Tide: Wikis

  
  
  



























































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Photo of boat in water next to a dock
The Bay of Fundy at high tide
Photo of boat resting on bottom next to dock
The Bay of Fundy at low tide
.Tides are the rise and fall of sea levels caused by the combined effects of the rotation of the Earth and the gravitational forces exerted by the Moon and the Sun.^ Tides - The periodic rise and fall of a body of water resulting from gravitational interactions among the sun, moon, and earth.

^ The tides are the regular rising and falling of sea level.
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

^ The tidal forces produced by the Moon and Sun, in combination with Earth's rotation, are responsible for the generation of the tides.
  • Tidal Power 20 September 2009 13:12 UTC www.tqnyc.org [Source type: Reference]

.The tides occur with a period of approximately 12 and a half hours and are influenced by the shape of the near-shore bottom.^ The tides occur with a period of approximately 12 and a half hours and are influenced by the shape of the near-shore bottom .
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ These rapid changes occur at exactly the same periods as the tides themselves -- half-daily, daily, etc.
  • Tides and the Earth's Rotation 19 September 2009 20:15 UTC bowie.gsfc.nasa.gov [Source type: Academic]

^ Semi-diurnal tides have a period of 12 hrs and 25 min, and theoretically have a wavelength of more than half the circumference of Earth.
  • Ocean Motion : Background :Types of Tides 19 September 2009 20:15 UTC oceanmotion.org [Source type: Academic]

[1][2][3]
.Most coastal areas experience two daily high (and two low) tides.^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

^ Frequency of Tides - Most coastal areas, with some exceptions, experience two high tides and two low tides every lunar day.

^ Certain locations have two high and two low tides per day.

.This is because at the point right "under" the Moon (the sub-lunar point), the water is at its closest to the Moon, so it experiences stronger gravity and rises.^ This is because at the point right "under" the Moon (the sub-lunar point), the water is at its closest to the Moon, so it experiences stronger gravity and rises.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ At the point right "under" the Moon, the water is closer than the solid Earth; so it is pulled more and rises.
  • Deltawerken - Tidal physics 20 September 2009 13:12 UTC www.deltawerken.com [Source type: FILTERED WITH BAYES]

^ Here, follow a step-through animation that explains why water rises on the side of the Earth away from the moon.
  • NOVA | Sinking City of Venice | What Causes the Tides? | PBS 19 September 2009 20:15 UTC www.pbs.org [Source type: FILTERED WITH BAYES]

.On the opposite side of the Earth (the antipodal point), the water is at its farthest from the moon, so it is pulled less; at this point the Earth moves more toward the Moon than the water does—causing that water to "rise" (relative to the Earth) as well.^ Because the earth is spinning there will be a bulge on the opposite side of the earth as well.
  • Why Tides? 19 September 2009 20:15 UTC www.sfgate.com [Source type: FILTERED WITH BAYES]

^ The moon’s gravity pulls more strongly on the side of Earth that faces it and causes the water here to bulge.
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

^ On the opposite side of the Earth (the antipodal point), the water is at its farthest from the moon, so it is pulled less; at this point the Earth moves more toward the Moon than the water does—causing that water to "rise" (relative to the Earth) as well.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.In between the sub-lunar and antipodal points, the force on the water is diagonal or transverse to the sub-lunar/antipodal axis (and always towards that axis), resulting in low tide.^ In between the sub-lunar and antipodal points, the force on the water is diagonal or transverse to the sub-lunar/antipodal axis (and always towards that axis), resulting in low tide.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ The period of tide between high water and low water.
  • Glossary of Ocean Terms -- Beach-Net 20 September 2009 12:18 UTC www.beach-net.com [Source type: FILTERED WITH BAYES]

^ Some waters are not navigable at low tide.
  • Puget Sound Shorelines: Beaches - Tides 19 September 2009 20:15 UTC www.ecy.wa.gov [Source type: FILTERED WITH BAYES]

[4]
.Tide prediction is important for coastal navigation.^ Tide prediction is important for coastal navigation .
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Tide predictions are important for fun and safety .
  • San Diego Tides 19 September 2009 20:15 UTC www.hribar.com [Source type: General]

^ Because the depth of coastal waters is important for navigation, an average low-water reference is established.

.The intertidal zone, the strip of seashore that high tide submerges and low tide exposes, is an important ecological product of ocean tides.^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

^ High tide or low tide Lyrics .
  • BEN HARPER - HIGH TIDE OR LOW TIDE LYRICS 17 September 2009 11:40 UTC www.metrolyrics.com [Source type: General]

^ The strip of seashore that is submerged at high tide and exposed at low tide, the intertidal zone , is an important ecological product of ocean tides (see Intertidal ecology ).
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

.While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in storm surges, especially in shallow seas and near coasts.^ Near-open Coast Tide Stations .
  • USGS Open-File Report 2005-1027, An Operational Mean High Water Datum for Determination of Shoreline Position from Topographic Lidar Data, Data Set and Methods 19 September 2009 20:15 UTC pubs.usgs.gov [Source type: FILTERED WITH BAYES]

^ A tide prediction can differ from the actual sea level that will be observed as a result of the tide.

^ While tides are usually the largest source of short-term sea-level fluctuations, sea levels are also subject to forces such as wind and barometric pressure changes, resulting in storm surge s, especially in shallow seas and near coasts.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.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.^ 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.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ More generally, tidal phenomena can occur in other systems besides the ocean, whenever a gravitational field that varies in time and space is present (see Other tides ).
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ The whole system was time synchronized such that the pencil tracings of the risings and fallings of the tide could later be scaled to determine the heights and times of various stages of the tides.

.For example, the solid part of the Earth is affected by tides.^ For example, the solid part of the Earth is affected by tides.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Solid earth tides .

^ For example, irregularities in the Bay of Fundy and the northern part of the Gulf of California cause tides of exceedingly high ranges, 50 and 30 feet, respectively.

Contents

Characteristics

Three graphs. <a name=.The first shows the twice-daily rising and falling tide pattern with nearly regular high and low elevations.^ The tides are the regular rising and falling of sea level.
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

^ If so, then you are familiar with its regular rise and fall.
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

.The second shows the much more variable high and low tides that form a "mixed tide".^ Which picture shows high tide?

^ So, when this occurs there is little variation between a high and low tide.
  • Untitled Document 15 September 2009 3:03 UTC www.padillabay.gov [Source type: FILTERED WITH BAYES]

^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

.The third shows the day-long period of a diurnal tide."^ In other regions, such as the Gulf of Mexico, there is only one high tide per day called a diurnal tide, with a period of 24 hr and 50 min.
  • tide Facts, information, pictures | Encyclopedia.com articles about tide 18 January 2010 0:43 UTC www.encyclopedia.com [Source type: FILTERED WITH BAYES]
  • Tide - Facts from the Encyclopedia - Yahoo! Education 18 January 2010 0:43 UTC education.yahoo.com [Source type: FILTERED WITH BAYES]

^ True tidal waves, also known as tide waves, are long-period waves associated with the tide-producing forces of the moon and the sun and which are identified with the rising and falling of the tide.
  • What is the difference between a tidal wave and a tsunami? 20 September 2009 13:12 UTC www.funtrivia.com [Source type: General]

^ This happens two times a day (this is called a semi-diurnal tide,) unless, in rare cases, a location experiences a diurnal tide which is when there's only one high tide and one low tide a day.

src="http://images-mediawiki-sites.thefullwiki.org/11/1/1/2/91369393828223573.gif" width="300" height="415" class="thumbimage" />
Fig. 1: Types of tides
Tide changes proceed via the following stages:
  • Sea level rises over several hours, covering the intertidal zone; flood tide.
  • The water rises to its highest level, reaching high tide.
  • Sea level falls over several hours, revealing the intertidal zone; ebb tide.
  • The water stops falling, reaching low tide.
.Tides produce oscillating currents known as tidal streams.^ Tides produce oscillating currents known as tidal streams.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Accompanying the vertical rise and fall of water are various horizontal or lateral movements commonly known as tidal currents or tidal streams, which are very different from the common ocean currents.
  • Tides, Clam Tides, Tide Tables for Long Beach WA, ocean park wa, klipsan beach, leadbetter point, baker bay, ilwaco, seaview, surfside 19 September 2009 20:15 UTC www.funbeach.com [Source type: FILTERED WITH BAYES]

^ Print this section Accompanying the vertical rise and fall of water are various horizontal or lateral movements commonly known as tidal currents or tidal streams, which are very different from the common ocean currents ( see Ocean and Oceanography ).
  • Tide - MSN Encarta 19 September 2009 20:15 UTC encarta.msn.com [Source type: FILTERED WITH BAYES]
  • Tide - MSN Encarta 19 September 2009 20:15 UTC ca.encarta.msn.com [Source type: FILTERED WITH BAYES]

.The moment that the tidal current ceases is called slack water or slack tide.^ Because tidal currents cease this is also called slack water or slack tide.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ This is not the same as slack water; this is a tidal (vertical) occurence, not a tidal current (horizontal) occurence.

^ This is called slack water .

.The tide then reverses direction and is said to be turning.^ The tide reverses direction and is said to be turning.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ The tide then reverses direction and is said to be turning.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.Slack water usually occurs near high water and low water.^ The arithmetic mean of mean high water and mean low water.

^ Slack water usually occurs near high water and low water.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ How High tides and Low Tides Occur?
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

.But there are locations where the moments of slack tide differ significantly from those of high and low water.^ The difference between high tide and low tide is called the tide range.

^ So, when this occurs there is little variation between a high and low tide.
  • Untitled Document 15 September 2009 3:03 UTC www.padillabay.gov [Source type: FILTERED WITH BAYES]

^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

[5]
.Tides are most commonly semidiurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day).^ In parts of the northern Gulf of Mexico and Southeast Asia, tides have one high and one low water per tidal day.
  • When does the high tide & low tide happens in the sea? - Yahoo! Answers 18 January 2010 0:43 UTC answers.yahoo.com [Source type: General]

^ The equilibrium tidal theory predicts tides that are semidiurnal, which means two high and two low tides each day.

^ Low tide: High Tide: .
  • The Physics of Tides 19 September 2009 20:15 UTC www.iit.edu [Source type: FILTERED WITH BAYES]

.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 tables.^ In a mixed system, it refers to higher high and lower high water and higher low and lower low waters.

^ The difference in height of the two high waters of each tidal day for a mixed or semidiurnal tide.

^ Thus the two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), and again.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.Similarly, the two low waters each day are the higher low water and the lower low water.^ In a mixed system, it refers to higher high and lower high water and higher low and lower low waters.

^ In these tides, we have a higher high-water and lower high-water as well as higher low-water and lower low-water.
  • Tide - Encyclopedia of Earth 18 January 2010 0:43 UTC www.eoearth.org [Source type: Academic]

^ The arithmetic mean of mean higher high water and mean lower low water.

.The daily inequality is not consistent and is generally small when the Moon is over the equator.^ The daily inequality changes with time and is generally small when the Moon is over the equator .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ The daily inequality is not consistent and is generally small when the Moon is over the equator .
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ We have seen in § 13 that the potential of the tide-generating force of the moon consists of three terms, one being approximately semi-diurnal, one approximately diurnal, and one varying slowly.

[6]

Tidal constituents

.Tidal changes are the net result of multiple influences that act over varying periods.^ As a result, tidal patterns vary.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Tidal changes are the net result of multiple influences that act over varying periods.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Changing tidal flows by damming a bay or estuary could, however, result in negative impacts on aquatic and shoreline ecosystems, as well as navigation and recreation.
  • Tidal Energy | Pros for Wave and Tidal Power 20 September 2009 13:12 UTC www.oceanenergycouncil.com [Source type: FILTERED WITH BAYES]

.These influences are called tidal constituents.^ These influences are called tidal constituents.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ 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 .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ The various frequencies of orbital forcing which contribute to tidal variations are called constituents .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

.Tides vary on timescales ranging from hours to years.^ Tides vary on timescales ranging from hours to years.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Tides vary on timescales ranging from hours to years, so to make accurate records tide gauges measure the water level over time at fixed stations which are screened from variations caused by waves shorter than minutes in period.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ Spring tides are when the range from high tide to low tide (about a six hour period) is most different.
  • How does the tidal range change from neap to spring tide and from... 15 September 2009 3:03 UTC www.answerbag.com [Source type: General]

.To make accurate records tide gauges at fixed stations measure the water level over time.^ Water depths are measured from this level and recorded on navigational charts.

^ Tides vary on timescales ranging from hours to years, so to make accurate records tide gauges measure the water level over time at fixed stations which are screened from variations caused by waves shorter than minutes in period.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ To make accurate records tide gauges at fixed stations measure the water level over time.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.The gauges ignore variations caused by waves with periods shorter than minutes.^ The gauges ignore variations caused by waves with periods shorter than minutes.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Tides vary on timescales ranging from hours to years, so to make accurate records tide gauges measure the water level over time at fixed stations which are screened from variations caused by waves shorter than minutes in period.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ Real amplitudes differ considerably, not only because of variations in ocean depth, and the obstacles to flow caused by the continents, but also because the natural period of wave propagation is of the same order of magnitude as the rotation period: about 30 hours.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

.These data are compared to the reference (or datum) level usually called mean sea level.^ These data are compared to the reference (or datum) level usually called mean sea level.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ A synonym for Sea-level Datum of 1929.

^ These data are compared to the reference (or datum) level usually called mean sea level .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

[7]

Principal lunar semidiurnal constituent

.In most locations, the largest constituent is the "principal lunar semidiurnal", also known as the M2 (or M2) tidal constituent.^ In most locations, tides are semidiurnal .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ In most locations, the largest is the "principal lunar semidiurnal" constituent, also known as the M2 (or M 2 ) tidal constituent.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ Smaller lunar elliptic semidiurnal 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.^ The wavelength of the two tidal waves is one-half the circumference of Earth.

^ 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.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ The earth rotates once a day.

.This is the constituent tracked by simple tide clocks.^ This is the constituent tracked by simple tide clock s.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ This is the constituent tracked by simple tide clocks .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

.The lunar day is longer than the earth day because the Moon orbits in the same direction the Earth spins.^ Earth and the Moon are moving in the same direction along their orbit with the Sun.

^ While the earth is turning the moon moves in its orbit.

^ This is because the earth is not only turning on its own axis, but the moon and earth are also rotating on their common barycenter, which means that the moon is not at the same location after 24 hours, but has moved 12.2 degrees to the east, and the earth must rotate another 50 minutes for the moon to come overhead again.

.Compare this to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05 (not at 1:00).^ Compare this to the minute hand on a watch crossing the hour hand at 12:00 and then again at about 1:05 (not at 1:00).
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ The long opening scene of HAL on the beach is all about process as we watch his daily routine over a period of perhaps hours or even weeks.

^ 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.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

Range variation: springs and neaps

The types of tides
.The semidiurnal tidal range (the difference in height between high and low waters over about a half day) varies in a two-week cycle.^ The equilibrium tidal theory predicts tides that are semidiurnal, which means two high and two low tides each day.

^ So, when this occurs there is little variation between a high and low tide.
  • Untitled Document 15 September 2009 3:03 UTC www.padillabay.gov [Source type: FILTERED WITH BAYES]

^ That's a difference of two hours between high tide in the two locations.

