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{{short description|Rise and fall of the sea level under astronomical gravitational influences}}
{{other uses}}
{{Redirect2|Ebbing|Ebb tide|other uses|Ebbing (disambiguation)|and|Ebb tide (disambiguation)}}
{{pp-semi-indef}}
[[File:tide overview.svg|300px|thumb|upright=1|Simplified schematic of only the lunar portion of Earth's tides, showing (exaggerated) high tides at the sublunar point and its [[antipodal point|antipode]] for the hypothetical case of an ocean of constant depth without land, and on the assumption that Earth is not rotating; otherwise there is a lag angle. Solar tides not shown.|alt=]]
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[[Tide table]]s can be used for any given locale to find the predicted times and [[amplitude]] (or "[[tidal range]]").
The predictions are influenced by many factors including the alignment of the Sun and Moon, the [[#Phase and amplitude|phase and amplitude of the tide]] (pattern of tides in the deep ocean), the [[amphidromic]] systems of the oceans, and the shape of the
Tides vary on timescales ranging from hours to years due to a number of factors, which determine the [[lunitidal interval]]. To make accurate records, [[tide gauge]]s at 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 called [[mean sea level]].<ref>{{cite web |url=http://www.oceanservice.noaa.gov/education/kits/tides/media/supp_tide05.html |title=Tidal lunar day |publisher=[[NOAA]] |access-date=2007-04-07 |archive-date=2018-08-17 |archive-url=https://web.archive.org/web/20180817075116/https://oceanservice.noaa.gov/education/kits/tides/media/supp_tide05.html |url-status=live }} Do not confuse with the astronomical [[lunar day]] on the Moon. A lunar zenith is the Moon's highest point in the sky.</ref>
While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to change from [[thermal expansion]], wind, and barometric pressure changes, resulting in [[storm surge]]s, especially in shallow seas and near coasts.
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[[File:Tide type.svg|thumb|Types of tides (See ''Timing'' (below) for coastal map)|alt=Three graphs. The first shows the twice-daily rising and falling tide pattern with nearly regular high and low elevations. The second shows the much more variable high and low tides that form a "mixed tide". The third shows the day-long period of a diurnal tide.]]
Four stages in the tidal cycle are named:
* {{anchor|Low|Low tide}}The water stops falling, reaching a [[local minimum]] called '''low tide'''.
* {{anchor|High|High tide}}The water stops rising, reaching a [[local maximum]] called '''high tide'''.▼
* {{anchor|Flood|Flood tide}}Sea level rises over several hours, covering the [[intertidal zone]]; '''flood tide'''.
▲* {{anchor|High|High tide}}The water stops rising, reaching a [[local maximum]] called '''high tide'''.
* {{anchor|Ebb|Ebb tide}}Sea level falls over several hours, revealing the intertidal zone; '''ebb tide'''.
Oscillating [[Current (fluid)|currents]] produced by tides are known as '''tidal streams''' or '''[[
Tides are commonly ''semi-diurnal'' (two high waters and two low waters each day), or ''diurnal'' (one tidal cycle per day). The two high waters on a given day are typically not the same height (the daily inequality); these are the ''higher high water'' and the ''lower high water'' in [[tide table]]s. Similarly, the two low waters each day are the ''higher low water'' and the ''lower low water''. The daily inequality is not consistent and is generally small when the Moon is over the [[Equator]].{{efn|Tide tables usually list ''mean lower low water'' (mllw, the 19 year average of mean lower low waters), ''mean higher low water'' (mhlw), ''mean lower high water'' (mlhw), ''mean higher high water'' (mhhw), as well as ''perigean tides''. These are ''mean'' values in the sense that they derive from mean data.<ref>{{cite web |url=http://www.ecy.wa.gov/programs/sea/swces/products/publications/glossary/words/H_M.htm |title=Glossary of Coastal Terminology: H–M |publisher=[[Washington Department of Ecology]], State of Washington |access-date=5 April 2007 |archive-date=21 November 2017 |archive-url=https://web.archive.org/web/20171121042259/http://www.ecy.wa.gov/programs/sea/swces/products/publications/glossary/words/H_M.htm |url-status=live }}</ref>}}
=== Reference levels ===
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* ''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.<ref>{{cite web |title=Definitions of tidal terms |url=http://www.linz.govt.nz/hydro/tidal-info/tidal-intro/definitions |website=Land Information New Zealand |access-date=20 February 2017 |archive-date=30 August 2014 |archive-url=https://web.archive.org/web/20140830114240/http://www.linz.govt.nz/hydro/tidal-info/tidal-intro/definitions |url-status=live }}</ref>
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=== Principal lunar semi-diurnal constituent ===
[[File:Global surface elevation of M2 ocean tide.webm|thumb|upright=1.7|Global surface elevation of M2 ocean tide (NASA)<ref name=NASA2016>{{Cite web |url=https://svs.gsfc.nasa.gov/4541 |title=Ocean Tides and Magnetic Fields |website=NASA Visualization Studio |publisher=[[NASA]] |date=30 December 2016 |access-date=20 November 2020 |archive-date=27 November 2020 |archive-url=https://web.archive.org/web/20201127195922/https://svs.gsfc.nasa.gov/4541 |url-status=live }}</ref>]]
In most locations, the largest constituent is the ''principal lunar semi-diurnal'', also known as the ''M2 tidal constituent'' or ''M<sub>2</sub> tidal constituent''. Its period is about 12 hours and 25.2 minutes, exactly half a ''tidal lunar day'', which is the average time separating one lunar [[zenith]] from the next, and thus is the time required for the Earth to rotate once relative to the Moon. Simple [[tide clock]]s track 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:{{frac|05
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 an [[hour angle]] of 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 to [[zenith]] or [[nadir]], but the period of the forcing still determines the time between high tides.
