retrieved 2012-03-20.[18] National Hurricane Center (2008). "SLOSH Model" (http:/ / www. nhc. noaa. gov/ HAW2/ english/ surge/ slosh. shtml). National Oceanic

and Atmospheric Administration. . Retrieved 2008-08-10.[19] NOAA (1999-04-19). "SLOSH Model Coverage" (http:/ / www. nws. noaa. gov/ mdl/ marine/ Basin. htm). National Oceanic and

Atmospheric Administration. . Retrieved 2008-08-11.[20] George Sambataro (2008). "Slosh Data... what is it" (http:/ / www. pcwp. com/ whatisslosh. html). PC Weather Products. . Retrieved

2008-08-11.[21] U.S. Army Corps of Engineers (2008). "National Hurricane Study Home Page" (http:/ / chps. sam. usace. army. mil/ USHESdata/

HESHOME. htm). Federal Emergency Management Agency. . Retrieved 2008-08-10.[22] U.S. Army Corps of Engineers (2008). "Jackson County, MS HES surge maps" (http:/ / chps. sam. usace. army. mil/ USHESdata/

Mississippi/ Jacksonsurgemapspage. htm). Federal Emergency Management Agency. . Retrieved 2008-08-10.[23] Rijkswaterstaat (2008-07-21). "Storm Surge Warning Service" (http:/ / www. svsd. nl/ index. cfm?taal=en). . Retrieved 2008-08-10.[24] Ports of the State (1999-03-01). "Storm surge forecast system" (http:/ / www. puertos. es/ externo/ clima/ Nivmar/ nivmareng. html).

Government of Spain. . Retrieved 2007-04-14.[25] Puertos del Estado (1999-03-01). "Sistema de previsión del mar a corto plazo" (http:/ / www. puertos. es/ externo/ clima/ Nivmar/ nivinht.

html) (in Spanish). Gobierno de España. . Retrieved 2008-08-10.[26] Stevens Institute of Technology (2008-08-10). "Storm Surge Warning System" (http:/ / hudson. dl. stevens-tech. edu/ SSWS/ ). New Jersey

Office of Emergency Management. . Retrieved 2008-08-11.[27] Donna Franklin (2008-08-11). "NWS StormReady Program, Weather Safety, Disaster, Hurricane, Tornado, Tsunami, Flash Flood..." (http:/ /

www. stormready. noaa. gov). National Weather Service. . Retrieved 2008-08-11.[28] National Flood Risk Systems Team (2007-04-14). "Current Flooding Situation" (http:/ / www. environment-agency. gov. uk/ subjects/ flood/

floodwarning/ ). Environment Agency. . Retrieved 2007-07-07.

Storm surge 99

[29] Floating houses built to survive Netherlands floods (http:/ / www. sfgate. com/ cgi-bin/ article. cgi?f=/ c/ a/ 2005/ 11/ 09/ HOG9RFI0IJ1.DTL) SFGate.com (San Francisco Chronicle)

[30] Read, Matt (27 May 2010). "Prepare for storm evacuations" (http:/ / www. floridatoday. com/ article/ 20100527/ COLUMNISTS0207/5270331/ Lay-Prepare-for-storm-evacuations-tar-balls). Melbourne, Florida: Florida Today. pp. 1B. .

References• Siddiqui, Zubair A. (April 2009). "Storm surge forecasting for the Arabian Sea" (http:/ / www. informaworld.

com/ index/ 911063396. pdf) (PDF). Marine Geodesy (Great Britain: Taylor & Francis) 32 (2): 19.• Anthes, Richard A. (1982). "Tropical Cyclones; Their Evolution, Structure and Effects, Meteorological

Monographs". American Meteorological Society (Ephrata, PA) 19 (41): 208.• Cotton, W.R. (1990). Storms. Fort Collins, Colorado: *ASTeR Press. p. 158. ISBN 0-9625986-0-7.• Dunn, Gordon E.; Banner I. Miller (1964). Atlantic Hurricanes. Baton Rouge, LA: Louisiana State University

Press. p. 377.• Finkl, C.W. Jnr. (1994). "Disaster Mitigation in the South Atlantic Coastal Zone (SACZ): A Prodrome for

Mapping Hazards and Coastal Land Systems Using the Example of Urban subtropical Southeastern Florida. In:Finkl, C.W., Jnr. (ed.), Coastal Hazards: Perception, Susceptibility and Mitigation.". Journal of Coastal Research(Charlottesville, Virginia: Coastal Education & Research Foundation) (Special Issue No. 12): 339–366.

• National Hurricane Center; Florida Department of Community Affairs, Division of Emergency Management(1995). Lake Okeechobee Storm Surge Atlas for 17.5' & 21.5' Lake Elevations. Ft. Myers, Florida: SouthwestFlorida Regional Planning Council.

• Gornitz, V.; R.C. Daniels, T.W. White, and K.R. Birdwell (1994). "The development of a coastal risk assessmentdatabase: Vulnerability to sea level rise in the U.S. southeast". Journal of Coastal Research (Coastal Education &Research Foundation) (Special Issue No. 12): 327–338.

• Granthem, K. N. (1953-10-01). "Wave Run-up on Sloping Structures". Transactions of the American GeophysicalUnion 34 (5): 720–724.

• Harris, D.L. (1963). "Characteristics of the Hurricane Storm Surge" (http:/ / www. csc. noaa. gov/ hes/ images/pdf/ CHARACTERISTICS_STORM_SURGE. pdf) (PDF). Technical Paper No. 48 (Washington, D.C.: U.S.Dept. of Commerce, Weather Bureau): 139.

• Hebert, Paul J.; Taylor, Glenn (1983). "The Deadliest, Costliest, and Most Intense United States Hurricanes ofThis Century (and other Frequently Requested Hurricane Facts)" (http:/ / www. nhc. noaa. gov/ pdf/NWS-NHC-1983-18. pdf) (PDF). NOAA Technical Memorandum NWS NHC 31 (Miami, Florida: NationalHurricane Center): 33.

• Hebert, P.J.; Jerrell, J., Mayfield, M. (1995). "The Deadliest, Costliest, and Most Intense United States Hurricanesof This Century (and other Frequently Requested Hurricane Facts)". NOAA Technical Memorandum NWS NHC31 (Coral Gables, Fla., In: Tait, Lawrence, (Ed.) Hurricanes...Different Faces In Different Places, (proceedings)17th Annual National Hurricane Conference, Atlantic City, N.J.): 10–50.

• Jarvinen, B.R.; Lawrence, M.B. (1985). "An evaluation of the SLOSH storm-surge model". AmericanMeteorological Society Bulletin 66 (11): 1408–1411.

• Jelesnianski, Chester P (1972). "SPLASH (Special Program To List Amplitudes of Surges From Hurricanes) I.Landfall Storms". NOAA Technical Memorandum NWS TDL-46 (Silver Spring, Maryland: National WeatherService Systems Development Office): 56.

• Jelesnianski, Chester P.; Jye Chen, Wilson A. Shaffer (1992). "SLOSH: Sea, Lake, and Overland Surges fromHurricanes". NOAA Technical Report NWS 48 (Silver Spring, Maryland: National Weather Service): 71.

• Lane, E.D. (1981). Environmental Geology Series, West Palm Beach Sheet; Map Series 101. Tallahassee, Florida:Florida Bureau of Geology. p. 1.

• Murty, T.S.; Flather, R.A. (1994). "Impact of Storm Surges in the Bay of Bengal. In: Finkl, C.W., Jnr. (ed.),Coastal Hazards: Perception, Susceptibility and Mitigation". Journal of Coastal Research (Special Issue No. 12):149–161.

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• Newman, C.J.; BR Jarvinen, CJ McAdie, JD Elms (1993). Tropical Cyclones of the North Atlantic Ocean,1871-1992. Asheville, North Carolina and National Hurricane Center, Coral Gables, Florida: National ClimaticData Center in cooperation with the National Hurricane Center. p. 193.

• Sheets, Dr. Robert C. (1995). Stormy Weather, In: Tait, Lawrence, (Ed.) Hurricanes... Different Faces InDifferent Places, (Proceedings) 17th Annual National Hurricane Conference. Atlantic City, N.J.. pp. 52–62.

• Simpson, R.H.; Arnold L. Sugg and Staff (1970-04-01). "The Atlantic Hurricane Season of 1969" (http:/ / docs.lib. noaa. gov/ rescue/ mwr/ 098/ mwr-098-04-0293. pdf) (PDF). Monthly Weather Review (Boston,Massachusetts: American Meteorological Society) 98 (4). Retrieved 2008-08-11. Summary page for article (http:// ams. allenpress. com/ perlserv/ ?request=get-abstract& doi=10. 1175/ 1520-0493(1970)098<0293:TAHSO>2. 3.CO;2)

• Simpson, R.H. (1971). A Proposed Scale for Ranking Hurricanes by Intensity (Speech). Miami, Florida.• Tannehill, I.R. (1956). Hurricanes. Princeton, New Jersey: Princeton University Press. p. 308.• United States National Weather Service (1993). Hurricane!: A Familiarization Booklet. NOAA PA 91001: U.S.

Dept. of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. p. 36.• Will, Lawrence E. (1978). Okeechobee Hurricane; Killer Storms in the Everglades. Belle Glade, Florida: Glades

Historical Society. p. 204.

External links• European Space Agency storm Surge Project home pages (http:/ / www. storm-surge. info/ )• Data on Bangladesh disasters (http:/ / nirapad. org/ care_nirapad/ Home/ Magazine/ chronology/ currentissue/

html/ news8. html) from NIRAPAD disaster response organisation.• NOAA National Hurricane Center storm surge page (http:/ / www. nhc. noaa. gov/ HAW2/ english/ storm_surge.

shtml)• "The 1953 English East Coast Floods" (http:/ / www. bbc. co. uk/ weather/ features/ understanding/ 1953_flood.

shtml)• DeltaWorks.Org (http:/ / www. deltawerken. com/ 89) North Sea Flood of 1953, includes images, video and

animations.• UK storm surge model outputs and real-time tide gauge information from the National Tidal and Sea Level

Facility (http:/ / www. pol. ac. uk/ ntslf/ )

Head of tide 101

Head of tideHead of tide is the farthest point upstream where a river is affected by tidal fluctuations. This applies to rivers whichflow into tidal bodies such as oceans, bays and sloughs. Though this point may vary due to storms and seasonal orannual differences in water flows, there is generally an average point which is accepted as the head of tide. A river'stidal data is recorded at various locations downstream of this point. A river's head of tide may be considered theupper boundary of its estuary.The head of tide is important in surveying, navigation, and fisheries management, and thus many jurisdictionsestablish a legal head of tide.The head of tide may be many miles upstream from the river's mouth. For example, on the Hudson River, it islocated 140 miles (unknown operator: u'strong' km) upstream, near Albany, New York. On the Saint LawrenceRiver, tides affect shipping upstream past Quebec City, which is located several hundred miles inland from the Gulfof Saint Lawrence and the Atlantic Ocean.

Tidal stream generator

Artist's impression of tidal turbines on a different typeof support structure.

Most tidal turbines resemble a wind turbine, mostcommonly the HAWT-type (centre).

A tidal stream generator, often referred to as a tidal energyconverter (TEC) is a machine that extracts energy from movingmasses of water, in particular tides, although the term is often usedin reference to machines designed to extract energy from run ofriver or tidal estuarine sites. Certain types of these machinesfunction very much like underwater wind turbines, and are thusoften referred to as tidal turbines. They were first conceived inthe 1970s during the oil crisis.[1]

Tidal stream generators are the cheapest and the least ecologicallydamaging among the three main forms of tidal powergeneration.[2]

Similarity to wind turbines

Tidal stream generators draw energy from water currents in muchthe same way as wind turbines draw energy from air currents.However, the potential for power generation by an individual tidalturbine can be greater than that of similarly rated wind energyturbine. The higher density of water relative to air (water is about800 times the density of air) means that a single generator canprovide significant power at low tidal flow velocities comparedwith similar wind speed.[3] Given that power varies with thedensity of medium and the cube of velocity, it is simple to see thatwater speeds of nearly one-tenth of the speed of wind provide the same power for the same size of turbine system;however this limits the application in practice to places where the tide moves at speeds of at least 2 knots (1 m/s)even close to neap tides. Furthermore, at higher speeds in a flow between 2 to 3 metres per second in seawater a tidalturbine can typically access four times as much energy per rotor swept area as a similarly rated power wind turbine.

Tidal stream generator 102

Types of tidal stream generatorsSince tidal stream generators are an immature technology, no standard technology has yet emerged as the clearwinner, but a large variety of designs are being experimented with, some very close to large scale deployment.Several prototypes have shown promise with many companies making bold claims, some of which are yet to beindependently verified, but they have not operated commercially for extended periods to establish performances andrates of return on investments.The European Marine Energy Centre[4] categorises them under four heads although a number of other approaches arealso being tried.

