Tide

Tide coming in, video stops about11⁄2hours before high tide

Tidesare the rise and fall ofsea levelscaused by the combined effects of thegravitationalforces exerted by theMoon(and to a much lesser extent, theSun) and are also caused by theEarthandMoonorbiting one another.

Tide tablescan be used for any given locale to find the predicted times andamplitude(or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, thephase and amplitude of the tide(pattern of tides in the deep ocean), theamphidromicsystems of the oceans, and the shape of thecoastlineand near-shorebathymetry(seeTiming). They are however only predictions, the actual time and height of the tide is affected by wind andatmospheric pressure.Many shorelines experiencesemi-diurnaltides—two nearly equal high and low tides each day. Other locations have adiurnaltide—one high and low tide each day. A "mixed tide" —two uneven magnitude tides a day—is a third regular category.^[1]^[2]^[a]

Tides vary on timescales ranging from hours to years due to a number of factors, which determine thelunitidal interval.To make accurate records,tide gaugesat fixed stations measure water level over time. Gauges ignore variations caused by waves with periods shorter than minutes. These data are compared to the reference (or datum) level usually calledmean sea level.^[3]

While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to change fromthermal expansion,wind, and barometric pressure changes, resulting instorm 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 that varies in time and space is present. For example, the shape of the solid part of the Earth is affected slightly byEarth tide,though this is not as easily seen as the water tidal movements.

Characteristics

Four stages in the tidal cycle are named:

The water stops falling, reaching alocal minimumcalledlow tide.
Sea level rises over several hours, covering theintertidal zone;flood tide.
The water stops rising, reaching alocal maximumcalledhigh tide.
Sea level falls over several hours, revealing the intertidal zone;ebb tide.

Oscillatingcurrentsproduced by tides are known astidal streamsortidal currents.The moment that the tidal current ceases is calledslack waterorslack tide.The tide then reverses direction and is said to be turning. Slack water usually occurs near high water and low water, but there are locations where the moments of slack tide differ significantly from those of high and low water.^[4]

Tides are commonlysemi-diurnal(two high waters and two low waters each day), ordiurnal(one tidal cycle per day). The two high waters on a given day are typically not the same height (the daily inequality); these are thehigher high waterand thelower high waterintide tables.Similarly, the two low waters each day are thehigher low waterand thelower low water.The daily inequality is not consistent and is generally small when the Moon is over theEquator.^[b]

Reference levels

The following reference tide levels can be defined, from the highest level to the lowest:

Highest astronomical tide(HAT) – The highest tide which can be predicted to occur. Note that meteorological conditions may add extra height to the HAT.
Mean high water springs(MHWS) – The average of the two high tides on the days of spring tides.
Mean high water neaps(MHWN) – The average of the two high tides on the days of neap tides.
Mean sea level(MSL) – This is the average sea level. The MSL is constant for any location over a long period.
Mean low water neaps(MLWN) – The average of the two low tides on the days of neap tides.
Mean low water springs(MLWS) – The average of the two low tides on the days of spring tides.
Lowest astronomical tide(LAT) – The lowest tide which can be predicted to occur.^[6]

Tidal constituents

Tidal constituentsare the net result of multiple influences impacting tidal changes over certain periods of time. Primary constituents include the Earth's rotation, the position of the Moon and Sun relative to the Earth, the Moon's altitude (elevation) above the Earth's Equator, andbathymetry.Variations with periods of less than half a day are calledharmonic constituents.Conversely, cycles of days, months, or years are referred to aslong periodconstituents.

Tidal forcesaffect the entire earth,but the movement of solid Earth occurs by mere centimeters. In contrast, the atmosphere is much more fluid and compressible so its surface moves by kilometers, in the sense of the contour level of a particular low pressure in the outer atmosphere.

Principal lunar semi-diurnal constituent

Global surface elevation of M2 ocean tide (NASA)^[7]

In most locations, the largest constituent is theprincipal lunar semi-diurnal,also known as theM2 tidal constituentorM₂tidal constituent.Its period is about 12 hours and 25.2 minutes, exactly half atidal lunar day,which is the average time separating one lunarzenithfrom the next, and thus is the time required for the Earth to rotate once relative to the Moon. Simpletide clockstrack this constituent. The lunar day is longer than the Earth day because the Moon orbits in the same direction the Earth spins. This is analogous to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05+1⁄2(not at 1:00).

The Moon orbits the Earth in the same direction as the Earth rotates on its axis, so it takes slightly more than a day—about 24 hours and 50 minutes—for the Moon to return to the same location in the sky. During this time, it has passed overhead (culmination) once and underfoot once (at anhour angleof 00:00 and 12:00 respectively), so in many places the period of strongest tidal forcing is the above-mentioned, about 12 hours and 25 minutes. The moment of highest tide is not necessarily when the Moon is nearest tozenithornadir,but the period of the forcing still determines the time between high tides.

Because the gravitational field created by the Moon weakens with distance from the Moon, it exerts a slightly stronger than average force on the side of the Earth facing the Moon, and a slightly weaker force on the opposite side. The Moon thus tends to "stretch" the Earth slightly along the line connecting the two bodies. The solid Earth deforms a bit, but ocean water, being fluid, is free to move much more in response to the tidal force, particularly horizontally (seeequilibrium tide).

As the Earth rotates, the magnitude and direction of the tidal force at any particular point on the Earth's surface change constantly; although the ocean never reaches equilibrium—there is never time for the fluid to "catch up" to the state it would eventually reach if the tidal force were constant—the changing tidal force nonetheless causes rhythmic changes in sea surface height.

When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called amixed semi-diurnal tide.^[8]

Range variation: springs and neaps

The semi-diurnal range (the difference in height between high and low waters over about half a day) varies in a two-week cycle. Approximately twice a month, aroundnew moonandfull moonwhen the Sun, Moon, and Earth form a line (a configuration known as asyzygy^[9]), thetidal forcedue to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this is called thespring tide.It is not named afterthe season,but, like that word, derives from the meaning "jump, burst forth, rise", as in a naturalspring. Spring tides are sometimes referred to assyzygy tides.^[10]

When the Moon is atfirst quarteror third quarter, the Sun and Moon are separated by 90° when viewed from the Earth, and the solar tidal force partially cancels the Moon's tidal force. At these points in the lunar cycle, the tide's range is at its minimum; this is called theneap tide,orneaps."Neap" is an Anglo-Saxon word meaning "without the power", as inforðganges nip(forth-going without-the-power).^[11] Neap tides are sometimes referred to asquadrature tides.^[10]

Spring tides result in high waters that are higher than average, low waters that are lower than average, "slack water"time that is shorter than average, and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven-day interval between springs and neaps.

Spring tide:Sun and Moon on the same side (0°)
Neap tide:Sun and Moon at 90°
Spring tide:Sun and Moon at opposite sides (180°)
Neap tide:Sun and Moon at 270°
Spring tide:Sun and Moon at the same side (cycle restarts)

Lunar distance

The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, atperigee,the range increases, and when it is atapogee,the range shrinks. Six or eight times a year perigee coincides with either a new or full moon causingperigean spring tideswith the largesttidal range.The difference between the height of a tide at perigean spring tide and the spring tide when the moon is at apogee depends on location but can be large as a foot higher.^[12]

Other constituents

These include solar gravitational effects, the obliquity (tilt) of the Earth's Equator and rotational axis, the inclination of 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.^[13]

Phase and amplitude

Because theM₂tidal constituent dominates in most locations, the stage orphaseof a tide, denoted by the time in hours after high water, is a useful concept. Tidal stage is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are calledcotidal lines,which are analogous tocontour linesof constant altitude ontopographical maps,and when plotted form acotidal maporcotidal chart.^[16]High water is reached simultaneously along the cotidal lines extending from the coast out into the ocean, and cotidal lines (and hence tidal phases) advance along the coast. Semi-diurnal and long phase constituents are measured from high water, diurnal from maximum flood tide. 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 must eventually meet at a common point, theamphidromic point.The amphidromic point is at once cotidal with high and low waters, which is satisfied byzerotidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand,IcelandandMadagascar.) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constantamplitude(half the distance between high and low water) which decrease to zero at the amphidromic point. For a semi-diurnal tide the amphidromic point can be thought of roughly like the center of a clock face, with the hour hand pointing in the direction of the high water cotidal line, which is directly opposite the low water cotidal line. High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. This rotation, caused by theCoriolis effect,is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere. The difference of cotidal phase from the phase of a reference tide is theepoch.The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian.^[17]

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

History

History of tidal theory

Investigation into tidal physics was important in the early development ofcelestial mechanics,with the existence of two daily tides being explained by the Moon's gravity. Later the daily tides were explained more precisely by the interaction of the Moon's and the Sun's gravity.

Seleucus of Seleuciatheorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned inPtolemy'sTetrabiblos.^[c]

InDe temporum ratione(The Reckoning of Time) of 725Bedelinked semidurnal tides and the phenomenon of varying tidal heights to the Moon and its phases. Bede starts by noting that the tides rise and fall 4/5 of an hour later each day, just as the Moon rises and sets 4/5 of an hour later.^[19]He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides.^[20]Bede then observes that the height of tides varies over the month. Increasing tides are calledmalinaeand decreasing tidesledonesand that the month is divided into four parts of seven or eight days with alternatingmalinaeandledones.^[21]In the same passage he also notes the effect of winds to hold back tides.^[21]Bede also records that the time of tides varies from place to place. To the north of Bede's location (Monkwearmouth) the tides are earlier, to the south later.^[22]He explains that the tide "deserts these shores in order to be able all the more to be able to flood other [shores] when it arrives there" noting that "the Moon which signals the rise of tide here, signals its retreat in other regions far from this quarter of the heavens".^[22]

Later medieval understanding of the tides was primarily based on works ofMuslim astronomers,which became available throughLatin translationstarting from the 12th century.^[23]Abu Ma'shar al-Balkhi(d. circa 886), in hisIntroductorium in astronomiam,taught that ebb and flood tides were caused by the Moon.^[23]Abu Ma'shar discussed the effects of wind and Moon's phases relative to the Sun on the tides.^[23]In the 12th century,al-Bitruji(d. circa 1204) contributed the notion that the tides were caused by the general circulation of the heavens.^[23]

Simon Stevin,in his 1608De spiegheling der Ebbenvloet(The theory of ebb and flood), dismissed a large number of misconceptions that still existed about ebb and flood. Stevin pleaded for the idea that the attraction of the Moon was responsible for the tides and spoke in clear terms about ebb, flood,spring tideandneap tide,stressing that further research needed to be made.^[24]^[25]

In 1609Johannes Kepleralso correctly suggested that the gravitation of the Moon caused the tides,^[d]which he based upon ancient observations and correlations.