.Around new and full moon when the Sun, Moon and Earth form a line (a condition known as syzygy[8] ), the tidal force due to the Sun reinforces that due to the Moon.^ Notice that this is around the time of the full moon AND when the moon is nearest the Earth.

^ Then explain that a spring tide is when the sun, earth, and moon are aligned (new and full moon).
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^ At full and new phases of the moon the Sun and Moon pull together.

.The tide's range is then at its maximum: this is called the spring tide, or just springs.^ The tide's range is then at its maximum: this is called the spring tide , or just springs .
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ This is called spring tide .
  • OceanLink | Ocean Info - Tides 19 September 2009 20:15 UTC oceanlink.island.net [Source type: FILTERED WITH BAYES]

^ The maximum range of the tide at Aden is 8 ft.

.It is not named after the season but, like that word, derives from an earlier meaning of "jump, burst forth, rise" as in a natural spring.^ It is not named after the season but, like that word, derives from an earlier meaning of "jump, burst forth, rise" as in a natural spring .
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Neap rise " is used to mean the average height between high-water of neap tides and low-water of spring tides.

^ The word is derived from the Greek klima, meaning inclination, and reflects the importance early scholars attributed to the sun's influence.
  • weather.com - Glossary 15 September 2009 3:03 UTC www.weather.com [Source type: FILTERED WITH BAYES]

.When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the Earth, and the solar gravitational force partially cancels the Moon's.^ When the moon is in first or third quarter, however, it is at right angles to the sun relative to the earth, and the height of the tides is subject to the opposing forces of the sun and moon.
  • Tides, Clam Tides, Tide Tables for Long Beach WA, ocean park wa, klipsan beach, leadbetter point, baker bay, ilwaco, seaview, surfside 19 September 2009 20:15 UTC www.funbeach.com [Source type: FILTERED WITH BAYES]

^ When the Moon is in first or in third quarter, however, it is at right angles to the Sun relative to Earth, and the height of the tides is subject to the opposing forces of the Sun and Moon.
  • Tide - MSN Encarta 19 September 2009 20:15 UTC encarta.msn.com [Source type: FILTERED WITH BAYES]

^ It is highest at new moon and full moon and lowest at first and third quarters.

.At these points in the lunar cycle, the tide's range is at its minimum: this is called the neap tide, or neaps (a word of uncertain origin).^ At these points in the lunar cycle, the tide's range is minimum: this is called the neap tide , or neaps .
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ At these points in the lunar cycle, the tide's range is minimum: this is called the neap tide, or neaps.
  • pleamar máxima viva equinoccial 15 September 2009 3:03 UTC www.proz.com [Source type: General]

^ These tides, called neap tides , also occur twice a month.
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

.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.^ These results to high tides that are unusually high and low tides that is unusually low.
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

^ High and low tides occur at the same times everywhere on earth.
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^ Note that spring low water is the lowest.
  • RYA navigation courses - Tides, spring, neap and chart datum: 6 tides. 15 September 2009 3:03 UTC www.sailingissues.com [Source type: FILTERED WITH BAYES]

.Neaps result in less extreme tidal conditions.^ Neaps result in less extreme tidal conditions.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ During the Moon’s first and last quarters the Sun and Moon act at right angles to each other, and the result is a much reduced tidal range called a “neap tide.” .

.There is about a seven day interval between springs and neaps.^ There is about a seven day interval between springs and neaps.
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^ The time between spring and neap is approximately 7 days.
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^ Tide day , the interval between the occurrences of two consecutive maxima of the resultant wave at the same place.
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.The changing distance separating the Moon and Earth also affects tide heights.^ The changing distance separating the Moon and Earth also affects tide heights.
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^ High Tide happens when the distance of moon from the earth is low.
  • When does the high tide & low tide happens in the sea? - Yahoo! Answers 18 January 2010 0:43 UTC answers.yahoo.com [Source type: General]

^ The changing distance of the Moon from the Earth also affects tide heights.
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.When the Moon is at perigee the range increases, and when it is at apogee the range shrinks.^ When the Moon is at perigee the range increases, and when it is at apogee the range shrinks.
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^ Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range .
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^ SPRING TIDE A tide of increased range, which occurs about every two weeks when the moon is new or full.
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.Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range.^ Spring Tide - Also known as perigean, a tide that occurs during or after a new Moon.
  • Massachusetts Tide Charts - Main Index 15 September 2009 3:03 UTC www.boatma.com [Source type: General]

^ Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range .
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^ Full moon madness: last low spring tide of 2008 .
  • Singapore Celebrates our Reefs!: Full moon madness: last low spring tide of 2008 15 September 2009 3:03 UTC iyor08singapore.blogspot.com [Source type: General]

.If a storm happens to be moving onshore at this time, the consequences (property damage, etc.^ If a storm happens to be moving onshore at this time, the consequences (property damage, etc.
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^ If a storm happens to be moving onshore at this time, the consequences (in the form of property damage, etc.
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) can be especially severe.

Semidiurnal range differences

.When there are two high tides each day but with different heights (and two low tides also of different heights), the pattern is called a mixed semidiurnal tide.^ Heights and times of low and high water on each day are published in tide tables.
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^ The equilibrium tidal theory predicts tides that are semidiurnal, which means two high and two low tides each day.

^ So, when this occurs there is little variation between a high and low tide.
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[9]

Bathymetry

.The shape of the shoreline and the ocean floor change the way that tides propagate, so there is no simple, general rule for predicting the time of high water from the Moon's position in the sky.^ The daily inequality changes with time and is generally small when the Moon is over the equator .
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^ The shape of the shoreline and the ocean floor change the way that tides propagate, so there is no simple, general rule for predicting the time of high water from the Moon's position in the sky.
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^ Tides and the environment Would the world be different had there been no tides, no moon?

.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.^ That's a difference of two hours between high tide in the two locations.

^ The difference in height of the two high waters of each tidal day for a mixed or semidiurnal tide.

^ The difference in height of the two low waters of each tidal day for a mixed or semidiurnal tide.

.However, for a given location the relationship between lunar 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.^ High and low tides occur at the same times everywhere on earth.
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^ So, when this occurs there is little variation between a high and low tide.
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^ That's a difference of two hours between high tide in the two locations.

.For example, the high tide at Norfolk, Virginia predictably occurs approximately two and a half hours before the moon passes directly overhead.^ That's a difference of two hours between high tide in the two locations.

^ For example, the high tide at Norfolk, Virginia predictably occurs approximately two and a half hours before the moon passes directly overhead.
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^ How High tides and Low Tides Occur?
  • How the Moon Affects Tides | Bukisa.com 18 January 2010 0:43 UTC www.bukisa.com [Source type: FILTERED WITH BAYES]

.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.^ 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.
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^ The Prediction of Tides Detailed prediction of ocean tides from theories of classical mechanics and hydrodynamics has not been entirely successful, largely because of complications introduced by the irregular shape of the ocean basins and coastlines.
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^ CONTINENTAL SHELF The zone around the continents extending from the low-water mark seaward, typically ending in steep slope to the depths of the ocean floor.
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.As a result, tidal patterns vary.^ As a result, tidal patterns vary.
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^ 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.
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^ Tidal changes are the net result of multiple influences that act over varying periods.
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.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.^ 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.
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^ Nevertheless, Strabo quotes from Posidonius a clear account of the tides on the Atlantic coast of Spain , and connects the tides correctly with the motion of the moon.

^ It is well known that there are strongly marked diurnal and semi-diurnal inequalities of the barometer due to the sun's heat, and they may be described as atmospheric meteorological tides.'

[10][11][12]

Other constituents

.Factors include gravitational effects due to the Sun, 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 orbits of the Moon and the Earth.^ Factors include gravitational effects due to the Sun, 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 orbits of the Moon and the Earth.
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^ This accelerates the Moon in its orbit, and decelerates the rotation of the Earth.
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^ Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit ".
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.Variations with periods of less than half a day are called harmonic constituents.^ Variations with periods of less than half a day are called harmonic constituents .
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^ Variations with periods of less than half a day are called harmonic constituents.
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^ Conversely, long period constituents cycle over days, months, or years.
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.Conversely, long period constituents cycle over days, months, or years.^ Conversely, long period constituents cycle over days, months, or years.
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^ Long period constituents have periods of days, months, or years.
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^ 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 nodal tidal constituent .
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Phase and amplitude

Map showing relative tidal magnitudes of different ocean areas
Fig. 4: The M2 tidal constituent. .Amplitude is indicated by color, and the white lines are cotidal differing by 1 hour.^ High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines.
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^ In the M 2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.
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^ As we have already indicated, the tide in British seas has mainly a progressive character, and the general march of the wave may be exhibited on a chart by what are called cotidal lines.

.The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period.^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ There are also nodal points in the ocean where there are no tides, these no-tide places are called amphidromic points.

^ In the open ocean, the tidal currents are rotary, shifting through all directions of the compass in a period matching that of the local tide.
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[13][14]
.Because the M2 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.^ Because the M 2 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.
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^ In most locations, tides are semidiurnal .
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^ Because tidal currents cease this is also called slack water or slack tide.
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.Tidal stage is also measured in degrees, with 360° per tidal cycle.^ It is also measured in degrees, with 360° per tidal cycle.
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^ Tidal stage is also measured in degrees, with 360° per tidal cycle.
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^ Tides may be semidiurnal (two high waters and two low waters each day), or diurnal (one tidal cycle per day).
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.Lines of constant tidal phase are called cotidal lines, analogous to lines on topographical maps.^ Lines of constant tidal phase are called cotidal lines .
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^ Lines of constant tidal phase are called cotidal lines , analogous to lines on topographical maps.
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^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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.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.^ Lines of constant tidal phase are called cotidal lines .
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^ 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.
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^ In Europe around 730 AD, the Venerable Bede described 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.
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.Semidiurnal and long phase constituents are measured from high water, diurnal from maximum flood tide.^ Semidiurnal and long phase constituents are measured from high water, diurnal from maximum flood tide.
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^ The bulges represent the crests of the two tidal waves (high tide), directly opposite each other, and the low water areas are the two troughs (low tide).

^ Because the M 2 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.
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.This and the discussion that follows is precisely true only for a single tidal constituent.^ This and the discussion that follows is precisely true only for a single tidal constituent.
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^ Tidal prediction is only possible when accurate observations have been made of the phenomena to be predicted; and the like is true of verification after prediction.

^ While the theorem remains true and the tidal height could be analysed in terms of a single frequency and its harmonics, a large number of significant terms would be required.
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.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.^ 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.
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^ 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 .
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^ The Prediction of Tides Detailed prediction of ocean tides from theories of classical mechanics and hydrodynamics has not been entirely successful, largely because of complications introduced by the irregular shape of the ocean basins and coastlines.
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.The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion.^ The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion.
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^ An amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion.
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^ During times of high tide accompanied by high wind and low pressure, as during a hurricane , a tidal surge can occur, causing coastal erosion, flooding, and damage to coastal cities.
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.(The rare exception occurs when the tide encircles an island, as it does around New Zealand and Madagascar.^ (The rare exception occurs when the tide circles around an island, as it does around New Zealand .
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^ (The rare exception occurs when the tide encircles an island, as it does around New Zealand and Madagascar.
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^ Either working independently or in groups, ask students to explain in their notebooks the sun and moon's placement when the most extreme high and low tides occur (at the new moon).
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) .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.^ Lines of constant tidal phase are called cotidal lines .
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^ The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion.
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^ Indeed tidal motion generally lessens moving away from the continental coasts, so that crossing the cotidal lines are contours of constant amplitude (half of the distance between high and low water) which decrease to zero at the amphidromic point.
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.For a semidiurnal 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.
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^ This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high water across from low water.
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^ For a 12 hour semidiurnal tide the amphidromic point behaves roughly like 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.
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.High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines.^ High water rotates about the amphidromic point once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines.
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^ The amphidromic point is at once cotidal with high and low waters, which is satisfied by zero tidal motion.
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^ High water rotates about once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines.
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.This rotation is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused by the Coriolis effect.^ CYCLONIC FLOW Winds that blow in and around a cyclone , that is counterclockwise in the Northern Hemisphere, clockwise in the Southern Hemisphere.
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^ This rotation is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused by the Coriolis effect.
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^ The circulation is counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
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.The difference of cotidal phase from the phase of a reference tide is the epoch.^ The difference of cotidal phase from the phase of a reference tide is the epoch .
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^ In the M 2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.
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^ An obvious fallback then is to have several tidal power generation stations, at locations where the tide phase is different enough so that low power from one station is filled in by high power from another.
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.The reference tide is the hypothetical constituent equilibrium tide on a landless Earth measured at 0° longitude, the Greenwich meridian.^ The reference tide is the hypothetical constituent equilibrium tide on a landless Earth measured at 0° longitude, the Greenwich meridian.
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^ If e denotes the equilibrium height of the tide, it is a function of colatitude and longitude, and may be expanded in a series of spherical surface harmonics e i.

^ Rotate the earth through one full solar day, so that the Greenwich meridian goes around in one full circle.

.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.^ 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.
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^ These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea.
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^ For example, the high tide arrives in Santa Cruz two hours earlier than it arrives at the Golden Gate Bridge, a mere 60 miles north, even though the moon is over both places at the same time.

.South of Cape Hatteras the tidal forces are more complex, and cannot be predicted reliably based on the North Atlantic cotidal lines.^ 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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^ Other advantages over wind and solar include predictable energy output as cyclical tidal patterns allow electricity outputs from ocean energy facilities to be accurately predicted far in advance, providing reliable base power for integration with electrical grids.
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^ Lines of constant tidal phase are called cotidal lines .
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Physics

On the current appearance of the moon, the general tide can be derived

History of tidal physics

.Tidal physics was important in the early development of heliocentrism and celestial mechanics, with the existence of two daily tides being explained by the moon's gravity.^ Tidal physics was important in the early development of heliocentrism and celestial mechanics , with the existence of two daily tides being explained by the moon's gravity, more precisely explained by universal gravitation, the interaction of the moon's gravity and the sun's gravity explaining the variation of tides.
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^ Two theories help explain tides.

^ The gravity of the moon does create the tides.

.More precisely the daily tides were explained by universal gravitation involving the interaction of the moon's gravity and the sun's gravity to cause the variation of tides.^ Tidal physics was important in the early development of heliocentrism and celestial mechanics , with the existence of two daily tides being explained by the moon's gravity, more precisely explained by universal gravitation, the interaction of the moon's gravity and the sun's gravity explaining the variation of tides.
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^ The gravity of the moon does create the tides.

^ Is the moon more effective than the sun at producing a tide?
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.An early explanation of tides was given by Galileo Galilei in his 1632 Dialogue Concerning the Two Chief World Systems, whose working title was Dialogue on the Tides.^ An early explanation of tides was given by Galileo Galilei in his 1632 Dialogue Concerning the Two Chief World Systems, whose working title was Dialogue on the Tides .
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^ In a general tide-table 1 References may be given to two papers by G. H. Darwin on this subject, viz.

^ However original any future contribution to the science of the tides may be, it would seem as though it must perforce be based on the work of these two.