Axial turbines

Evopod - A semi-submerged floating approach tested in StrangfordLough.

These are close in concept to traditional windmillsoperating under the sea and have the most prototypescurrently operating. These include:The AR-1000, a 1MW tidal turbine developed byAtlantis Resources Corporation which was successfullydeployed and commissioned at the EMEC facilityduring the summer of 2011. The AR series turbines arecommercial scale Horizontal Axis Turbines designedfor open ocean deployment in the harshestenvironments on the planet. AR turbines feature asingle rotor set with highly efficient fixed pitch blades.The AR turbine is rotated as required with each tidalexchange. This is done in the slack period betweentides and fixed in place for the optimal heading for thenext tide. AR turbines are rated at 1MW @ 2.65m/s ofwater flow velocity.Further information about Atlantis Resources Corporation can be found here. [5]

Kvalsund, south of Hammerfest, Norway.[6] Although still a prototype, a turbine with a reported capacity of 300 kWwas connected to the grid on 13 November 2003.A 300 kW Periodflow marine current propeller type turbine — Seaflow — was installed by Marine Current Turbinesoff the coast of Lynmouth, Devon, England, in 2003.[7] The 11m diameter turbine generator was fitted to a steel pilewhich was driven into the seabed. As a prototype, it was connected to a dump load, not to the grid.Since April 2007 Verdant Power[8] has been running a prototype project in the East River between Queens andRoosevelt Island in New York City; it was the first major tidal-power project in the United States.[9] The strongcurrents pose challenges to the design: the blades of the 2006 and 2007 prototypes broke off, and new reinforcedturbines were installed in September 2008.[10][11]

Following the Seaflow trial, a full-size prototype, called SeaGen, was installed by Marine Current Turbines inStrangford Lough in Northern Ireland in April 2008. The turbine began to generate at full power of just over 1.2 MWin December 2008[12] and is reported to have fed 150 kW into the grid for the first time on 17 July 2008, and hasnow contributed more than a gigawatt hour to consumers in Northern Ireland.[13] It is currently the only commercialscale device to have been installed anywhere in the world.[14] SeaGen is made up of two axial flow rotors, each ofwhich drive a generator. The turbines are capable of generating electricity on both the ebb and flood tides becausethe rotor blades can pitch through 180˚.[15]

OpenHydro,[16] an Irish company exploiting the Open-Centre Turbine developed in the U.S., has a prototype beingtested at the European Marine Energy Centre (EMEC), in Orkney, Scotland.

Tidal stream generator 103

A prototype semi-submerged floating tethered tidal turbine called Evopod has been tested since June 2008[17] inStrangford Lough, Northern Ireland at 1/10 scale. The company developing it is called Ocean Flow Energy Ltd,[18]

and they are based in the UK. The advanced hull form maintains optimum heading into the tidal stream and it isdesigned to operate in the peak flow of the water column.Tenax Energy of Australia is proposing to put 450 turbines off the coast of the Australian city Darwin, in theClarence Strait. The turbines feature a rotor section that is approximately 15 metres in diameter with a gravity basewhich is slighter larger than this to support the structure. The turbines will operate in deep water well below shippingchannels. Each turbine is forecast to produce energy for between 300 and 400 homes.[19]

Tidalstream, a UK-based company, has commissioned a scaled-down Triton 3 turbine in the Thames, see picture onthe right, and photographs maintained on their website [20].[21] It can be floated out to site, installed without cranes,jack-ups or divers, and then ballasted into operating position. At full scale the Triton 3 in 30-50m deep water has a3MW capacity, and the Triton 6 in 60-80m water has a capacity of up to 10MW, depending on the flow. Bothplatforms have man-access capability both in the operating position and in the float-out maintenance position.

Vertical and horizontal axis crossflow turbinesInvented by Georges Darreius in 1923 and Patented in 1929, these turbines that can be deployed either vertically orhorizontally.The Gorlov turbine[22] is a variant of the Darrieus design featuring a helical design which is being commerciallypiloted on a large scale in S. Korea,[23] starting with a 1MW plant that started in May 2009[24] and expanding to90MW by 2013. Neptune Renewable Energy has developed Proteus[25] a shrouded vertical axis turbine which can beused to form an array in mainly estuarine conditions. The Musgrove vertical Axis Wind Turbine with vertical selfstarting free hinged aerodynamic blades is probably the inspiration for the this turbine.In late April 2008, Ocean Renewable Power Company, LLC (ORPC) [26] successfully completed the testing of itsproprietary turbine-generator unit (TGU) prototype at ORPC's Cobscook Bay and Western Passage tidal sites nearEastport, Maine.[27] The TGU is the core of the OCGen technology and utilizes advanced design cross-flow (ADCF)turbines to drive a permanent magnet generator located between the turbines and mounted on the same shaft. ORPChas developed TGU designs that can be used for generating power from river, tidal and deep water ocean currents.Trials in the Strait of Messina, Italy, started in 2001 of the Kobold concept.[28]

Flow augmented turbinesUsing flow augmentation measures, for example a duct or shroud, the incident power available to a turbine can beincreased. The most common example uses a shroud to increase the flow rate through the turbine, which can be ofeither the axial or crossflow type.The Australian company Tidal Energy Pty Ltd undertook successful commercial trials of efficient shrouded tidalturbines on the Gold Coast, Queensland in 2002. Tidal Energy has commenced a rollout of their shrouded turbine fora remote Australian community in northern Australia where there are some of the fastest flows ever recorded(11 m/s, 21 knots) – two small turbines will provide 3.5 MW. Another larger 5 meter diameter turbine, capable of800 kW in 4 m/s of flow, is planned for deployment as a tidal powered desalination showcase near BrisbaneAustralia in October 2008.

Tidal stream generator 104

Oscillating devicesOscillating devices do not have a rotating component, instead making use of aerofoil sections which are pushedsideways by the flow. Oscillating stream power extraction was proven with the omni- or bi-directional Wing'd Pumpwindmill.[29] During 2003 a 150 kW oscillating hydroplane device, the Stingray, was tested off the Scottish coast.[30]

The Stingray uses hydrofoils to create oscillation, which allows it to create hydraulic power. This hydraulic power isthen used to power a hydraulic motor, which then turns a generator.[1]

Pulse Tidal operate an oscillating hydrofoil device in the Humber estuary.[31] Having secured funding from the EU,they are developing a commercial scale device to be commissioned 2012.[32]

The bioSTREAM tidal power conversion system, uses the biomimicry of swimming species, such as shark, tuna, andmackerel using their highly efficient Thunniform mode propulsion. It is produced by Australian company BioPowerSystems.A 2 kW prototype relying on the use of two oscillating hydrofoils in a tandem configuration has been developed atLaval University and tested successfully near Quebec City, Canada, in 2009. A hydrodynamic efficiency of 40% hasbeen achieved during the field tests.[33]

Venturi effectVenturi effect devices use a shroud or duct in order to generate a pressure differential which is used to run asecondary hydraulic circuit which is used to generate power. A device, the Hydro Venturi, is to be tested in SanFrancisco Bay.[34]

Commercial plansRWE's npower announced that it is in partnership with Marine Current Turbines to build a tidal farm of SeaGenturbines off the coast of Anglesey in Wales,[35] near the Skerries.[36]

In November 2007, British company Lunar Energy announced that, in conjunction with E.ON, they would bebuilding the world's first deep-sea tidal energy farm off the coast of Pembrokshire in Wales. It will provideelectricity for 5,000 homes. Eight underwater turbines, each 25 metres long and 15 metres high, are to be installed onthe sea bottom off St David's peninsula. Construction is due to start in the summer of 2008 and the proposed tidalenergy turbines, described as "a wind farm under the sea", should be operational by 2010.British Columbia Tidal Energy Corp. plans to deploy at least three 1.2 MW turbines in the Campbell River or in thesurrounding coastline of British Columbia by 2009.[37]

An organisation named Alderney Renewable Energy Ltd [38] is planning to use tidal turbines to extract power fromthe notoriously strong tidal races around Alderney in the Channel Islands. It is estimated that up to 3 GW could beextracted. This would not only supply the island's needs but also leave a considerable surplus for export.[39]

Nova Scotia Power has selected OpenHydro's turbine for a tidal energy demonstration project in the Bay of Fundy,Nova Scotia, Canada and Alderney Renewable Energy Ltd for the supply of tidal turbines in the Channel Islands.Open Hydro [40]

Pulse Tidal [41] are designing a commercial device with seven other companies who are expert in their fields.[42] Theconsortium was awarded an €8 million EU grant to develop the first device, which will be deployed in 2012 andgenerate enough power for 1,000 homes. Pulse is in a good position to scale up production because the supply chainis already in place.ScottishPower Renewables [43] are planning to deploy ten 1MW HS1000 devices designed by Hammerfest Strom [44]

in the Sound of Islay.[45]

Tidal stream generator 105

Energy calculations

Turbine powerTidal energy converters can have varying modes of operating and therefore varying power output. If the powercoefficient of the device " " is known, the equation below can be used to determine the power output of thehydrodynamic subsystem of the machine. This available power cannot exceed that imposed by the Betz limit on thepower coefficient, although this can be circumvented to some degree by placing a turbine in a shroud or duct. Thisworks, in essence, by forcing water which would not have flowed through the turbine through the rotor disk. In thesesituations it is the frontal area of the duct, rather than the turbine, which is used in calculating the power coefficientand therefore the Betz limit still applies to the device as a whole.The energy available from these kinetic systems can be expressed as:

where:= the turbine power coefficient

P = the power generated (in watts)= the density of the water (seawater is 1027 kg/m³)

A = the sweep area of the turbine (in m²)V = the velocity of the flow

Relative to an open turbine in free stream, ducted turbines are capable of as much as 3 to 4 times the power of thesame turbine rotor in open flow. .[46]

Resource assessmentWhile initial assessments of the available energy in a channel have focus on calculations using the kinetic energyflux model, the limitations of tidal power generation are significantly more complicated. For example, the maximumphysical possible energy extraction from a strait connecting two large basins is given to within 10% by:[47][48]

where= the density of the water (seawater is 1027 kg/m³)

g = gravitational acceleration (9.80665 m/s2)= maximum differential water surface elevation across the channel

= maximum volumetric flow rate though the channel.

Potential sitesAs with wind power, selection of location is critical for the tidal turbine. Tidal stream systems need to be located inareas with fast currents where natural flows are concentrated between obstructions, for example at the entrances tobays and rivers, around rocky points, headlands, or between islands or other land masses. The following potentialsites are under serious consideration:• Pembrokeshire in Wales[49]

• River Severn between Wales and England[50]

• Cook Strait in New Zealand[51]

• Kaipara Harbour in New Zealand[52]

• Bay of Fundy[53] in Canada.

Tidal stream generator 106

• East River[54][55] in the USA• Golden Gate in the San Francisco Bay[56]

• Piscataqua River in New Hampshire[57]

• The Race of Alderney and The Swinge in the Channel Islands[39]

• The Sound of Islay, between Islay and Jura in Scotland[58]

• Pentland Firth between Caithness and the Orkney Islands, Scotland• Humboldt County, California in the United States• Columbia River, Oregon in the United StatesModern advances in turbine technology may eventually see large amounts of power generated from the ocean,especially tidal currents using the tidal stream designs but also from the major thermal current systems such as theGulf Stream, which is covered by the more general term marine current power. Tidal stream turbines may be arrayedin high-velocity areas where natural tidal current flows are concentrated such as the west and east coasts of Canada,the Strait of Gibraltar, the Bosporus, and numerous sites in Southeast Asia and Australia. Such flows occur almostanywhere where there are entrances to bays and rivers, or between land masses where water currents areconcentrated.

Environmental impactsVery little direct research or observation of tidal stream systems exists. Most direct observations consist of releasingtagged fish upstream of the device(s) and direct observation of mortality or impact on the fish.One study of the Roosevelt Island Tidal Energy (RITE, Verdant Power) project in the East River (New York City),utilized 24 split beam hydroacoustic sensors (scientific echosounder) to detect and track the movement of fish bothupstream and downstream of each of six turbines. The results suggested (1) very few fish using this portion of theriver, (2) those fish which did use this area were not using the portion of the river which would subject them to bladestrikes, and (3) no evidence of fish traveling through blade areas.Work is currently being conducted by the Northwest National Marine Renewable Energy Center (NNMREC[59])toexplore and establish tools and protocols for assessment of physical and biological conditions and monitorenvironmental changes associated with tidal energy development.

References[1][1] Jones, Anthony T., and Adam Westwood. "Power from the oceans: wind energy industries are growing, and as we look for alternative power

sources, the growth potential is through the roof. Two industry watchers take a look at generating energy from wind and wave action and thepotential to alter." The Futurist 39.1 (2005): 37(5). GALE Expanded Academic ASAP. Web. 8 October 2009.