Galileo Galileiin his 1632Dialogue Concerning the Two Chief World Systems,whose working title wasDialogue on the Tides,gave an explanation of the tides. The resulting theory, however, was incorrect as he attributed the tides to the sloshing of water caused by the Earth's movement around the Sun. He hoped to provide mechanical proof of the Earth's movement. The value of his tidal theory is disputed. Galileo rejected Kepler's explanation of the tides.

Isaac Newton(1642–1727) was the first person to explain tides as the product of the gravitational attraction of astronomical masses. His explanation of the tides (and many other phenomena) was published in thePrincipia(1687)^[27]^[28]and used histheory of universal gravitationto explain the lunar and solar attractions as the origin of the tide-generating forces.^[e] Newton and others beforePierre-Simon Laplaceworked the problem from the perspective of a static system (equilibrium theory), that provided an approximation that described the tides that would occur in a non-inertial ocean evenly covering the whole Earth.^[27]The tide-generating force (or its correspondingpotential) is still relevant to tidal theory, but as an intermediate quantity (forcing function) rather than as a final result; theory must also consider the Earth's accumulated dynamic tidal response to the applied forces, which response is influenced by ocean depth, the Earth's rotation, and other factors.^[29]

In 1740, theAcadémie Royale des Sciencesin Paris offered a prize for the best theoretical essay on tides.Daniel Bernoulli,Leonhard Euler,Colin MaclaurinandAntoine Cavallerishared the prize.^[30]

Maclaurin used Newton's theory to show that a smooth sphere covered by a sufficiently deep ocean under the tidal force of a single deforming body is aprolatespheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth'srotational effectson motion. Euler realized that the tidal force'shorizontalcomponent (more than the vertical) drives the tide. In 1744Jean le Rond d'Alembertstudied tidal equations for the atmosphere which did not include rotation.

In 1770James Cook'sbarque HMSEndeavourgrounded on theGreat Barrier Reef.Attempts were made to refloat her on the following tide which failed, but the tide after that lifted her clear with ease. Whilst she was being repaired in the mouth of theEndeavour RiverCook observed the tides over a period of seven weeks. At neap tides both tides in a day were similar, but at springs the tides rose 7 feet (2.1 m) in the morning but 9 feet (2.7 m) in the evening.^[31]

Pierre-Simon Laplace formulated a system ofpartial differential equationsrelating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. TheLaplace tidal equationsare still in use today.William Thomson, 1st Baron Kelvin,rewrote Laplace's equations in terms ofvorticitywhich allowed for solutions describing tidally driven coastally trapped waves, known asKelvin waves.^[32]^[33]^[34]

Others including Kelvin andHenri Poincaréfurther developed Laplace's theory. Based on these developments and thelunar theoryofE W Browndescribing the motions of the Moon,Arthur Thomas Doodsondeveloped and published in 1921^[35]the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.^[36]Some of his methods remain in use.^[37]

History of tidal observation

From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the Sun and moon.Pytheastravelled to theBritish Islesabout 325 BC and seems to be the first to have related spring tides to the phase of the moon.

In the 2nd century BC, theHellenistic astronomer Seleucus of Seleuciacorrectly described the phenomenon of tides in order to support hisheliocentrictheory.^[38]He correctly theorized that tides were caused by themoon,although he believed that the interaction was mediated by thepneuma.He noted that tides varied in time and strength in different parts of the world. According toStrabo(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's position relative to the Sun.^[39]

TheNaturalis HistoriaofPliny the Eldercollates many tidal observations, e.g., the spring tides are a few days after (or before) new and full moon and are highest around the equinoxes, though Pliny noted many relationships now regarded as fanciful. In hisGeography,Strabo described tides in thePersian Gulfhaving their greatest range when the moon was furthest from the plane of the Equator. All this despite the relatively small amplitude ofMediterraneanbasin tides. (The strong currents through theEuripus Straitand theStrait of MessinapuzzledAristotle.)Philostratusdiscussed tides in Book Five ofThe Life ofApollonius of Tyana.Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the VenerableBededescribed how the rising tide on one coast of the British Isles coincided with the fall on the other and described the time progression of high water along the Northumbrian coast.

The firsttide tableinChinawas recorded in 1056 AD primarily for visitors wishing to see the famoustidal borein theQiantang River.The first known British tide table is thought to be that of John Wallingford, who died Abbot of St. Albans in 1213, based on high water occurring 48 minutes later each day, and three hours earlier at theThamesmouth than upriver atLondon.^[40]

In 1614Claude d'Abbevillepublished the work "Histoire de la mission de pères capucins en l'Isle de Maragnan et terres circonvoisines",where he exposed that theTupinambá peoplealready had an understanding of the relation between the Moon and the tides before Europe.^[41]

William Thomson (Lord Kelvin)led the first systematicharmonic analysisof tidal records starting in 1867. The main result was the building of atide-predicting machineusing a system of pulleys to add together six harmonic time functions. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s.^[42]

The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in theThames Estuary.Many large ports had automatic tide gauge stations by 1850.

John Lubbockwas one of the first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840.^[43]William Whewellexpanded this work ending with a nearly global chart in 1836.^[44]In order to make these maps consistent, he hypothesized the existence of a region with no tidal rise or fall where co-tidal lines meet in the mid-ocean. The existence of such anamphidromic point,as they are now known, was confirmed in 1840 byCaptain William Hewett, RN,from careful soundings in theNorth Sea.^[45]^[46]^[32]

Much later, in the late 20th century, geologists noticed tidalrhythmites,which document the occurrence of ancient tides in the geological record, notably in theCarboniferous.^[47]^[48]

Physics

Forces

The 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.

Whereas thegravitational forcesubjected by a celestial body on Earth varies inversely as the square of its distance to the Earth, the maximal tidal force varies inversely as, approximately, the cube of this distance.^[49]If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to thefree fallof the whole Earth, not only the oceans, towards these bodies) a different pattern of tidal forces would be observed, e.g. with a much stronger influence from the Sun than from the Moon: 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 overall proportionality is

{\text{tidal force}}\propto {\frac {M}{d^{3}}}\propto \rho \left({\frac {r}{d}}\right)^{3},

where $M$ is the mass of the heavenly body, $d$ is its distance, $ρ$ is its average density, and $r$ is its radius. The ratio $r / d$ is related to the angle subtended by the object in the sky. Since the Sun and the Moon have practically the same diameter in the sky, the tidal force of the Sun is less than that of the Moon because its average density is much less, and it is only 46% as large as the lunar,^[f]thus during a spring tide, the Moon contributes 69% while the Sun contributes 31%. More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1×10⁻⁷g,while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52×10⁻⁷g,wheregis thegravitational accelerationat the Earth's surface.^[g]The effects of the other planets vary as their distances from Earth vary. When Venus is closest to Earth, its effect is 0.000113 times the solar effect.^[50]At other times, Jupiter or Mars may have the most effect.

The ocean's surface is approximated by a surface referred to as thegeoid,which takes into consideration the gravitational force exerted by the earth as well ascentrifugal forcedue to rotation. Now consider the effect of massive external bodies such as the Moon and Sun. These bodies have strong gravitational fields that diminish with distance and cause the ocean's surface to deviate from the geoid. They establish a new equilibrium ocean surface which bulges toward the moon on one side and away from the moon on the other side. The earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface tends toward this equilibrium shape, which is constantly changing, and never quite attains it. When the ocean surface is not aligned with it, it's as though the surface is sloping, and water accelerates in the down-slope direction.

Equilibrium

Theequilibrium tideis the idealized tide assuming a landless Earth.^[51] It would produce a tidal bulge in the ocean, elongated towards the attracting body (Moon or Sun). It isnotcaused by the vertical pull nearest or farthest from the body, which is very weak; rather, it is caused by the tangential ortractivetidal force, which is strongest at about 45 degrees from the body, resulting in a horizontal tidal current.^[h] ^[i] ^[j]^[55]

Laplace's tidal equations

Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can bemodelledusing theLaplace tidal equationswhich incorporate the following features:

The vertical (or radial) velocity is negligible, and there is no verticalshear—this is a sheet flow.
The forcing is only horizontal (tangential).
TheCoriolis effectappears as an inertial force (fictitious) acting laterally to the direction of flow and proportional to velocity.
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 (inertial force) steers flows moving towards the Equator to the west and flows moving away from the Equator toward the east, allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity.

Amplitude and cycle time

The theoreticalamplitudeof oceanic tides caused by the Moon is about 54 centimetres (21 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 (9.8 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 (31 in), while at neap tide the theoretical level is reduced to 29 centimetres (11 in). Since the orbits of the Earth about the Sun, and the Moon about the Earth, are elliptical, tidal amplitudes change somewhat as a result of the varying Earth–Sun and Earth–Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 centimetres (37 in).