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[[File:Tide schematic.svg|thumb|left|alt=Spring tide: the Sun, moon, and earth form a straight line. Neap tide: the Sun, moon, and earth form a right angle.|The types of tides]]
{{anchor|springtide|Spring}}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, around [[new moon]] and [[full moon]] when the Sun, Moon, and Earth form a line (a configuration known as a [[syzygy (astronomy)|syzygy]]<ref>{{Cite book |title=Mathematical astronomy in Copernicus's De revolutionibus |volume=1 |first1=Noel M. |last1=Swerdlow |first2=Otto |last2=Neugebauer |publisher=Springer-Verlag |date=1984 |isbn=0-387-90939-7 |page=76 |url=https://books.google.com/books?id=4YDvAAAAMAAJ&q=Syzygy |via=[[Google Books]] |access-date=2020-11-22 |archive-date=2023-09-16 |archive-url=https://web.archive.org/web/20230916153030/https://books.google.com/books?id=4YDvAAAAMAAJ&q=Syzygy |url-status=live }}</ref>), the [[tidal force]] due to the Sun reinforces that due to the Moon. The tide's range is then at its maximum; this is called the '''spring tide'''. It is not named after the [[Spring (season)|season]], but, like that word, derives from the meaning "jump, burst forth, rise", as in a natural [[Spring (hydrosphere)|spring]].
Spring tides are sometimes referred to as ''syzygy tides''.<ref name="Harris1981">{{cite book |last=Harris |first=D.L. |title=Tides and Tidal Datums in the United States |publisher=[[United States Army Corps of Engineers]], Coastal Engineering Research Center |series=Special report (Coastal Engineering Research Center (U.S.))) |year=1981 |url=https://books.google.com/books?id=kbIse3HQ74wC&pg=PA32 |access-date=2021-08-24 |page=32 |via=[[Google Books]] |archive-date=2023-09-16 |archive-url=https://web.archive.org/web/20230916153028/https://books.google.com/books?id=kbIse3HQ74wC&pg=PA32 |url-status=live }}</ref>
{{anchor|Neap}}When the Moon is at [[Gibbous|first quarter]] or 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 the '''neap tide''', or '''neaps'''. "Neap" is an Anglo-Saxon word meaning "without the power", as in ''forðganges nip'' (forth-going without-the-power).<ref>{{cite OED2|neap²}} Old English (example given from AD 469: ''forðganges nip'' – without the power of advancing). The Danish ''niptid'' is probably from the English. The English term neap-flood (from which neap tide comes) seems to have been in common use by AD 725.</ref>
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[[File:Atlantic coast at low tide, Bar Harbor IMG 2262.JPG|thumb|Low tide at [[Bar Harbor, Maine|Bar Harbor]], [[Maine]], U.S. (2014)]]
The changing distance separating the Moon and Earth also affects tide heights. When the Moon is closest, at [[perigee]], the range increases, and when it is at [[apogee]], the range shrinks. Six or eight times a year perigee coincides with either a new or full moon causing [[perigean spring tide]]s with the largest ''[[tidal 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.<ref>{{cite web |title=What is a perigean spring tide? |url=https://oceanservice.noaa.gov/facts/perigean-spring-tide.html |publisher=National Oceanic and Atmospheric Administration |date=26 February 2021 |access-date=16 July 2021 |archive-date=30 July 2021 |archive-url=https://web.archive.org/web/20210730210313/https://oceanservice.noaa.gov/facts/perigean-spring-tide.html |url-status=live }}</ref>
=== Other constituents ===
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=== Phase and amplitude ===
[[File:M2 tidal constituent.jpg|thumb|''M''<sub>2</sub> tidal constituent. Red is most extreme (highest highs, lowest lows), with blues being least extreme. White cotidal lines converge in blue areas indicating little or no tide.
</ref>|alt=Map showing relative tidal magnitudes of different ocean areas]]
Because the ''M''<sub>2</sub> tidal constituent dominates in most locations, the stage or ''phase'' of 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 called ''[[cotidal line]]s'', which are analogous to [[contour lines]] of constant altitude on [[topographical maps]], and when plotted form a ''cotidal map'' or ''cotidal chart''.<ref>{{Cite book |url=https://books.google.com/books?id=E3uhBQAAQBAJ&q=tidal+map&pg=PT28 |title=Dynamics of Ocean Tides |isbn=9789400925717 |last1=Marchuk |first1=Guri I. |last2=Kagan |first2=B. A. |date=6 December 2012 |publisher=Springer |via=[[Google Books]] |access-date=22 November 2020 |archive-date=16 September 2023 |archive-url=https://web.archive.org/web/20230916153029/https://books.google.com/books?id=E3uhBQAAQBAJ&q=tidal+map&pg=PT28 |url-status=live }}</ref> 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, the [[amphidromic point]]. The amphidromic point is at once cotidal with high and low waters, which is satisfied by ''zero'' tidal motion. (The rare exception occurs when the tide encircles an island, as it does around New Zealand, [[Iceland]] and [[Madagascar]].) Tidal motion generally lessens moving away from continental coasts, so that crossing the cotidal lines are contours of constant ''amplitude'' (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 the [[Coriolis 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 the ''epoch''. The reference tide is the hypothetical constituent "equilibrium tide" on a landless Earth measured at 0° longitude, the Greenwich meridian.<ref>{{cite book |last=Schureman |first=Paul |title=Manual of harmonic analysis and prediction of tides |date=1971 |publisher=U.S. Coast and geodetic survey |page=204 |url=https://www.biodiversitylibrary.org/ia/manualofharmonic00schu#page/220/mode/1up |access-date=2018-01-14 |archive-date=2017-08-08 |archive-url=https://web.archive.org/web/20170808200945/http://www.biodiversitylibrary.org/ia/manualofharmonic00schu#page/220/mode/1up |url-status=live }}</ref>
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.