[2] "Tidal power" (http:/ / www. esru. strath. ac. uk/ EandE/ Web_sites/ 01-02/ RE_info/ Tidal Power. htm#streams). . Retrieved 1 November2010.

[3] "Surfing Energy's New Wave" Time International 16 June 2003: 52+. http:/ / www. time. com/ time/ magazine/ article/ 0,9171,457348,00.html

[4] EMEC. "Tidal Energy Devices" (http:/ / www. emec. org. uk/ tidal_devices. htm). . Retrieved 5 October 2008.[5] http:/ / www. atlantisresourcescorporation. com/[6] First power station to harness Moon opens - September 22, 2003 - New Scientist (http:/ / www. newscientist. com/ article. ns?id=dn4188)[7] REUK: "Read about the first open-sea tidal turbine generator off Lynmouth, Devon" (http:/ / www. reuk. co. uk/

Worlds-First-Open-Sea-Tidal-Turbine. htm)[8] Verdant Power (http:/ / www. verdantpower. com/ what-initiative)[9] MIT Technology Review, April 2007 (http:/ / www. technologyreview. com/ Energy/ 18567/ ). Retrieved August 24, 2008.[10] Robin Shulman (September 20, 2008). "N.Y. Tests Turbines to Produce Power. City Taps Current Of the East River" (http:/ / www.

washingtonpost. com/ wp-dyn/ content/ article/ 2008/ 09/ 19/ AR2008091903729. html). Washington Post. . Retrieved 2008-10-09.[11] Kate Galbraith (September 22, 2008). "Power From the Restless Sea Stirs the Imagination" (http:/ / www. nytimes. com/ 2008/ 09/ 23/

business/ 23tidal. html?em). New York Times. . Retrieved 2008-10-09.[12] http:/ / www. marineturbines. com/ 3/ news/[13] First connection to the grid (http:/ / www. marineturbines. com/ 3/ news/ / )[14] · Sea Generation Tidal Turbine (http:/ / www. marineturbines. com/ 18/ projects/ 19/ seagen/ )

Tidal stream generator 107

[15] Marine Current Turbines. "Technology." Marine Current Turbines. Marine Current Turbines, n.d. Web. 5 October 2009.<http://www.marineturbines.com/21/ technology/>.

[16] OpenHydro (http:/ / www. openhydro. com/ )[17] (http:/ / www. oceanflowenergy. com/ news-details. aspx?id=6) Ocean Flow Energy Ltd announce the start of their testing in Strangford

Lough[18] Ocean Flow Energy company website (http:/ / www. oceanflowenergy. com/ )[19] Nigel Adlam (2010-01-29). "Tidal power project could run all homes" (http:/ / www. ntnews. com. au/ article/ 2010/ 01/ 29/

119431_ntnews. html). Northern Territory News. . Retrieved 2010-06-06.[20] http:/ / www. tidalstream. co. uk[21] (http:/ / www. tidalstream. co. uk)[22] Gorlov Turbine (http:/ / www. gcktechnology. com/ )[23] Gorlov Turbines in Koreas (http:/ / www. worldchanging. com/ archives/ 002383. html)[24] "South Korea starts up, to expand 1-MW Jindo Uldolmok tidal project" (http:/ / www. hydroworld. com/ index/ display/ article-display/

2336952618/ articles/ hrhrw/ hydroindustrynews/ ocean-tidal-streampower/ south-korea_starts. html). Hydro World. 2009. .[25] Proteus (http:/ / www. neptunerenewableenergy. com/ )[26] http:/ / www. oceanrenewablepower. com[27] "Tide is slowly rising in interest in ocean power" (http:/ / www. masshightech. com/ stories/ 2008/ 07/ 28/

weekly9-Tide-is-slowly-rising-in-interest-in-ocean-power. html/ ). Mass High Tech: The Journal of New England Technology. August 1,2008. . Retrieved 2008-10-11.

[28] A.D.A.Group (http:/ / www. dpa. unina. it/ adag/ eng/ renewable_energy. html)[29] Wing'd Pump Windmill (http:/ / econologica. org/ watermill. htm)[30] Stingray (http:/ / www. engb. com/ )[31] BBC Look North "A tidal power project in the Humber has generated its first batch of electricity" (http:/ / www. youtube. com/

watch?v=z07OV0d9NS4)[32] EU Grant reported by The Engineer (http:/ / www. theengineer. co. uk/ pulse-tidal-receives-eu-grant/ 1000213. article)[33] HAO turbine (http:/ / hydrolienne. fsg. ulaval. ca/ en)[34] San Francisco Bay Guardian News (http:/ / www. sfbg. com/ 38/ 43/ news_tidal. html)[35] "RWE plans 10.5 MW sea current power plant off Welsh coast - Forbes.com" (http:/ / www. forbes. com/ markets/ feeds/ afx/ 2008/ 02/ 07/

afx4626015. html). .[36] RWE npower renewables Sites > Projects in Development > Marine > Skerries > The Proposal : Anglesey Skerries Tidal Stream Array

(http:/ / www. rwe. com/ web/ cms/ en/ 309778/ rwe-npower-renewables/ sites/ projects-in-development/ marine/ skerries/ the-proposal/ ).Retrieved February 26, 2010.

[37] Tidal Power Coming to West Coast of Canada (http:/ / www. alternative-energy-news. info/ press/ tidal-power-west-coast-canada/ )[38] http:/ / www. are. gb. com/ index. php[39] Alderney Renewable Energy Ltd (http:/ / www. are. gb. com/ index. php)[40] http:/ / www. openhydro. com[41] http:/ / www. pulsetidal. com[42] Pulse Press Release: Consortium members signed up with EU Grant: Bosch Rexroth will provide the hydraulics; Herbosch Kiere the

installation; DNV the certification; IT Power the engineering; Niestern Sander the construction; the Fraunhofer IWES the control systems; andGurit the composites (http:/ / www. pulsegeneration. co. uk/ ?q=node/ 54)

[43] http:/ / www. scottishpowerrenewables. com[44] http:/ / www. hammerfeststrom. com[45] Islay Energy Trust (http:/ / www. islayenergytrust. org. uk)[46] http:/ / www. cyberiad. net/ library/ pdf/ bk_tidal_paper25apr06. pdf tidal paper on cyberiad.net[47] Atwater, J.F., Lawrence, G.A. (2008) Limitations on Tidal Power Generation in a Channel, Proceedings of the 10th World Renewable

Energy Congress. (pp 947–952)[48] Garrett, C. and Cummins, P. (2005). "The power potential of tidal currents in channels." Proceedings of the Royal Society A: Mathematical,

Physical and Engineering Sciences, Vol. 461, London. The Royal Society, 2563–2572[49] Builder & Engineer - Pembrokeshire tidal barrage moves forward (http:/ / www. builderandengineer. co. uk/ news/ general/

pembrokeshire-tidal-barrage-moves-forward-934. html)[50] Severn balancing act (http:/ / www. walesonline. co. uk/ news/ politics-news/ tm_headline=severn-balancing-act-hain& method=full&

objectid=19718602& siteid=50082-name_page. html)[51] NZ: Chance to turn the tide of power supply | EnergyBulletin.net | Peak Oil News Clearinghouse (http:/ / www. energybulletin. net/ 6046.

html)[52] "Harnessing the power of the sea" (http:/ / www. contrafedpublishing. co. nz/ Energy+ NZ/ Harnessing+ the+ power+ of+ the+ sea. html).

Energy NZ, Vol 1, No 1. Winter 2007. .[53] Bay of Fundy to get three test turbines | Cleantech.com (http:/ / media. cleantech. com/ 2269/ bay-of-fundy-to-get-three-test-turbines)[54] Shulman, Robin (September 20, 2008). "N.Y. Tests Turbines to Produce Power" (http:/ / www. washingtonpost. com/ wp-dyn/ content/

article/ 2008/ 09/ 19/ AR2008091903729. html?hpid=topnews& sub=AR). The Washington Post. ISSN 0740-5421. . Retrieved 2008-09-20.

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[55] Verdant Power (http:/ / verdantpower. com/ what-initiative)[56] http:/ / deanzaemtp. googlepages. com/ PGEbacksnewstudyofbaystidalpower. pdf[57] Tidal power from Piscataqua River? (http:/ / www. seacoastonline. com/ apps/ pbcs. dll/ article?AID=/ 20070519/ NEWS/ 705190344)[58] Islay Energy Trust - Developing Renewables for the community (http:/ / www. islayenergytrust. org. uk)[59] (http:/ / depts. washington. edu/ nnmrec/ )

Tidal barrage

The Rance Tidal Power Station, a tidal barrage inFrance.

A tidal barrage is a dam-like structure used to capture the energyfrom masses of water moving in and out of a bay or river due to tidalforces.[1][2]

Instead of damming water on one side like a conventional dam, a tidalbarrage first allows water to flow into a bay or river during high tide,and releasing the water back during low tide. This is done bymeasuring the tidal flow and controlling the sluice gates at key times ofthe tidal cycle. Turbines are then placed at these sluices to capture theenergy as the water flows in and out.[1]

Tidal barrages are among the oldest methods of tidal power generation,with projects being developed as early as the 1960s, such as the 1.7megawatt Kislaya Guba Tidal Power Station in Kislaya Guba, Russia.

Generating methods

An artistic impression of a tidal barrage,including embankments, a ship lock and caissons

housing a sluice and two turbines.

The barrage method of extracting tidal energy involves building abarrage across a bay or river that is subject to tidal flow. Turbinesinstalled in the barrage wall generate power as water flows in and outof the estuary basin, bay, or river. These systems are similar to a hydrodam that produces Static Head or pressure head (a height of waterpressure). When the water level outside of the basin or lagoon changesrelative to the water level inside, the turbines are able to producepower.

The basic elements of a barrage are caissons, embankments, sluices,turbines, and ship locks. Sluices, turbines, and ship locks are housed incaissons (very large concrete blocks). Embankments seal a basin whereit is not sealed by caissons.

The sluice gates applicable to tidal power are the flap gate, vertical rising gate, radial gate, and rising sector.Only a few such plants exist. The first was the Rance Tidal Power Station, on the Rance river, in France, which hasbeen operating since 1966, and generates 240MW. A larger 254MW plant began operation at Sihwa Lake, Korea, in2011. Smaller plants include one on the Bay of Fundy, and another across a tiny inlet in Kislaya Guba, Russia). Anumber of proposals have been considered for a Severn barrage across the River Severn, from Brean Down inEngland to Lavernock Point near Cardiff in Wales.Barrage systems are affected by problems of high civil infrastructure costs associated with what is in effect a dambeing placed across estuarine systems, and the environmental problems associated with changing a large ecosystem.

Tidal barrage 109

Ebb generationThe basin is filled through the sluices until high tide. Then the sluice gates are closed. (At this stage there may be"Pumping" to raise the level further). The turbine gates are kept closed until the sea level falls to create sufficienthead across the barrage, and then are opened so that the turbines generate until the head is again low. Then thesluices are opened, turbines disconnected and the basin is filled again. The cycle repeats itself. Ebb generation (alsoknown as outflow generation) takes its name because generation occurs as the tide changes tidal direction.

Flood generationThe basin is filled through the turbines, which generate at tide flood. This is generally much less efficient than ebbgeneration, because the volume contained in the upper half of the basin (which is where ebb generation operates) isgreater than the volume of the lower half (filled first during flood generation). Therefore the available leveldifference – important for the turbine power produced – between the basin side and the sea side of the barrage,reduces more quickly than it would in ebb generation. Rivers flowing into the basin may further reduce the energypotential, instead of enhancing it as in ebb generation. Of course this is not a problem with the "lagoon" model,without river inflow.

PumpingTurbines are able to be powered in reverse by excess energy in the grid to increase the water level in the basin athigh tide (for ebb generation). This energy is more than returned during generation, because power output is stronglyrelated to the head. If water is raised 2 ft (61 cm) by pumping on a high tide of 10 ft (3 m), this will have been raisedby 12 ft (3.7 m) at low tide. The cost of a 2 ft rise is returned by the benefits of a 12 ft rise. This is because thecorrelation between the potential energy is not a linear relationship, but rather, is related by the square of the tidalheight variation.

Two-basin schemesAnother form of energy barrage configuration is that of the dual basin type. With two basins, one is filled at high tideand the other is emptied at low tide. Turbines are placed between the basins. Two-basin schemes offer advantagesover normal schemes in that generation time can be adjusted with high flexibility and it is also possible to generatealmost continuously. In normal estuarine situations, however, two-basin schemes are very expensive to construct dueto the cost of the extra length of barrage. There are some favourable geographies, however, which are well suited tothis type of scheme.