Real amplitudes differ considerably, not only because of depth variations and continental obstacles, but also because wave propagation across the ocean has a natural period of the same order of magnitude as the rotation period: if there were no land masses, it would take about 30 hours for a long wavelength surface wave to propagate along the Equator halfway around the Earth (by comparison, the Earth'slithospherehas 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 both significant and further complicate the ocean's response to tidal forces.

Dissipation

Earth's tidal oscillations introduce dissipation at anaveragerate of about 3.75terawatts.^[56]About 98% of this dissipation is by marine tidal movement.^[57]Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation. This tidal drag creates torque on the moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–moon separation. The equal and opposite torque on the Earth correspondingly decreases its rotational velocity. Thus, over geologic time, the moon recedes from the Earth, at about 3.8 centimetres (1.5 in)/year, lengthening the terrestrial day.^[k]

Day length has increasedby about 2 hours in the last 600 million years. Assuming (as a crude approximation) that the deceleration rate has been constant, this would imply that 70 million years ago, day length was on the order of 1% shorter with about 4 more days per year.

Bathymetry

The shape of the shoreline and the ocean floor changes the way that tides propagate, so there is no simple, general rule that predicts the time of high water from the Moon's position in the sky. Coastal characteristics such as underwaterbathymetryand coastline shape mean that individual location characteristics affect tide forecasting; actual high water time and height may differ from model predictions due to the coastal morphology's effects on tidal flow. However, for a given location the relationship between lunaraltitudeand the time of high or low tide (thelunitidal interval) is relatively constant and predictable, as is the time of high or low tide relative to other points on the same coast. For example, the high tide atNorfolk, Virginia,U.S., predictably occurs approximately 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 shapes and sizes affect the size of tidal frequencies. As a result, tidal patterns vary. For example, in the U.S., the East coast has predominantly semi-diurnal tides, as do Europe's Atlantic coasts, while the West coast predominantly has mixed tides.^[59]^[60]^[61]Human changes to the landscape can also significantly alter local tides.^[62]

Observation and prediction

Timing

The tidal forces due to the Moon and Sun generate very long waves which travel all around the ocean following the paths shown inco-tidal charts.The time when the crest of the wave reaches a port then gives the time of high water at the port. The time taken for the wave to travel around the ocean also means that there is a delay between the phases of the Moon and their effect on the tide. Springs and neaps in theNorth Sea,for example, are two days behind the new/full moon and first/third quarter moon. This is called the tide'sage.^[63]^[64]

The oceanbathymetrygreatly influences the tide's exact time and height at a particularcoastalpoint. There are some extreme cases; theBay of Fundy,on the east coast of Canada, is often stated to have the world's highest tides because of its shape, bathymetry, and its distance from the continental shelf edge.^[65]Measurements made in November 1998 at Burntcoat Head in the Bay of Fundy recorded a maximum range of 16.3 metres (53 ft) and a highest predicted extreme of 17 metres (56 ft).^[66]^[67]Similar measurements made in March 2002 at Leaf Basin,Ungava Bayin northernQuebecgave similar values (allowing for measurement errors), a maximum range of 16.2 metres (53 ft) and a highest predicted extreme of 16.8 metres (55 ft).^[66]^[67]Ungava Bay and the Bay of Fundy lie similar distances from the continental shelf edge, but Ungava Bay is only free ofpack icefor about four months every year while the Bay of Fundy rarely freezes.

Southamptonin the United Kingdom has a double high water caused by the interaction between theM₂andM₄tidal constituents(Shallow water overtides of principal lunar).^[68]Portlandhas double low waters for the same reason. TheM₄tide is found all along the south coast of the United Kingdom, but its effect is most noticeable between theIsle of WightandPortlandbecause theM₂tide is lowest in this region.

Because the oscillation modes of theMediterranean Seaand theBaltic Seado not coincide with any significant astronomical 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 theGulf of MexicoandSea of Japan.Elsewhere, as along the southern coast ofAustralia,low tides can be due to the presence of a nearbyamphidrome.

Analysis

Isaac Newton's theory of gravitation first enabled an explanation of why there were generally two tides a day, not one, and offered hope for a detailed understanding of tidal forces and behavior. Although it may seem that tides could be predicted via a sufficiently detailed knowledge of instantaneous astronomical forcings, the actual tide at a given location is determined by astronomical forces accumulated by the body of water over many days. In addition, accurate results would require detailed knowledge of the shape of all the ocean basins—theirbathymetry,and coastline shape.

Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s byWilliam 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 each significant tide-generating frequency to be distinguished by analysis, and to extract the tidal constants for a sufficient number of the strongest known components of the astronomical tidal forces to enable practical tide prediction. The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component. Because astronomical frequencies and phases can be calculated with certainty, the tide height at other times can then be predicted once the response to the harmonic components of the astronomical tide-generating forces has 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 variation

TheHighest Astronomical Tideis the perigean spring tide when both the Sun and Moon are closest to the Earth.

When confronted by a periodically varying function, the standard approach is to employFourier series,a form of analysis that usessinusoidalfunctions as abasisset, having frequencies that are zero, one, two, three, etc. times the frequency of a particular fundamental cycle. These multiples are calledharmonicsof the fundamental frequency, and the process is termedharmonic 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 are suitable for tides.

For the analysis of tide heights, the Fourier series approach has in practice to be made more elaborate than the use of a single frequency and its harmonics. The tidal patterns are decomposed into many sinusoids having many fundamental frequencies, corresponding (as in thelunar theory) to many different combinations of the motions of the Earth, the Moon, and the angles that define the shape and location of their orbits.

For tides, then,harmonic analysisis not limited to harmonics of a single frequency.^[l]In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier 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 be valid.

The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), andGeorge Darwin.A.T. Doodsonextended their work, introducing theDoodson Numbernotation to organise the hundreds of resulting 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_{o}\cos(\ Omega t+p),

where

A o

is the amplitude,

ω

is the angular frequency, usually given in degrees per hour, corresponding to

t

measured in hours,

p

is the phase offset with regard to the astronomical state at timet= 0.

There is one term for the Moon and a second term for the Sun. The phase $p$ of the first harmonic for the Moon term is called thelunitidal intervalor high water interval.

The next refinement is to accommodate the harmonic terms due to the elliptical shape of the orbits. To do so, the value of the amplitude is taken to be not a constant, but varying with time, about the average amplitude $A o$ .To do so, replace $A o$ in the above equation with $A (t)$ where $A$ is another sinusoid, similar to the cycles and epicycles ofPtolemaic theory.This gives

A(t)=A_{o}{\bigl (}1+A_{a}\cos(\ Omega _{a}t+p_{a}){\bigr )},

which is to say an average value $A o$ with a sinusoidal variation about it of magnitude $A a$ ,with frequency $ω a$ and phase $p a$ .Substituting this for $A o$ in the original equation gives a product of two cosine factors:

A_{o}{\bigl (}1+A_{a}\cos(\ Omega _{a}t+p_{a}){\bigr )}\cos(\ Omega t+p).

Given that for any $x$ and $y$

\cos x\cos y={\tfrac {1}{2}}\cos(x+y)+{\tfrac {1}{2}}\cos(x-y),

it is clear that a compound term involving the product of two cosine terms each with their own frequency is the same asthreesimple cosine terms that are to be added at the original frequency and also at frequencies which are the sum and 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) is above or below the plane of the Equator, and that these attributes have their own periods also incommensurable with a day and a month, and it is clear that many combinations result. With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences to form the frequency of each simple cosine term.

Remember that astronomical tides donotinclude weather effects. Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.) away from those prevailing at the measurement time affect the tide's actual timing and magnitude. Organisations quoting a "highest astronomical tide" for some location may exaggerate the figure as a safety factor against analytical uncertainties, distance from the nearest measurement point, changes since the last observation time, ground subsidence, etc., to avert liability should an engineering work be overtopped. Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide.

Careful Fourierdata analysisover a nineteen-year period (theNational Tidal Datum Epochin the U.S.) uses frequencies called thetidal harmonic constituents.Nineteen years is preferred because the Earth, Moon and Sun's relative positions repeat almost exactly in theMetonic cycleof 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 forcingperiod,but without detailed understanding of the mathematical derivation, which means that useful tidal tables have been constructed for centuries.^[69]The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (thesemi-diurnalconstituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day orfortnightly,monthly, and semiannual. Semi-diurnal tides dominated coastline, but some areas such as theSouth China Seaand theGulf of Mexicoare primarily diurnal. In the semi-diurnal areas, the primary constituentsM₂(lunar) andS₂(solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).^[70]

In theM₂plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich. The lines rotate around theamphidromic pointscounterclockwise in the northern hemisphere so that fromBaja California PeninsulatoAlaskaand fromFrancetoIrelandtheM₂tide propagates northward. In the southern hemisphere this direction is clockwise. On the other hand,M₂tide propagates counterclockwise around New Zealand, but this is because the islands act as a dam and permit the tides to have different heights on the islands' opposite sides. (The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.)

The exception is atCook Straitwhere the tidal currents periodically link high to low water. This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high water across from low water at each end of Cook Strait. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so theM₂patterns cannot be used for other tide components.

Example calculation

Graph with a single line rising and falling between 4 peaks around 3 and four valleys around −3 — Tides atBridgeport, Connecticut,U.S. during a 50-hour period.

Graph with a single line showing tidal peaks and valleys gradually cycling between higher highs and lower highs over a 14-day period — Tides at Bridgeport, Connecticut, U.S. during a 30-day period.

Graph showing with a single line showing only a minimal annual tidal fluctuation — Tides at Bridgeport, Connecticut, U.S. during a 400-day period.

Graph showing 6 lines with two lines for each of three cities. Nelson has two monthly spring tides, while Napier and Wellington each have one. — Tidal patterns in Cook Strait. The south part (Nelson) has two spring tides per month, versus only one on the north side (Wellington and Napier).