.However, the resulting theory was incorrect - he attributed the tides to water sloshing due to the Earth's movement around the Sun, hoping to provide mechanical proof of the Earth's movement - and the value of the theory is disputed, as discussed there.^ However, the resulting theory was incorrect - he attributed the tides to water sloshing due to the earth's movement around the sun, hoping to provide mechanical proof of the earth's movement - and the value of the theory is disputed, as discussed there.
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^ The Prediction of Tides Detailed prediction of ocean tides from theories of classical mechanics and hydrodynamics has not been entirely successful, largely because of complications introduced by the irregular shape of the ocean basins and coastlines.
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^ Neap tide, having the minimum range, occurs during the moon's first and last quarters, when the moon, earth, and sun form a right angle.
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.At the same time Johannes Kepler correctly suggested that the Moon caused the tides, based upon ancient observation and correlations, which was rejected by Galileo.^ At the same time Johannes Kepler correctly suggested that the moon caused the tides, based upon ancient observation and correlations, which was rejected by Galileo.
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^ The importance of tides for maritime activities has prompted the compilation of tide tables for harbors, which give the time and height of high water and low water based on past observations and corrected for the varying positions of celestial bodies.
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^ During times of high tide accompanied by high wind and low pressure, as during a hurricane , a tidal surge can occur, causing coastal erosion, flooding, and damage to coastal cities.
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.It was originally mentioned in Ptolemy's Tetrabiblos as being derived from ancient observation.^ It was originally mentioned in Ptolemy 's Tetrabiblos as being derived from ancient observation.
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^ It will be understood, therefore, that in the following schedules the " argument " is that part of the argument which is derived from theory, the true complete argument being the " argument " -K, where is derived from observation.

.Isaac Newton (1642–1727) was the first person to explain tides scientifically.^ Isaac Newton (1642 -1727) was the first person to explain tides scientifically.
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^ Isaac Newton laid the foundations for the mathematical explanation of tides in the Philosophiae Naturalis Principia Mathematica ( 1687 ).
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^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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.His explanation of the tides (and many other phenomena) was published in 1686, in the second volume of the Principia.^ His explanation of the tides (and many other phenomena) was published in 1686, in the second volume of the Principia.
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^ Isaac Newton laid the foundations for the mathematical explanation of tides in the Philosophiae Naturalis Principia Mathematica ( 1687 ).
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^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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.Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).^ Isaac Newton laid the foundations for the mathematical explanation of tides in the Philosophiae Naturalis Principia Mathematica ( 1687 ).
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^ Tide-generating Force.

^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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[15][16] .Newton first applied the theory of universal gravitation to account for the tides as due to the lunar and solar attractions,[17] offering an initial theory of the tide-generating force.^ Tide-generating Force.

^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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^ Based on these developments and the lunar theory of E W Brown , Arthur Thomas Doodson developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.
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.Newton and others before Pierre-Simon Laplace worked with an equilibrium theory, largely concerned with an approximation that describes the tides that would occur in a non-inertial ocean evenly covering the whole Earth.^ Newton and others before Pierre-Simon Laplace worked with an equilibrium theory, largely concerned with an approximation that describes the tides that would occur in a non-inertial ocean evenly covering the whole Earth.
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^ An early explanation of tides was given by Galileo Galilei in his 1632 Dialogue Concerning the Two Chief World Systems, whose working title was Dialogue on the Tides .
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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 with major axis directed toward the deforming body.
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[15] .The tide-generating force (or its corresponding potential) is still relevant to tidal theory, but as an intermediate quantity rather than as a final result; theory has to consider also the Earth's dynamic tidal response to the force, a response that is influenced by bathymetry, Earth's rotation, and other factors.^ The other consequence of the tidal acceleration is the deceleration of the rotation of the Earth.
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^ Tidal locking Tidal force Tides .
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^ The tide-generating force (or its corresponding potential ) is still relevant to tidal theory, but as an intermediate quantity rather than as a final result; theory has to consider also the Earth's dynamic tidal response to the force, a response that is influenced by bathymetry, Earth's rotation, and other factors.
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[18]
.In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides.^ In 1738 the Academy of Sciences of Paris offered, as a subject for a prize, the theory of the tides.

^ In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides.
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^ Another monograph on tides, treating especially the mathematical developments, is Maurice Levy's La The'orie des marees (Paris, 1898).

.Daniel Bernoulli, Leonhard Euler, Colin Maclaurin and Antoine Cavalleri shared the prize.^ Daniel Bernoulli , Leonhard Euler, Colin Maclaurin and Antoine Cavalleri shared the prize.
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^ Daniel Bernoulli , Antoine Cavalleri, Leonhard Euler , and Colin Maclaurin shared the prize.
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^ Daniel Bernoulli , Leonhard Euler , Cohn Maclaurin and Antoine Cavalleri.

.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 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.
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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 with major axis directed toward the deforming body.
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^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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.Maclaurin was the first to write about the Earth's rotational effects on motion.^ Maclaurin was the first to write about the Earth's rotational effects on motion.
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^ If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon.
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^ If other effects were ignored, tidal acceleration would continue until the rotational period of the Earth matched the orbital period of the Moon.
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.Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide.^ Tidal locking Tidal force Tides .
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^ Euler realized that the tidal force's horizontal component (more than the vertical) drives the tide.
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^ Euler realized that the horizontal component of the tidal force (more than the vertical) drives the tide.
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.In 1744 Jean le Rond d'Alembert studied tidal equations for the atmosphere which did not include rotation.^ In 1744 Jean le Rond d'Alembert studied tidal equations for the atmosphere which did not include rotation.
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^ In 17 4 6 Jean-le-Rond D'Alembert wrote a paper in which he treated the tides of the atmosphere; but this work, like Maclaurin's, is chiefly remarkable for the importance of collateral points.

.Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides.^ The first major theoretical formulation for water tides was made by Pierre-Simon Laplace , who formulated a system of partial differential equations relating the horizontal flow to the surface height of the ocean.
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^ As the tides change, currents must flow to redistribute the ocean's water.
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^ Pierre-Simon Laplace formulated a system of partial differential equations relating the ocean's horizontal flow to its surface height, the first major dynamic theory for water tides.
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.The Laplace tidal equations are still in use today.^ Laplace's tidal equations .
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^ The Laplace tidal equations are still in use today.
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^ Laplace tidal equation .
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.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 waves.^ Laplace's tidal equations .
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^ William Thomson, 1st Baron Kelvin , rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, which are known as Kelvin waves .
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^ Laplace tidal equation .
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[19] [20] [21]
.Others including Kelvin and Henri Poincare further developed Laplace's theory.^ Others including Kelvin and Henri Poincare further developed Laplace's theory.
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^ Laplace's theory without these complications, but the theory is now accessible in H. Lamb's Hydrodynamics and other works of the kind.

.Based on these developments and the lunar theory of E W Brown, Arthur Thomas Doodson developed and published in 1921[22] the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.^ Based on these developments and the lunar theory of E W Brown , Arthur Thomas Doodson developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.
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^ Neap tide, having the minimum range, occurs during the moon's first and last quarters, when the moon, earth, and sun form a right angle.
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^ Isaac Newton laid the foundations of scientific tidal studies with his mathematical explanation of tide-generating forces in the Philosophiae Naturalis Principia Mathematica (1687).
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[23] .Some of his methods remain in use.^ Some of his methods remain in use.
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[24]

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.^ 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.
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^ The center of mass of the earth orbits the center of mass of the earth-moon system, held into its orbit by the gravitational pull of the moon.

^ The moon produces two tidal bulges on the earth on a line connecting the centers of the earth and moon.

.Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).^ The derivative of 1/ r 2 , with r = distance to originating body, varies as the inverse cube.
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^ Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
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^ Thus, the tidal force depends not on the strength of the gravitational field of the Moon, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body; see NASA ).
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[4] .[25] 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 gravitational force exerted on the Earth by the Sun is on average 179 times stronger than that exerted on the Earth by the Moon, but because the Sun is on average 389 times farther from the Earth, the gradient of its field is weaker.
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^ 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.
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^ According to »NASA the lunar tidal force is 2.21 times larger than the solar.
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.The solar tidal force is 46% as large as the lunar.^ The solar tidal force is 46% as large as the lunar.
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^ Thus, the tidal force depends not on the strength of the lunar gravitational field, but on its gradient (which falls off approximately as the inverse cube of the distance to the originating gravitational body).
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^ More precisely, the lunar tidal acceleration (along the Moon-Earth axis, at the Earth's surface) is about 1.1 × 10 −7 g , while the solar tidal acceleration (along the Sun-Earth axis, at the Earth's surface) is about 0.52 × 10 −7 g , where g is the gravitational acceleration at the Earth's surface.
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[26] .More precisely, the lunar tidal acceleration (along the Moon-Earth axis, at the Earth's surface) is about 1.1 × 10−7 g, while the solar tidal acceleration (along the Sun-Earth axis, at the Earth's surface) is about 0.52 × 10−7 g, where g is the gravitational acceleration at the Earth's surface.^ More precisely, the lunar tidal acceleration (along the Moon-Earth axis, at the Earth's surface) is about 1.1 × 10 −7 g , while the solar tidal acceleration (along the Sun-Earth axis, at the Earth's surface) is about 0.52 × 10 −7 g , where g is the gravitational acceleration at the Earth's surface.
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^ Neap tide, having the minimum range, occurs during the moon's first and last quarters, when the moon, earth, and sun form a right angle.
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^ When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the earth, and the forces due to the Sun partially cancel those of the Moon.
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[27] .Venus has the largest effect of the other planets, at 0.000113 times the solar effect.^ The effect of the other planets is much, much smaller, with the largest being Venus at 0.000113 times that of the Sun.
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^ Venus has the largest effect of the other planets, at 0.000113 times the solar effect.
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^ Nevertheless it must be admitted that the effect produced by solar tidal friction on Jupiter and Saturn has not been nearly so great as on the interior planets.

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.
Fig. .6: The lunar gravity differential field at the Earth's surface is known as the tide-generating force.^ The Moon's (or Sun's) gravity differential field at the surface of the earth is known as the Tide Generating Force.
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^ Earth's surface is known as the tide-generating force .
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^ Graphic of tidal forces; the gravity field is generated by a body to the right.
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This is the primary mechanism that drives tidal action and explains two equipotential tidal bulges, accounting for two daily high waters.
.Tidal forces can also be analyzed this way: each point of the Earth experiences the Moon's radially decreasing gravity differently; they are subject to the tidal forces of Figure 6, which dominate.^ Tidal forces can also be analyzed this way: each point of the Earth experiences the Moon's radially decreasing gravity differently; they are subject to the tidal force''s of Figure 6, which dominate.
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^ When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the earth, and the forces due to the Sun partially cancel those of the Moon.
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^ Reference: "marea viva" / spring tide Reference information: Around new and full moon when the Sun, Moon and Earth form a line (a condition known as syzygy), the tidal forces due to the Sun reinforce those of the Moon.
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.Finally, most importantly, only the tidal forces' horizontal components actually tidally accelerate the water particles since there is small resistance.^ The forcing is only horizontal ( tangent ial).
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^ Finally, most importantly, only the horizontal components of the tidal forces actually contribute tidal acceleration to the water particles since there is small resistance.
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^ Tidal forces are also responsible for tidal locking and tidal acceleration .
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.The tidal force on a particle equals about one ten millionth that of Earth's gravitational force.^ They are caused by the gravitational force of one or...
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^ The actual tidal force on a particle is only about a ten millionth of the force caused by the Earth's gravity.
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^ The tidal force on a particle equals about one ten millionth that of Earth's gravitational force.
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.The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the geoid.^ The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) which is commonly referred to as the geoid .
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^ The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the geoid .
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^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, the part of the Earth nearest the Moon, and the farthest part.
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.Since the gravitational force is equal to the potential's gradient, there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium.^ Since the gravitational force is equal to the potential's gradient , there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium.
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^ Since the gravitational force is equal to the gradient of the potential, there are no tangential forces on such a surface, and the ocean surface is thus in gravitational equilibrium.
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^ If the augmentation due to mutual attraction of the water is not included, b i becomes equal to unity; there is no longer any necessity to use spherical harmonic analysis, and we see that if the equation to the surface of an ocean be p= a+S, where S is a function of latitude and longitude , it is in equilibrium under forces due to a potential whose value at the surface of the sphere (where p=a ) is gS. In treating the theory of tidal observation we shall specify the tide-generating forces in this way, and then by means of " the principle of forced vibrations," referred to in § 7 as used by Laplace for discussing the actual oscillations of the sea, we shall pass to the actual tides at the port of observation.

.Now consider the effect of massive external bodies such as the Moon and Sun.^ Now consider the effect of external, massive bodies such as the Moon and Sun.
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^ Now consider the effect of massive external bodies such as the Moon and Sun.
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^ Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant.
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.These bodies have strong gravitational fields that diminish with distance in space and which act to alter the shape of an equipotential surface on the Earth.^ These bodies have strong gravitational fields that diminish with distance in space and which act to alter the shape of an equipotential surface on the Earth.
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^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, the part of the Earth nearest the Moon, and the farthest part.
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^ Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant.
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.This deformation has a fixed spatial orientation relative to the influencing body.^ This deformation has a fixed spatial orientation relative to the influencing body.
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.The Earth's rotation relative to this shape causes the daily tidal cycle.^ The Earth's rotation relative to this shape causes the daily tidal cycle.
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^ 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 nodal tidal constituent .
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^ If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon.
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.Gravitational forces follow an inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube of the distance.^ Gravitational forces follow an inverse-square law (force is inversely proportional to the square of the distance), but tidal forces are inversely proportional to the cube of the distance.
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^ This effect is directly proportional to the mass of the body causing the tide but inversely proportional to the cube of the distance between the bodies.
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^ The retarding force in apogee acts exactly inversely, and diminishes the perigean distance.

.The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, which occurs on the part of the Earth nearest to and furthest from the Moon.^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, the part of the Earth nearest the Moon, and the farthest part.
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^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, which occurs on the part of the Earth nearest to and furthest from the Moon.
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^ This is the primary mechanism that drives tidal action and explains two tidal equipotential bulges, accounting for two high tides per day.
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.When the tidal equipotential changes, the ocean surface is no longer aligned with it, so that the apparent direction of the vertical shifts.^ When the tidal equipotential changes, the ocean surface is no longer aligned with it, so that the apparent direction of the vertical shifts.
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^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, the part of the Earth nearest the Moon, and the farthest part.
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^ In the open ocean, the tidal currents are rotary, shifting through all directions of the compass in a period matching that of the local tide.
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.The surface then experiences a down slope, in the direction that the equipotential has risen.^ The surface then experiences a down slope, in the direction that the equipotential has risen.
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^ When the tidal equipotential changes, the ocean surface is no longer aligned with it, so that the apparent direction of the vertical shifts.
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Laplace's tidal equations

.Ocean depths are much smaller than their horizontal extent.^ Ocean depths are much smaller than their horizontal extent.
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^ The depth of the oceans is much smaller than their horizontal extent; thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features: The vertical (or radial) velocity is negligible, and there is no vertical shear —this is a sheet flow.
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^ If this is so in the simple case of an ocean of uniform depth, how much more must it be true of oceans of various depths interrupted by continents?

Thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features:
.
  1. The vertical (or radial) velocity is negligible, and there is no vertical shear—this is a sheet flow.
  2. The forcing is only horizontal (tangential).
  3. The Coriolis effect appears as a fictitious lateral forcing proportional to velocity.
  4. The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth.^ The forcing is only horizontal ( tangent ial).
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    ^ The Coriolis effect appears as a fictitious lateral forcing proportional to velocity.
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    ^ The rate of change of the surface height is proportional to the negative divergence of velocity multiplied by the depth.
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    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 boundary conditions dictate no flow across the coastline and free slip at the bottom.
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.The Coriolis effect steers waves to the right in the northern hemisphere and to the left in the southern allowing coastally trapped waves.^ This rotation is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused by the Coriolis effect.
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^ In the Northern Hemisphere, air is deflected to the right of its path, while in the Southern Hemisphere, air is deflected to the left of its path.
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^ The Coriolis effect steers waves to the right in the northern hemisphere and to the left in the southern allowing coastally trapped waves.
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.Finally, a dissipation term can be added which is an analog to viscosity.^ Finally, a dissipation term can be added which is an analog to viscosity.
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[28]

Amplitude and cycle time

.The theoretical amplitude of 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 not rotating.^ This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.
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^ In addition to oceanic tides, there are atmospheric tides as well as earth tides .
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^ The theoretical amplitude of oceanic tides caused by the Moon is about 54 cm 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 not rotating.
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.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.^ This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.
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^ The Sun similarly causes tides, of which the theoretical amplitude is about 25 cm (46% of that of the Moon) with a cycle time of 12 hours.
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^ The Sun similarly causes tides, of which the theoretical amplitude is about (46% of that of the Moon) with a cycle time of 12 hours.
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.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).^ At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to .
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^ At spring tide the two effects add to each other to a theoretical level of 79 cm, while at neap tide the theoretical level is reduced to 29 cm.
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^ The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary, and many large ports had automatic tide gage stations by 1850.
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.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.^ The Sun also cycles from north to south of the equator, while the Earth–Sun and Earth–Moon distances change on their own cycles.
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^ This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.
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^ The changing distance separating the Moon and Earth also affects tide heights.
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.This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.^ This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.
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^ When the Moon is at first quarter or third quarter, the Sun and Moon are separated by 90° when viewed from the earth, and the forces due to the Sun partially cancel those of the Moon.
  • pleamar máxima viva equinoccial 15 September 2009 3:03 UTC www.proz.com [Source type: General]

^ 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 nodal tidal constituent .
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.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).^ If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 cm.
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^ If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach .
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^ According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the Moon's position relative to the Sun.
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.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's lithosphere has a natural period of about 57 minutes).^ Real amplitudes differ considerably, not only because of variations in ocean depth, and the obstacles to flow caused by the continents, but also because the natural period of wave propagation is of the same order of magnitude as the rotation period: about 30 hours.
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^ If there were no land masses, it would take about 30 hours for a long wavelength ocean surface wave to propagate along the equator halfway around the Earth (by comparison, the natural period of the Earth's lithosphere is about 57 minutes).
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^ There ain't no land here.'
  • The Ebb-Tide by Robert Louis Stevenson in collaboration with Lloyde Osbourne - Full Text Free Book (Part 2/3) 20 September 2009 12:18 UTC www.fullbooks.com [Source type: Original source]

Dissipation

.Earth's tidal oscillations introduce dissipation at an average rate of about 3.75 terawatt.^ The tidal oscillations of the Earth introduce dissipation, at an average rate of about 3.75 terawatt.
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^ Earth's tidal oscillations introduce dissipation at an average rate of about 3.75 terawatt .
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^ 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.
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[29] .About 98% of this dissipation is by marine tidal movement.^ About 98% of this dissipation is by marine tidal movement.
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^ About 98% of this dissipation is by the tidal movement in the seas and oceans.
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^ The tidal oscillations of the Earth introduce dissipation, at an average rate of about 3.75 terawatt.
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[30] .Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation.^ The dissipation arises as the basin-scale tidal flow drives smaller-scale flows which experience turbulent dissipation.
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^ Dissipation arises as basin-scale tidal flows drive smaller-scale flows which experience turbulent dissipation.
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.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 Moon's orbital angular momentum also increases.
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^ This tidal drag creates torque on the Moon that gradually transfers angular momentum to its orbit, and a gradual increase in Earth–Moon separation.
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^ Effectively, energy and angular momentum are transferred from the rotation of the Earth to the orbital motion of the Moon.
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.The equal and opposite torque on the Earth correspondingly decreases its rotational velocity.^ The equal and opposite torque on the Earth correspondingly decreases its rotational velocity.
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^ As a result of the equal and opposite torque on the Earth, the rotational velocity of the Earth is correspondingly slowed.
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^ The rotational angular momentum of the Earth decreases and consequently the length of the day increases.
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.Thus, over geologic time, the Moon recedes from the Earth, at about 3.8 centimetres (1.5 in)/year, lengthening the terrestrial day.^ Thus, over geologic time, the Moon recedes from the Earth, at about year, lengthening the terrestrial day.
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^ Thus, over geologic time, the Moon recedes from the Earth, at about 3.8 cm/year, and the length of the terrestrial day increases, meaning that there is about 1 fewer day per 100 million years.
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^ At that time, the Moon would always be overhead of a single fixed place on Earth.
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[31] .Day length has increased by about 2 hours in the last 600 million years.^ Day length has increased by about 2 hours in the last 600 million years.
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^ 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.
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^ Thus, over geologic time, the Moon recedes from the Earth, at about year, lengthening the terrestrial day.
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.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.^ Day length has increased by about 2 hours in the last 600 million years.
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^ 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.
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^ This geological record is consistent with these conditions 620 million years ago: the day was 21.9±0.4 hours, and there were 13.1±0.1 synodic months/year and 400±7 solar days/year.
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Observation and prediction

History

Brouscon's Almanach of 1546: Compass bearings of high waters in the Bay of Biscay (left) and the coast from Brittany to Dover (right).
Brouscon's Almanach of 1546: Tidal diagrams "according to the age of the Moon".
.From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the Sun and Moon.^ From ancient times, tides have been observed and discussed with increasing sophistication, first noting the daily recurrence, then its relationship to the Sun and Moon.
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^ From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the Sun and Moon.
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^ Tidal Observation: the Tide-gauge.

.Pytheas travelled to the British Isles about 325 BC and seems to be the first to have related spring tides to the phase of the Moon.^ Pytheas travelled to the British Isles about 325 BC and seems to be the first to have related spring tides to the phase of the Moon.
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^ Pytheas travelled to the British Isles and seems to be the first to have related spring tides to the phase of the Moon.
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^ Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range .
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.In the 2nd century BC, the Babylonian astronomer, Seleucus of Seleucia, correctly described the phenomenon of tides in order to support his heliocentric theory.^ In the 2nd century BC, the Babylonian astronomer , Seleucus of Seleucia , correctly described the phenomenon of tides in order to support his heliocentric theory.
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^ He also gives the law of the tide in the Indian Ocean as observed by Seleucus the Babylonian, and the passage shows that Seleucus had unravelled the law which governs the diurnal inequality of the tide in that sea.

[32] .He correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the pneuma.^ He correctly theorized that tides were caused by the Moon , although he believed that the interaction was mediated by the pneuma.
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^ He correctly theorized that tides were caused by the Moon , although he believed that the interaction was mediated by the pneuma .
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^ At the same time Johannes Kepler correctly suggested that the moon caused the tides, based upon ancient observation and correlations, which was rejected by Galileo.
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.He noted that tides varied in time and strength in different parts of the world.^ He noted that tides varied in time and strength in different parts of the world.
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^ He noted that the tides varied in time and strength in different parts of the world.
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^ From ancient times, tides have been observed and discussed with increasing sophistication, first noting the daily recurrence, then its relationship to the Sun and Moon.
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.According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the Moon's position relative to the Sun.^ According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the Moon's position relative to the Sun.
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^ According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.
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^ 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 nodal tidal constituent .
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[33]
.The Naturalis Historia of Pliny the Elder collates 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.^ Tidal Observation: the Tide-gauge.

^ The Naturalis Historia of Pliny the Elder collates many observations of detail: the spring tides being a few days after (or before) new and full moon, and that the spring tides around the time of the equinoxes were the highest, though there were also many relationships now regarded as fanciful.
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^ This is the primary mechanism that drives tidal action and explains two tidal equipotential bulges, accounting for two high tides per day.
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.In his Geography, Strabo described tides in the Persian Gulf having their greatest range when the Moon was furthest from the plane of the equator.^ In his Geography , Strabo described tides in the Persian Gulf having their greatest range when the Moon was furthest from the plane of the equator.
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^ Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range .
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^ According to Strabo (1.1.9), Seleucus was the first to link tides to the lunar attraction, and that the height of the tides depends on the Moon's position relative to the Sun.
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.All this despite the relatively small amplitude of Mediterranean basin tides.^ All this despite the relatively small amplitude of Mediterranean basin tides.
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^ All this despite the relatively feeble tides in the Mediterranean basin, though there are strong currents through the Strait of Messina and between Greece and the island of Euboea through the Euripus that puzzled Aristotle .
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^ The tides which we omit from the schedules are of relatively unimportant, but nevertheless commonly evaluated in accurate tidal work, are all lunar tides, viz.

.(The strong currents through the Strait of Messina and between Greece and the island of Euboea through the Euripus puzzled Aristotle).^ All this despite the relatively feeble tides in the Mediterranean basin, though there are strong currents through the Strait of Messina and between Greece and the island of Euboea through the Euripus that puzzled Aristotle .
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^ (The strong currents through the Strait of Messina and between Greece and the island of Euboea through the Euripus puzzled Aristotle ).
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^ The tidal flow through Cook Strait between 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.
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.Philostratus discussed tides in Book Five of The Life of Apollonius of Tyana.^ Philostratus discussed tides in Book Five of The Life of Apollonius of Tyana.
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.Philostratus mentions the moon, but attributes tides to "spirits". In Europe around 730 AD, the Venerable Bede described 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.^ In Europe around 730 AD, the Venerable Bede described 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.
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^ The water rises to its highest level, reaching high tide.
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^ Philostratus mentions the moon, but attributes tides to "spirits".
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In the 9th century, the Arabian earth-scientist, Al-Kindi (Alkindus), wrote a treatise entitled Risala fi l-Illa al-Failali l-Madd wa l-Fazr (Treatise on the Efficient Cause of the Flow and Ebb), in which he presents an argument on tides which "depends on the changes which take place in bodies owing to the rise and fall of temperature."[34] He describes a clear and precise laboratory experiment that proved his argument.[35]
.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 tide table in China was recorded in 1056 AD primarily for visitors wishing to see the famous tidal bore in the Qiantang River .
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^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
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^ Semidiurnal tides dominated coastline, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal.
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.The first known British tide table is thought to be that of John, Abbott of Wallingford (d.^ The first known British tide table is thought to be that of John, Abbott of Wallingford (d.
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^ The first known tide table is thought to be that of John, Abbott of Wallingford (d.
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^ The first tide table in China was recorded in 1056 A.D, primarily for the benefit of visitors wishing to see the famous tidal bore in the Qiantang River .
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.1213), based on high water occurring 48 minutes later each day, and three hours earlier at the Thames mouth than upriver at London.^ London than at the mouth of the Thames .
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^ Thames mouth than upriver at London.
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^ Bridgeport is north of the equator, so when the Moon is north of the equator also and shining upon Bridgeport, Bridgeport is closer to its maximum effect than approximately twelve hours later when Bridgeport is on the far side of the Earth from the Moon and the high tide bulge at Bridgeport's longitude has its maximum south of the equator.
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.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.^ Tides in asynchronous binary systems Tide predictions .
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^ The main result was the building of a tide-predicting machine using a system of pulleys to add together six harmonic functions of time.
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^ William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867.
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.It was "programmed" by resetting gears and chains to adjust phasing and amplitudes.^ It was "programmed" by resetting gears and chains to adjust phasing and amplitudes.
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.Similar machines were used until the 1960s.^ Similar machines were used until the 1960s.
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[36]
.The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary.^ The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary, and many large ports had automatic tide gage stations by 1850.
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^ The first known sea-level record of an entire spring–neap cycle was made in 1831 on the Navy Dock in the Thames Estuary.
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^ At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to .
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Many large ports had automatic tide gage stations by 1850.
.William Whewell first mapped co-tidal lines ending with a nearly global chart in 1836. In order to make these maps consistent, he hypothesized the existence of amphidromes where co-tidal lines meet in the mid-ocean.^ William Whewell first mapped co-tidal lines ending with a nearly global chart in 1836.
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^ In order to make these maps consistent, he hypothesized the existence of amphidromes where co-tidal lines meet in the mid-ocean.
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^ William Thomson (Lord Kelvin) led the first systematic harmonic analysis of tidal records starting in 1867.
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.These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea.^ These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea.
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^ At these points in the lunar cycle, the tide's range is minimum: this is called the neap tide , or neaps .
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^ Sea level measured by coastal tide gauges may also be strongly affected by wind.
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[19]

Timing

World map showing the location of diurnal, semi-diurnal, and mixed semi-diurnal tides. <a name=.The European and African west coasts are exclusively semidiurnal, and North America's West coast is mixed semi-diurnal, but elsewhere the different patterns are highly intermixed, although a given pattern may cover hundreds to 1-2,000 kilometres (−1,242.1 mi)."^ It is well known that there are strongly marked diurnal and semi-diurnal inequalities of the barometer due to the sun's heat, and they may be described as atmospheric meteorological tides.'

^ Similarly the astronomical tide K2 may be perturbed by a semi-annual inequality in the semi-diurnal astronomical tide of speed 2(y - n).

^ U S National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section), »map showing world distribution of tide patterns , semidiurnal, diurnal and mixed semidiurnal.
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src="http://images-mediawiki-sites.thefullwiki.org/01/3/5/2/95333013673219586.jpg" width="300" height="147" class="thumbimage" />
Fig. 7: The same tidal forcing has different results depending on many factors, including coast orientation, continental shelf margin, water body dimensions.
.In most places there is a delay between the phases of the Moon and the effect on the tide.^ In most places there is a delay between the phases of the Moon and the effect on the tide.
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^ Because the M 2 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.
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^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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.Springs and neaps in the North Sea, for example, are two days behind the new/full Moon and first/third quarter.^ In the Wadden Sea, this actually occurs on average three days after a full or new moon.

^ Springs and neaps in the North Sea , for example, are two days behind the new/full Moon and first/third quarter.
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^ On the days after new and full moon the range of tide is at its maximum, and on the day after the first and third quarter at its minimum.

.This is called the tide's age.^ This is called the tide's age .
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^ This is called the age of the tide .
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^ This period has accordingly been called " the age of the tide."

[37]
.The local bathymetry greatly influences the tide's exact time and height at a particular coastal point.^ The local bathymetry greatly influences the tide's exact time and height at a particular coast al point.
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^ The exact time and height of the tide at a particular coastal point is also greatly influenced by the local bathymetry .
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^ If the sun be now introduced we have another similar tide of about half the height, and this depends on solar time, giving low-water somewhere about noon and midnight.