Tidal lagoon powerTidal pools[3] are independent enclosing barrages built on high level tidal estuary land that trap the high water andrelease it to generate power, single pool, around 3.3W/m2. Two lagoons operating at different time intervals canguarantee continuous power output, around 4.5W/m2. Enhanced pumped storage[4] tidal series of lagoons raises thewater level higher than the high tide, and uses intermittent renewables for pumping, around 7.5W/m2. i.e.10 × 10 km2 delivers 750MW constant output 24/7. These independent barrages do not block the flow of the riverand are a viable alternative to the Severn Barrage.

Tidal barrage 110

Environmental impactThe placement of a barrage into an estuary has a considerable effect on the water inside the basin and on theecosystem. Many governments have been reluctant in recent times to grant approval for tidal barrages. Throughresearch conducted on tidal plants, it has been found that tidal barrages constructed at the mouths of estuaries posesimilar environmental threats as large dams. The construction of large tidal plants alters the flow of saltwater in andout of estuaries, which changes the hydrology and salinity and possibly negatively affects the marine mammals thatuse the estuaries as their habitat[5] The La Rance plant, off the Brittany coast of northern France, was the first andlargest tidal barrage plant in the world. It is also the only site where a full-scale evaluation of the ecological impactof a tidal power system, operating for 20 years, has been made[6]

French researchers found that the isolation of the estuary during the construction phases of the tidal barrage wasdetrimental to flora and fauna, however; after ten years, there has been a "variable degree of biological adjustment tothe new environmental conditions"[6]

Some species lost their habitat due to La Rance's construction, but other species colonized the abandoned space,which caused a shift in diversity. Also as a result of the construction, sandbanks disappeared, the beach of St. Servanwas badly damaged and high-speed currents have developed near sluices, which are water channels controlled bygates[7]

TurbidityTurbidity (the amount of matter in suspension in the water) decreases as a result of smaller volume of water beingexchanged between the basin and the sea. This lets light from the Sun penetrate the water further, improvingconditions for the phytoplankton. The changes propagate up the food chain, causing a general change in theecosystem.

Tidal fences and turbinesTidal fences and turbines can have varying environmental impacts depending on whether or not fences and turbinesare constructed with regard to the environment. The main environmental impact of turbines is their impact on fish. Ifthe turbines are moving slowly enough, such as low velocities of 25-50 rpm, fish kill is minimalized and silt andother nutrients are able to flow through the structures[5] For example, a 20 kW tidal turbine prototype built in the St.Lawrence Seaway in 1983 reported no fish kills[5] Tidal fences block off channels, which makes it difficult for fishand wildlife to migrate through those channels. In order to reduce fish kill, fences could be engineered so that thespaces between the caisson wall and the rotor foil are large enough to allow fish to pass through[5] Larger marinemammals such as seals or dolphins can be protected from the turbines by fences or a sonar sensor auto-breakingsystem that automatically shuts the turbines down when marine mammals are detected[5] Overall, many researcheshave argued that while tidal barrages pose environmental threats, tidal fences and tidal turbines, if constructedproperly, are likely to be more environmentally benign. Unlike barrages, tidal fences and turbines do not blockchannels or estuarine mouths, interrupt fish migration or alter hydrology, thus, these options offer energy generatingcapacity without dire environmental impacts[5]

Tidal barrage 111

SalinityAs a result of less water exchange with the sea, the average salinity inside the basin decreases, also affecting theecosystem. "Tidal Lagoons" do not suffer from this problem.

Sediment movementsEstuaries often have high volume of sediments moving through them, from the rivers to the sea. The introduction ofa barrage into an estuary may result in sediment accumulation within the barrage, affecting the ecosystem and alsothe operation of the barrage.

FishFish may move through sluices safely, but when these are closed, fish will seek out turbines and attempt to swimthrough them. Also, some fish will be unable to escape the water speed near a turbine and will be sucked through.Even with the most fish-friendly turbine design, fish mortality per pass is approximately 15% (from pressure drop,contact with blades, cavitation, etc.). Alternative passage technologies (fish ladders, fish lifts, fish escalators etc.)have so far failed to solve this problem for tidal barrages, either offering extremely expensive solutions, or oneswhich are used by a small fraction of fish only. Research in sonic guidance of fish is ongoing. The Open-Centreturbine reduces this problem allowing fish to pass through the open centre of the turbine.Recently a run of the river type turbine has been developed in France. This is a very large slow rotating Kaplan typeturbine mounted on an angle. Testing for fish mortality has indicated fish mortality figures to be less than 5%. Thisconcept also seems very suitable for adaption to marine current/tidal turbines.[8]

Energy calculationsThe energy available from a barrage is dependent on the volume of water. The potential energy contained in avolume of water is:[9]

where:• h is the vertical tidal range,• A is the horizontal area of the barrage basin,• ρ is the density of water = 1025 kg per cubic meter (seawater varies between 1021 and 1030 kg per cubic meter)

and• g is the acceleration due to the Earth's gravity = 9.81 meters per second squared.The factor half is due to the fact, that as the basin flows empty through the turbines, the hydraulic head over the damreduces. The maximum head is only available at the moment of low water, assuming the high water level is stillpresent in the basin.

Tidal barrage 112

Example calculation of tidal power generationAssumptions:

•• The tidal range of tide at a particular place is 32 feet = 10 m (approx)• The surface of the tidal energy harnessing plant is 9 km² (3 km × 3 km)= 3000 m × 3000 m = 9 × 106 m2

• Density of sea water = 1025.18 kg/m3

Mass of the sea water = volume of sea water × density of sea water= (area × tidal range) of water × mass density= (9 × 106 m2 × 10 m) × 1025.18 kg/m3

= 92 × 109 kg (approx)Potential energy content of the water in the basin at high tide = ½ × area × density × gravitational acceleration × tidalrange squared

= ½ × 9 × 106 m2 × 1025 kg/m3 × 9.81 m/s2 × (10 m)2

=4.5 × 1012 J (approx)Now we have 2 high tides and 2 low tides every day. At low tide the potential energy is zero.Therefore the total energy potential per day = Energy for a single high tide × 2

= 4.5 × 1012 J × 2= 9 × 1012 J

Therefore, the mean power generation potential = Energy generation potential / time in 1 day= 9 × 1012 J / 86400 s= 104 MW

Assuming the power conversion efficiency to be 30%: The daily-average power generated = 104 MW * 30%= 31 MW (approx)

Because the available power varies with the square of the tidal range, a barrage is best placed in a location with veryhigh-amplitude tides. Suitable locations are found in Russia, USA, Canada, Australia, Korea, the UK. Amplitudes ofup to 17 m (56 ft) occur for example in the Bay of Fundy, where tidal resonance amplifies the tidal range.

EconomicsTidal barrage power schemes have a high capital cost and a very low running cost. As a result, a tidal power schememay not produce returns for many years, and investors may be reluctant to participate in such projects.Governments may be able to finance tidal barrage power, but many are unwilling to do so also due to the lag timebefore investment return and the high irreversible commitment. For example the energy policy of the UnitedKingdom[10] recognizes the role of tidal energy and expresses the need for local councils to understand the broadernational goals of renewable energy in approving tidal projects. The UK government itself appreciates the technicalviability and siting options available, but has failed to provide meaningful incentives to move these goals forward.

Tidal barrage 113

References[1] "Tidal barrage" (http:/ / www. esru. strath. ac. uk/ EandE/ Web_sites/ 01-02/ RE_info/ Tidal Power. htm#barrage). . Retrieved 2 November

2010.[2] "Tidal barrages and tidal turbines" (http:/ / www. rise. org. au/ info/ Tech/ tidal/ index. html). . Retrieved 2 November 2010.[3] http:/ / wwww. tidalelectric. com[4] http:/ / www. inference. phy. cam. ac. uk/ sustainable/ book/ tex/ Lagoons. pdf[5] Pelc, Robin and Fujita, Rob. Renewable energy from the ocean. (http:/ / www. sciencedirect. com/ science?_ob=ArticleURL&

_udi=B6VCD-47CGCRD-6& _user=10& _rdoc=1& _fmt=& _orig=search& _sort=d& view=c& _acct=C000050221& _version=1&_urlVersion=0& _userid=10& md5=7a620f2b0dbe9238f4dd14565b4f205a)

[6] Retiere, C. Tidal power and aquatic environment of La Rance. (http:/ / www. sciencedirect. com/ science?_ob=ArticleURL&_udi=B6WBR-45P0YSY-18& _user=607017& _coverDate=01/ 31/ 1994& _alid=807589306& _rdoc=7& _fmt=high& _orig=search&_cdi=6717& _sort=d& _docanchor=& view=c& _ct=13& _acct=C000031527& _version=1& _urlVersion=0& _userid=607017&md5=a1bf5bed8436ee57584961d337274b71)

[7] Charlier, Roger. Forty candles for the Rance River TPP tides provide renewable and sustainable power generation (http:/ / www.sciencedirect. com/ science?_ob=ArticleURL& _udi=B6VMY-4K7FFMT-1& _user=607017& _coverDate=12/ 31/ 2007&_alid=807601279& _rdoc=2& _fmt=high& _orig=mlkt& _cdi=6163& _sort=v& _st=17& _docanchor=& view=c& _ct=743&_acct=C000031527& _version=1& _urlVersion=0& _userid=607017& md5=3cedbf77e95163ad11903503d4f6775e)

[8] VLH TURBINE (http:/ / www. vlh-turbine. com)[9] Lamb, H. (1994). Hydrodynamics (6th ed.). Cambridge University Press. ISBN 978-0-521-45868-9. §174, p. 260.[10] (http:/ / www. odpm. gov. uk/ index. asp?id=1143914#TopOfPage) (see for example key principles 4 and 6 within Planning Policy

Statement 22)

Marine energyMarine energy or marine power (also sometimes referred to as ocean energy or ocean power) refers to the energycarried by ocean waves, tides, salinity, and ocean temperature differences. The movement of water in the world’soceans creates a vast store of kinetic energy, or energy in motion. This energy can be harnessed to generateelectricity to power homes, transport and industries.The term marine energy encompasses both wave power — power from surface waves, and tidal power — obtainedfrom the kinetic energy of large bodies of moving water. Offshore wind power is not a form of marine energy, aswind power is derived from the wind, even if the wind turbines are placed over water.The oceans have a tremendous amount of energy and are close to many if not most concentrated populations. Oceanenergy has the potential of providing a substantial amount of new renewable energy around the world.[1]

Potential of ocean energyThe theoretical potential is equivalent to 4-18 million ToE.

Theoretical global ocean energy resource[2]

Capacity(GW)

Annual gen.(TW·h)

Form

5,000 50,000 Marine current power[3]

20 2,000 Osmotic power

1,000 10,000 Ocean thermal energy

90 800 Tidal energy

1,000—9,000 8,000—80,000 Wave energy

Indonesia as archipelagic country with three quarter of the area is ocean, has 49 GW recognized potential oceanenergy and has 727 GW theoritical potential ocean energy.[4]

Marine energy 114

Forms of ocean energy

RenewableThe oceans represent a vast and largely untapped source of energy in the form of surface waves, fluid flow, salinitygradients, and thermal.

Marine current power

The energy obtained from ocean currents

Osmotic power

The energy from salinity gradients.

Ocean thermal energy

The power from temperature differences at varying depths.

Tidal power

The energy from moving masses of water — a popular form of hydroelectric power generation. Tidal powergeneration comprises three main forms, namely: tidal stream power, tidal barrage power, and dynamic tidal power.

Wave power

The power from surface waves.

Non-renewablePetroleum and natural gas beneath the ocean floor are also sometimes considered a form of ocean energy. An oceanengineer directs all phases of discovering, extracting, and delivering offshore petroleum (via oil tankers andpipelines,) a complex and demanding task. Also centrally important is the development of new methods to protectmarine wildlife and coastal regions against the undesirable side effects of offshore oil extraction.