Because the Moon is moving in its orbit around the Earth and in the same sense as the Earth's rotation, a point on the Earth must rotate slightly further to catch up so that the time between semi-diurnal tides is not twelve but 12.4206 hours—a bit over twenty-five minutes extra. The two peaks are not equal. The two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), 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 main influences combine to produce spring tides; when the two forces are opposing each other as when the angle Moon–Earth–Sun is close to ninety degrees, neap tides result. As the Moon moves around its orbit it changes from north of the Equator to south of the Equator. The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the Moon is above the Equator), then redevelop but with the other polarity, wa xing to a maximum difference and then waning again.

Current

The tides' influence oncurrentor flow is much more difficult to analyze, and data is much more difficult to collect. A tidal height is ascalar quantityand varies smoothly over a wide region. A flow is avector quantity,with magnitude and direction, both of which can vary substantially with depth and over short distances due to local bathymetry. Also, although a water channel's center is the most useful measuring site, mariners object when current-measuring equipment obstructs waterways. A flow proceeding up a curved channel may have similar magnitude, even though its direction varies continuously along the channel. Surprisingly, flood and ebb flows are often not in opposite directions. Flow direction is determined by the upstream channel's shape, not the downstream channel's shape. Likewise,eddiesmay form in only one flow direction.

Nevertheless, tidal current analysis is similar to tidal heights analysis: in the simple case, at a given location the flood flow is in mostly one direction, and the ebb flow in another direction. Flood velocities are given positive sign, and ebb velocities negative sign. Analysis proceeds as though these are tide heights.

In more complex situations, the main ebb and flood flows do not dominate. Instead, the flow direction and magnitude trace an ellipse over a tidal cycle (on a polar plot) instead of along the ebb and flood lines. In this case, analysis might proceed along pairs of directions, with the primary and secondary directions at right angles. An alternative is to treat the tidal flows as complex numbers, as each value has both a magnitude and a direction.

Tide flow information is most commonly seen onnautical charts,presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides. The timing is relative to high water at some harbour where 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 weather conditions, which cancompletelychange the outcome.

The tidal flow throughCook Straitbetween the two main islands of New Zealand is particularly interesting, as the tides on each side of the strait are almost exactly out of phase, so that one side's high water is simultaneous with the other's low water. Strong currents result, with almost zero tidal height change in the strait's center. Yet, although the tidal surge normally flows in one direction for six hours and in the reverse direction for six hours, a particular surge might last eight or ten hours with the reverse surge enfeebled. In especially boisterous weather conditions, the reverse surge might be entirely overcome so that the flow continues in the same direction through three or more surge periods.

A further complication for Cook Strait's flow pattern is that the tide at the south side (e.g. atNelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the north side's tidal pattern has onlyonecycle per month, as on the east side:Wellington,andNapier.

The graph of Cook Strait's tides shows separately the high water and low water height and time, through November 2007; these arenotmeasured values but instead are calculated from tidal parameters derived from years-old measurements. Cook Strait's nautical chart offers tidal current information. For instance the January 1979 edition for41°13.9′S174°29.6′E/ 41.2317°S 174.4933°E/-41.2317; 174.4933(northwest ofCape Terawhiti) refers timings toWestportwhile the January 2004 issue refers to Wellington. Near Cape Terawhiti in the middle of Cook Strait the tidal height variation is almost nil while the tidal current reaches its maximum, especially near the notorious Karori Rip. Aside from weather effects, the actual currents through Cook Strait are influenced by the tidal height differences between the two ends of the strait and as can be seen, only one of the two spring tides at the north west end of the strait near Nelson has a counterpart spring tide at the south east end (Wellington), so the resulting behaviour follows neither reference harbour.^{[citation needed]}

Power generation

Tidal energy can be extracted by two means: inserting a waterturbineinto a tidal current, or building ponds that release/admit water through a turbine. In the first case, the energy amount is entirely determined by the timing and tidal current magnitude. However, the best currents may be unavailable because the turbines would obstruct ships. In the second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, ship navigation is disrupted. However, with multiple ponds, power can be generated at chosen times. So far, there are few installed systems for tidal power generation (most famously,La RanceatSaint Malo,France) which face many difficulties. Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineering challenges.

Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects. While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates. Since the power available from a flow is proportional to the cube of the flow speed, the times during which high power generation is possible are brief.

Tidal flows are important for navigation, and significant errors in position occur if they are not accommodated. Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significantdraftfrom entering at low tide.

Until the advent of automated navigation, competence in calculating tidal effects was important to naval officers. The certificate of examination for lieutenants in theRoyal Navyonce declared that the prospective officer was able to "shift his tides".^[71]

Tidal flow timings and velocities appear intide chartsor atidal stream atlas.Tide charts come in sets. Each chart covers a single hour between one high water and another (they ignore the leftover 24 minutes) and show the average tidal 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"which relate 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 (or DR) from travel distance and direction, (2) mark the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the tide's direction. The distance the tide moves the boat along this line is computed by the tidal speed, and this gives an" estimated position "or EP (traditionally marked with a dot in a triangle).

Nautical chartsdisplay the water's "charted depth" at specific locations with "soundings"and the use of bathymetriccontour linesto depict the submerged surface's shape. These depths are relative to a "chart datum",which is typically the water level at the lowest possible astronomical tide (although other datums are commonly used, especially historically, and tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle." Drying heights "may also be shown on the chart, which are the heights of the exposedseabedat the lowest astronomical tide.

Tide tables list each day's high and low water heights and times. To calculate the actual water depth, add the charted depth to the published tide height. Depth for other times can be derived from tidal curves published for major ports. Therule of twelfthscan suffice if an accurate curve is not available. This approximation presumes that the increase in depth in the six hours between 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

Intertidal ecology

Intertidal ecology is the study ofecosystemsbetween the low- and high-water lines along a shore. At low water, the intertidal zone is exposed (oremersed), whereas at high water, it is underwater (orimmersed). Intertidalecologiststherefore study the interactions between intertidal organisms and their environment, as well as among thedifferent species.The most important interactions may vary according to the type of intertidal community. The broadest classifications are based on substrates —rocky shoreor soft bottom.

Intertidal organisms experience a highly variable and often hostile environment, and haveadaptedto cope with and even exploit these conditions. One easily visible feature isvertical zonation,in which the community divides into distinct horizontal bands of specific species at each elevation above low water. A species' ability to cope withdesiccationdetermines its upper limit, whilecompetitionwith other species sets its lower limit.

Humansuse intertidal regionsfor food and recreation.Overexploitationcan damage intertidals directly. Other anthropogenic actions such as introducinginvasive speciesandclimate changehave large negative effects.Marine Protected Areasare one option communities can apply to protect these areas and aid scientificresearch.

Biological rhythms

The approximately 12-hour and fortnightly tidal cycle has large effects on intertidal^[72]and marine organisms.^[73]Hence theirbiological rhythmstend to occur in rough multiples of these periods.^[74]Many other animals such as thevertebrates,display similar circatidal rhythms.^[75]Examples includegestationand egg hatching. In humans, themenstrual cyclelasts roughly alunar month,an even multiple of the tidal period. Such parallels at least hint at thecommon descentof all animals from a marine ancestor.^[76]

Other tides

When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generateinternal waveswith tidal frequencies. Such waves are calledinternal tides.

Shallow areas in otherwise open water can experience rotary tidal currents, flowing in directions that continually change and thus the flow direction (not the flow) completes a full rotation in12+1⁄2hours (for example, theNantucket Shoals).^[77]

In addition to oceanic tides, large lakes can experience small tides and even planets can experienceatmospheric tidesandEarth tides.These arecontinuum mechanicalphenomena. The first two take place influids.The third affects the Earth's thinsolidcrust surrounding its semi-liquid interior (with various modifications).

Lake tides

Large lakes such asSuperiorandEriecan experience tides of 1 to 4 cm (0.39 to 1.6 in), but these can be masked by meteorologically induced phenomena such asseiche.^[78]The tide inLake Michiganis described as 1.3 to 3.8 cm (0.5 to 1.5 in)^[79]or4.4 cm (1+3⁄4in).^[80]This is so small that other larger effects completely mask any tide, and as such these lakes are considered non-tidal.^[81]

Atmospheric tides

Atmospheric tides are negligible at ground level and aviation altitudes, masked byweather's much more important effects. Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about 80 to 120 kilometres (50 to 75 mi), above which the molecular density becomes too low to support fluid behavior.

Earth tides

Earth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquidgyroscopewith a very thin crust. The Earth's crust shifts (in/out, east/west, north/south) in response to lunar and solar gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, terrestrial tides' semi-diurnal amplitude can reach about 55 centimetres (22 in) at the Equator—15 centimetres (5.9 in) due to the Sun—which is important inGPScalibration andVLBImeasurements. Precise astronomical angular measurements require knowledge of the Earth's rotation rate andpolar motion,both of which are influenced by Earth tides. The semi-diurnalM₂Earth tides are nearly in phase with the Moon with a lag of about two hours.^{[citation needed]}

Galactic tides

Galactic tidesare the tidal forces exerted by galaxies on stars within them andsatellite galaxiesorbiting them. The galactic tide's effects on theSolar System'sOort cloudare believed to cause 90 percent of long-period comets.^[82]

Misnomers

Tsunamis,the large waves that occur after earthquakes, are sometimes calledtidal waves,but this name is given by theirresemblanceto the tide, rather than any causal link to the tide. Other phenomena unrelated to tides but using the wordtidearerip tide,storm tide,hurricane tide,andblackorred tides.Many of these usages are historic and refer to the earlier meaning of tide as "a portion of time, a season" and "a stream, current or flood".^[83]