.There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the world's largest well-documented tidal ranges, 16 metres (52 ft) because of its shape.^ There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the world's largest well-documented tidal ranges, because of its shape.
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^ There are some extreme cases: the Bay of Fundy , on the east coast of Canada , features the largest well-documented tidal ranges in the world, 16 meters (53 ft), because of the shape of the bay.
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^ Some experts believe Ungava Bay in northern Quebec to have even higher tidal ranges, but it is free of pack ice for only about four months every year, while the Bay of Fundy rarely freezes.
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[38] .Some experts believe Ungava Bay in northern Quebec to have even higher tidal ranges, but it is free of pack ice for only about four months every year, while the Bay of Fundy rarely freezes.^ Some experts believe Ungava Bay in northern Quebec to have even higher tidal ranges, but it is free of pack ice for only about four months every year, while the Bay of Fundy rarely freezes.
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^ Ungava Bay in northern Quebec , is believed by some experts to have higher tidal ranges than the Bay of Fundy, but it is free of pack ice for only about four months every year, whereas the Bay of Fundy rarely freezes.
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^ There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the world's largest well-documented tidal ranges, because of its shape.
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.Southampton in the United Kingdom has a double high water caused by the interaction between the region's different tidal harmonics.^ A double high-water exists at Southampton .

^ Southampton in the United Kingdom has a double high water caused by the interaction between the different tidal harmonics within the region.
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^ Southampton in the United Kingdom has a double high water caused by the interaction between the region's different tidal harmonics.
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.This is contrary to the popular belief that the flow of water around the Isle of Wight creates two high waters.^ This is contrary to the popular belief that the flow of water around the Isle of Wight creates two high waters.
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^ In Europe around 730 AD, the Venerable Bede described 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.
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^ In Europe around 730 AD, the Venerable Bede described how the rise of tide on one coast of the British Isles coincided with the fall on the other and described the progression in times of the same high water along the Northumbrian coast.
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.The Isle of Wight is important, however, since it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water.^ The Isle of Wight is important, however, since it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water.
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^ In Europe around 730 AD, the Venerable Bede described 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.
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^ In Europe around 730 AD, the Venerable Bede described how the rise of tide on one coast of the British Isles coincided with the fall on the other and described the progression in times of the same high water along the Northumbrian coast.
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[39]
.Because the oscillation modes of the Mediterranean Sea and the Baltic Sea do not coincide with any significant astronomical forcing period, the largest tides are close to their narrow connections with the Atlantic Ocean.^ Because the oscillation modes of the Mediterranean Sea and the Baltic Sea do not coincide with any significant astronomical forcing period, the largest tides are close to their narrow connections with the Atlantic Ocean.
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^ April 24, 2008 Because the oscillation modes of the Mediterranean Sea and the Baltic Sea do not coincide with any significant astronomical forcing period, the largest tides are close to their narrow connections with the Atlantic Ocean.
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^ Every 7½ lunations (the full cycle from full moon to new to full), perigee coincides with either a new or full moon causing perigean spring tides with the largest tidal range .
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.Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan.^ Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan .
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^ Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan.
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^ Semidiurnal tides dominated coastline, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal.
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.On the southern coast of Australia, because the coast is mainly straight (partly because of the tiny quantities of runoff flowing from rivers), tidal ranges are equally small.^ On the southern coast of Australia , because the coast is mainly straight (partly because of the tiny quantities of runoff flowing from rivers), tidal ranges are equally small.
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^ On the southern coast of Australia, because the coast is mainly straight (partly because of the tiny quantities of runoff flowing from rivers), tidal ranges are equally small.
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^ There are some extreme cases: the Bay of Fundy, on the east coast of Canada, features the world's largest well-documented tidal ranges, because of its shape.
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Analysis

A regular water level chart
.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 detailed understanding.^ 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 detailed understanding.
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^ It was Isaac Newton 's universal theory of gravitation that first enabled an explanation of why there were two tides a day, not one, and, via calculation of the forces, offered hope of detailed understanding.
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^ Based on these developments and the lunar theory of E W Brown , Arthur Thomas Doodson developed and published in 1921 the first modern development of the tide-generating potential in harmonic form: Doodson distinguished 388 tidal frequencies.
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.Although it may seem that tides could be predicted via a sufficiently detailed knowledge of the instantaneous astronomical forcings, the actual tide at a given location is determined by astronomical forces accumulated over many days.^ Although it may seem that tides could be predicted via a sufficiently detailed knowledge of the instantaneous astronomical forcings, the actual tide at a given location is determined by astronomical forces accumulated over many days.
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^ Although it may seem that tides could be predicted via a sufficiently detailed knowledge of the astronomical forcing terms, the actual tide at a given location is determined by the response of the oceans to the astronomical forces accumulated over a period of many days.
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^ Small uninhabited islands and sands are counted from boats or are reached by foot during low tide; many of those are only counted from May to October.

.Precise results require detailed knowledge of the shape of all the ocean basins—their bathymetry and coastline shape.^ To calculate this response requires a detailed knowledge of the shape of all the ocean basins — their bathymetry and coastline shape.
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^ Precise results require detailed knowledge of the shape of all the ocean basins—their bathymetry and coastline shape.
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^ Also to make precise astronomical angular measurements requires knowledge of the Earth's rate of rotation and nutation , both of which are influenced by earth tides.
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.Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by William Thomson.^ Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by William Thomson .
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^ We shall not follow the analytical processes in detail, but the formulae given show the possibility of replacing the symbols used in the method of harmonic analysis by others involving R.A., declination and parallax.

^ The tides' influence on current flow is much more difficult to analyse, and data is much more difficult to collect.
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.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.^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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^ 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.
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^ In most places there is a delay between the phases of the Moon and the effect on the tide.
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.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.
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^ Long Period Tides; General Coefficient = 1- sin2X .

^ The tide heights are compared to the known frequencies of the astronomical tide-raising forces.
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.The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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^ The following schedules, then, give h the height of tide.

^ The behaviour of the tide heights is expected to follow the behaviour of the tide force, with the amplitude and delays of those responses remaining constant.
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.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 tide heights are compared to the known frequencies of the astronomical tide-raising forces.
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^ Because astronomical frequencies and phases can be calculated with certainty, the tide height at other times can be predicted once the response to the astronomical states has been found.
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^ 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.
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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
.The Highest Astronomical Tide is the perigean spring tide when both the Sun and the Moon are closest to the Earth.^ The Highest Astronomical Tide is the perigean spring tide when both the Sun and the Moon are closest to the Earth.
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^ Also the sun raises tides in both.

^ The Naturalis Historia of Pliny the Elder collates 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.
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.When confronted by a periodically varying function, the standard approach is to employ Fourier series, a form of orthogonal analysis that uses sinusoidal functions as a basis set, having frequencies that are zero, one, two, three, etc.^ When confronted by a periodically varying function, the standard approach is to employ Fourier series , a form of orthogonal analysis that uses sinusoid al functions as a basis set, having frequencies that are zero, one, two, three, etc.
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^ When confronted by a periodically varying function, the standard approach is to employ Fourier series , a form of orthogonal analysis that uses sinusoidal functions as a basis set, having frequencies that are zero, one, two, three, etc.
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^ A much more compact decomposition for the tides involves a combination of sinusoids having more than one fundamental frequency.
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times the frequency of a particular fundamental cycle. .These multiples are called harmonics of the fundamental frequency, and the process is termed harmonic analysis.^ For tides then, although the process is still termed harmonic analysis , it is not limited to harmonics of a single frequency.
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^ These multiples are called harmonics of the fundamental frequency, and the process is termed harmonic analysis .
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^ See the article Harmonic Analysis for the numerical processes by which Ao.

.If the basis set of sinusoidal functions suit the behaviour being modelled, relatively few harmonic terms need to be added.^ If the basis set of sinusoidal functions suit the behaviour being modelled, relatively few harmonic terms need to be added.
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^ If the basis set of sinusoidal functions are well-suited to the behaviour being modelled, relatively few harmonic terms need to be carried in the analysis.
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^ The X-Y-Z functions being simple time-harmonics, the principle of forced oscillations allows us to conclude that the forces corresponding to V in (47) will generate oscillations in the ocean of the same periods and types as the terms in V, but of unknown amplitudes and phases.

.Orbital paths are very nearly circular, so sinusoidal variations are suitable for tides.^ Orbital paths are very nearly circular, so sinusoidal variations are suitable for tides.
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^ Fortunately orbital paths are very nearly circular, so sinusoidal variations are suitable for tides.
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^ It alone would carry the satellite farther from C than it would be dragged back by the central force towards C. The satellite would describe a spiral , the coils of which would be very nearly circular and very nearly coincident.

.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.^ For tides then, although the process is still termed harmonic analysis , it is not limited to harmonics of a single frequency.
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^ For the analysis of tide heights, the Fourier series approach is best made more elaborate.
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^ For tides, then, harmonic analysis is not limited to harmonics of a single frequency.
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.The tidal patterns are decomposed into many sinusoids having many fundamental frequencies, corresponding (as in the lunar 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.^ The tidal patterns are decomposed into many sinusoids having many fundamental frequencies, corresponding (as in the lunar 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.
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^ 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 nodal tidal constituent .
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^ Coastal characteristics such as underwater topography and coastline shape mean that individual location characteristics need to be taken into consideration when forecasting tides; high water time may differ from that suggested by a model such as the one above due to the effects of coastal morphology on tidal flow.
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.For tides, then, harmonic analysis is not limited to harmonics of a single frequency.^ For tides then, although the process is still termed harmonic analysis , it is not limited to harmonics of a single frequency.
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^ For tides, then, harmonic analysis is not limited to harmonics of a single frequency.
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^ Current procedure for analysing tides follows the method of harmonic analysis introduced in the 1860s by William Thomson .
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[40] .In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier series approach.^ In other words, the harmonies are multiples of many fundamental frequencies, not just of the one fundamental frequency of the simpler Fourier series approach.
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^ In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier series approach.
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^ For the analysis of tide heights, the Fourier series approach is best made more elaborate.
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.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.^ In other words, the harmonies are multiples of many fundamental frequencies, not just of the one fundamental frequency of the simpler Fourier series approach.
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^ In other words, the harmonies are multiples of many fundamental frequencies, not just of the fundamental frequency of the simpler Fourier series approach.
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^ That is, the sum of two sinusoids, one at the Sun's frequency and the second at the Moon's frequency, requires those two terms only, but their representation as a Fourier series having only one fundamental frequency and its (integer) multiples would require many terms.
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.The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin.^ The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin .
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^ The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin.
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^ William Thomson, 1st Baron Kelvin , rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, which are known as Kelvin waves .
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.A.T. Doodson extended their work, introducing the Doodson Number notation to organise the hundreds of resulting terms.^ Their work was extended by A.T. Doodson who introduced the Doodson Number notation to organise the hundreds of terms that result.
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^ A.T. Doodson extended their work, introducing the Doodson Number notation to organise the hundreds of resulting terms.
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^ With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences of them to form the frequency of each simple cosine term.
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.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.^ 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.
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^ Since the mean value of A is s - h (the difference of the mean longitudes), and since the mean values of p and p, are 2Km, it follows that the mean value of the period elapsing after full moon and change of moon up to spring tide is ( K, - Km)/2(a - n).

^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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Each term is of the form
A·cos(w·t + p)
where .A is the amplitude, w is the angular frequency usually given in degrees per hour corresponding to t measured in hours, and p is the phase offset with regard to the astronomical state at time t = 0 .^ Each term is of the form : A ·cos( w · t + p ) where A is the amplitude, w is the angular frequency usually given in degrees per hour corresponding to t measured in hours, and p is the phase offset with regard to the astronomical state at time t = 0 .
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^ Each term is of the form A ·cos( w · t + p ) where A is the amplitude, w is the angular frequency usually given in degrees per hour corresponding to t measured in hours, and p is the phase offset with regard to the astronomical state at time t = 0 .
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^ Tidal stage is also measured in degrees, with 360° per tidal cycle.
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.There is one term for the Moon and a second term for the Sun.^ There is one term for the Moon and a second term for the Sun.
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^ In the diagram there are two balanced pulleys and one movable one; a second unit would require one more movable pulley and one more balanced one.

^ Terms There are certain terms in the tide-generating forces of t of the moon, depending on the longitude of the moon's Motion 's nodes, which complete their revolution in 18.6 years.

.The phase p of the first harmonic for the Moon term is called the lunitidal interval or high water interval.^ The phase p of the first harmonic for the Moon term is called the lunitidal interval or high water interval.
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^ That ordinate of high-water intervals which is coincident with the greatest ordinate of high-water heights gives the mean establishment.

^ Now we have seen from 03) that e (which is proportional to V ) has terms of three kinds, the first depending on twice the moon's (or sun's) hour-angle, the second on the hour-angle, and the third independent thereof.

.The next step is to accommodate the harmonic terms due to the elliptical shape of the orbits.^ The next step is to accommodate the harmonic terms due to the elliptical shape of the orbits.
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^ Factors include gravitational effects due to the Sun, 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 orbits of the Moon and the Earth.
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^ In the method of harmonic analysis we conceive the tidal forces or potential due to each disturbing body to be developed in a series of terms each consisting of a constant (determined by the elements of the planet's orbit and the obliquity of the ecliptic) multiplied by a simple harmonic function of the time.

.Accordingly, the value of A is not a constant but also varying with time, slightly, about some average figure.^ Accordingly, the value of A is not a constant but also varying with time, slightly, about some average figure.
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^ Strictly speaking, u should be taken as the same function of the longitude of the moon's node, varying as the node moves; but, as the variation is but small in the course of a year, u may be treated as a constant and put equal to an average value for the year, which average value is taken as the true value of u at exactly mid year.

^ It follows from these two results that there must be some intermediate periodic time of the satellite for which the eccentricity does not tend to vary.