References[1] Carbon Trust, Future Marine Energy. Results of the Marine Energy Challenge: Cost competitiveness and growth of wave and tidal stream

energy, January 2006[2][2] International Energy Agency, Implementing Agreement on Ocean Energy Systems (IEA-OES), Annual Report 2007[3] US Department of the Interior (May 2006). "Ocean Current Energy Potential on the U.S. Outer Continental Shelf" (http:/ / ocsenergy. anl.

gov/ documents/ docs/ OCS_EIS_WhitePaper_Current. pdf) (pdf). . Retrieved 2 November 2010.[4] Indonesian Ocean Energy (http:/ / jakarta. indopos. co. id/ ?p=4742)

External links• The Ocean Energy Systems Implementing Agreement (http:/ / www. ocean-energy-systems. org)• European Ocean Energy Association (http:/ / www. eu-oea. com)• Ocean Energy Council (http:/ / www. oceanenergycouncil. com)• SuperGen UK Centre for Marine Energy Research (http:/ / www. supergen-marine. org. uk)

Article Sources and Contributors 115

Article Sources and ContributorsTide  Source: http://en.wikipedia.org/w/index.php?oldid=492910855  Contributors: (jarbarf), +Virtue+, 2D, 5 albert square, A-giau, A. Parrot, A1r, AaronSw, Aaroneddie123, Abce2,Abhishekbh, Ace of Spades, Acebulf, Acroterion, Ahoerstemeier, Aidsgang, Aitias, Ajahnjohn, Ajay5150, Alan16, AlanSiegrist, Alansohn, AlexiusHoratius, Alpha 4615, Alynna Kasmira,Andonic, Andres, Andrew Dalby, AndrewDressel, Andrewpmack, Andy M. Wang, Andyjsmith, Anna Lincoln, Apbiologyrocks, Art LaPella, ArthurDuhurst, Arunsingh16, Aslan83, Atif.t2,Atoll, AubreyEllenShomo, Avala, Aveh8, Avono, BD2412, Bagatelle, Barek, Bassbonerocks, Becobu26, Before My Ken, Benc, Bender235, Bensin, Big iron, Biggins, Bigjimr, Bilbicus, Billturnill, Binary TSO, Blockyt, Bob Hu, Bobblewik, Bobby122, Bobianite, Bobo192, Bongwarrior, Bookandcoffee, Brambleclawx, Brandon5485, Brendan Moody, Brews ohare, Briaboru, BrianHuffman, Brian0918, BrianEd, Brianga, Bryan Derksen, BryanD, Bsadowski1, Bubba73, Bucephalus, CRGreathouse, CWii, Camw, Can't sleep, clown will eat me, Canthusus, Canton japan,CapitalR, Carikate, CatherineMunro, Cebra, CharlesC, Cherkash, Chihuahua State, Chris Scoones, Chris the speller, Christopher Cooper, Civil Engineer III, Cjdavidson, Closedmouth,Cmdrjameson, Coastobs, Coldipa, Colonel Warden, Conversion script, Courcelles, Coylemj, Crowsnest, Cryptic C62, Crystallina, D, D. Recorder, DARTH SIDIOUS 2, DHN, DVdm,DaKid1996, Dalta, Danh, Daniel Collins, DanielBeaver, Danorton, Davewild, Davezelenka, David J Wilson, David Webb, David.Monniaux, DavidK93, Davidhorman, Dbowen, Dcenters,Ddesonie, Deeb, Deflective, Dekimasu, Delldot, Denseatoms, Derlay, Dgw, Dialectric, Digihoe, Discospinster, Dlohcierekim, Dr Greg, Dreadstar, Drf5n, Drmies, Dspradau, Dsspiegel, Duk,Duncancumming, Duncanogi, Dzhim, EEPROM Eagle, Edgar181, Editor 362, Edxguy, Eike Welk, Ejbrun, Elemesh, Eliashedberg, Ellywa, EndlessBob, Enginear, Enviroboy, Epbr123,Epicstonemason, Epipelagic, Erianna, Eric Kvaalen, Espetkov, Estudiarme, Evgeni Sergeev, Excirial, Extransit, FNX, Falcon8765, Farosdaughter, FayssalF, Ferred, Fitzy03, Floor Anthoni,FlyingToaster, ForestAngel, Fremsley, FritzG, Frodet, Froth, FunPika, Fxmastermind, Fæ, GUGGIE BONDSCON, Gaff, Gaius Cornelius, Galoubet, Gandalf61, Gderrin, Geoeg, Geologician,Geremia, Gerry Lynch, Gianfranco, GianniG46, Glenn, Gnowor, Gogo Dodo, Graham87, Green caterpillar, Grundig, Gruntler, Gtwkndhpqu, Gutsul, Gökhan, Hadal, Happyhacker101,Happylittlehakker10101, Haus, Hbackman, Headbomb, Hemmer, Hemmingsen, Heron, HexaChord, Hiddndragn, HighKing, Hightidelowtideforkidsfunzie, Hilosoph, Hippietrail, Hobartimus,Hqb, Hydrogen Iodide, ILovePlankton, IRP, IVAN3MAN, Iankap99, Ikh, Ilovetides99899, Imperi, Inbetweener, Internaltide, Invertzoo, Inwind, Iridescent, Isnow, Ixfd64, J.delanoy, JCM83,JEBrown87544, JForget, JTheo, Ja 62, Jackehammond, Jagged 85, Jan eissfeldt, Jano 34, Jared, Jarich, Jayen466, Jcastel3, JeLuF, Jebba, Jeff G., Jfire, Jhbdel, Jluu, Jmundo, Joffan, Johnhen,Johnluick, Johnuniq, Jokestress, Jonathan.s.kt, Jonathanfvk, Jossi, Jsnyder, Juliancolton, Junckerg, Jusdafax, Just an astrophysicist, KVDP, Kaf, Karada, Karuna8, Katalaveno, Kdliss, Kelisi, KenGallager, Kgrad, Killdevil, King of Hearts, Kingpin13, Kkailas, KnowledgeOfSelf, Kostmo, Kubigula, Lahiru k, LeilaniLad, Lemmiwinks2, Letterofmarque, Lfstevens, Lindenso, Little Mountain5, Llustman, Logical2u, Loren.wilton, Loren36, Lotje, Lstocks, Luna Santin, Lunokhod, Lysy, MBisanz, MC MasterChef, MCalamari, MER-C, MJJRy, MK8, MPF, MaNeMeBasat, Malcolmxl5,Maradja, Mark.murphy, Martarius, Martyx, Master Jay, Materialscientist, Matt Rules34, MattTomczak, Mattisse, Mayur, Mboverload, Mbrowning69, Mbz1, McSly, MesserWoland, MichaelHardy, MichaelBillington, Mikayh3, Mike Gale, Mikethecar, Miss Manzana, Mister Flash, Mister Matt, Misza13, Mithridates, Mlaffs, Monch1962, Mongol, MortimerCat, MrOllie, Mukinduri,Myden, Mygerardromance, NHRHS2010, Nakon, Natcase, NawlinWiki, Nbarth, Neilanderson, Neurolysis, NewEnglandYankee, Nick, Nick Number, NickW557, NickyMcLean, Nivix, Njd27,Non-dropframe, NorwegianBlue, Now3d, Nsaa, Ntc.bom, NuclearWarfare, NuncAutNunquam, Occultations, Odie5533, Ojigiri, Olahus, Oliver Pereira, Olivier Debre, Ondewelle,One-dimensional Tangent, Oreo Priest, Orphan Wiki, Ouishoebean, Ourshalf ourshalf, Owen, OwenBlacker, Ozga, P. 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Burton, Paiev, Palmeira, Palmiped, Panarjedde, PapaTonyB,PatGallacher, Patrick, Paul-L, Pearle, Pequod76, Per Honor et Gloria, Persian Poet Gal, Petit06, Pfly, Philip Trueman, PhotoBox, Phr en, Piano non troppo, Piet Delport, Pinethicket, Pjf,Plumbago, Pmronchi, Ponydepression, Postlewaight, Pqrtv, Qubert, Qwanqwa, Qxz, RDBury, RJBurkhart, RJaguar3, RaCha'ar, Racerx11, Radon210, RandomP, Rex Germanus, RexNL, Rhianne12, Rich Farmbrough, Richard.bourgerie, Richard001, Richhoncho, RickBeton, Rjd0060, Rjstott, Rjwilmsi, Rmo13, RobertDahlstrom, RobertG, Robma, RockMagnetist, Rockfang, Roisterer,Romanskolduns, Ron Ritzman, Rorro, Rracecarr, Rror, Rsocol, SCFilm29, SEIBasaurus, SPUI, Saalstin, Sam, Sashidandy, SchuminWeb, Sean.hoyland, Seaphoto, Semperf, Senator Palpatine,Serendipodous, Serpent's Choice, Servicesong, Shalom Yechiel, Shekk12, Shobhitg, Shoeofdeath, Sikon, Silverchemist, Simeon H, Simoniester, Sionnach1, Sixit, Sjc, Skier Dude, Skizzik, Slakr,Sliker Hawk, Snabbi, Snori, Solipsist, Sonett72, Spiel496, Spitfire19, Splintercellguy, StarryGrandma, Starshipenterprise, Steinsky, Stephenb, Stevenmitchell, Stringanomaly, Student7, Surachit,Swaroophoppy, TGCP, THEN WHO WAS PHONE?, TOttenville8, Taco hot, Tamfang, Tchannon, Teles, Tempshill, Terry0051, TexasDawg, TharkunColl, The Thing That Should Not Be,TheCustomOfLife, TheMaestro, TheseNuts123, Thingg, Thompsontough, Thorncrag, Thrawnlives, Tide rolls, TigerShark, Tiles, Tim Goodwin, Tim1988, Timtwickham, Timwi, Tom Peters,Tommy2010, Tomruen, Tox, Trewornan, Trilobite, TriviaMonth2011, Trixt, Tsange, TubularWorld, Tyrol5, Ufwuct, Ukexpat, Uncle Dick, Unint, Unknown1321, Urhixidur, UserXresu,Utcursch, VI, Vanished 6551232, Vdm, Vegaswikian, Vianello, Violetriga, Viriditas, Vjwsoo, Vrenator, Vriekerk, Vsmith, Vyznev Xnebara, WODUP, WOTMoon, Wavelength, Wbruceis,Webdinger, Welsh, Wenli, WereSpielChequers, West Brom 4ever, Whatapie1, Whispering, Wikibob, Wikiklaas, Wikipelli, Will Beback, William Avery, William M. Connolley, Winterst, Wj32,Woodstone, Wugo, Xdenizen, Xiglofre, Xzqx, Yamamoto Ichiro, Yath, ZBrannigan, Zaheen, Zfr, Zoe, Zzuuzz, 1033 ,מלמד כץ anonymous edits

Sea level  Source: http://en.wikipedia.org/w/index.php?oldid=490989548  Contributors: Adamsan, Ahoerstemeier, Ahunt, Alan Liefting, AlexanderWinston, Alexh19740110, Alfio, AndreasJS,Anna Frodesiak, Anorak2, Antarctic-adventurer, Anthony.army, Arbanak, ArgentTurquoise, AshLin, Auntof6, Awickert, Awostrack, Bamadude, BarrelProof, Baseball Bugs, Bermicourt,Berthold Werner, BillC, Bjulee, Blimpguy, Bobathon71, Bovineone, Bryan Derksen, CarFan1234, Catgut, Charlesfrhutchinson, Charlie pearce, Cleared as filed, Correogsk, Crowsnest, Cxbrx,Cyrius, DadaNeem, Daedalus969, Davezelenka, David Edgar, Dcljr, Dianareale, Dmeranda, Docu, Donarreiskoffer, Dontdoit, Dragons flight, Dyvroeth, Eclecticology, Ed Poor, Eekerz, EggCentric, Egil, EncMstr, Enquire, Epipelagic, Escape Orbit, Evil saltine, Ezra Wax, FocalPoint, Forever Dusk, FoxyNet, FrostyBytes, Fungible, GRAHAMUK, Galloping Moses, Geanixx,Geol310LB, Georg Slickers, Golbez, Gothmog.es, Graham87, GregBenson, Grunt, Gyrobo, Haham hanuka, Haidata, Helix84, Heljqfy, HuskyHuskie, Imnotminkus, InspectorTiger, J.delanoy,JForget, JWSchmidt, Jan.Kamenicek, Jcmo, Jeepday, Joy, JuanFox, Jusdafax, Just plain Bill, Jwpurple, KFM206, Kansan, Karn, Kcordina, Kevin Steinhardt, Knowledge Seeker, Knowledgeum,Koyn, Krator, Kwinkunks, Len Raymond, Lightmouse, Lulu087, Mac Davis, Maddox1, Marx01, Mbcannell, Mckelroy88, Meelar, Melchoir, Michael Hardy, Michaelas10, Mikenorton, Mikue,Monowiki, Mxbn0, New Nothing, Nguyen Thanh Quang, Nickkid5, Nossac, OlEnglish, Omnipaedista, Pairadox, Pallida Mors, Parsa, Philip Trueman, Piano non troppo, Plumbago, Pstaveley,Purslane, Qfl247, Quintote, Qyy, RJHall, Richard001, Rjwilmsi, RockMagnetist, Rorshacma, Rrburke, STarry, Salvio giuliano, Samw, Shadowscorpio, Shafei, Shantavira, Shekk12, Shrigley,Sietse Snel, Sjoffutt, Sky Attacker, Slawojarek, Slightsmile, Smith609, Sneesby, Solipsist, South Bay, Speciate, Srleffler, Stephen Morley, TaintedMustard, Tangotango, The High Fin SpermWhale, The Thing That Should Not Be, TheGeneralUser, TheSeer, Tom Peters, Totalbomb, Treisijs, Trimp, Triskaideka, Twinsday, V.narsikar, Vermeer, Vicki Rosenzweig, Volcanoguy, Vsmith,Wayne Slam, WhatsHisFace2, Whkoh, William M. Connolley, Willking1979, WisdomFromIntrospect, Zaheen, 240 anonymous edits