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Investigation into tidal physics was important in the early development of [[celestial 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 Seleucia]] theorized around 150 BC that tides were caused by the Moon. The influence of the Moon on bodies of water was also mentioned in [[Ptolemy]]'s ''[[Tetrabiblos]]''.{{efn|"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,
In {{lang|la|De temporum ratione}} (''[[The Reckoning of Time]]'') of 725 [[Bede]] linked 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.<ref name=Wallis>{{cite book |author=Bede |author-link=Bede |translator-last=Wallis |translator-first=Faith |title=The Reckoning of Time |year=1999 |publisher=[[Liverpool University Press]] |isbn=0-85323-693-3 |url=https://books.google.com/books?id=yFsw-Vaup6sC |access-date=1 June 2018 |page=82 |via=[[Google Books]] |archive-date=9 April 2023 |archive-url=https://web.archive.org/web/20230409160418/https://books.google.com/books?id=yFsw-Vaup6sC |url-status=live }}</ref> He goes on to emphasise that in two lunar months (59 days) the Moon circles the Earth 57 times and there are 114 tides.{{sfn|Bede|1999|p=83}} Bede then observes that the height of tides varies over the month. Increasing tides are called ''malinae'' and decreasing tides ''ledones'' and that the month is divided into four parts of seven or eight days with alternating ''malinae'' and ''ledones''.{{sfn|Bede|1999|p=84}} In the same passage he also notes the effect of winds to hold back tides.{{sfn|Bede|1999|p=84}} 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.{{sfn|Bede|1999|p=85}} 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".{{sfn|Bede|1999|p=85}}
[[Simon Stevin]], in his 1608 {{lang|nl|De 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 tide]] and [[neap tide]], stressing that further research needed to be made.<ref>{{cite web |url=http://www.vliz.be/imisdocs/publications/224466.pdf |title=Simon Stevin |publisher=Flanders Marine Institute |type=pdf |language=nl |access-date=2014-06-01 |archive-date=2014-08-05 |archive-url=https://web.archive.org/web/20140805054735/http://www.vliz.be/imisdocs/publications/224466.pdf |url-status=live }}</ref><ref>{{Cite book |last1=Palmerino |first1=Carla Rita |first2=J.M.M.H. |last2=Thijssen |url=https://books.google.com/books?id=a5lkdlMPi1AC&dq=%22johannes+kepler%22+%22simon+stevin%22+ebb&pg=PA200 |title=The Reception of the Galilean Science of Motion in Seventeenth-Century Europe |date=31 August 2004 |publisher=[[Springer Science+Business Media]] |isbn=978-1-4020-2455-9 |page=200 |via=[[Google Books]] |access-date=29 November 2022 |archive-date=12 April 2022 |archive-url=https://web.archive.org/web/20220412060701/https://books.google.com/books?id=a5lkdlMPi1AC&pg=PA200&dq=%22johannes+kepler%22+%22simon+stevin%22+ebb |url-status=live }}</ref>
In 1609 [[Johannes Kepler]] also correctly suggested that the gravitation of the Moon caused the tides,{{efn|''"Orbis virtutis tractoriæ, quæ est in Luna, porrigitur utque ad Terras, & prolectat aquas sub Zonam Torridam,
[[Galileo Galilei]] in his 1632 ''[[Dialogue Concerning the Two Chief World Systems]]'', whose working title was ''Dialogue 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 the ''[[Philosophiae Naturalis Principia Mathematica|Principia]]'' (1687)<ref name=slc-ch2>{{cite book |author-link=Eugenie Lisitzin |last=Lisitzin |first=E. |title=Sea-Level Changes, (Elsevier Oceanography Series) |volume=8 |date=1974 |chapter=2 "Periodical sea-level changes: Astronomical tides" |page=5}}</ref><ref>{{cite web |publisher=U.S. [[National Oceanic and Atmospheric Administration]] (NOAA) National Ocean Service (Education section) |url=http://oceanservice.noaa.gov/education/kits/tides/tides02_cause.html |title=What Causes Tides? |access-date=2009-09-06 |archive-date=2016-08-20 |archive-url=https://web.archive.org/web/20160820055655/http://oceanservice.noaa.gov/education/kits/tides/tides02_cause.html |url-status=live }}</ref> and used his [[Newton's law of universal gravitation|theory of universal gravitation]] to explain the lunar and solar attractions as the origin of the tide-generating forces.{{efn|1=See for example, in the 'Principia' (Book 1) (1729 translation), [https://books.google.com/books?id=Tm0FAAAAQAAJ&pg=PA251 Corollaries 19 and 20 to Proposition 66, on pages 251–254], referring back to page 234 et seq.; and in Book 3 [https://archive.org/details/bub_gb_6EqxPav3vIsC/page/n279 <!-- pg=255 --> Propositions 24, 36 and 37, starting on page 255].}}
Newton and others before [[Pierre-Simon Laplace]] worked 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.<ref name=slc-ch2 /> The tide-generating force (or its corresponding [[scalar potential|potential]]) 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.<ref>{{cite book |last=Wahr |first=J. |title=Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1 |pages=40–46 |date=1995}}</ref>
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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 a [[prolate]] spheroid (essentially a three-dimensional oval) with major axis directed toward the deforming body. Maclaurin was the first to write about the Earth's [[Coriolis effect|rotational effects]] on motion. Euler realized that the tidal force's ''horizontal'' component (more than the vertical) drives the tide. In 1744 [[Jean le Rond d'Alembert]] studied tidal equations for the atmosphere which did not include rotation.