.Replace it then by A(t) where A is another sinusoid, similar to the cycles and epicycles of Ptolemaic theory.^ It turns out that another sinusoid gives an excellent approximation for the changing amplitude, similar to the cycles and epicycles of Ptolemaic theory .
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Accordingly,
A(t) = A·(1 + Aa·cos(wa·t + pa)) ,
which is to say an average value .A with a sinusoidal variation about it of magnitude Aa , with frequency wa and phase pa .^ Accordingly, A ( t ) = A ·(1 + A a ·cos( w a · t + p a )) , which is to say an average value A with a sinusoidal variation about it of magnitude A a , with frequency w a and phase p a .
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^ Accordingly, : A ( t ) = A ·(1 + A a ·cos( w a · t + p a )) , which is to say an average value A with a sinusoidal variation about it of magnitude A a , with frequency w a and phase p a .
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Thus the simple term is now the product of two cosine factors:
A·[1 + Aa·cos(wa + pa)]·cos(w·t + p)
Given that for any x and y
cos(x)·cos(y) = ½·cos( x + y ) + ½·cos( xy ) ,
it is clear that a compound term involving the product of two cosine terms each with their own frequency is the same as .three simple 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.^ Thus the simple term is now the product of two cosine factors: : A · »+ A a ·cos( w a + p a ) ·cos( w · t + p ) Given that for any x and y :cos( x )·cos( y ) = ½·cos( x + y ) + ½·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 as three simple 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.
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^ Thus the simple term is now a compound term, the product of two cosine factors: A ·[1 + A a ·cos( w a + p a )]·cos( w · t + p ) Now, given that for any x and y cos( x )·cos( y ) = ½·cos( x + y ) + ½·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 as three simple cosine terms that are to be added, at the original frequency and also at the sum and difference of the two frequencies of the product term.
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^ With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences of them to form the frequency of each simple cosine term.
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.(Three, not two terms, since the whole expression is (1 + cos(x))·cos(y) .^ (Three, not two terms, since the whole expression is (1 + cos( x ))·cos( y ) .
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^ Thus the simple term is now the product of two cosine factors: : A · »+ A a ·cos( w a + p a ) ·cos( w · t + p ) Given that for any x and y :cos( x )·cos( y ) = ½·cos( x + y ) + ½·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 as three simple 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.
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^ Thus the simple term is now a compound term, the product of two cosine factors: A ·[1 + A a ·cos( w a + p a )]·cos( w · t + p ) Now, given that for any x and y cos( x )·cos( y ) = ½·cos( x + y ) + ½·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 as three simple cosine terms that are to be added, at the original frequency and also at the sum and difference of the two frequencies of the product term.
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) .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.^ 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.
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^ The Naturalis Historia of Pliny the Elder collates 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.
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^ If the satellite be close to the planet the rate of increase of the satellite's periodic time or month is large compared with the rate of increase of the period of planetary rotation or day; but if the satellite is far off the converse is true.

.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.^ With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences of them to form the frequency of each simple cosine term.
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^ 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.
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^ Their work was extended by A.T. Doodson who introduced the Doodson Number notation to organise the hundreds of terms that result.
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Graph showing one line each for M 2, S 2, N 2, K 1, O 1, P 1, and one for their summation, with the X axis spanning slightly more than a single day
Fig. 8: Tidal prediction summing constituent parts.
.Remember that astronomical tides do not include weather effects.^ Remember that astronomical tides do not include weather effects.
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^ Remember that astronomical tides do not include the effect of weather, and changes to local conditions (sandbank movement, dredging harbour mouths, etc.
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^ Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide.
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.Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.^ Also, changes to local conditions (sandbank movement, dredging harbour mouths, etc.
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^ Remember that astronomical tides do not include the effect of weather, and changes to local conditions (sandbank movement, dredging harbour mouths, etc.
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^ Remember always that calculated tidal heights take no account of weather effects, nor include any changes to conditions since the coefficients were determined, such as movement of sandbanks or dredging, etc.
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) 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.^ 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.
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^ Organisations quoting a "highest astronomical tide" for some location can exaggerate the figure as a safety factor against uncertainties of analysis, extrapolation from the nearest point of measurement, changes since the time of observation, possible ground subsidence, etc., to protect the organisation against blame should an engineering work be overtopped.
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^ At the same time Johannes Kepler correctly suggested that the moon caused the tides, based upon ancient observation and correlations, which was rejected by Galileo.
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.Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide.^ Special care is needed when assessing the size of a "weather surge" by subtracting the astronomical tide from the observed tide.
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^ It is estimated by subtracting the normal astronomic tide from the observed storm tide.
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^ If the size of a "weather surge" is assessed by subtracting the astronomical tide from the observed tide at the time, care is needed.
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.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.^ 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 .
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^ These influences are called tidal constituents.
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^ 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 nodal tidal constituent .
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.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 nodal tidal constituent.^ Conversely, long period constituents cycle over days, months, or years.
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^ Nineteen years is preferred because the relative positions of the Earth, Moon and Sun repeat almost exactly in the Metonic cycle of 18.6 years.
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^ The Earth's rotation relative to this shape causes the daily tidal cycle.
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.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.^ 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.
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^ This analysis can be done using only the knowledge of the period of forcing, but without detailed understanding of the mathematical derivation, which means that useful tidal tables have been constructed for centuries.
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^ 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 .
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[41] .The resulting amplitudes and phases can then be used to predict the expected tides.^ The resulting amplitudes and phases can then be used to predict the expected tides.
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^ Because the M 2 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.
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^ The main result was the building of a tide-predicting machine using a system of pulleys to add together six harmonic functions of time.
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.These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours (diurnal) as well.^ These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours ( diurnal ) as well.
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^ Because the M 2 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.
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^ The tides occur with a period of approximately 12 and a half hours and are influenced by the shape of the near-shore bottom .
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.Longer term constituents are 14 day or fortnightly, monthly, and semiannual.^ Longer term constituents are 14 day or fortnightly , monthly, and semiannual.
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^ In the semidiurnal areas, the primary constituents M 2 (lunar) and S 2 (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).
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.Semidiurnal tides dominated coastline, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal.^ Semidiurnal tides dominated coastline, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal.
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^ Most of the coastline is dominated by semidiurnal tides, but some areas such as the South China Sea and the Gulf of Mexico are primarily diurnal.
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^ W. This must be the same, if such an island exists, which is very doubtful, and totally disbelieved in by South Sea traders.'
  • The Ebb-Tide by Robert Louis Stevenson in collaboration with Lloyde Osbourne - Full Text Free Book (Part 2/3) 20 September 2009 12:18 UTC www.fullbooks.com [Source type: Original source]

.In the semidiurnal areas, the primary constituents M2 (lunar) and S2 (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).^ In the semidiurnal areas, the primary constituents M 2 (lunar) and S 2 (solar) periods differ slightly, so that the relative phases, and thus the amplitude of the combined tide, change fortnightly (14 day period).
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^ Principal lunar semidiurnal constituent .
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^ Longer term constituents are 14 day or fortnightly , monthly, and semiannual.
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[42]
.In the M2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.^ In the M 2 plot above, each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.
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^ The difference of cotidal phase from the phase of a reference tide is the epoch .
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^ In the M 2 plot above each cotidal line differs by one hour from its neighbors, and the thicker lines show tides in phase with equilibrium at Greenwich.
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.The lines rotate around the amphidromic points counterclockwise in the northern hemisphere so that from Baja California to Alaska and from France to Ireland the M2 tide propagates northward.^ The lines rotate around the amphidromic points counterclockwise in the northern hemisphere so that from Baja California to Alaska and from France to Ireland the M 2 tide propagates northward.
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^ The lines rotate around the amphidromic point s counterclockwise in the northern hemisphere so that from Baja California to Alaska and from France to Ireland the M 2 tide propagates northward.
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^ 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.
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.In the southern hemisphere this direction is clockwise.^ In the southern hemisphere this direction is clockwise.
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^ This rotation is generally clockwise in the southern hemisphere and counterclockwise in the northern hemisphere, and is caused by the Coriolis effect.
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.On the other hand M2 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.^ On the other hand M 2 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.
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^ On the other hand M 2 tide propagates counterclockwise around New Zealand, but this because the islands act as a dam and permit the tides to have different heights on opposite sides of the islands.
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^ (The rare exception occurs when the tide circles around an island, as it does around New Zealand .
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.(The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.^ (The tides do propagate northward on the east side and southward on the west coast, as predicted by theory.
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^ (But the tides do propagate northward on the east side and southward on the west coast, as predicted by theory.
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^ Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier .
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)
.The exception is at Cook Strait where the tidal currents periodically link high to low water.^ The exception is the Cook Strait where the tidal currents periodically link high to low water.
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^ Cook Strait's nautical chart offers tidal current information.
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^ The exception is at Cook Strait where the tidal currents periodically link high to low water.
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.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.^ The exception is the Cook Strait where the tidal currents periodically link high to low water.
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^ This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high water across from low water.
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^ 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.
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.Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M2 patterns cannot be used for other tide components.^ Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M 2 patterns cannot be used for other tide components.
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^ The resulting amplitudes and phases can then be used to predict the expected tides.
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^ Because the M 2 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.
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Example calculation

Graph with a single line rising and falling between 4 peaks around 3 and four valleys around -3
Fig. 9: Tides at Bridgeport, Connecticut, U.S.A. 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
Fig. 10: Tides at Bridgeport, Connecticut, U.S.A. during a 30 day period.
Graph showing with a single line showing only a minimal annual tidal fluctuation
Fig. .11: Tides at Bridgeport, Connecticut, U.S.A. during a 400 day period.
Graph showing 6 lines with two lines for each of three cities.</span><span class=^ The number f is a fraction such that its reciprocal is twice the number of sidereal days in the period of the tide.

^ All tides whose period is an exact multiple or submultiple of a mean solar day, or of a tropical year, are affected by meteorological Meteoro- conditions.

.Nelson has two monthly spring tides, while Napier and Wellington each have one."^ Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier .
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^ At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to .
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^ Now observation shows that at this port the two tides are nearly equal to one another, and that their greatest difference is not a thirtieth of their sum.

src="http://images-mediawiki-sites.thefullwiki.org/03/3/3/5/7431007621418437.png" width="250" height="158" class="thumbimage" />
Fig. 12: Two spring tides per month vs. one.
.Figure 9 shows the common pattern of two daily tidal peaks (the precise cycle time is 12.4206 hours).^ U.S.A. during a 50 hour period.|alt=Graph with a single line rising and falling between 4 peaks around 3 and four valleys around -3]] Figure 9 shows the common pattern of two daily tidal peaks (the precise cycle time is 12.4206 hours).
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^ Figure 10 shows the common pattern of two tidal peaks in a day, though remember that the repeat time is not exactly twelve hours but 12.4206 hours.
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^ Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier .
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.The two peaks are not equal: the twin tidal bulges beneath the Moon and on the opposite side of the Earth align with the Moon.^ The two peaks are not equal: the twin tidal bulges beneath the Moon and on the far side of the Earth are aligned with the Moon.
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^ Bridgeport is north of the equator, so when the Moon is north of the equator also and shining upon Bridgeport, Bridgeport is closer to its maximum effect than approximately twelve hours later when Bridgeport is on the far side of the Earth from the Moon and the high tide bulge at Bridgeport's longitude has its maximum south of the equator.
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^ The ocean surface moves to adjust to changing tidal equipotential, tending to rise when the tidal potential is high, the part of the Earth nearest the Moon, and the farthest part.
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.Bridgeport is north of the equator, so when the Moon is north of the equator also and shining upon Bridgeport, Bridgeport is closer to its maximum tide than approximately twelve hours later when Bridgeport is on the opposite side of the Earth from the Moon and the high tide bulge at Bridgeport's longitude has its maximum south of the equator.^ The Sun also cycles from north to south of the equator, while the Earth–Sun and Earth–Moon distances change on their own cycles.
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^ Bridgeport is north of the equator, so when the Moon is north of the equator also and shining upon Bridgeport, Bridgeport is closer to its maximum tide than approximately twelve hours later when Bridgeport is on the opposite side of the Earth from the Moon and the high tide bulge at Bridgeport's longitude has its maximum south of the equator.
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^ As the Moon moves around its orbit it changes from north of the equator to south of the equator.
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.Thus the two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), and again.^ Thus the two high tides a day alternate in maximum heights: lower high (just under three feet), higher high (just over three feet), and again.
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^ Similarly, the two low waters each day are the higher low water and the lower low water .
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^ Similarly, the two low waters each day are referred to as the higher low water and the lower low water .
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.Likewise for the low tides.^ Likewise for the low tides.
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.Figure 10 shows the spring tide/neap tide cycle in tidal amplitudes as the Moon orbits the Earth from being in line (Sun–Earth–Moon, or Sun–Moon–Earth) when the two main influences combine to give the spring tides, to when the two forces are opposing each other as when the angle Moon–Earth–Sun is close to ninety degrees, producing the neap tides.^ At spring tide the two effects add to each other to a theoretical level of , while at neap tide the theoretical level is reduced to .
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^ Figure 11 shows the spring tide / neap tide cycle in the amplitudes of the tides as the Moon orbits the Earth from being in line (Sun–Earth–Moon, or Sun–Moon–Earth) when the two main influences combine to give the spring tides, to when the two forces are opposing each other as when the angle Moon–Earth–Sun is close to ninety degrees producing the neap tides.
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^ This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun.
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.As the Moon moves around its orbit it changes from north of the equator to south of the equator.^ This was not the case when the moon was deemed to move on the equator.

^ The Sun also cycles from north to south of the equator, while the Earth–Sun and Earth–Moon distances change on their own cycles.
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^ Note also as the Moon moves around its orbit it also changes from north of the equator to south of the equator.
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.The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the Moon is above the equator), then redevelops but with the other polarity, waxing to a maximum difference and then waning again.^ The alternation in the heights of the high tides becomes smaller, until they are the same (the Moon is above the equator), then redevelops but with the other polarity, waxing to a maximum difference and then waning again.
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^ The alternation in high tide heights becomes smaller, until they are the same (at the lunar equinox, the Moon is above the equator), then redevelops but with the other polarity, waxing to a maximum difference and then waning again.
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^ At the same time Johannes Kepler correctly suggested that the moon caused the tides, based upon ancient observation and correlations, which was rejected by Galileo.
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.Figure 11 shows just over a year's worth of tidal height calculations.^ Figure 11 shows just over a year's worth of tidal height calculations.
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^ Figure 12 shows just over a year's worth of tidal height calculations.
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^ Figure 12 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.
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.The Sun also cycles from north to south of the equator, while the Earth–Sun and Earth–Moon distances change on their own cycles.^ The Sun also cycles between being north or south of the equator and as well the Earth–Sun and Earth–Moon distances change on their own cycles.
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^ The Sun also cycles from north to south of the equator, while the Earth–Sun and Earth–Moon distances change on their own cycles.
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^ The changing distance separating the Moon and Earth also affects tide heights.
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.None of the various cycle periods are commensurate.^ None of the various cycle periods are commensurate.
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[citation needed]

Current

.The tides' influence on current flow is much more difficult to analyse, and data is much more difficult to collect.^ The tides' influence on current flow is much more difficult to analyse, and data is much more difficult to collect.
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^ The flow pattern caused by tidal influence is much more difficult to analyse, and also, data is much more difficult to collect.
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^ A much more compact decomposition for the tides involves a combination of sinusoids having more than one fundamental frequency.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

.A tidal height is a simple number which applies to a wide region simultaneously.^ A tidal height is a simple number which applies to a wide region simultaneously — often as far as the eye can see.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ A tidal height is a simple number which applies to a wide region simultaneously.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ While the theorem remains true and the tidal height could be analysed in terms of a single frequency and its harmonics, a large number of significant terms would be required.
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.A flow has both a magnitude and a direction, both of which can vary substantially with depth and over short distances due to local bathymetry.^ A flow has both a magnitude and a direction, both of which can vary substantially with depth and over short distances due to local bathymetry.
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^ A flow has both a magnitude and a direction, which both can vary substantially over just a short distance due to local bathymetry, and also vary with depth below the water surface.
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^ Real amplitudes differ considerably, not only because of variations in ocean depth, and the obstacles to flow caused by the continents, but also because the natural period of wave propagation is of the same order of magnitude as the rotation period: about 30 hours.
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.Also, although a water channel's center is the most useful measuring site, mariners object when current-measuring equipment obstructs waterways.^ Also, although the centre of a channel is the most useful measuring site, mariners will not accept a current measuring installation obstructing navigation, so a flexible approach is required.
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^ Also, although a water channel's center is the most useful measuring site, mariners object when current-measuring equipment obstructs waterways.
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^ Because the M 2 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.
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.A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel.^ A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel.
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^ Variations in barometric pressure also ' p ' Land- runs in the direction analogous to up stream for three §4.