Tide table  Source: http://en.wikipedia.org/w/index.php?oldid=464552994  Contributors: A1call, Bumm13, Cjdavidson, Danthemankhan, Duncanogi, Longhair, LyshMac, Mark.murphy, MisterFlash, Rockfang, SGBailey, SchuminWeb, Terry0051, Tewy, Timtwickham, Trewornan, Wbruceis, Your Lord and Master, 凌 雲, 14 anonymous edits

Slack water  Source: http://en.wikipedia.org/w/index.php?oldid=492097967  Contributors: Autarch, Bahudhara, Bloblaw, Cmdrjameson, Coolliam123, Deeb, Dell Adams, DuncanHill, ErikKennedy, Flodded, Funandtrvl, Grutness, Inaspicious, Jabencarsey, Jlpriestley, Jonathan.s.kt, Joseph Solis in Australia, Lodestoneman, Maelnuneb, Mark.murphy, Mister Flash,NewEnglandYankee, P199, Pbsouthwood, Pjf, Pnkrockr, Rockfang, Steveprutz, Tefalstar, Valich, Vincent Ramos, 23 anonymous edits

Bathymetry  Source: http://en.wikipedia.org/w/index.php?oldid=485082719  Contributors: AlexD, Altenmann, Athelwulf, Balthazarduju, Beautyod, Beland, Belg4mit, Bioneer1, Borgx, Bozoid,Bradjuhasz, Carmen56, Chicagocowboy412, Danim, David Biddulph, Dejvas, Dj Capricorn, Drf5n, Edinburgh Wanderer, Epipelagic, Fratrep, Friedputty, GregU, Gzornenplatz, Havanafreestone,Interiot, Jolio81, Leevanjackson, Linuxbeak, Loren36, Macedonian, Martin451, Michaelwraftery, Mnc4t, Natcase, Nathan Johnson, Parag.agarkar, Plumbago, RP459, Richy, Rjwilmsi, Scythia,Searchme, Semolo75, Shmooty, SimonP, StanislavT, Substar, Tetracube, The Thing That Should Not Be, TheSpectator, UCI67315651, Ultrasonicspeed, Upior polnocy, Victor Blacus, Wardog,Wavelength, Woodstone, Xzqx, 66 anonymous edits

Lunitidal interval  Source: http://en.wikipedia.org/w/index.php?oldid=479313212  Contributors: A2Kafir, Andro Lee, Arminius, Aua, Autarch, Avocado, Barticus88, Caltrop, Daedalus-Prime,Djr32, Edcolins, Epipelagic, Glueball, Hyacinth, Jluu, LilHelpa, Loren36, Melcombe, Modulechanger, Qubert, Qwfp, Rockfang, SWAdair, TimBentley, Whitejay251, 21 anonymous edits

Amphidromic point  Source: http://en.wikipedia.org/w/index.php?oldid=492343033  Contributors: Angela, Antandrus, Charles Matthews, Chetvorno, Chris857, Crowsnest, Dav4is, EagleFan,EoGuy, Epipelagic, Eric Kvaalen, FF2010, Fathomharvill, Fig wright, Fxmastermind, Jeff3000, Jonmagne, Just granpa, Mark, Mjmcb1, Nolens Volens, Poulpy, RedWolf, Rich Farmbrough,Rmo13, Rockfang, Seattle Skier, SimonP, Skier Dude, Waleswatcher, Wheelie Willy, Wikiklaas, 10 anonymous edits

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Theory of tides  Source: http://en.wikipedia.org/w/index.php?oldid=417813582  Contributors: A little insignificant, AnnaFrance, Arjayay, Crowsnest, Cuvette, Derlay, Discospinster, JohnHyams, MFNickster, Ma lack, Michael Hardy, Mxcatania, Rami radwan, Rich Farmbrough, Rmo13, Siddhant, Splintercellguy, Terry0051, The undertow, Tidevann, Trafford09, Woodstone,Zelmerszoetrop, 15 anonymous edits

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Lunokhod, MAGZine, Maximaximax, Mejor Los Indios, Melchoir, Michael Hardy, NOrbeck, Natoland, Nick Mks, NickyMcLean, Novangelis, PJtP, Patrick, RJHall, Rjwilmsi, RobertMel,Rockfang, Sakkura, Search4Lancer, Skoosh, Snoyes, Steve2011, SteveMcCluskey, Svmich, Tauʻolunga, Terry0051, Tide rolls, Tim Goodwin, Tom Peters, Tompeters, Tregoweth, Urhixidur,Wdanwatts, Wellithy, WolfmanSF, Woodstone, Yevgeny Kats, Zhatt, 63 anonymous edits

Tidal power  Source: http://en.wikipedia.org/w/index.php?oldid=492924433  Contributors: 10metreh, 2CentsOfMine, 2help, A8UDI, ABF, AMD, Adambro, Adashiel, Addshore, Aditya.m4,AeguorAgricola, Agreatnate, Ahoerstemeier, Aitias, Aksi great, Alan012, Alanbrowne, Alansohn, Aleenf1, Alex Ramon, Alex.muller, Alexkin, Alfio, Alfredlebum, Aliwalla, Altenmann,Alterrabe, AluminumHaste, Amwhitesell, Anclation, Andonic, Andrij Kursetsky, Andy pyro, Andy4789, Andymacdon, Anetode, Angry mob mulls options, Angrysockhop, AniRaptor2001,Anlace, Anna Lincoln, Anonymous101, Anthony717, Arunsingh16, Ashanda, Atomota, Auntof6, Azxten, Bachrach44, Badgernet, Badinfinity, Barek, Bart133, Beagel, Bearcat, Bears16,Beetstra, Behun, Beland, Bento00, Berkut, Bernd in Japan, Billymac00, Blanchardb, BlckKnght, Blue8425, BlueAg09, Bm gub, Bmcclure, BobJhonson91, Bobblewik, Bobet, Bobnorwal,Bobo192, Bongwarrior, BrentN, Brewmastermk, Brian Everlasting, Brianhe, Bruce1ee, Bushytails, CIreland, CRGreathouse, CTZMSC3, Caeruleancentaur, Calabe1992, Calltech, Caltas, Calvin1998, CambridgeBayWeather, Camelhumps, Can't sleep, clown will eat me, CanadianLinuxUser, Capricorn42, Captain panda, Captain-tucker, Cartman02au, Casagiada, Casmith 789, Cazlsj,Ccoonnoorr0088, Censorship Workaround, Cheesy mike, Chiselbash, Chowbok, Chris55, Chrisdafish, Christian75, Christopher140691, Chriswaterguy, Ciphergoth, Ckatz, Clarky11, Cmprince,Codetiger, Colin Gross, Collabi, Colonies Chris, Comet Tuttle, CommonsDelinker, Corella, Costas Skarlatos, Couposanto, Coxt001, Crazysane, Crimsonthorn, Crowsnest, Cst17, Cureden, Curps,CyrilB, DARTH SIDIOUS 2, DMG413, DVD R W, Dabomb87, Dabreeze, Dadude3320, Dampferzeuger, Dan Fiorucci, Dancter, Danh, DariusRex, DarkArcher, Darry2385, DavidOaks, DawnBard, Deb, Dee Jay Randall, Denisarona, Derek Andrews, Derek Ross, Dezen, Dialectric, Diannaa, Dina, Discospinster, Dispenser, Diwakark86, Dlohcierekim, Doomedtx, Doyley, Dresdnhope,Duk, Dynabee, Dyraneque, E8, ESkog, Eclipse996, 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Sustainabilityproject, Sxc123, SynergyBlades, Tabby, Tamás Kádár, Taxa, Tbhotch, Teratornis,TerriersFan, The Thing That Should Not Be, The Utahraptor, TheNewPhobia, Theo F, Theresa knott, Thingg, ThreeDee912, Thumperward, Thunderboltz, Tidalenergy, Tidaljohn, Tide rolls,TigerShark, Tim1988, Tizio, Toastyman, Tobi, Tom harrison, TomSheffield, Tony Corsini, Trusilver, Tsunade, Tv316, Twested, TyA, UNguyinChina, Uncle Dick, Vanished User 1004,Vanished user 39948282, Vanisheduser12345, Vary, VasilievVV, Vegaswikian, Ventolin, VinceBowdren, Viriditas, Vivio Testarossa, Vortexrealm, Vrenator, Vsmith, Waggers, Wavelength,WayneMokane, Weglinton, Weskokemor, Wetman, Wheasley, Where, Whitepaw, WikipedianMarlith, Wikipelli, Willking1979, Winchelsea, Winvirus, Witbcoedus, Wjmcqueen, Wmahan,Wolfkeeper, WpZurp, Wtmitchell, Wtshymanski, Wwoods, Xaosflux, Xulin, Yamamoto Ichiro, Yngvarr, Ytrottier, Zaxzaxzax, Žiedas, Ζεύς, மாதவன், 2026 anonymous edits

Intertidal ecology  Source: http://en.wikipedia.org/w/index.php?oldid=482981154  Contributors: Bcasterline, Bender235, BrownHairedGirl, Calliopejen1, Choij, Colincbn, DrSatan, Epipelagic,Hesperian, Horny 12 year old girl, Iridescent, Kaarel, Kaikoura, Mbz1, MortimerCat, Pachyana, Phil Polychaete, PhilMacD, Pietrow, Pinethicket, Radon210, Rayvier, Rich257, Richard001, RiseAbove the Vile, Snowolfd4, Stealthbreed, Stemonitis, WJBscribe, Xuz, 37 anonymous edits

Internal tide  Source: http://en.wikipedia.org/w/index.php?oldid=492544638  Contributors: Chris the speller, Dbfirs, DiverDave, Epipelagic, Fxmastermind, Internaltide, Mandarax, Meaghan,Oldag07, RHaworth, Rjwilmsi, Rorro, 1 anonymous edits

Earth tide  Source: http://en.wikipedia.org/w/index.php?oldid=492919463  Contributors: 123Hedgehog456, Carbonaceous, Cuvette, Danorton, Drf5n, Dthomsen8, Epipelagic, Hu, Inwind, MCB,MichaelRWolf, Mikenorton, NatureA16, NickyMcLean, Nurg, Pargy, Richhoncho, Rjwilmsi, Rmo13, Rockfang, Rracecarr, Sailsbystars, Seattle Skier, TristramBrelstaff, Tuttt, Vsmith,WordSurd, 30 anonymous edits

Galactic tide  Source: http://en.wikipedia.org/w/index.php?oldid=465438161  Contributors: Antonsusi, Bryan Derksen, Buettcher, CommonsDelinker, Deuar, Długosz, Headbomb, Kelisi,Kostmo, Larryisgood, M-le-mot-dit, Mangojuice, Mnmngb, Prjaeger, RJHall, Rotational, Saros136, Serendipodous, Spiral Wave, StuRat, 6 anonymous edits

Tidal locking  Source: http://en.wikipedia.org/w/index.php?oldid=491935795  Contributors: 7, Alex.g, Anotherben, Anyeverybody, Armeria, Art LaPella, Autonova, B.d.mills, Basawala,Bdell555, BlueMoonlet, Bongdentoiac, Bryan Derksen, Bzorro, CP\M, Chaos syndrome, Chris the speller, CimanyD, Clementi, Cvgittings, Cyrius, Deuar, Doady, Donald Albury,Donarreiskoffer, Double sharp, Dracontes, Drstupid phd, Duccio, Ed Poor, Email4mobile, Emurphy42, Fan of Physics, FirstPrinciples, Foobar, FormerNukeSubmariner, FractalFusion,Freederick, Geologyguy, Ggb667, Gulliveig, HexenX, Hibernian, Jalwikip, Jonathan Wheeler, JorisvS, JuJube, Keenan Pepper, KlappCK, Kosebamse, Kuyabribri, Latitude0116, Leptictidium,Ligar, Lkesteloot, Looxix, Lowellian, Lunokhod, M.O.X, Martin Rizzo, Mboverload, Melongrower, Mentock, Michael Hardy, Mini-Geek, Mipadi, Misza13, Monsterman222, MrBell,MushroomCloud, Nmagedman, NorCalHistory, NuncAutNunquam, Oliphaunt, Omegatron, Pagarus, Pericles Xanthippou, Phancy Physicist, Pinethicket, RJBurkhart, RJHall, Rangergordon,Rfluchel, Ricardv46, Rich Farmbrough, Richhoncho, Rjwilmsi, Rmhermen, RobertG, Roentgenium111, RoyBoy, SS, SchuminWeb, Sghvd, Shawn81, Shirik, Shoefly, Shoessss, Sjaffredo,Spacetweek, Special-T, Stebulus, Stephan Leeds, Susurrus, Sverdrup, Swamibooba, TastyCakes, The Yeti, Thryduulf, Tideflat, Timothykinney, Tktktk, Tnxman307, Tom Peters, TonyClarke,Trulystand700, UnitedStatesian, V. Szabolcs, Waninge, Wikicheng, WikiediaUser, Wikiwert, William M. Connolley, WilyD, Woohookitty, Zyqqh, 96 anonymous edits