Notes

^Coastal orientation and geometry affects the phase, direction, and amplitude ofamphidromic systems,coastalKelvin wavesas well as resonantseichesin bays. Inestuaries,seasonal river outflows influence tidal flow.
^Tide tables usually listmean 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 asperigean tides.These aremeanvalues in the sense that they derive from mean data.^[5]
^"The moon, too, as the heavenly body nearest the earth, bestows her effluence most abundantly upon mundane things, for most of them, animate or inanimate, are sympathetic to her and change in company with her; the rivers increase and diminish their streams with her light, the seas turn their own tides with her rising and setting,..."^[18]
^"Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam,... Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem,..."(The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone,... However the moon flies swiftly across the zenith; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west,... "^[26]
^See for example, in the 'Principia' (Book 1) (1729 translation),Corollaries 19 and 20 to Proposition 66, on pages 251–254,referring back to page 234 et seq.; and in Book 3Propositions 24, 36 and 37, starting on page 255.
^According toNASAthe lunar tidal force is 2.21 times larger than the solar.
^SeeTidal force – Mathematical treatmentand sources cited there.
^"The ocean does not produce tides as a direct response to the vertical forces at the bulges. The tidal force is only about 1 ten millionth the size of the gravitational force owing to the Earth's gravity. It is the horizontal component of the tidal force that produces the tidal bulge, causing fluid to converge at the sublunar and antipodal points and move away from the poles, causing a contraction there." (...) "The projection of the tidal force onto the horizontal direction is called the tractive force (see Knauss, Fig. 10.11). This force causes an acceleration of water towards the sublunar and antipodal points, building up water until the pressure gradient force from the bulging sea surface exactly balances the tractive force field."^[52]
^"While the solar and lunar envelopes are thought of as representing the actual ocean waters, another very important factor must be recognized. The components of the tide-generating forces acting tangentially along the water surface turn out to be the most important. Just as it is easier to slide a bucket of water across a floor rather than to lift it, the horizontal tractive components move the waters toward the points directly beneath and away from the sun or moon far more effectively than the vertical components can lift them. These tractive forces are most responsible for trying to form the ocean into the symmetrical egg-shaped distensions (the tide potential, the equilibrium tide). They reach their maximums in rings 45° from the points directly beneath and away from the sun or moon."^[53]
^"... the gravitational effect that causes the tides is much too weak to lift the oceans 12 inches vertically away from the earth. It is possible, however, to move the oceans horizontally within the earth's gravitational field. This gathers the oceans toward two points where the height of the water becomes elevated by the converging volume of water."^[54]
^The day is currently lengthening at a rate of about 0.002 seconds per century.^[58]
^To demonstrate thisTides Home Pageoffers a tidal height pattern converted into an.mp3sound file, and the rich sound is quite different from a pure tone.