^ A flow has both a magnitude and a direction, both of which can vary substantially with depth and over short distances due to local bathymetry.
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.Surprisingly, flood and ebb flows are often not in opposite directions.^ But contrary even to the obvious expectation, flood and ebb flows are often not in opposite directions.
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^ Surprisingly, flood and ebb flows are often not in opposite directions.
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^ Nevertheless, analysis of currents proceeds on the same basis as tides: At a given location in the simple case, the great majority of the flood flow will be in one direction, and the ebb flow in another (not necessarily opposite) direction.
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.Flow direction is determined by the upstream channel's shape, not the downstream channel's shape.^ Flow direction is determined by the upstream channel's shape, not the downstream channel's shape.
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^ A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel.
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.Likewise, eddies may form in only one flow direction.^ Likewise, eddies can form in one direction but not the other.
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^ Likewise, eddies may form in only one flow direction.
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^ There are therefore four ways in which the system may degrade, according to the way it was started; but we shall only consider one, that corresponding to the portion ABba of the figure.

.Nevertheless, current analysis is similar to tidal analysis: in the simple case, at a given location the flood flow is in mostly one direction, and the ebb flow in another direction.^ Nevertheless, analysis of currents proceeds on the same basis as tides: At a given location in the simple case, the great majority of the flood flow will be in one direction, and the ebb flow in another (not necessarily opposite) direction.
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies.
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.Flood velocities are given positive sign, and ebb velocities negative sign.^ The velocities measured along the flood direction are taken as positive, and along the ebb direction as negative, and analysis proceeds as if these were tide height figures.
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.Analysis proceeds as though these are tide heights.^ Analysis proceeds as though these are tide heights.
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^ However original any future contribution to the science of the tides may be, it would seem as though it must perforce be based on the work of these two.

^ The study of tide height by harmonic analysis was begun by Laplace, William Thomson (Lord Kelvin), and George Darwin .
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.In more complex situations, the main ebb and flood flows do not dominate.^ More Men near Ebb And flow .
  • Ebb And flow singles - Ebb And flow dating - Ebb And flow personals 22 September 2009 16:32 UTC uk.match.com [Source type: General]

^ More Women near Ebb And flow .
  • Ebb And flow singles - Ebb And flow dating - Ebb And flow personals 22 September 2009 16:32 UTC uk.match.com [Source type: General]

^ In more complex situations, the main ebb and flood flows do not dominate.
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.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 more complex situations, the flow will not be dominated by the main ebb and flow directions, with the flow direction and magnitude tracing out an ellipse over a tidal cycle (on a polar plot) instead of along the two lines of ebb and flow direction.
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^ Surprisingly, flood and ebb flows are often not in opposite directions.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ 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.
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.In this case, analysis might proceed along pairs of directions, with the primary and secondary directions at right angles.^ In this case, analysis might proceed along pairs of directions, with the primary and secondary directions at right angles.
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^ In this case, analysis might proceed along two pairs of directions, the primary flow directions and the secondary directions at right angles.
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^ Thus we see that the tidal forces tend to pull the water towards and away from the moon, and to depress the water at right angles to that direction.

.An alternative is to treat the tidal flows as complex numbers, as each value has both a magnitude and a direction.^ An alternative is to treat the tidal flows as complex numbers, as each value has both a magnitude and a direction.
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ The relative magnitudes of the tidal forces are given by the numbers on the figure.

.Tide flow information is most commonly seen on nautical charts, presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides.^ Tide flow information is most commonly seen on nautical chart s, presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides.
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^ Tide tables Tide charts Tide detergent coup...
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ 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.
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.The timing is relative to high water at some harbour where the tidal behaviour is similar in pattern, though it may be far away.^ The timing is relative to high water at some harbour where the tidal behaviour is similar in pattern, though it may be far away.
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^ These depths are relative to a " chart datum ", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle.
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^ If the sun be now introduced we have another similar tide of about half the height, and this depends on solar time, giving low-water somewhere about noon and midnight.

.As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weather conditions, which can completely change the outcome.^ As with tide height predictions, tide flow predictions based only on astronomical factors do not take account of weather conditions, which can completely change the situation.
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^ As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weather conditions, which can completely change the outcome.
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^ The only tides in which it has hitherto been thought necessary to represent this change of form belong to the principal lunar and principal solar series.

.The tidal flow through Cook Strait between 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.^ Again, New Zealand has particularly interesting opportunities.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ The exception is the Cook Strait where the tidal currents periodically link high to low water.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ A further complication for Cook Strait's flow pattern is that the tide at the north side(e.g.
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.Strong currents result, with almost zero tidal height change in the strait's center.^ Strong currents result, with almost zero tidal height change in the strait's center.
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^ Strong currents result, with almost zero tidal height change in the centre of the strait.
  • Tide encyclopedia topics | Reference.com 18 January 2010 0:43 UTC www.reference.com [Source type: FILTERED WITH BAYES]

^ (The strong currents through the Strait of Messina and between Greece and the island of Euboea through the Euripus puzzled Aristotle ).
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.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.^ 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.
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ And he could have found in his heart to regret that she was not a goddess, nor yet he a pagan, that he might have bowed down before her in that hour of difficulty.
  • The Ebb-Tide by Robert Louis Stevenson in collaboration with Lloyde Osbourne - Full Text Free Book (Part 2/3) 20 September 2009 12:18 UTC www.fullbooks.com [Source type: Original source]

.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.^ 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.
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^ A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ As with tide height predictions, tide flow predictions based only on astronomical factors do not incorporate weather conditions, which can completely change the outcome.
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A further complication for Cook Strait's flow pattern is that the tide at the north side(e.g. at .Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier.^ Nelson) follows the common bi-weekly spring–neap tide cycle (as found along the west side of the country), but the south side's tidal pattern has only one cycle per month, as on the east side: Wellington, and Napier .
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^ 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).
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^ 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 end (Nelson) has a counterpart spring tide at the south end (Wellington), so the resulting behaviour follows neither reference harbour.
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.Figure 12 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.^ Figure 12 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.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Figure 11 shows just over a year's worth of tidal height calculations.
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^ Tide tables list each day's high and low water heights and times.
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.Cook Strait's nautical chart offers tidal current information.^ Cook Strait's nautical chart offers tidal current information.
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^ 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.
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^ Tide flow information is most commonly seen on nautical chart s, presented as a table of flow speeds and bearings at hourly intervals, with separate tables for spring and neap tides.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.For instance the January 1979 edition for 41°13·9’S 174°29·6’E (north west of Cape Terawhiti) refers timings to Westport while the January 2004 issue refers to Wellington.^ For instance the January 1979 edition for 41°13·9’S 174°29·6’E (north west of Cape Terawhiti) refers timings to Westport while the January 2004 issue refers to Wellington.
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.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.^ 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.
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^ Strong currents result, with almost zero tidal height change in the strait's center.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Cook Strait's nautical chart offers tidal current information.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.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 end (Nelson) has a counterpart spring tide at the south end (Wellington), so the resulting behaviour follows neither reference harbour.^ Strong currents result, with almost zero tidal height change in the strait's center.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ 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 end (Nelson) has a counterpart spring tide at the south end (Wellington), so the resulting behaviour follows neither reference harbour.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Cook Strait's nautical chart offers tidal current information.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

[citation needed]

Power generation

.Tidal energy can be extracted by two means: inserting a water turbine into a tidal current, or building ponds that release/admit water through a turbine.^ Tidal energy can be extracted by two means: inserting a water turbine into a tidal current, or building ponds that release/admit water through a turbine.
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^ There are, it is true, diurnal tidal currents, but they are so arranged that the water level remains unchanged.

^ In the first case, the energy amount is entirely determined by the timing and tidal current magnitude.
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.In the first case, the energy amount is entirely determined by the timing and tidal current magnitude.^ In the first case, the energy amount is entirely determined by the timing and tidal current magnitude.
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^ The equations are It would seem at first sight as if these equations would suffice to determine all the C's in terms of C2, and that C2 would remain indeterminate; but we shall show that this is not the case.

^ From ancient times, tidal observation and discussion has increased in sophistication, first marking the daily recurrence, then tides' relationship to the Sun and Moon.
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.However, the best currents may be unavailable because the turbines would obstruct ships.^ However, the best currents may be unavailable because the turbines would obstruct ships.
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^ However original any future contribution to the science of the tides may be, it would seem as though it must perforce be based on the work of these two.

.In the second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, ship navigation is disrupted.^ In the second, the impoundment dams are expensive to construct, natural water cycles are completely disrupted, ship navigation is disrupted.
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.However, with multiple ponds, power can be generated at chosen times.^ However, with multiple ponds, power can be generated at chosen times.
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^ 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.
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.So far, there are few installed systems for tidal power generation (most famously, La Rance by Saint Malo, France) which faces many difficulties.^ So far, there are few installed systems for tidal power generation (most famously, La Rance by Saint Malo , France) which faces many difficulties.
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^ While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates.
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^ Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects.
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.Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineering challenges.^ Aside from environmental issues, simply withstanding corrosion and biological fouling pose engineering challenges.
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.Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects.^ Tidal power proponents point out that, unlike wind power systems, generation levels can be reliably predicted, save for weather effects.
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^ So far, there are few installed systems for tidal power generation (most famously, La Rance by Saint Malo , France) which faces many difficulties.
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^ 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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.While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates.^ While some generation is possible for most of the tidal cycle, in practice turbines lose efficiency at lower operating rates.
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^ So far, there are few installed systems for tidal power generation (most famously, La Rance by Saint Malo , France) which faces many difficulties.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ These depths are relative to a " chart datum ", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle.
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.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.^ 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.
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^ However, with multiple ponds, power can be generated at chosen times.
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^ In the curve of high-water intervals the ordinate corresponding to XII. is the establishment, since it gives the time of high-water at full moon and change of moon.

Navigation

Chart illustrating that tidal heights enter in calculations of legally significant data such as boundary lines between the high seas and territorial waters. <a name=.Chart shows an exemplar coastline, identifying bottom features such as longshore bar and berms, tidal heights such as mean higher high water, and distances from shore such as the 12 mile limit."^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
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^ 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.
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^ In fact, observation shows that it is more nearly lowwater than high-water when the moon is on the meridian.

src="http://images-mediawiki-sites.thefullwiki.org/05/3/6/0/30266932426421908.gif" width="425" height="282" class="thumbimage" />
Fig. 13: Civil and maritime uses of tidal data
.Tidal flows are important for navigation, and significant errors in position occur if they are not accommodated.^ Tidal flows are important for navigation, and significant errors in position occur if they are not accommodated.
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^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
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^ When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
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^ If the sun be now introduced we have another similar tide of about half the height, and this depends on solar time, giving low-water somewhere about noon and midnight.

^ The tide heights are expected to follow the tidal force, with a constant amplitude and phase delay for each component.
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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".[43]
.Tidal flow timings and velocities appear in tide charts or a tidal stream atlas.^ Tidal flow timings and velocities appear in tide charts or a tidal stream atlas .
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ But the use of the adjective " tidal " appears to us erroneous in this context, for the tide is a rising and falling of the water of the sea produced by the attraction of the sun and moon .

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.^ 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.
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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^ Intertidal ecology is the study of intertidal ecosystems, where organisms live between the low and high water lines.
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.An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots) for spring and neap tides.^ Neap rise " is used to mean the average height between high-water of neap tides and low-water of spring tides.

^ Thus both at springs and neaps the term " rise " refers to the rise above the level of low-water at spring tide.

^ As we have already indicated, the tide in British seas has mainly a progressive character, and the general march of the wave may be exhibited on a chart by what are called cotidal lines.

.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.^ 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.
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^ 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.
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^ 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).
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.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 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.
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^ 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).
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

.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).^ 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).
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ 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.
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.Nautical charts display the water's "charted depth" at specific locations with "soundings" and the use of bathymetric contour lines to depict the submerged surface's shape.^ Nautical chart s display the water's "charted depth" at specific locations with "soundings" and the use of bathymetric contour line s to depict the submerged surface's shape.
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^ To calculate the actual water depth, add the charted depth to the published tide height.
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^ 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.
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.These depths are relative to a "chart datum", which is typically the water level at the lowest possible astronomical tide (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 exposed seabed at the lowest astronomical tide.
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^ These depths are relative to a " chart datum ", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle.
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^ An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots ) for spring and neap tides.
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."Drying heights" may also be shown on the chart, which are the heights of the exposed seabed at the lowest astronomical tide.^ "Drying heights" may also be shown on the chart, which are the heights of the exposed seabed at the lowest astronomical tide.
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^ If e denotes the equilibrium height of the tide, it is a function of colatitude and longitude, and may be expanded in a series of spherical surface harmonics e i.

^ These depths are relative to a " chart datum ", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle.
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.Tide tables list each day's high and low water heights and times.^ Tide tables list each day's high and low water heights and times.
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^ Tidal heights are also important; for example many rivers and harbours have a shallow "bar" at the entrance which prevents boats with significant draft from entering at low tide.
  • � Tide Data �"; 18 January 2010 0:43 UTC www.aadet.com [Source type: FILTERED WITH BAYES]

^ In Europe around 730 AD, the Venerable Bede described 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.
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.To calculate the actual water depth, add the charted depth to the published tide height.^ To calculate the actual water depth, add the charted depth to the published tide height.
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^ "Drying heights" may also be shown on the chart, which are the heights of the exposed seabed at the lowest astronomical tide.
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^ These depths are relative to a " chart datum ", which is typically the water level at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum possible water depth during the tidal cycle.
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.Depth for other times can be derived from tidal curves published for major ports.^ Depth for other times can be derived from tidal curves published for major ports.
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^ 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.
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.The rule of twelfths can suffice if an accurate curve is not available.^ The rule of twelfths can suffice if an accurate curve is not available.
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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

Photo of partially submerged rock showing horizontal bands of different color and texture, where each band represents a different fraction of time spent submerged.
Fig. 14: A rock, seen at low water, exhibiting typical intertidal zonation.
.Intertidal ecology is the study of intertidal ecosystems, where organisms live between the low and high water lines.^ Neap rise " is used to mean the average height between high-water of neap tides and low-water of spring tides.

^ In considering any single oscillation of water level we find, especially in estuaries, that the interval from high to low-water is longer than that from low to high-water, and the difference between these two intervals is greater at springs than at neaps.

^ The " diurnal inequality " of the tide denotes the fact that successive high-waters and successive low-waters are unequal to one another.

.At low water, the intertidal is exposed (or ‘emersed’) whereas at high water, the intertidal is underwater (or ‘immersed’).^ Neap rise " is used to mean the average height between high-water of neap tides and low-water of spring tides.

^ The " diurnal inequality " of the tide denotes the fact that successive high-waters and successive low-waters are unequal to one another.