Tidal prism  Source: http://en.wikipedia.org/w/index.php?oldid=468683080  Contributors: Biscuittin, Dondegroovily, Dv82matt, John of Reading, Katharineamy, Leahbeckett, Phil Whiston,R'n'B, Rich Farmbrough, Ww2censor

Tidal range  Source: http://en.wikipedia.org/w/index.php?oldid=491682836  Contributors: (jarbarf), 790, Animum, Art LaPella, BrokenSegue, Christopher Cooper, DMG413, Dufydtaf,Epipelagic, Feministo, Fransvannes, Gnusmas, Goudzovski, Hu12, Interchange88, Ixfd64, JRPG, Jared, Johan Lont, KevinP, Klemen Kocjancic, Leafyplant, Leevanjackson, LilHelpa, Mets501,Mikenorton, Mindmatrix, Monkey Bounce, Riana, Rockfang, Seattle Skier, ShakataGaNai, SpuriousQ, Stemonitis, Tide rolls, WikHead, Wolfadeus, 53 anonymous edits

Tidal resonance  Source: http://en.wikipedia.org/w/index.php?oldid=426986127  Contributors: Andrewpmack, Anthony Ivanoff, Crazytales, David Webb, Dcljr, Epipelagic, Gareth Owen,Germendax, Jonathan.s.kt, Mark Yen, Mark.murphy, Michael Hardy, Omegatron, PetaRZ, PigFlu Oink, RJBurkhart, Rmhermen, Rockfang, Splintercellguy, UmptanumRedux, 4 anonymous edits

Tide pool  Source: http://en.wikipedia.org/w/index.php?oldid=492723538  Contributors: (jarbarf), 78.26, 867-5309, @pple, AGK, Aitias, Akkida, Alan Liefting, Altenmann, Andrewpmack,Animum, Avenue, Baconquesadilla, Banpei, BernardH, Bobber0001, Bobo192, Bucketsofg, Celarnor, Chris 73, Chrisfow, Cieran 91, Clayoquot, Cometstyles, Cwmhiraeth, DanielCD, Dreadstar,E0steven, Editmeister3000, Ennerk, Epbr123, Epipelagic, Falstaft, Fluffy42, Freakmighty, Fuzzbox, Gatoclass, God989, GorillaWarfare, Grafen, GrahamBould, Hakunamenta, Hesperian,Hmains, Hoovernj, Icelight, ImperatorExercitus, India14, Invertzoo, J.delanoy, J04n, JAF1970, JeR, JohnnyRush10, Jonadin93, Kaarel, Keilana, Keri3294, King of Hearts, KnowledgeOfSelf,Kubigula, Leonard G., Leuko, Lfstevens, LilHelpa, Luciferwildcat, MER-C, Mark.murphy, Maxis ftw, Mbz1, Meaghan, Merbabu, Mikeethesitch, Molly7242, Moreschi, NJR ZA, Naniwako,NawlinWiki, Neutrality, Nonpareil, Paphrag, Philip Trueman, Pinethicket, Polylerus, Rich Farmbrough, Richerman, Rjwilmsi, Rockfang, Seaphoto, Shalom Yechiel, Shirik, Slon02, Sophiemeans wisdom, Squids and Chips, Storm Rider, Tad Lincoln, TerraFrost, Tester12354, The Arbiter, The High Fin Sperm Whale, The Thing That Should Not Be, TheTooth, Tide rolls, Tiles,Tom.k, Tomer T, Tomlburton, Vegaswikian, Viriditas, WJBscribe, Wetman, Woohookitty, Zazpot, Zenten, Zotel, 210 anonymous edits

Tideline  Source: http://en.wikipedia.org/w/index.php?oldid=414034344  Contributors: Buster7, Crowsnest, Discospinster, Epipelagic, FayssalF, Gmckenna, Hermzz, Nz101, Pb30, Rockfang,Woohookitty, 5 anonymous edits

Tidal bore  Source: http://en.wikipedia.org/w/index.php?oldid=492587406  Contributors: 16@r, Andy Dingley, Antandrus, Art LaPella, Asiaticus, Astanhope, Bbrnrd, BenFrantzDale, Benstrider, Big iron, Bo Basil, BoH, Bongwarrior, Cassowary, Chansonh, Chris075, Colonies Chris, Crowsnest, Danny, Dicklyon, Dino, Dkettle, Donfbreed, Dvagabundo, Earth, EddEdmondson,

Article Sources and Contributors 117

Ei2g, Emerson7, Epipelagic, Facts707, Fh235, Flatfishfool, Frangle Plazma Goat, Graham87, Hankwang, Hans yulun lai, Haukurth, Helium4, Heqs, Hu12, Iridescent, Jeffwarnica, Joaquin008,John, Karada, Karl Palmen, Koavf, Lightmouse, Luna Santin, MCBastos, MDCollins, Marcg106, Mark.murphy, Marokwitz, Maxbeer, Maximus Rex, Mayalld, Mhockey, Michael Hardy, Mirv,Muu-karhu, NellieBly, Nico niko, Omegatron, Orodreth, OwenBlacker, P199, PRiis, Pablo X, Parkwells, Parsa, Peruvianllama, Picapica, Pokerface am, Prof307, Pyrotec, Ranveig, Raygirvan,Rcsprinter123, Remicles2, Rhobite, Rich Farmbrough, Rjwilmsi, Rlcantwell, Rockfang, SYSS Mouse, Sam, Saperaud, Shawn in Montreal, Shiftchange, Shoombooly, Siberian T, Sonjaaa,Supaluminal, Swanny18, Syukri Abd Rahman, Takeaway, The Lord Of The Dance, Thingg, Tokek, Tom Radulovich, Torturella, VIGNERON, Verne Equinox, Wavelength, Wefalck,Williamborg, Yggdriedi, Zeimusu, 129 anonymous edits

Storm surge  Source: http://en.wikipedia.org/w/index.php?oldid=492163040  Contributors: AdamRoach, Alansohn, Allstrak, ArchibolCunningham, Bachrach44, BalticPat22, Bender235,Breawycker, Cadsuane Melaidhrin, Caiaffa, Calliopejen, Canterbury Tail, Capecodeph, Carbenium, Carcharoth, Casper2k3, Cdcollura, Cfarquhar 220276, Chacor, Cherkash, Coastobs, Coredesat,Corvus cornix, Cyberpower678, Cyrius, Dan100, Dankelley, Danny, Dave.Dunford, DerHexer, Dmron, Drf5n, Drunken Pirate, Dupz, Edderso, Emperorbma, Epbr123, Erianna, Filanca, Fratrep,GcSwRhIc, Gidonb, Giftlite, Gioto, HarveyHenkelmann, Headbomb, Hede2000, Howboutchamon, Howcheng, Hurontario, Hurricaneg, Iridescent, Ja 62, Jamesontai, Jason Rees, Jaxl, Jdorje,Jengod, Jetwag, Johan Jönsson, Joyous!, Juliancolton, Kimiko, Kizor, Kummi, Leonard G., Lexter John, Lightmouse, Lotje, Mailseth, Mandypedia, Mathewignash, Mild Bill Hiccup, Mkieper,Moheroy, Mosesofmason, Munificent, Naraht, Neelix, Nehrams2020, Nhl hockey 541@hotmail.com, Nick Number, NickyMcLean, Nv8200p, Octahedron80, Oliphaunt, Oroso, PVSpud, Paul012, Plasticup, QuiteUnusual, RIUSABruce, RWFanMS, RanEagle, RattleMan, Redpants6677, Revoranii, Rich Farmbrough, Rjwilmsi, Rlove, Rmashhadi, Ruakh, RyanCross, SaintedLegion,Sam Hocevar, Scott5114, Sdornan, Severa, Shanel, Shenme, SiliconDioxide, Skybum, Solipsist, Splash, Student7, Tagishsimon, Tbhotch, Tdftyg, Terra Xin, Tesscass, The Thing That Should NotBe, TheCoffee, Thegreatdr, Titoxd, Toddst1, Tom, Tpbradbury, Trixt, Tropische Storm Sven, Vsmith, WadeSimMiser, Wat Tyler, Wavelength, Weatherdude2, Weiwensg, Whouk, Why Not ADuck, Wiki13, Wxornot, XyKyWyKy, Yachtsman1, Zubair71, Еdit, っ, 170 anonymous edits

Head of tide  Source: http://en.wikipedia.org/w/index.php?oldid=371464027  Contributors: Boo Twitty, Epipelagic, Fiftytwo thirty, Peter Horn, Rockfang, Shalom Yechiel, 4 anonymous edits

Tidal stream generator  Source: http://en.wikipedia.org/w/index.php?oldid=484730894  Contributors: Airplaneman, Chris the speller, Crowsnest, Ernestfax, Giancarlo Rossi, IohannesAnimosus, Johnarmstrong1, Le5zek, McGeddon, Nolabob, OliverWragg, Optimist on the run, Pakaraki, Rehman, Rich Farmbrough, Tommo97, UNguyinChina, WTM, Websterwebfoot, 12anonymous edits

Tidal barrage  Source: http://en.wikipedia.org/w/index.php?oldid=491878002  Contributors: Arthena, Chase me ladies, I'm the Cavalry, Corella, Crowsnest, Drieux, Epipelagic, Napoleon0,Ohconfucius, Rehman, RoflSloth, SBaker43, Sreejithk2000, Tide rolls, Verne Equinox, Websterwebfoot, 9 anonymous edits

Marine energy  Source: http://en.wikipedia.org/w/index.php?oldid=483054952  Contributors: Andy Dingley, Brewmastermk, Chris55, Correctionwriter, Dawnseeker2000, DirkvdM, Epipelagic,Eszwaqeszwaq, Gsarwa, Iridescent, Jessicaowen, Jonathan Oldenbuck, Manning Bartlett, Masters Marketer, Mathew Topper, MrOllie, Nimur, NuclearEnergy, Peterkingiron, Rehman, RichFarmbrough, Shinkansen Fan, Vegaswikian, Wavelength, 16 anonymous edits