References

^Reddy, M.P.M. & Affholder, M. (2002).Descriptive physical oceanography: State of the Art.Taylor & Francis.p. 249.ISBN 90-5410-706-5.OCLC 223133263.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.
^Hubbard, Richard (1893).Boater's Bowditch: The Small Craft American Practical Navigator.McGraw-HillProfessional. p. 54.ISBN 0-07-136136-7.OCLC 44059064.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.
^"Tidal lunar day".NOAA.Archivedfrom the original on 2018-08-17.Retrieved2007-04-07.Do not confuse with the astronomicallunar dayon the Moon. A lunar zenith is the Moon's highest point in the sky.
^Mellor, George L. (1996).Introduction to physical oceanography.Springer. p. 169.ISBN 1-56396-210-1.
^"Glossary of Coastal Terminology: H–M".Washington Department of Ecology,State of Washington.Archivedfrom the original on 21 November 2017.Retrieved5 April2007.
^"Definitions of tidal terms".Land Information New Zealand.Archivedfrom the original on 30 August 2014.Retrieved20 February2017.
^"Ocean Tides and Magnetic Fields".NASA Visualization Studio.NASA.30 December 2016.Archivedfrom the original on 27 November 2020.Retrieved20 November2020.
^"Types and causes of tidal cycles".U.S. National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section). Archived fromthe originalon February 1, 2012.
^Swerdlow, Noel M.; Neugebauer, Otto (1984).Mathematical astronomy in Copernicus's De revolutionibus.Vol. 1. Springer-Verlag. p. 76.ISBN 0-387-90939-7.Archivedfrom the original on 2023-09-16.Retrieved2020-11-22– viaGoogle Books.
^^a ^bHarris, D.L. (1981).Tides and Tidal Datums in the United States.Special report (Coastal Engineering Research Center (U.S.))).United States Army Corps of Engineers,Coastal Engineering Research Center. p. 32.Archivedfrom the original on 2023-09-16.Retrieved2021-08-24– viaGoogle Books.
^"neap²".Oxford English Dictionary(2nd ed.).Oxford University Press.1989.Old English (example given from AD 469:forðganges nip– without the power of advancing). The Danishniptidis probably from the English. The English term neap-flood (from which neap tide comes) seems to have been in common use by AD 725.
^"What is a perigean spring tide?".National Oceanic and Atmospheric Administration. 26 February 2021.Archivedfrom the original on 30 July 2021.Retrieved16 July2021.
^Le Provost, Christian (1991). "Generation of Overtides and compound tides (review)". In Parker, Bruce B. (ed.).Tidal Hydrodynamics.John Wiley & Sons.ISBN 978-0-471-51498-5.
^Accad, Y. & Pekeris, C.L. (November 28, 1978). "Solution of the Tidal Equations for the M₂and S₂Tides in the World Oceans from a Knowledge of the Tidal Potential Alone ".Philosophical Transactions of the Royal Society of London A.290(1368): 235–266.Bibcode:1978RSPTA.290..235A.doi:10.1098/rsta.1978.0083.S2CID 119526571.
^"Tide forecasts".New Zealand: National Institute of Water & Atmospheric Research. Archived fromthe originalon 2008-10-14.Retrieved2008-11-07.Including animations of the M2, S2 and K1 tides for New Zealand.
^Marchuk, Guri I.; Kagan, B. A. (6 December 2012).Dynamics of Ocean Tides.Springer.ISBN 9789400925717.Archivedfrom the original on 16 September 2023.Retrieved22 November2020– viaGoogle Books.
^Schureman, Paul (1971).Manual of harmonic analysis and prediction of tides.U.S. Coast and geodetic survey. p. 204.Archivedfrom the original on 2017-08-08.Retrieved2018-01-14.
^Ptolemy(1940). "2".Tetrabiblos.Vol. 1. Translated by Robbins, Frank E. Cambridge, Massachusetts:Harvard University Press.
^Bede(1999).The Reckoning of Time.Translated by Wallis, Faith.Liverpool University Press.p. 82.ISBN 0-85323-693-3.Archivedfrom the original on 9 April 2023.Retrieved1 June2018– viaGoogle Books.
^Bede 1999,p. 83.
^^a ^bBede 1999,p. 84.
^^a ^bBede 1999,p. 85.
^^a ^b ^c ^dTolmacheva, Marina (2014). Glick, Thomas F. (ed.).Geography, Chorography.Routledge.p. 188.ISBN 978-1135459321.{{cite book}}:|work=ignored (help)
^"Simon Stevin"(PDF)(pdf) (in Dutch). Flanders Marine Institute.Archived(PDF)from the original on 2014-08-05.Retrieved2014-06-01.
^Palmerino, Carla Rita; Thijssen, J.M.M.H. (31 August 2004).The Reception of the Galilean Science of Motion in Seventeenth-Century Europe.Springer Science+Business Media.p. 200.ISBN 978-1-4020-2455-9.Archivedfrom the original on 12 April 2022.Retrieved29 November2022– viaGoogle Books.
^Johannes Kepler,Astronomia nova... (1609), p. 5 of theIntroductio in hoc opus(Introduction to this work).From page 5:
^^a ^bLisitzin, E.(1974). "2" Periodical sea-level changes: Astronomical tides "".Sea-Level Changes, (Elsevier Oceanography Series).Vol. 8. p. 5.
^"What Causes Tides?".U.S.National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section).Archivedfrom the original on 2016-08-20.Retrieved2009-09-06.
^Wahr, J. (1995).Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1.pp. 40–46.
^Euler, Leonhard;Aiton, Eric J. (1996).Commentationes mechanicae et astronomicae ad physicam pertinentes.Springer Science+Business Media.pp. 19–.ISBN 978-3-7643-1459-0– viaGoogle Books.
^Thomson, Thomas,ed. (March 1819)."On Capt. Cook's Account of the Tides".Annals of Philosophy.XIII.London: Baldwin, Cradock and Joy: 204.Archivedfrom the original on 26 August 2016.Retrieved25 July2015.
^^a ^bZuosheng, Y.; Emery, K.O. & Yui, X. (July 1989)."Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables".Limnology and Oceanography.34(5): 953–957.Bibcode:1989LimOc..34..953Z.doi:10.4319/lo.1989.34.5.0953.
^Cartwright, David E. (1999).Tides: A Scientific History.Cambridge, UK:Cambridge University Press.ISBN 9780521621458.
^Case, James (March 2000). "Understanding Tides – From Ancient Beliefs to Present-day Solutions to the Laplace Equations".SIAM News.33(2).
^Doodson, A.T. (December 1921)."The Harmonic Development of the Tide-Generating Potential".Proceedings of the Royal Society of London A.100(704): 305–329.Bibcode:1921RSPSA.100..305D.doi:10.1098/rspa.1921.0088.
^Casotto, S. & Biscani, F. (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.Bibcode:2004DDA....35.0805C.
^Moyer, T.D. (2003).Formulation for observed and computed values of Deep Space Network data types for navigation(PDF).Deep-space communications and navigation. Vol. 3.Wiley.pp. 126–128.ISBN 0-471-44535-5.Archived fromthe original(PDF)on 2004-10-16.
^Flussi e riflussi[Ebbs and flows] (in Italian). Milano: Feltrinelli. 2003.ISBN 88-07-10349-4.
^van der Waerden, B.L.(1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy".Annals of the New York Academy of Sciences.500(1): 525–545 [527].Bibcode:1987NYASA.500..525V.doi:10.1111/j.1749-6632.1987.tb37224.x.S2CID 222087224.
^Cartwright, D.E. (1999)."Tides, A Scientific History".Eos Transactions.80(36): 11, 18.Bibcode:1999EOSTr..80..408A.doi:10.1029/99EO00304.
^"Astronomia indígena prevê influência da lua sobre as marés antes de Galileu e Newton"[Indigenous astronomy predicts moon's influence on tides before Galileo and Newton] (in Brazilian Portuguese). 2009-06-19.Retrieved2021-12-11.
^"The Doodson–Légé Tide Predicting Machine".Proudman Oceanographic Laboratory. Archived fromthe originalon 2009-03-20.Retrieved2008-10-03.
^Lubbock, J.W. (1831)."On the tides on the coast of Great Britain".The Philosophical Magazine.9(53): 333–335.doi:10.1080/14786443108647618.
^Whewell, William (1836)."Researches on the tides, sixth series. On the results of an extensive system of tide observations made on the coasts of Europe and America in June 1835".Philosophical Transactions of the Royal Society of London.126:289–341.
^Hewett, William (1841)."Tide observations in the North Sea".The Nautical Magazine:180–183.
^Cartwright, David Edgar (17 August 2000).Tides: A Scientific History.Cambridge University Press.ISBN 978-0-521-79746-7.OCLC 1001932580.
^Kuecher, Gerald J.; Woodland, Bertram G.; Broadhurst, Frederick M. (1 September 1990)."Evidence of deposition from individual tides and of tidal cycles from the Francis Creek Shale (host rock to the Mazon Creek Biota), Westphalian D (Pennsylvanian), northeastern Illinois".Sedimentary Geology.68(3): 211–221.Bibcode:1990SedG...68..211K.doi:10.1016/0037-0738(90)90113-8.ISSN 0037-0738.
^Archer, Allen W; Kuecher, Gerald J; Kvale, Erik P (1995)."The Role of Tidal-Velocity Asymmetries in the Deposition of Silty Tidal Rhythmites (Carboniferous, Eastern Interior Coal Basin, U.S.A.)".SEPM Journal of Sedimentary Research.65:408–416.doi:10.1306/d42680d6-2b26-11d7-8648000102c1865d.
^Young, C. A. (1889).A Textbook of General Astronomy(PDF).p. 288.Archived(PDF)from the original on 2019-10-05.Retrieved2018-08-13.
^"Interplanetary Low Tide".Science Mission Directorate.2000-05-03.Archivedfrom the original on 2023-06-04.Retrieved2023-06-25.
^"Equilibrium tide".AMS Glossary.2020-09-02.Archivedfrom the original on 2020-08-01.Retrieved2020-09-02.
^Thompson, LuAnne(2006)."Physical Processes in the Ocean"(PDF).Archived(PDF)from the original on 2020-09-28.Retrieved2020-06-27.
^Hicks, S.D. (2006).Understanding Tides(PDF)(Report).NOAA.Archived(PDF)from the original on 2022-01-20.Retrieved2020-09-02.
^Mccully, James Greig (2006).Beyond The Moon: A Conversational, Common Sense Guide To Understanding The Tides, World Scientific.World Scientific.ISBN 9789814338189.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.
^"What Physics Teachers Get Wrong about Tides! - PBS Space Time".PBSLearningMedia.2020-06-17.Archivedfrom the original on 2020-10-21.Retrieved2020-06-27.
^Munk, W.; Wunsch, C. (1998). "Abyssal recipes II: energetics of tidal and wind mi xing".Deep-Sea Research Part I.45(12): 1977.Bibcode:1998DSRI...45.1977M.doi:10.1016/S0967-0637(98)00070-3.
^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.S2CID 4367240.
^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.
^"map showing world distribution of tide patterns, semi-diurnal, diurnal and mixed semi-diurnal".U.S.National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section).Archivedfrom the original on 2018-08-27.Retrieved2009-09-05.
^Thurman, H.V. (1994).Introductory Oceanography(7th ed.). New York:Macmillan Publishers.pp. 252–276.ref
^Ross, D.A. (1995).Introduction to Oceanography.New York:HarperCollins.pp. 236–242.
^Witze, Alexandra (5 July 2020)."How humans are altering the tides of the oceans".BBC Future.BBC.Archivedfrom the original on 6 July 2020.Retrieved8 July2020.
^"Glossary of Meteorology".American Meteorological Society.Archivedfrom the original on 2021-05-08.Retrieved2021-04-02.
^Webster, Thomas (1837).The elements of physics.Printed for Scott, Webster, and Geary. p.168.
^"FAQ".Archived fromthe originalon February 12, 2012.RetrievedJune 23,2007.
^^a ^bO'Reilly, C.T.R.; Solvason, Ron & Solomon, Christian (2005). Ryan, J. (ed.). "Where are the World's Largest Tides".BIO Annual Report "2004 in Review".Washington, D.C.: Biotechnol. Ind. Org.: 44–46.
^^a ^bO'reilly, Charles T.; Solvason, Ron; Solomon, Christian (2005)."Resolving the World's largest tides"(PDF).In Percy, J.A; Evans, A.J.; Wells, P.G.; Rolston, S.J. (eds.).The Changing Bay of Fundy-Beyond 400 years, Proceedings of the 6th Bay of Fundy Workshop, Cornwallis, Nova Scotia, Sept. 29, 2004 to October 2, 2004. Environment Canada-Atlantic Region, Occasional Report no. 23. Dartmouth, N.S. and Sackville, N.B.Archived(PDF)from the original on August 27, 2016.RetrievedApril 1,2013.
^Pingree, R.D.; Maddock, L. (1978). "Deep-Sea Research".25:53–63.{{cite journal}}:Cite journal requires|journal=(help)
^Center for Operational Oceanographic Products and Services, National Ocean Service,National Oceanic and Atmospheric Administration(January 2000)."Tide and Current Glossary"(PDF).Silver Spring, MD.Archived(PDF)from the original on 2007-01-28.Retrieved2007-04-05.{{cite web}}:CS1 maint: multiple names: authors list (link)
^"Harmonic Constituents".NOAA.Archivedfrom the original on 2007-03-17.Retrieved2007-04-05.
^Society for Nautical Research (1958).The Mariner's Mirror.Archivedfrom the original on 2023-09-16.Retrieved2009-04-28– viaGoogle Books.
^Bos, A.R.; Gumanao, G.S.; van Katwijk, M.M.; Mueller, B.; Saceda, M.M. & Tejada, R.P. (2011)."Ontogenetic habitat shift, population growth, and burrowing behavior of the Indo-Pacific beach starArchaster typicus(Echinodermata: Asteroidea) ".Marine Biology.158(3): 639–648.Bibcode:2011MarBi.158..639B.doi:10.1007/s00227-010-1588-0.PMC3873073.PMID 24391259.
^Bos, A.R. & Gumanao, G.S. (2012). "The lunar cycle determines availability of coral reef fishes on fish markets".Journal of Fish Biology.81(6): 2074–2079.Bibcode:2012JFBio..81.2074B.doi:10.1111/j.1095-8649.2012.03454.x.PMID 23130702.
^Naylor, Ernest (2010-02-04). "Chapter 5: Lunar and semilunar biorhythms".Chronobiology of Marine Organisms.Cambridge University Press.ISBN 978-1-139-48494-7.Archivedfrom the original on 2023-09-16.Retrieved2022-01-03– viaGoogle Books.
^Zhu, Bokai; Dacso, Clifford C.; O'Malley, Bert W. (2018-07-01)."Unveiling" Musica Universalis "of the Cell: A Brief History of Biological 12-Hour Rhythms".Journal of the Endocrine Society.2(7): 727–752.doi:10.1210/js.2018-00113.ISSN 2472-1972.PMC6025213.PMID 29978151.Archivedfrom the original on 2023-09-16.Retrieved2022-01-03.
^Darwin, Charles(1871).The Descent of Man, and Selection in Relation to Sex.London: John Murray.
^Le Lacheur, Embert A. (April 1924)."Tidal currents in the open sea: Subsurface tidal currents at Nantucket Shoals Light Vessel".Geographical Review.14(2): 282–286.Bibcode:1924GeoRv..14..282L.doi:10.2307/208104.JSTOR 208104.Archivedfrom the original on 16 September 2023.Retrieved4 February2012.
^"Do the Great Lakes have tides?".Great Lakes Information Network. October 1, 2000. Archived fromthe originalon 2017-12-30.Retrieved2010-02-10.
^Calder, Vince."Tides on Lake Michigan".Argonne National Laboratory.Archivedfrom the original on 2019-08-15.Retrieved2019-08-14.
^Dunkerson, Duane."moon and Tides".Astronomy Briefly.Archivedfrom the original on 2010-01-15.Retrieved2010-02-10.
^"Do the Great Lakes have tides?".National Ocean Service.NOAA.Archivedfrom the original on 2016-04-23.Retrieved2016-04-26.
^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".Oxford English Dictionary.Vol. XVIII (2nd ed.).Oxford University Press.1989. p. 64.

External links

[3] Coastal orientation and geometry affects the phase, direction, and amplitude ofamphidromic systems,coastalKelvin wavesas well as resonantseichesin bays. Inestuaries,seasonal river outflows influence tidal flow.

[7] Tide tables usually listmean 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 asperigean tides.These aremeanvalues in the sense that they derive from mean data.^[5]

[21] "The moon, too, as the heavenly body nearest the earth, bestows her effluence most abundantly upon mundane things, for most of them, animate or inanimate, are sympathetic to her and change in company with her; the rivers increase and diminish their streams with her light, the seas turn their own tides with her rising and setting,..."^[18]

[30] "Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam,... Celeriter vero Luna verticem transvolante, cum aquæ tam celeriter sequi non possint, fluxus quidem fit Oceani sub Torrida in Occidentem,..."(The sphere of the lifting power, which is [centered] in the moon, is extended as far as to the earth and attracts the waters under the torrid zone,... However the moon flies swiftly across the zenith; because the waters cannot follow so quickly, the tide of the ocean under the torrid [zone] is indeed made to the west,... "^[26]

[33] See for example, in the 'Principia' (Book 1) (1729 translation),Corollaries 19 and 20 to Proposition 66, on pages 251–254,referring back to page 234 et seq.; and in Book 3Propositions 24, 36 and 37, starting on page 255.