In 1770 [[James Cook]]'s [[barque]] [[HMS Endeavour|HMS ''Endeavour'']] grounded on the [[Great 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 the [[Endeavour River]] Cook 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 {{convert|7|feet}} in the morning but {{convert|9|feet}} in the evening.<ref name=Cook>{{cite journal |editor-last=Thomson |editor-first=Thomas |editor-link=Thomas Thomson (chemist) |title=On Capt. Cook's Account of the Tides |date=March 1819 |publisher=Baldwin, Cradock and Joy |place=London |journal=[[Annals of Philosophy]] |volume=XIII |page=204 |url=https://www.biodiversitylibrary.org/page/15877750 |access-date=25 July 2015 |archive-date=26 August 2016 |archive-url=https://web.archive.org/web/20160826094842/http://biodiversitylibrary.org/page/15877750 |url-status=live }}</ref>
Pierre-Simon Laplace formulated a system of [[partial differential equation]]s relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides. The [[Laplace's tidal equations|Laplace tidal equations]] are still in use today. [[William Thomson, 1st Baron Kelvin]], rewrote Laplace's equations in terms of [[vorticity]] which allowed for solutions describing tidally driven coastally trapped waves, known as [[Kelvin wave]]s.<ref name="tidhist">{{cite journal |title=Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables |journal=Limnology and Oceanography |volume=34 |issue=5 |date=July 1989 |pages=953–957 |last1=Zuosheng |first1=Y. |last2=Emery |first2=K.O. |last3=Yui |first3=X. |name-list-style=amp |doi=10.4319/lo.1989.34.5.0953 |bibcode=1989LimOc..34..953Z |doi-access=free}}</ref><ref>{{cite book |title=Tides: A Scientific History |url=https://archive.org/details/tidesscientifich0000cart |url-access=registration |last=Cartwright |first=David E. |publisher=[[Cambridge University Press]] |location=Cambridge, UK |date=1999 |isbn=9780521621458}}</ref><ref>{{cite journal |title=Understanding Tides – From Ancient Beliefs to Present-day Solutions to the Laplace Equations |first=James |last=Case |journal=SIAM News |volume=33 |issue=2 |date=March 2000}}</ref>
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The first [[tide table]] in [[China]] was recorded in 1056 AD primarily for visitors wishing to see the famous [[tidal bore]] in the [[Qiantang 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 the [[Thames]] mouth than upriver at [[London]].<ref>{{cite journal |last=Cartwright |first=D.E. |date=1999 |title=Tides, A Scientific History |journal=Eos Transactions |volume=80 |issue=36 |pages=11, 18|doi=10.1029/99EO00304 |bibcode=1999EOSTr..80..408A |doi-access=free }}</ref>
In 1614 [[Claude d'Abbeville]] published the work "{{lang|fr|Histoire de la mission de pères capucins en
[[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] led the first systematic [[harmonic analysis]] of tidal records starting in 1867. The main result was the building of a [[tide-predicting machine]] using 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.<ref>{{cite web |url=http://www.pol.ac.uk/home/insight/doodsonmachine.html |title=The Doodson–Légé Tide Predicting Machine |access-date=2008-10-03 |publisher=Proudman Oceanographic Laboratory |url-status=dead |archive-url=https://web.archive.org/web/20090320184406/http://www.pol.ac.uk/home/insight/doodsonmachine.html |archive-date=2009-03-20}}</ref>
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[[Sir John Lubbock, 3rd Baronet|John Lubbock]] was one of the first to map co-tidal lines, for Great Britain, Ireland and adjacent coasts, in 1840.<ref>{{cite journal |last1=Lubbock |first1=J.W. |title=On the tides on the coast of Great Britain |journal=The Philosophical Magazine |date=1831 |volume=9 |issue=53 |pages=333–335 |doi=10.1080/14786443108647618 |url=https://archive.org/details/lubbock-1831-philosophical-magazine-s-2id-13416500}}</ref> [[William Whewell]] expanded this work ending with a nearly global chart in 1836.<ref>{{cite journal |last1=Whewell |first1=William |title=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 |journal=[[Philosophical Transactions of the Royal Society of London]] |date=1836 |volume=126 |pages=289–341 |url=https://archive.org/details/jstor-108036}}</ref> 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 an [[amphidromic point]], as they are now known, was confirmed in 1840 by [[William Hewett (died 1840)|Captain William Hewett, RN]], from careful soundings in the [[North Sea]].<ref>{{cite journal |last1=Hewett |first1=William |title=Tide observations in the North Sea |journal=The Nautical Magazine |date=1841 |pages=180–183 |url=https://archive.org/details/199-1841-hewett-fairy-the-nautical-magazine-1841}}</ref><ref name="Cartwright2000">{{cite book |first1=David Edgar |last1=Cartwright |date=17 August 2000 |title=Tides: A Scientific History |publisher=[[Cambridge University Press]] |isbn=978-0-521-79746-7 |oclc=1001932580}}</ref><ref name="tidhist"/>
Much later, in the late 20th century, geologists noticed tidal [[Rhythmite|rhythmites]], which document the occurrence of ancient tides in the geological record, notably in the [[Carboniferous]].<ref name="Kuecher et al. 1990">{{cite journal |last1=Kuecher |first1=Gerald J. |last2=Woodland |first2=Bertram G. |last3=Broadhurst |first3=Frederick M. |title=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 |journal=Sedimentary Geology |date=1 September 1990 |volume=68 |issue=3 |pages=211–221 |doi=10.1016/0037-0738(90)90113-8 |bibcode=1990SedG...68..211K |url=https://doi.org/10.1016/0037-0738(90)90113-8 |issn=0037-0738}}</ref><ref name="Archer et al. 1995">{{cite journal |last1=Archer |first1=Allen W |last2=Kuecher |first2=Gerald J |last3=Kvale |first3=Erik P |title=The Role of Tidal-Velocity Asymmetries in the Deposition of Silty Tidal Rhythmites (Carboniferous, Eastern Interior Coal Basin, U.S.A.) |journal=SEPM Journal of Sedimentary Research |date=1995 |volume=65 |pages=408–416 |doi=10.1306/d42680d6-2b26-11d7-8648000102c1865d |url=https://doi.org/10.1306/D42680D6-2B26-11D7-8648000102C1865D |language=en}}</ref>
== Physics ==
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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 the [[gravitational force]] subjected 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.<ref>{{cite book |last=Young |first=C. A. |date=1889 |title=A Textbook of General Astronomy |url=https://www.gutenberg.org/files/37275/37275-pdf.pdf |page=288 |access-date=2018-08-13 |archive-date=2019-10-05 |archive-url=https://web.archive.org/web/20191005003655/http://www.gutenberg.org/files/37275/37275-pdf.pdf |url-status=live }}</ref> If the tidal force caused by each body were instead equal to its full gravitational force (which is not the case due to the [[free fall]] of 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