Image Sources, Licenses and Contributors 118

Image Sources, Licenses and ContributorsImage:Bay of Fundy High Tide.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Bay_of_Fundy_High_Tide.jpg  License: GNU Free Documentation License  Contributors: BeforeMy Ken, Benoit Rochon, GeorgHH, Sam, Sanao, ShizhaoImage:Bay of Fundy Low Tide.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Bay_of_Fundy_Low_Tide.jpg  License: GNU Free Documentation License  Contributors: Before MyKen, Benoit Rochon, GeorgHH, Sam, Sanao, Shizhao, SpiritiaImage:Tide type.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_type.gif  License: unknown  Contributors: J. Spencer, Monkeybait, Nichalp, Rmo13, Stannered, 1 anonymouseditsImage:Tide schematic.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_schematic.svg  License: Public Domain  Contributors: User:KVDP, SVG conversion by SurachitFile:Negative low tide at Ocean Beach 1.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Negative_low_tide_at_Ocean_Beach_1.jpg  License: Creative CommonsAttribution-Sharealike 3.0  Contributors: Brocken InagloryImage:M2 tidal constituent.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:M2_tidal_constituent.jpg  License: Public Domain  Contributors: Original uploader was Rmo13 aten.wikipediaImage:Field tidal.png  Source: http://en.wikipedia.org/w/index.php?title=File:Field_tidal.png  License: GNU Free Documentation License  Contributors: Bryan Derksen, Ciaurlec, Cwbm(commons), Duk, Lambdadra, Pieter KuiperFile:Brouscon Almanach 1546 Compass bearing of high waters in the Bay of Biscay left Brittany to Dover right.jpg  Source:http://en.wikipedia.org/w/index.php?title=File:Brouscon_Almanach_1546_Compass_bearing_of_high_waters_in_the_Bay_of_Biscay_left_Brittany_to_Dover_right.jpg  License: Public Domain Contributors: Geagea, Mu, World ImagingFile:Brouscon Almanach 1546 Tidal diagrams according to the age of the Moon.jpg  Source:http://en.wikipedia.org/w/index.php?title=File:Brouscon_Almanach_1546_Tidal_diagrams_according_to_the_age_of_the_Moon.jpg  License: Public Domain  Contributors: Geagea, Mu, WorldImagingImage:Diurnal tide types map.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Diurnal_tide_types_map.jpg  License: Public Domain  Contributors: KVDPImage:Water surface level changes with tides.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Water_surface_level_changes_with_tides.svg  License: Public Domain  Contributors:KVDP, SVG conversion by SurachitImage:Tidal constituent sum.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_constituent_sum.gif  License: Public Domain  Contributors: Monkeybait, Rmo13Image:Tide.Bridgeport.50h.png  Source: http://en.wikipedia.org/w/index.php?title=File:Tide.Bridgeport.50h.png  License: Public Domain  Contributors: NickyMcLeanImage:Tide.Bridgeport.30d.png  Source: http://en.wikipedia.org/w/index.php?title=File:Tide.Bridgeport.30d.png  License: Public Domain  Contributors: NickyMcLeanImage:Tide.Bridgeport.400d.png  Source: http://en.wikipedia.org/w/index.php?title=File:Tide.Bridgeport.400d.png  License: Public Domain  Contributors: NickyMcLeanImage:Tide.NZ.November.png  Source: http://en.wikipedia.org/w/index.php?title=File:Tide.NZ.November.png  License: Creative Commons Attribution 3.0  Contributors: Nicky McLeanNickyMcLean (talk)Image:Tide legal use.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_legal_use.gif  License: Public Domain  Contributors: Monkeybait, Rmo13, 1 anonymous editsImage:Tidal Indicator Delaware River ca1897.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_Indicator_Delaware_River_ca1897.jpg  License: Public Domain  Contributors:Superintendent Of The Coast & Geodetic SurveyImage:Intertide zonation at Kalaloch.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Intertide_zonation_at_Kalaloch.jpg  License: Public Domain  Contributors: Angrense, BeforeMy Ken, Docu, ShizhaoFile:Israel Sea Level BW 1.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Israel_Sea_Level_BW_1.JPG  License: Public Domain  Contributors: Berthold WernerFile:Recent Sea Level Rise.png  Source: http://en.wikipedia.org/w/index.php?title=File:Recent_Sea_Level_Rise.png  License: unknown  Contributors: ALE!, Angrense, Dragons flight, ElGrafo, Glenn, Hadlock, Hmoulding, Pflatau, Smith609, 2 anonymous editsImage:Geoida.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Geoida.svg  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors: MesserWolandImage:BadwaterSL.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:BadwaterSL.JPG  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Qfl247 (talk). Originaluploader was Qfl247 at en.wikipediaFile:Mass balance atmospheric circulation.png  Source: http://en.wikipedia.org/w/index.php?title=File:Mass_balance_atmospheric_circulation.png  License: Public Domain  Contributors:NASAFile:Sea level temp 140ky.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Sea_level_temp_140ky.gif  License: unknown  Contributors: Bender235, Emmanuel.boutet, Glenn,White-Silent-NightFile:Phanerozoic Sea Level.png  Source: http://en.wikipedia.org/w/index.php?title=File:Phanerozoic_Sea_Level.png  License: unknown  Contributors: Angrense, Ciaurlec, Dragons flight,Flappiefh, Glenn, Pflatau, Smith609, Teratornis, ZimbresFile:Post-Glacial Sea Level.png  Source: http://en.wikipedia.org/w/index.php?title=File:Post-Glacial_Sea_Level.png  License: unknown  Contributors: Angrense, Dragons flight, Glenn, Pflatau,2 anonymous editsImage:Tide table 01.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_table_01.jpg  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors: TewyFile:AYool topography 15min.png  Source: http://en.wikipedia.org/w/index.php?title=File:AYool_topography_15min.png  License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: PlumbagoFile:Rear map.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Rear_map.jpg  License: Public Domain  Contributors: Matthew Fontaine MauryFile:Atlantic-trench.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Atlantic-trench.JPG  License: Public Domain  Contributors: Original uploader was Vsmith at en.wikipediaFile:M2 tidal constituent.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:M2_tidal_constituent.jpg  License: Public Domain  Contributors: Original uploader was Rmo13 aten.wikipediaFile:Shoemaker-levy-tidal-forces.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Shoemaker-levy-tidal-forces.jpg  License: Public Domain  Contributors: Maksim, Pieter Kuiper,VestaFile:Field tidal.png  Source: http://en.wikipedia.org/w/index.php?title=File:Field_tidal.png  License: GNU Free Documentation License  Contributors: Bryan Derksen, Ciaurlec, Cwbm(commons), Duk, Lambdadra, Pieter KuiperFile:Saturn-cassini-March-27-2004.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Saturn-cassini-March-27-2004.jpg  License: Public Domain  Contributors: Avron, Bricktop,Gentgeen, Ischa1, Juiced lemon, O'Dea, Rursus, Ruslik0, 1 anonymous editsFile:Tidal-forces.png  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal-forces.png  License: GNU Free Documentation License  Contributors: Bryan Derksen, Eman, Justass, Mdd,Pieter Kuiper, RuM, Tano4595, WikipediaMasterImage:Tideforcenw.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tideforcenw.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Tideforcese.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tideforcese.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:The Earth and the Moon photographed from Mars orbit.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:The_Earth_and_the_Moon_photographed_from_Mars_orbit.jpg License: Public Domain  Contributors: NASA/JPL-Caltech/University of ArizonaImage:Tidal braking.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_braking.svg  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors:AndrewBuckFile:Tide type.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_type.gif  License: unknown  Contributors: J. Spencer, Monkeybait, Nichalp, Rmo13, Stannered, 1 anonymouseditsFile:SeaGen installed.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:SeaGen_installed.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Fundy (Fundy)File:DTP T dam top-down view.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:DTP_T_dam_top-down_view.jpg  License: Public Domain  Contributors: UNguyinChinaImage:Anjajavy forest meets sea.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Anjajavy_forest_meets_sea.jpg  License: Creative Commons Attribution-Sharealike 2.5 Contributors: Original uploader was Anlace at en.wikipedia

Image Sources, Licenses and Contributors 119

Image:Barnacles.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Barnacles.jpg  License: Copyrighted free use  Contributors: StemonitisImage:Tide pools in santa cruz.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tide_pools_in_santa_cruz.jpg  License: Creative Commons Attribution-Sharealike 3.0,2.5,2.0,1.0 Contributors: Brocken InagloryImage:Hermit crabs scavenge at Gumboot chiton 2.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Hermit_crabs_scavenge_at_Gumboot_chiton_2.jpg  License: CreativeCommons Attribution-Share Alike  Contributors: Brocken InagloryFile:interfacial.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Interfacial.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: InternaltideFile:tpelev.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tpelev.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Internaltide, MeaghanFile:scripps internal wave T.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Scripps_internal_wave_T.jpg  License: Creative Commons Attribution 3.0  Contributors: InternaltideImage:Sectorialvert.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Sectorialvert.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Sectorialeastwest.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Sectorialeastwest.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Sectorialnorthsouth.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Sectorialnorthsouth.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Tesseralvert.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tesseralvert.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Tesseraleastwest.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tesseraleastwest.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Tesseralnorthsouth.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tesseralnorthsouth.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:Zonalvert.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Zonalvert.jpg  License: Creative Commons Attribution-Sharealike 2.5  Contributors: Rmo13Image:NGC4676.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:NGC4676.jpg  License: Public domain  Contributors: NASA, H. Ford (JHU), G. Illingworth (UCSC/LO),M.Clampin (STScI), G. Hartig (STScI), the ACS Science Team, and ESAImage:Roche limit (far away sphere).PNG  Source: http://en.wikipedia.org/w/index.php?title=File:Roche_limit_(far_away_sphere).PNG  License: GNU Free Documentation License Contributors: MarsveImage:Roche limit (tidal sphere).PNG  Source: http://en.wikipedia.org/w/index.php?title=File:Roche_limit_(tidal_sphere).PNG  License: GNU Free Documentation License  Contributors:MarsveFile:NGC40384039 large.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:NGC40384039_large.jpg  License: Public Domain  Contributors: Friendlystar, WilyDImage:M31bobo.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:M31bobo.jpg  License: Creative Commons Attribution 3.0  Contributors: Boris Štromar Vedran Vrhovac has askedme to share my photographs of Messier objects M8, M31, M46 and M47 for use on Wikipedia. I hereby state that these photos can freely be used for educational and commercial purposes onWikipedia as long as I'm cited as the author of these photos. Vedran is allowed to modify this photos.Image:Kuiper oort.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Kuiper_oort.jpg  License: Public Domain  Contributors: NASAFile:MoonTorque.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:MoonTorque.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: SghvdImage:Synchronous rotation.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Synchronous_rotation.svg  License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: SmurrayinchesterImage:Moon PIA00302.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Moon_PIA00302.jpg  License: Public Domain  Contributors: Karn, Pringles, TheDJ, 姫 宮 南, 4 anonymouseditsImage:Tidal Range.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_Range.jpg  License: Public Domain  Contributors: Original uploader was Jared at en.wikipediaImage:PortisheadDocks NearHighTide.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:PortisheadDocks_NearHighTide.JPG  License: Creative Commons Attribution 3.0 Contributors: David WebbImage:PortisheadDocks LowTide.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:PortisheadDocks_LowTide.JPG  License: Creative Commons Attribution 3.0  Contributors:David WebbFile:Porto Covo February 2009-2.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Porto_Covo_February_2009-2.jpg  License: Creative Commons Attribution-Sharealike 3.0 Contributors: AlvesgasparFile:Tide pools in Santa Cruz from Spray-splash zone to low tide zone.jpg  Source:http://en.wikipedia.org/w/index.php?title=File:Tide_pools_in_Santa_Cruz_from_Spray-splash_zone_to_low_tide_zone.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors:Brocken InagloryFile:Pteropurpura trialata is laying the eggs 1.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Pteropurpura_trialata_is_laying_the_eggs_1.jpg  License: GNU Free DocumentationLicense  Contributors: Brocken InagloryFile:Anthopleura sola is consuming Velella velella.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Anthopleura_sola_is_consuming_Velella_velella.jpg  License: CreativeCommons Attribution-Sharealike 3.0  Contributors: Brocken InagloryFile:Postelsia palmaeformis 2.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Postelsia_palmaeformis_2.jpg  License: Creative Commons Attribution-Sharealike 3.0,2.5,2.0,1.0 Contributors: Brocken Inaglory(Original uploader was Brocken Inaglory)File:Starfishmussel.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Starfishmussel.jpg  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors: Liné1,Mbz1, 4 anonymous editsFile:Close-up of clone war of sea anemones.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Close-up_of_clone_war_of_sea_anemones.jpg  License: Creative CommonsAttribution-Share Alike  Contributors: Brocken InagloryFile:Turnagain-bore.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Turnagain-bore.jpg  License: Public Domain  Contributors: Korrigan, Man vyi, Ozhiker, SaperaudFile:Undular bore Araguari River-Brazil-USGS-bws00026.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Undular_bore_Araguari_River-Brazil-USGS-bws00026.jpg  License:Public Domain  Contributors: CrowsnestFile:Trent Aegir 2.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Trent_Aegir_2.JPG  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors: Originaluploader was Chris075 at en.wikipediaFile:Trent Aegir 3.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Trent_Aegir_3.JPG  License: Creative Commons Attribution-ShareAlike 3.0 Unported  Contributors: Originaluploader was Chris075 at en.wikipediaFile:River Ribble bore.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:River_Ribble_bore.jpg  License: Creative Commons Attribution-Sharealike 3.0  Contributors: Frangle PlazmaGoatFile:Tidal bore.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_bore.jpg  License: GNU Free Documentation License  Contributors: Arria Belli, Benoit Rochon, Bouchecl, Manvyi, SaperaudImage:Surge-en.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Surge-en.svg  License: Public Domain  Contributors: SuperManuImage:Storm surge graphic.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Storm_surge_graphic.svg  License: Public Domain  Contributors: Howcheng. Original graphic by RobertSimmon, NASA GSFC.Image:Sloshrun.gif  Source: http://en.wikipedia.org/w/index.php?title=File:Sloshrun.gif  License: Public Domain  Contributors: NOAA National Hurricane Center, Sweetwater, Florida.File:TidalStream Tidal Farm Pic.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:TidalStream_Tidal_Farm_Pic.JPG  License: Creative Commons Attribution-ShareAlike 3.0Unported  Contributors: SelfFile:HAWT and VAWTs in operation medium.gif  Source: http://en.wikipedia.org/w/index.php?title=File:HAWT_and_VAWTs_in_operation_medium.gif  License: Public Domain Contributors: SsgxnhFile:Evopod July 2009.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Evopod_July_2009.JPG  License: Creative Commons Attribution-Sharealike 3.0  Contributors:Mindlessworker. Original uploader was Mindlessworker at en.wikipediaFile:Rance tidal power plant.JPG  Source: http://en.wikipedia.org/w/index.php?title=File:Rance_tidal_power_plant.JPG  License: Creative Commons Attribution-ShareAlike 3.0 Unported Contributors: User:Dani 7C3File:Tidal power conceptual barrage.jpg  Source: http://en.wikipedia.org/w/index.php?title=File:Tidal_power_conceptual_barrage.jpg  License: Creative Commons Attribution-ShareAlike 3.0Unported  Contributors: Original uploader was Evgeni Sergeev at en.wikipedia

License 120

LicenseCreative Commons Attribution-Share Alike 3.0 Unported//creativecommons.org/licenses/by-sa/3.0/