[55] According toNASAthe lunar tidal force is 2.21 times larger than the solar.

[56] SeeTidal force – Mathematical treatmentand sources cited there.

[60] "The ocean does not produce tides as a direct response to the vertical forces at the bulges. The tidal force is only about 1 ten millionth the size of the gravitational force owing to the Earth's gravity. It is the horizontal component of the tidal force that produces the tidal bulge, causing fluid to converge at the sublunar and antipodal points and move away from the poles, causing a contraction there." (...) "The projection of the tidal force onto the horizontal direction is called the tractive force (see Knauss, Fig. 10.11). This force causes an acceleration of water towards the sublunar and antipodal points, building up water until the pressure gradient force from the bulging sea surface exactly balances the tractive force field."^[52]

[62] "While the solar and lunar envelopes are thought of as representing the actual ocean waters, another very important factor must be recognized. The components of the tide-generating forces acting tangentially along the water surface turn out to be the most important. Just as it is easier to slide a bucket of water across a floor rather than to lift it, the horizontal tractive components move the waters toward the points directly beneath and away from the sun or moon far more effectively than the vertical components can lift them. These tractive forces are most responsible for trying to form the ocean into the symmetrical egg-shaped distensions (the tide potential, the equilibrium tide). They reach their maximums in rings 45° from the points directly beneath and away from the sun or moon."^[53]

[64] "... the gravitational effect that causes the tides is much too weak to lift the oceans 12 inches vertically away from the earth. It is possible, however, to move the oceans horizontally within the earth's gravitational field. This gathers the oceans toward two points where the height of the water becomes elevated by the converging volume of water."^[54]

[69] The day is currently lengthening at a rate of about 0.002 seconds per century.^[58]

[80] To demonstrate thisTides Home Pageoffers a tidal height pattern converted into an.mp3sound file, and the rich sound is quite different from a pure tone.

[Reddy-1] Reddy, M.P.M. & Affholder, M. (2002).Descriptive physical oceanography: State of the Art.Taylor & Francis.p. 249.ISBN 90-5410-706-5.OCLC 223133263.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.

[Hubbard-2] Hubbard, Richard (1893).Boater's Bowditch: The Small Craft American Practical Navigator.McGraw-HillProfessional. p. 54.ISBN 0-07-136136-7.OCLC 44059064.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.

[4] "Tidal lunar day".NOAA.Archivedfrom the original on 2018-08-17.Retrieved2007-04-07.Do not confuse with the astronomicallunar dayon 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] "Glossary of Coastal Terminology: H–M".Washington Department of Ecology,State of Washington.Archivedfrom the original on 21 November 2017.Retrieved5 April2007.

[8] "Definitions of tidal terms".Land Information New Zealand.Archivedfrom the original on 30 August 2014.Retrieved20 February2017.

[NASA2016-9] "Ocean Tides and Magnetic Fields".NASA Visualization Studio.NASA.30 December 2016.Archivedfrom the original on 27 November 2020.Retrieved20 November2020.

[noaa7-10] "Types and causes of tidal cycles".U.S. National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section). Archived fromthe originalon February 1, 2012.

[11] Swerdlow, Noel M.; Neugebauer, Otto (1984).Mathematical astronomy in Copernicus's De revolutionibus.Vol. 1. Springer-Verlag. p. 76.ISBN 0-387-90939-7.Archivedfrom the original on 2023-09-16.Retrieved2020-11-22– viaGoogle Books.

[Harris1981-12] Harris, D.L. (1981).Tides and Tidal Datums in the United States.Special report (Coastal Engineering Research Center (U.S.))).United States Army Corps of Engineers,Coastal Engineering Research Center. p. 32.Archivedfrom the original on 2023-09-16.Retrieved2021-08-24– viaGoogle Books.

[13] "neap²".Oxford English Dictionary(2nd ed.).Oxford University Press.1989.Old English (example given from AD 469:forðganges nip– without the power of advancing). The Danishniptidis probably from the English. The English term neap-flood (from which neap tide comes) seems to have been in common use by AD 725.

[14] "What is a perigean spring tide?".National Oceanic and Atmospheric Administration. 26 February 2021.Archivedfrom the original on 30 July 2021.Retrieved16 July2021.

[leprovost-15] Le Provost, Christian (1991). "Generation of Overtides and compound tides (review)". In Parker, Bruce B. (ed.).Tidal Hydrodynamics.John Wiley & Sons.ISBN 978-0-471-51498-5.

[16] Accad, Y. & Pekeris, C.L. (November 28, 1978). "Solution of the Tidal Equations for the M₂and S₂Tides in the World Oceans from a Knowledge of the Tidal Potential Alone ".Philosophical Transactions of the Royal Society of London A.290(1368): 235–266.Bibcode:1978RSPTA.290..235A.doi:10.1098/rsta.1978.0083.S2CID 119526571.

[17] "Tide forecasts".New Zealand: National Institute of Water & Atmospheric Research. Archived fromthe originalon 2008-10-14.Retrieved2008-11-07.Including animations of the M2, S2 and K1 tides for New Zealand.

[18] Marchuk, Guri I.; Kagan, B. A. (6 December 2012).Dynamics of Ocean Tides.Springer.ISBN 9789400925717.Archivedfrom the original on 16 September 2023.Retrieved22 November2020– viaGoogle Books.

[19] Schureman, Paul (1971).Manual of harmonic analysis and prediction of tides.U.S. Coast and geodetic survey. p. 204.Archivedfrom the original on 2017-08-08.Retrieved2018-01-14.

[20] Ptolemy(1940). "2".Tetrabiblos.Vol. 1. Translated by Robbins, Frank E. Cambridge, Massachusetts:Harvard University Press.

[Wallis-22] Bede(1999).The Reckoning of Time.Translated by Wallis, Faith.Liverpool University Press.p. 82.ISBN 0-85323-693-3.Archivedfrom the original on 9 April 2023.Retrieved1 June2018– viaGoogle Books.

[FOOTNOTEBede199983-23] Bede 1999,p. 83.

[FOOTNOTEBede199984-24] Bede 1999,p. 84.

[FOOTNOTEBede199985-25] Bede 1999,p. 85.

[Tolmacheva-26] Tolmacheva, Marina (2014). Glick, Thomas F. (ed.).Geography, Chorography.Routledge.p. 188.ISBN 978-1135459321.{{cite book}}:|work=ignored (help)

[27] "Simon Stevin"(PDF)(pdf) (in Dutch). Flanders Marine Institute.Archived(PDF)from the original on 2014-08-05.Retrieved2014-06-01.

[28] Palmerino, Carla Rita; Thijssen, J.M.M.H. (31 August 2004).The Reception of the Galilean Science of Motion in Seventeenth-Century Europe.Springer Science+Business Media.p. 200.ISBN 978-1-4020-2455-9.Archivedfrom the original on 12 April 2022.Retrieved29 November2022– viaGoogle Books.

[29] Johannes Kepler,Astronomia nova... (1609), p. 5 of theIntroductio in hoc opus(Introduction to this work).From page 5:

[slc-ch2-31] Lisitzin, E.(1974). "2" Periodical sea-level changes: Astronomical tides "".Sea-Level Changes, (Elsevier Oceanography Series).Vol. 8. p. 5.

[32] "What Causes Tides?".U.S.National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section).Archivedfrom the original on 2016-08-20.Retrieved2009-09-06.

[34] Wahr, J. (1995).Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1.pp. 40–46.

[EulerAiton1996-35] Euler, Leonhard;Aiton, Eric J. (1996).Commentationes mechanicae et astronomicae ad physicam pertinentes.Springer Science+Business Media.pp. 19–.ISBN 978-3-7643-1459-0– viaGoogle Books.

[Cook-36] Thomson, Thomas,ed. (March 1819)."On Capt. Cook's Account of the Tides".Annals of Philosophy.XIII.London: Baldwin, Cradock and Joy: 204.Archivedfrom the original on 26 August 2016.Retrieved25 July2015.

[tidhist-37] Zuosheng, Y.; Emery, K.O. & Yui, X. (July 1989)."Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables".Limnology and Oceanography.34(5): 953–957.Bibcode:1989LimOc..34..953Z.doi:10.4319/lo.1989.34.5.0953.

[38] Cartwright, David E. (1999).Tides: A Scientific History.Cambridge, UK:Cambridge University Press.ISBN 9780521621458.

[39] Case, James (March 2000). "Understanding Tides – From Ancient Beliefs to Present-day Solutions to the Laplace Equations".SIAM News.33(2).

[40] Doodson, A.T. (December 1921)."The Harmonic Development of the Tide-Generating Potential".Proceedings of the Royal Society of London A.100(704): 305–329.Bibcode:1921RSPSA.100..305D.doi:10.1098/rspa.1921.0088.

[41] Casotto, S. & Biscani, F. (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.Bibcode:2004DDA....35.0805C.

[42] Moyer, T.D. (2003).Formulation for observed and computed values of Deep Space Network data types for navigation(PDF).Deep-space communications and navigation. Vol. 3.Wiley.pp. 126–128.ISBN 0-471-44535-5.Archived fromthe original(PDF)on 2004-10-16.

[43] Flussi e riflussi[Ebbs and flows] (in Italian). Milano: Feltrinelli. 2003.ISBN 88-07-10349-4.

