Editing Tide (section)

=== 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.