: <math>\text{tidal force} \propto \frac{M}{d^3} \propto \rho\left(\frac{r}{d}\right)^3,</math>
where {{mvar|M}} is the mass of the heavenly body, {{mvar|d}} is its distance, {{mvar|ρ}} is its average density, and {{mvar|r}} is its radius. The ratio {{math|''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,<!-- numbers double-checked by User:JEBrown87544, 03 Jan 2007 -->{{efn|According to [https://web.archive.org/web/19980224174548/http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/961029b.html NASA] the lunar tidal force is 2.21 times larger than the solar.}} 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{{e|−7}} ''g'', while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52{{e|−7}} ''g'', where ''g'' is the [[standard gravity|gravitational acceleration]] at the Earth's surface.{{efn|See [[Tidal force#Formulation|Tidal force – Mathematical treatment]] and sources cited there.}} 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.<ref name="Science Mission Directorate 2000">{{cite web | title=Interplanetary Low Tide | website=Science Mission Directorate | date=2000-05-03 | url=https://science.nasa.gov/science-news/science-at-nasa/2000/ast04may_1m | access-date=2023-06-25 | archive-date=2023-06-04 | archive-url=https://web.archive.org/web/20230604014510/https://science.nasa.gov/science-news/science-at-nasa/2000/ast04may_1m | url-status=live }}</ref> At other times, Jupiter or Mars may have the most effect.
[[File:
▲[[File:Field tidal.svg|thumb|The lunar [[gravity]] differential [[Vector field|field]] at the Earth's surface is known as the [[Tidal force|tide-generating force]]. This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters.|alt=Diagram showing a circle with closely spaced arrows pointing away from the reader on the left and right sides, while pointing towards the user on the top and bottom.]]
The ocean's surface is approximated by a surface referred to as the [[geoid]], which takes into consideration the gravitational force exerted by the earth as well as [[centrifugal force]] due 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 ===
The '''equilibrium tide''' is the idealized tide assuming a landless Earth.<ref name="AMS Glossary 2020">{{cite web |title=Equilibrium tide |website=AMS Glossary |date=2020-09-02 |url=http://glossary.ametsoc.org/wiki/Equilibrium_tide |access-date=2020-09-02 |archive-date=2020-08-01 |archive-url=https://web.archive.org/web/20200801165541/http://glossary.ametsoc.org/wiki/Equilibrium_tide |url-status=live }}</ref>
It would produce a tidal bulge in the ocean, elongated towards the attracting body (Moon or Sun).
It is ''not'' caused by the vertical pull nearest or farthest from the body, which is very weak; rather, it is caused by the
{{efn|"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."<ref name="Hicks2006">{{cite report |last=Hicks |first=S.D. |title=Understanding Tides |publisher=[[NOAA]] |year=2006 |url=https://tidesandcurrents.noaa.gov/publications/Understanding_Tides_by_Steacy_finalFINAL11_30.pdf |language=en |access-date=2020-09-02 |archive-date=2022-01-20 |archive-url=https://web.archive.org/web/20220120232639/http://www.tidesandcurrents.noaa.gov/publications/Understanding_Tides_by_Steacy_finalFINAL11_30.pdf |url-status=live }}</ref>}}
{{efn|"... 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."<ref>{{cite book |first=James Greig |last=Mccully |date=2006 |title=Beyond The Moon: A Conversational, Common Sense Guide To Understanding The Tides, World Scientific |publisher=World Scientific |isbn=9789814338189 |url=https://books.google.com/books?id=aKLICgAAQBAJ&q=tractal |via=[[Google Books]] |access-date=2022-01-05 |archive-date=2023-09-16 |archive-url=https://web.archive.org/web/20230916153030/https://books.google.com/books?id=aKLICgAAQBAJ&q=tractal |url-status=live }}</ref>}}<ref name="PBS LearningMedia 2020">{{cite web |title=What Physics Teachers Get Wrong about Tides! - PBS Space Time |website=[[PBS]] LearningMedia |date=2020-06-17 |url=https://www.pbslearningmedia.org/resource/what-physics-teachers-pbs-space-time/what-physics-teachers-pbs-space-time/ |access-date=2020-06-27 |archive-date=2020-10-21 |archive-url=https://web.archive.org/web/20201021020010/https://www.pbslearningmedia.org/resource/what-physics-teachers-pbs-space-time/what-physics-teachers-pbs-space-time/ |url-status=live }}</ref>
=== Laplace's tidal equations ===
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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 underwater [[bathymetry]] and 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 lunar [[altitude (astronomy)|altitude]] and the time of high or low tide (the [[lunitidal 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 at [[Norfolk, 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.<ref name=noaa7b>{{cite web |website=U.S. [[National Oceanic and Atmospheric Administration]] (NOAA) National Ocean Service (Education section) |url=http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide07b.html |title=map showing world distribution of tide patterns, semi-diurnal, diurnal and mixed semi-diurnal |access-date=2009-09-05 |archive-date=2018-08-27 |archive-url=https://web.archive.org/web/20180827211303/http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide07b.html |url-status=live }}</ref><ref>{{cite book |first=H.V. |last=Thurman |date=1994 |title=Introductory Oceanography |edition=7th |location=New York |publisher=[[Macmillan Publishers]] |pages=252–276}}ref</ref><ref>{{cite book |first=D.A. |last=Ross |date=1995 |title=Introduction to Oceanography |location=New York |publisher=[[HarperCollins]] |pages=236–242}}</ref> Human changes to the landscape can also significantly alter local tides.<ref>{{cite news |last1=Witze |first1=Alexandra |title=How humans are altering the tides of the oceans |url=https://www.bbc.com/future/article/20200703-how-humans-are-altering-the-tides-of-the-oceans |access-date=8 July 2020 |work=BBC Future |publisher=[[BBC]] |date=5 July 2020 |archive-date=6 July 2020 |archive-url=https://web.archive.org/web/20200706134113/https://www.bbc.com/future/article/20200703-how-humans-are-altering-the-tides-of-the-oceans |url-status=live }}</ref>
== Observation and prediction ==
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=== Timing ===
[[File:Diurnal tide types map.jpg|thumb|The same tidal forcing has different results depending on many factors, including coast orientation, continental shelf margin, water body dimensions.|alt=World map showing the location of diurnal, semi-diurnal, and mixed semi-diurnal tides. The European and African west coasts are exclusively semi-diurnal, and North America's West coast is mixed semi-diurnal, but elsewhere the different patterns are highly intermixed, although a given pattern may cover {{convert|200|-|2000|km|mi}}.]]