[44] van der Waerden, B.L.(1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy".Annals of the New York Academy of Sciences.500(1): 525–545 [527].Bibcode:1987NYASA.500..525V.doi:10.1111/j.1749-6632.1987.tb37224.x.S2CID 222087224.

[45] Cartwright, D.E. (1999)."Tides, A Scientific History".Eos Transactions.80(36): 11, 18.Bibcode:1999EOSTr..80..408A.doi:10.1029/99EO00304.

[46] "Astronomia indígena prevê influência da lua sobre as marés antes de Galileu e Newton"[Indigenous astronomy predicts moon's influence on tides before Galileo and Newton] (in Brazilian Portuguese). 2009-06-19.Retrieved2021-12-11.

[47] "The Doodson–Légé Tide Predicting Machine".Proudman Oceanographic Laboratory. Archived fromthe originalon 2009-03-20.Retrieved2008-10-03.

[48] Lubbock, J.W. (1831)."On the tides on the coast of Great Britain".The Philosophical Magazine.9(53): 333–335.doi:10.1080/14786443108647618.

[49] Whewell, William (1836)."Researches on the tides, sixth series. On the results of an extensive system of tide observations made on the coasts of Europe and America in June 1835".Philosophical Transactions of the Royal Society of London.126:289–341.

[50] Hewett, William (1841)."Tide observations in the North Sea".The Nautical Magazine:180–183.

[Cartwright2000-51] Cartwright, David Edgar (17 August 2000).Tides: A Scientific History.Cambridge University Press.ISBN 978-0-521-79746-7.OCLC 1001932580.

[Kuecher_et_al._1990-52] Kuecher, Gerald J.; Woodland, Bertram G.; Broadhurst, Frederick M. (1 September 1990)."Evidence of deposition from individual tides and of tidal cycles from the Francis Creek Shale (host rock to the Mazon Creek Biota), Westphalian D (Pennsylvanian), northeastern Illinois".Sedimentary Geology.68(3): 211–221.Bibcode:1990SedG...68..211K.doi:10.1016/0037-0738(90)90113-8.ISSN 0037-0738.

[Archer_et_al._1995-53] Archer, Allen W; Kuecher, Gerald J; Kvale, Erik P (1995)."The Role of Tidal-Velocity Asymmetries in the Deposition of Silty Tidal Rhythmites (Carboniferous, Eastern Interior Coal Basin, U.S.A.)".SEPM Journal of Sedimentary Research.65:408–416.doi:10.1306/d42680d6-2b26-11d7-8648000102c1865d.

[54] Young, C. A. (1889).A Textbook of General Astronomy(PDF).p. 288.Archived(PDF)from the original on 2019-10-05.Retrieved2018-08-13.

[Science_Mission_Directorate_2000-57] "Interplanetary Low Tide".Science Mission Directorate.2000-05-03.Archivedfrom the original on 2023-06-04.Retrieved2023-06-25.

[AMS_Glossary_2020-58] "Equilibrium tide".AMS Glossary.2020-09-02.Archivedfrom the original on 2020-08-01.Retrieved2020-09-02.

[59] Thompson, LuAnne(2006)."Physical Processes in the Ocean"(PDF).Archived(PDF)from the original on 2020-09-28.Retrieved2020-06-27.

[Hicks2006-61] Hicks, S.D. (2006).Understanding Tides(PDF)(Report).NOAA.Archived(PDF)from the original on 2022-01-20.Retrieved2020-09-02.

[63] Mccully, James Greig (2006).Beyond The Moon: A Conversational, Common Sense Guide To Understanding The Tides, World Scientific.World Scientific.ISBN 9789814338189.Archivedfrom the original on 2023-09-16.Retrieved2022-01-05– viaGoogle Books.

[PBS_LearningMedia_2020-65] "What Physics Teachers Get Wrong about Tides! - PBS Space Time".PBSLearningMedia.2020-06-17.Archivedfrom the original on 2020-10-21.Retrieved2020-06-27.

[Munk1998-66] Munk, W.; Wunsch, C. (1998). "Abyssal recipes II: energetics of tidal and wind mi xing".Deep-Sea Research Part I.45(12): 1977.Bibcode:1998DSRI...45.1977M.doi:10.1016/S0967-0637(98)00070-3.

[Ray1996-67] 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.S2CID 4367240.

[68] 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.

[noaa7b-70] "map showing world distribution of tide patterns, semi-diurnal, diurnal and mixed semi-diurnal".U.S.National Oceanic and Atmospheric Administration(NOAA) National Ocean Service (Education section).Archivedfrom the original on 2018-08-27.Retrieved2009-09-05.

[71] Thurman, H.V. (1994).Introductory Oceanography(7th ed.). New York:Macmillan Publishers.pp. 252–276.ref

[72] Ross, D.A. (1995).Introduction to Oceanography.New York:HarperCollins.pp. 236–242.

[73] Witze, Alexandra (5 July 2020)."How humans are altering the tides of the oceans".BBC Future.BBC.Archivedfrom the original on 6 July 2020.Retrieved8 July2020.

[74] "Glossary of Meteorology".American Meteorological Society.Archivedfrom the original on 2021-05-08.Retrieved2021-04-02.

[75] Webster, Thomas (1837).The elements of physics.Printed for Scott, Webster, and Geary. p.168.

[76] "FAQ".Archived fromthe originalon February 12, 2012.RetrievedJune 23,2007.

[BIO2004-77] O'Reilly, C.T.R.; Solvason, Ron & Solomon, Christian (2005). Ryan, J. (ed.). "Where are the World's Largest Tides".BIO Annual Report "2004 in Review".Washington, D.C.: Biotechnol. Ind. Org.: 44–46.

[FundyWorkshop-78] O'reilly, Charles T.; Solvason, Ron; Solomon, Christian (2005)."Resolving the World's largest tides"(PDF).In Percy, J.A; Evans, A.J.; Wells, P.G.; Rolston, S.J. (eds.).The Changing Bay of Fundy-Beyond 400 years, Proceedings of the 6th Bay of Fundy Workshop, Cornwallis, Nova Scotia, Sept. 29, 2004 to October 2, 2004. Environment Canada-Atlantic Region, Occasional Report no. 23. Dartmouth, N.S. and Sackville, N.B.Archived(PDF)from the original on August 27, 2016.RetrievedApril 1,2013.

[Pingree_1978-79] Pingree, R.D.; Maddock, L. (1978). "Deep-Sea Research".25:53–63.{{cite journal}}:Cite journal requires|journal=(help)

[81] Center for Operational Oceanographic Products and Services, National Ocean Service,National Oceanic and Atmospheric Administration(January 2000)."Tide and Current Glossary"(PDF).Silver Spring, MD.Archived(PDF)from the original on 2007-01-28.Retrieved2007-04-05.{{cite web}}:CS1 maint: multiple names: authors list (link)

[82] "Harmonic Constituents".NOAA.Archivedfrom the original on 2007-03-17.Retrieved2007-04-05.

[83] Society for Nautical Research (1958).The Mariner's Mirror.Archivedfrom the original on 2023-09-16.Retrieved2009-04-28– viaGoogle Books.

[84] Bos, A.R.; Gumanao, G.S.; van Katwijk, M.M.; Mueller, B.; Saceda, M.M. & Tejada, R.P. (2011)."Ontogenetic habitat shift, population growth, and burrowing behavior of the Indo-Pacific beach starArchaster typicus(Echinodermata: Asteroidea) ".Marine Biology.158(3): 639–648.Bibcode:2011MarBi.158..639B.doi:10.1007/s00227-010-1588-0.PMC3873073.PMID 24391259.

[85] Bos, A.R. & Gumanao, G.S. (2012). "The lunar cycle determines availability of coral reef fishes on fish markets".Journal of Fish Biology.81(6): 2074–2079.Bibcode:2012JFBio..81.2074B.doi:10.1111/j.1095-8649.2012.03454.x.PMID 23130702.

[86] Naylor, Ernest (2010-02-04). "Chapter 5: Lunar and semilunar biorhythms".Chronobiology of Marine Organisms.Cambridge University Press.ISBN 978-1-139-48494-7.Archivedfrom the original on 2023-09-16.Retrieved2022-01-03– viaGoogle Books.

[87] Zhu, Bokai; Dacso, Clifford C.; O'Malley, Bert W. (2018-07-01)."Unveiling" Musica Universalis "of the Cell: A Brief History of Biological 12-Hour Rhythms".Journal of the Endocrine Society.2(7): 727–752.doi:10.1210/js.2018-00113.ISSN 2472-1972.PMC6025213.PMID 29978151.Archivedfrom the original on 2023-09-16.Retrieved2022-01-03.

[Descent-88] Darwin, Charles(1871).The Descent of Man, and Selection in Relation to Sex.London: John Murray.

[rocur-89] Le Lacheur, Embert A. (April 1924)."Tidal currents in the open sea: Subsurface tidal currents at Nantucket Shoals Light Vessel".Geographical Review.14(2): 282–286.Bibcode:1924GeoRv..14..282L.doi:10.2307/208104.JSTOR 208104.Archivedfrom the original on 16 September 2023.Retrieved4 February2012.

[90] "Do the Great Lakes have tides?".Great Lakes Information Network. October 1, 2000. Archived fromthe originalon 2017-12-30.Retrieved2010-02-10.

[91] Calder, Vince."Tides on Lake Michigan".Argonne National Laboratory.Archivedfrom the original on 2019-08-15.Retrieved2019-08-14.

[92] Dunkerson, Duane."moon and Tides".Astronomy Briefly.Archivedfrom the original on 2010-01-15.Retrieved2010-02-10.

[93] "Do the Great Lakes have tides?".National Ocean Service.NOAA.Archivedfrom the original on 2016-04-23.Retrieved2016-04-26.

[94] 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.

[95] "tide".Oxford English Dictionary.Vol. XVIII (2nd ed.).Oxford University Press.1989. p. 64.

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