Editing Tide (section)

== Tidal constituents{{anchor|Constituents}} == <!-- [[tidal constituent]] and [[tidal constituents]] redirect here -->
{{further|Theory of tides#Tidal constituents|Long-period tides}}
{{see also|Earth tide#Tidal constituents}}

''Tidal constituents'' are 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, and [[bathymetry]]. Variations with periods of less than half a day are called ''harmonic constituents''. Conversely, cycles of days, months, or years are referred to as ''long period'' constituents.

Tidal forces [[Earth tide|affect 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 ===
[[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.

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.

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 (see [[equilibrium 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.

[[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.]]

When there are two high tides each day with different heights (and two low tides also of different heights), the pattern is called a ''mixed semi-diurnal tide''.<ref name=noaa7>{{cite web |publisher=[[National Oceanic and Atmospheric Administration|U.S. National Oceanic and Atmospheric Administration]] (NOAA) National Ocean Service (Education section) |url=http://oceanservice.noaa.gov/education/kits/tides/tides07_cycles.html |title=Types and causes of tidal cycles |archive-url=https://web.archive.org/web/20120201145550/http://oceanservice.noaa.gov/education/kits/tides/tides07_cycles.html |archive-date=February 1, 2012}}</ref>

=== Lunar distance ===
[[File:Bangchuidao Island.JPG|thumb|Low tide at Bangchuidao scenic area, [[Dalian]], [[Liaoning Province]], [[China]]]]
[[File:Negative low tide at Ocean Beach 1.jpg|thumb|Low tide at [[Ocean Beach, San Francisco, California|Ocean Beach]] in [[San Francisco]], [[California]], U.S.]]
[[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 ===
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.<ref name="leprovost">{{cite book |last=Le Provost |first=Christian |date=1991 |chapter=Generation of Overtides and compound tides (review) |editor1-last=Parker |editor1-first=Bruce B. |title=Tidal Hydrodynamics |publisher=[[John Wiley & Sons]] |isbn=978-0-471-51498-5}}</ref>

=== 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. Around these convergences, called [[amphidromic point]]s, curved arrows show the direction of the tides, each indicating a synchronized 6-hour period. Tidal ranges generally increase with increasing distance from amphidromic points. Tide waves move around these points, generally counterclockwise in the N. Hemisphere and clockwise in the S. Hemisphere <ref>{{cite journal |title=Solution of the Tidal Equations for the M<sub>2</sub> and S<sub>2</sub> Tides in the World Oceans from a Knowledge of the Tidal Potential Alone |journal=Philosophical Transactions of the Royal Society of London A |volume=290 |issue=1368 |date=November 28, 1978 |pages=235–266 |last1=Accad |first1=Y. |last2=Pekeris |first2=C.L. |name-list-style=amp |doi=10.1098/rsta.1978.0083 |bibcode=1978RSPTA.290..235A |s2cid=119526571}}</ref><ref>{{cite web |url=http://www.niwa.cri.nz/rc/prog/chaz/news/coastal#tide |title=Tide forecasts |publisher=National Institute of Water & Atmospheric Research |location=New Zealand |access-date=2008-11-07 |url-status=dead |archive-url=https://web.archive.org/web/20081014152423/http://www.niwa.cri.nz/rc/prog/chaz/news/coastal#tide |archive-date=2008-10-14}} Including animations of the M2, S2 and K1 tides for New Zealand.
</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.