The tidal forces due to the Moon and Sun generate very long waves which travel all around the ocean following the paths shown in [[#Phase and amplitude|co-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 the [[North Sea]], for example, are two days behind the new/full moon and first/third quarter moon. This is called the tide's ''age''.<ref>{{cite web |url=https://glossary.ametsoc.org/wiki/Age |title=Glossary of Meteorology |website=[[American Meteorological Society]] |access-date=2021-04-02 |archive-date=2021-05-08 |archive-url=https://web.archive.org/web/20210508194219/https://glossary.ametsoc.org/wiki/Age |url-status=live }}</ref><ref>{{cite book
|title=The elements of physics |first1=Thomas |last1=Webster |publisher=Printed for Scott, Webster, and Geary |date=1837 |page=[https://archive.org/details/elementsphysics00websgoog/page/n184 168] |url=https://archive.org/details/elementsphysics00websgoog}}</ref>
The ocean [[bathymetry]] greatly influences the tide's exact time and height at a particular [[coast]]al point. There are some extreme cases; the [[Bay 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.<ref>{{cite web |url=http://www.waterlevels.gc.ca/english/FrequentlyAskedQuestions.shtml#importantes |title=FAQ |access-date=June 23, 2007 |archive-date=February 12, 2012 |archive-url=https://web.archive.org/web/20120212231548/http://www.waterlevels.gc.ca/english/FrequentlyAskedQuestions.shtml#importantes |url-status=dead}}</ref> Measurements made in November 1998 at Burntcoat Head in the Bay of Fundy recorded a maximum range of {{convert|16.3|m|ft}} and a highest predicted extreme of {{convert|17|m|ft}}.<ref name=BIO2004>{{cite journal |last1=O'Reilly |first1=C.T.R. |first2=Ron |last2=Solvason |first3=Christian |last3=Solomon |name-list-style=amp |title=Where are the World's Largest Tides |journal=BIO Annual Report "2004 in Review" |date=2005 |pages=44–46 |editor1-first=J. |editor1-last=Ryan |publisher=Biotechnol. Ind. Org. |location=Washington, D.C.}}</ref><ref name=FundyWorkshop>{{cite book |first1=Charles T. |last1=O'reilly |first2=Ron |last2=Solvason |first3=Christian |last3=Solomon |chapter-url=http://www.bofep.org/PDFfiles/BoFEP6thProceedings.pdf |chapter=Resolving the World's largest tides |editor1-first=J.A |editor1-last=Percy |editor2-first=A.J. |editor2-last=Evans |editor3-first=P.G. |editor3-last=Wells |editor4-first=S.J. |editor4-last=Rolston |date=2005 |title=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. |access-date=April 1, 2013 |archive-date=August 27, 2016 |archive-url=https://web.archive.org/web/20160827202033/http://www.bofep.org/PDFfiles/BoFEP6thProceedings.pdf |url-status=live }}</ref> Similar measurements made in March 2002 at Leaf Basin, [[Ungava Bay]] in northern [[Quebec]] gave similar values (allowing for measurement errors), a maximum range of {{convert|16.2|m|ft}} and a highest predicted extreme of {{convert|16.8|m|ft}}.<ref name=BIO2004 /><ref name=FundyWorkshop /> Ungava Bay and the Bay of Fundy lie similar distances from the continental shelf edge, but Ungava Bay is only free of [[pack ice]] for about four months every year while the Bay of Fundy rarely freezes.
[[Southampton]] in the United Kingdom has a double high water caused by the interaction between the ''M''<sub>2</sub> and [[Theory of tides#Short period|''M''<sub>4</sub> tidal constituents]] (Shallow water overtides of principal lunar).<ref name=Pingree_1978>{{cite journal |last1=Pingree |first1=R.D. |first2=L. |last2=Maddock |title=Deep-Sea Research |year=1978 |volume=25 |pages=53–63}}</ref> [[Isle of Portland|Portland]] has double low waters for the same reason. The ''M''<sub>4</sub> tide is found all along the south coast of the United Kingdom, but its effect is most noticeable between the [[Isle of Wight]] and [[Isle of Portland|Portland]] because the ''M''<sub>2</sub> tide is lowest in this region.
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Remember that astronomical tides do ''not'' include 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 Fourier [[data analysis]] over a nineteen-year period (the ''National Tidal Datum Epoch'' in the U.S.) uses frequencies called the ''tidal harmonic constituents''. Nineteen years is preferred because the Earth, Moon and Sun's relative positions repeat almost exactly in the [[Metonic cycle]] of 19 years, which is long enough to include the 18.613 year [[Lunar node|lunar nodal]] [[Earth tide#Tidal constituents|tidal constituent]]. This analysis can be done using only the knowledge of the forcing ''period'', but without detailed understanding of the mathematical derivation, which means that useful tidal tables have been constructed for centuries.<ref>{{cite web |url=http://tidesandcurrents.noaa.gov/publications/glossary2.pdf |title=Tide and Current Glossary |author=Center for Operational Oceanographic Products and Services, National Ocean Service, [[National Oceanic and Atmospheric Administration]] |location=Silver Spring, MD |date=January 2000 |access-date=2007-04-05 |archive-date=2007-01-28 |archive-url=https://web.archive.org/web/20070128171521/http://tidesandcurrents.noaa.gov/publications/glossary2.pdf |url-status=live }}</ref> The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the ''semi-diurnal'' constituents), but there are major constituents near 24 hours (''diurnal'') as well. Longer term constituents are 14 day or ''fortnightly'', monthly, and semiannual. Semi-diurnal tides dominated coastline, but some areas such as the [[South China Sea]] and the [[Gulf of Mexico]] are primarily diurnal. In the semi-diurnal areas, the primary constituents ''M''<sub>2</sub> (lunar) and ''S''<sub>2</sub> (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).<ref>{{Cite web |url=http://tidesandcurrents.noaa.gov/harmonic_cons_defs.html |title=Harmonic Constituents |website=[[NOAA]] |access-date=2007-04-05 |archive-date=2007-03-17 |archive-url=https://web.archive.org/web/20070317043911/http://tidesandcurrents.noaa.gov/harmonic_cons_defs.html |url-status=live }}</ref>
In the ''M''<sub>2</sub> plot 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 the [[amphidromic point]]s counterclockwise in the northern hemisphere so that from [[Baja California Peninsula]] to [[Alaska]] and from [[France]] to [[Ireland]] the ''M''<sub>2</sub> tide propagates northward. In the southern hemisphere this direction is clockwise. On the other hand, ''M''<sub>2</sub> tide 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.)
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A further complication for Cook Strait's flow pattern is that the tide at the south side (e.g. at [[Nelson, New Zealand|Nelson]]) 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 only ''one'' cycle per month, as on the east side: [[Wellington]], and [[Napier, New Zealand|Napier]].
The graph of Cook Strait's tides shows separately the high water and low water height and time, through November 2007; these are ''not'' measured 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 for {{coord|41
=== Power generation ===
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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 significant [[Draft (hull)|draft]] from 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 the [[Royal Navy]] once declared that the prospective officer was able to "shift his tides".<ref>{{cite book |title=The Mariner's Mirror |url=https://books.google.com/books?id=lagPAAAAIAAJ&q=%22shift+his+tides%22 |author=Society for Nautical Research |date=1958 |access-date=2009-04-28 |via=[[Google Books]] |archive-date=2023-09-16 |archive-url=https://web.archive.org/web/20230916153531/https://books.google.com/books?id=lagPAAAAIAAJ&q=%22shift+his+tides%22 |url-status=live }}</ref>
Tidal flow timings and velocities appear in ''tide charts'' or a [[tidal 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 in [[Knot (unit)|knots]]) for spring and neap tides. If a tide chart is not available, most nautical charts have "[[tidal diamond]]s" which relate specific points on the chart to a table giving tidal flow direction and speed.
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=== Biological rhythms ===
The approximately 12-hour and fortnightly tidal cycle has large effects on intertidal<ref>{{cite journal |last1=Bos |first1=A.R. |last2=Gumanao |first2=G.S. |last3=van Katwijk |first3=M.M. |last4=Mueller |first4=B. |last5=Saceda |first5=M.M. |last6=Tejada |first6=R.P. |name-list-style=amp |date=2011 |title=Ontogenetic habitat shift, population growth, and burrowing behavior of the Indo-Pacific beach star ''Archaster typicus'' (Echinodermata: Asteroidea) |journal=[[Marine Biology (journal)|Marine Biology]] |volume=158 |issue=3 |pages=639–648 |doi=10.1007/s00227-010-1588-0 |pmid=24391259 |pmc=3873073|bibcode=2011MarBi.158..639B }}</ref> and marine organisms.<ref>{{cite journal |last1=Bos |first1=A.R. |last2=Gumanao |first2=G.S. |name-list-style=amp |date=2012 |title=The lunar cycle determines availability of coral reef fishes on fish markets |journal=[[Journal of Fish Biology]] |volume=81 |issue=6 |pages=2074–2079 |doi=10.1111/j.1095-8649.2012.03454.x |pmid=23130702|bibcode=2012JFBio..81.2074B }}</ref> Hence their [[biological rhythm]]s tend to occur in rough multiples of these periods.<ref>{{Cite book |last=Naylor |first=Ernest |url=https://books.google.com/books?id=7zLqjQlzM60C |title=Chronobiology of Marine Organisms |date=2010-02-04 |publisher=[[Cambridge University Press]] |isbn=978-1-139-48494-7 |language=en |chapter=Chapter 5: Lunar and semilunar biorhythms |via=[[Google Books]] |access-date=2022-01-03 |archive-date=2023-09-16 |archive-url=https://web.archive.org/web/20230916153532/https://books.google.com/books?id=7zLqjQlzM60C |url-status=live }}</ref> Many other animals such as the [[vertebrate]]s, display similar circatidal rhythms.<ref>{{Cite journal |last1=Zhu |first1=Bokai |last2=Dacso |first2=Clifford C. |last3=
== Other tides ==
When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate [[internal wave]]s with tidal frequencies. Such waves are called ''[[internal tide]]s''.
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 in {{frac|12|1|2}} hours (for example, the [[Nantucket Shoals]]).<ref name=rocur>{{cite journal |last=Le Lacheur |first=Embert A. |url=https://www.jstor.org/pss/208104 |title=Tidal currents in the open sea: Subsurface tidal currents at Nantucket Shoals Light Vessel |journal=[[Geographical Review]] |date=April 1924 |volume=14 |issue=2 |pages=282–286 |doi=10.2307/208104 |jstor=208104 |bibcode=1924GeoRv..14..282L |access-date=4 February 2012 |archive-date=16 September 2023 |archive-url=https://web.archive.org/web/20230916153559/https://www.jstor.org/stable/208104 |url-status=live }}</ref>
In addition to oceanic tides, large lakes can experience small tides and even planets can experience ''[[atmospheric tide]]s'' and ''[[Earth tide]]s''. These are [[continuum mechanics|continuum mechanical]] phenomena. The first two take place in [[fluid mechanics|fluid]]s. The third affects the Earth's thin [[Solid mechanics|solid]] crust surrounding its semi-liquid interior (with various modifications).
=== Lake tides ===
Large lakes such as [[Lake Superior|Superior]] and [[Lake Erie|Erie]] can experience tides of {{convert|1|to|4|cm|in|abbr=on|sigfig=2}}, but these can be masked by meteorologically induced phenomena such as [[seiche]].<ref>{{cite web |title=Do the Great Lakes have tides? |date=October 1, 2000 |url=http://www.great-lakes.net/teach/chat/answers/100100_tides.html |publisher=Great Lakes Information Network |access-date=2010-02-10 |archive-date=2017-12-30 |archive-url=https://web.archive.org/web/20171230003511/http://www.great-lakes.net/teach/chat/answers/100100_tides.html |url-status=dead}}</ref> The tide in [[Lake Michigan]] is described as {{convert|0.5|to|1.5|in|cm|abbr=on|order=flip}}<ref>{{cite web |last=Calder |first=Vince |title=Tides on Lake Michigan |url=https://wat.lewiscollard.com/archive/www.newton.dep.anl.gov/askasci/phy00/phy00330.htm |publisher=Argonne National Laboratory |access-date=2019-08-14 |archive-date=2019-08-15 |archive-url=https://web.archive.org/web/20190815033734/https://wat.lewiscollard.com/archive/www.newton.dep.anl.gov/askasci/phy00/phy00330.htm |url-status=live }}</ref> or {{convert|1+3/4|in|cm|order=flip|abbr=on}}.<ref>{{cite web |title=moon and Tides |url=http://www.thespaceguy.com/moontides.htm |publisher=Astronomy Briefly |last=Dunkerson |first=Duane |access-date=2010-02-10 |archive-date=2010-01-15 |archive-url=https://web.archive.org/web/20100115000607/http://www.thespaceguy.com/moontides.htm |url-status=live }}</ref> This is so small that other larger effects completely mask any tide, and as such these lakes are considered non-tidal.<ref>{{cite web |title=Do the Great Lakes have tides? |url=http://oceanservice.noaa.gov/facts/gltides.html |website=National Ocean Service |publisher=[[NOAA]] |access-date=2016-04-26 |archive-date=2016-04-23 |archive-url=https://web.archive.org/web/20160423224702/http://oceanservice.noaa.gov/facts/gltides.html |url-status=live }}</ref>
=== Atmospheric tides ===
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== Further reading ==
{{refbegin}}
* [http://tidesandcurrents.noaa.gov/publications/150_years_of_tides.pdf 150 Years of Tides on the Western Coast: The Longest Series of Tidal Observations in the Americas] {{Webarchive|url=https://web.archive.org/web/20110505153935/http://tidesandcurrents.noaa.gov/publications/150_years_of_tides.pdf |date=2011-05-05 }} NOAA (2004).
* [http://faculty.ifmo.ru/butikov/Projects/tides1.pdf Eugene I. Butikov: ''A dynamical picture of the ocean tides''] {{Webarchive|url=https://web.archive.org/web/20080911141308/http://faculty.ifmo.ru/butikov/Projects/tides1.pdf |date=2008-09-11 }}
* [http://www.vialattea.net/maree/eng/index.htm Tides and centrifugal force] {{Webarchive|url=https://web.archive.org/web/20070512004000/http://www.vialattea.net/maree/eng/index.htm |date=2007-05-12 }}: Why the centrifugal force does not explain the tide's opposite lobe (with nice animations).
* [https://arxiv.org/abs/astro-ph/0610563v1 O. Toledano ''et al.'' (2008): ''Tides in asynchronous binary systems''] {{Webarchive|url=https://web.archive.org/web/20170809040314/https://arxiv.org/abs/astro-ph/0610563v1 |date=2017-08-09 }}
* Gaylord Johnson [https://books.google.com/books?id=uSgDAAAAMBAJ&pg=PA50 "How Moon and Sun Generate the Tides"] {{Webarchive|url=https://web.archive.org/web/20230916153532/https://books.google.com/books?id=uSgDAAAAMBAJ&pg=PA50 |date=2023-09-16 }} ''Popular Science'', April 1934
{{refend}}
* {{cite book |last1=Simon |first1=Bernard |translator-last=Manley |translator-first=David |year=2013 |orig-date=2007 |title=Coastal Tides |url=https://diffusion.shom.fr/pro/coastal-tides-version-anglaise-de-la-maree-oceanique-cotiere.html |publisher=[[Institut océanographique, Fondation Albert Ier, Prince de Monaco]] |isbn=978-2-903581-83-1 |access-date=2021-10-18 |archive-date=2022-11-13 |archive-url=https://web.archive.org/web/20221113030309/https://diffusion.shom.fr/pro/coastal-tides-version-anglaise-de-la-maree-oceanique-cotiere.html |url-status=dead }}
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