^ In either case the observations may be made every hour, or the times and heights of high and low-water may be noted.

Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, as well as among the different species. The most important interactions may vary according to the type of intertidal community. The broadest classifications are based on substrates — rocky shore or soft bottom.
Intertidal organisms experience a highly variable and often hostile environment, and have adapted to cope with and even exploit these conditions. .One easily visible feature is vertical zonation, in which the community divides into distinct horizontal bands of specific species at each elevation above low water.^ The " diurnal inequality " of the tide denotes the fact that successive high-waters and successive low-waters are unequal to one another.

.A species' ability to cope with desiccation determines its upper limit, while competition with other species sets its lower limit.^ At any other state of the moon, except full and change, the " interval " or " lunitidal interval " means the interval between the moon's upper or lower transit and high-water.

Humans use intertidal regions for food and recreation. Overexploitation can damage intertidals directly. Other anthropogenic actions such as introducing invasive species and climate change have large negative effects. Marine Protected Areas are one option communities can apply to protect these areas and aid scientific research.

Biological rhythms

The approximately fortnightly tidal cycle has large effects on intertidal organisms. Hence their biological rhythms tend to occur in rough multiples of this period. Many other animals such as the vertebrates, display similar rhythms. Examples include gestation and egg hatching. .In humans, the menstrual cycle lasts roughly a month, an even multiple of the tidal period.^ In consequence of the tidal friction the periodic times both of the moon (or the month) and of the earth's rotation (or the day) increase; but the month increases in length at a much greater rate than the day.

Such parallels at least hint at the common descent of all animals from a marine ancestor.[44]

Other tides

.When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies.^ There are, it is true, diurnal tidal currents, but they are so arranged that the water level remains unchanged.

^ In ordinary parlance sailors very commonly use the term " tide " when they mean what may be more accurately described as a tidal current.

^ The resultant oscillation of the ocean must therefore be the summation of a series of partial waves generated at each instant by the moon and always falling behind her, and the aggregate wave, being the same at each instant, must travel 1000 m.

.Such waves are called internal tides.^ As we have already indicated, the tide in British seas has mainly a progressive character, and the general march of the wave may be exhibited on a chart by what are called cotidal lines.

.In addition to oceanic tides, large lakes can experience small tides and even planets can experience atmospheric tides and earth tides.^ Hence for steel the oceanic tides would be reduced to 1, and for glass to of the tides on a rigid earth.

^ Although the results would be practically the same for any system of frictionally resisted tides, we shall speak below of the planet or earth as a viscous body.'

^ True astronomical tides in the atmosphere would be shown by a ' Lord Kelvin shows that the attraction of the sun on these tides must produce an excessively small acceleration of the earth's rotation.

These are continuum mechanical phenomena. The first two take place in fluids. The third affects the Earth's thin solid crust surrounding its semi-liquid interior (with various modifications).

Lake tides

.Large lakes such as Superior and Erie can experience tides of 1 to 4 cm, but these can be masked by meteorologically induced phenomena such as seiche.^ Such alterations may be inextricably involved with the rise and fall of the true astronomical tide, but we shall here distinguish them as meteorological tides.

[45] The tide in Lake Michigan is described as 0.5 inches to 1.5 inches[46] or 1 and 3/4 inches.[47]

Atmospheric tides

.Atmospheric tides are negligible at ground level and aviation altitudes, masked by weather's much more important effects.^ That work also reproduces in more modern form Airy's investigation of the effects of friction on the tides of rivers.

^ Now it is more important in the theory of the tides to know what occurs at spring tide than what occurs at full and change of moon.

.Atmospheric tides are both gravitational and thermal in origin and are the dominant dynamics from about 80–120 kilometres (50–75 mi) above which the molecular density becomes too low to support fluid behavior.^ Thus both at springs and neaps the term " rise " refers to the rise above the level of low-water at spring tide.

Earth tides

Earth tides or terrestrial tides affect the entire Earth's mass, which acts similarly to a liquid gyroscope with 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' semidiurnal amplitude can reach about 55 centimetres (22 in) at the equator—15 centimetres (5.9 in) is due to the Sun—which is important in GPS calibration and VLBI measurements.^ This is the equation of continuity, and, together with (15), it forms the system which must be integrated in the general problem of the tides.

^ It is well known that there are strongly marked diurnal and semi-diurnal inequalities of the barometer due to the sun's heat, and they may be described as atmospheric meteorological tides.'

^ We shall only consider in detail the case of greatest interest, namely that of the most important of the tides generated by the attraction of the sun and moon.

.Precise astronomical angular measurements require knowledge of the Earth's rotation rate and nutation, both of which are influenced by earth tides.^ It must be clear from the sketch just given that the effect of tidal friction is that the angular motion of the moon round the earth is retarded, but not to so great an extent as the earth's rotation.

^ True astronomical tides in the atmosphere would be shown by a ' Lord Kelvin shows that the attraction of the sun on these tides must produce an excessively small acceleration of the earth's rotation.

^ In these units the present angular velocity of the Moment of earth's diurnal rotation is expressed by 0.7044, and the Momentum.

.The semi-diurnal M2 Earth tides are nearly in phase with the Moon with a lag of about two hours.^ The average age is about 36 hours as far as observations have yet been Tide.

^ It is best, then, only to attempt a partial synthesis, and to admit the existence of two diurnal tides.

^ Now yx 3 is equal to x 3 (h - x ), and this is a maximum when x = fh and the maximum number of days in the month is ( lh) 3 (h-1h ) or 33h4/44; if h is equal to 4, as is nearly the case for the earth and moon, this becomes 27.

[citation needed]
Some particle physics experiments must adjust for terrestrial tides.[48] .For instance, at CERN and SLAC, the very large particle accelerators account for terrestrial tides.^ Let Amounf of us now turn to such a port as Aden , where the weather Error at is very uniform, but the tides very complex on account Aden.

Among the relevant effects are circumference deformation for circular accelerators and particle beam energy.[49][50] .Since tidal forces generate currents in conducting fluids in the Earth's interior, they in turn affect the Earth's magnetic field.^ Hence the ellipticity of an earth of steel under tide-generating force would be a of that of a fluid earth, and the fraction for glass would be 6.

^ If the fluid in which the tides are raised were perfectly frictionless,' or if the earth were a perfect fluid or perfectly elastic, the apices of the tidal spheroid would be at M and M'.

^ There are, it is true, diurnal tidal currents, but they are so arranged that the water level remains unchanged.

Earth tides have also been linked to earthquakes.[51]

Galactic tides

Galactic tides are the tidal forces exerted by galaxies on stars within them and satellite galaxies orbiting them. .The galactic tide's effects on the Solar System's Oort cloud are believed to cause 90 percent of long-period comets.^ All tides whose period is an exact multiple or submultiple of a mean solar day, or of a tropical year, are affected by meteorological Meteoro- conditions.

^ Long Period Tides; General Coefficient = 1- sin2X .

^ By an examination of the probable effects of solar tidal friction on a contracting planetary mass, we have been led to assign a cause for the observed distribution of satellites in the solar Summary.

[52]

Misapplications

.Tsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is given by their resemblance to the tide, rather than any actual link to the tide.^ If we examine the progress of the tide-wave up a river we find that highwater occurs at the sea earlier than higher up.

^ Now it is more important in the theory of the tides to know what occurs at spring tide than what occurs at full and change of moon.

^ As we have already indicated, the tide in British seas has mainly a progressive character, and the general march of the wave may be exhibited on a chart by what are called cotidal lines.

.Other phenomena unrelated to tides but using the word tide are rip tide, storm tide, hurricane tide, and black or red tides.^ In other words we reach Laplace's remarkable conclusion that there is no diurnal rise and fall of the tides.

See also

Notes

  1. ^ M. P. M. Reddy, M. Affholder (2001). Descriptive physical oceanography: State of the Art. Taylor and Francis. pp. 249. ISBN 9054107065. OCLC 47801346 223133263 47801346. http://books.google.com/books?id=2NC3JmKI7mYC&pg=PA436&dq=tides+centrifugal+%22equilibrium+theory%22+date:2000-2010&lr=&as_brr=0&sig=ACfU3U0q243eRhAw2g0xIPsA_bpeb_TUIQ#PPA249,M1. 
  2. ^ Richard Hubbard (1893). Boater's Bowditch: The Small Craft American Practical Navigator. McGraw-Hill Professional. pp. 54. ISBN 0071361367. OCLC 44059064. http://books.google.com/books?id=nfWSxRr8VP4C&pg=PA54&dq=centrifugal+revolution+and+rotation+date:1970-2009&lr=&as_brr=0&sig=ACfU3U2e_gEEDUG4mB1nO2GS21kCJwUJVQ#PPA54,M1. 
  3. ^ Coastal orientation and geometry affects the phase, direction, and amplitude of amphidromic systems, coastal Kelvin waves as well as resonant seiches in bays. In estuaries seasonal river outflows influence tidal flow.
  4. ^ a b NASA (May 4, 2000). NASA "Interplanetary Low Tide". http://science.nasa.gov/headlines/y2000/ast04may_1m.htm NASA. Retrieved September 26, 2009. 
  5. ^ Mellor, George L. (1996). Introduction to physical oceanography. Springer. p. 169. ISBN 1563962101. 
  6. ^ Tide tables usually list mean lower low water (mllw, the 19 year average of mean lower low waters), mean higher low water (mhlw), mean lower high water (mlhw), mean higher high water (mhhw), as well as perigean tides. These are mean values in the sense that they derive from mean data."Glossary of Coastal Terminology: H–M"]. Washington Department of Ecology, State of Washington. http://www.ecy.wa.gov/programs/sea/swces/products/publications/glossary/words/H_M.htm. Retrieved 5 April 2007. 
  7. ^ "Tidal lunar day". NOAA. http://www.oceanservice.noaa.gov/education/kits/tides/media/supp_tide05.html. Do not confuse with the astronomical lunar day on the Moon. A lunar zenith is the Moon's highest point in the sky.
  8. ^ Swerdlow, Noel M.; Neugebauer, Otto (1984), Mathematical astronomy in Copernicus's De revolutionibus, Volume 1, Springer-Verlag, p. 76, ISBN 0387909397, 9780387909394, http://books.google.be/books?id=4YDvAAAAMAAJ&q=Syzygy&dq=Syzygy&lr=&cd=30 
  9. ^ "Types and causes of tidal cycles". U S National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section). http://oceanservice.noaa.gov/education/kits/tides/tides07_cycles.html. 
  10. ^ U S National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section), map showing world distribution of tide patterns, semidiurnal, diurnal and mixed semidiurnal.
  11. ^ H V Thurman (1994). Introductory Oceanography (7 ed.). New York, NY: Macmillan. pp. 252–276. ref
  12. ^ D A Ross (1995). Introduction to Oceanography. New York, NY: HarperCollins. pp. 236–242. 
  13. ^ Y. Accad, C. L. Pekeris (November 28, 1978). "Solution of the Tidal Equations for the M2 and S2 Tides in the World Oceans from a Knowledge of the Tidal Potential Alone". Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 290 (1368): 235–266. 
  14. ^ "Tide forecasts". New Zealand: National Institute of Water & Atmospheric Research. http://www.niwa.cri.nz/rc/prog/chaz/news/coastal#tide. Retrieved 2008-11-07.  Including animations of the M2, S2 and K1 tides for New Zealand.
  15. ^ a b E Lisitzin (1974). "2 "Periodical sea-level changes: Astronomical tides"". Sea-Level Changes, (Elsevier Oceanography Series). 8. p. 5. 
  16. ^ "What Causes Tides?". U S National Oceanic and Atmospheric Administration (NOAA) National Ocean Service (Education section). http://oceanservice.noaa.gov/education/kits/tides/tides02_cause.html. 
  17. ^ 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 3 Propositions 24, 36 and 37, starting on page 255.
  18. ^ J Wahr (1995). Earth Tides in "Global Earth Physics", American Geophysical Union Reference Shelf #1,. pp. 40–46. 
  19. ^ a b Yang Zuosheng, K. O. Emery, Xui Yui (July 1989). "Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables". Limnology and Oceanography 34 (5): 953–957. 
  20. ^ David E. Cartwright (1999). Tides: A Scientific History. Cambridge, UK: Cambridge University Press. 
  21. ^ Case, James (March 2000). "Understanding Tides—From Ancient Beliefs to Present-day Solutions to the Laplace Equations". SIAM News 33 (2). 
  22. ^ A T Doodson (December, 1921). "The Harmonic Development of the Tide-Generating Potential". Proceedings of the Royal Society of London. Series A 100 (704): 305–329. 
  23. ^ S Casotto, F Biscani (April 2004). "A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession, nutation, and perturbations due to figure and planetary terms". AAS Division on Dynamical Astronomy 36 (2): 67. 
  24. ^ See e.g. T D Moyer (2003), "Formulation for observed and computed values of Deep Space Network data types for navigation", vol.3 in Deep-space communications and navigation series, Wiley (2003), e.g. at pp.126-8.
  25. ^ Two points on either side of the Earth sample the imposed gravity at two nearby points, effectively providing a finite difference of the gravitational force that varies as the inverse square of the distance. The derivative of 1/r2, with r = distance to originating body, varies as the inverse cube.
  26. ^ According to NASA the lunar tidal force is 2.21 times larger than the solar.
  27. ^ See Tidal force - Mathematical treatment and sources cited there.
  28. ^ Hypothetically, if the ocean were a constant depth, there were no land, and the Earth did not rotate, high water would occur as two bulges in the oceans' height, one facing the Moon and the other facing away from the Moon. There would also be smaller, superimposed bulges on the sides facing toward and away from the Sun.
  29. ^ Munk, W. (1998). "Abyssal recipes II: energetics of tidal and wind mixing". Deep Sea Research Part I Oceanographic Research Papers 45: 1977. doi:10.1016/S0967-0637(98)00070-3. 
  30. ^ Ray, R. D. (1996). "Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry". Nature 381: 595. doi:10.1038/381595a0. 
  31. ^ Lecture 2: The Role of Tidal Dissipation and the Laplace Tidal Equations by Myrl Hendershott. GFD Proceedings Volume, 2004, WHOI Notes by Yaron Toledo and Marshall Ward.
  32. ^ Flussi e riflussi. Milano: Feltrinelli. 2003. ISBN 88-07-10349-4. 
  33. ^ "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences (500 (1)): 525–545 [527]. 1987. 
  34. ^ Al-Kindi, FSTC
  35. ^ Prioreschi, Plinio (2002). "Al-Kindi, A Precursor Of The Scientific Revolution". Journal of the International Society for the History of Islamic Medicine (2): 17–19 [17]. 
  36. ^ "The Doodson–Légé Tide Predicting Machine". Proudman Oceanographic Laboratory. http://www.pol.ac.uk/home/insight/doodsonmachine.html. Retrieved 2008-10-03. 
  37. ^ Glossary of Meteorology American Meteorological Society.
  38. ^ "FAQ". http://www.waterlevels.gc.ca/english/FrequentlyAskedQuestions.shtml#importantes. Retrieved June 23, 2007. 
  39. ^ http://www.bristolnomads.org.uk/stuff/double_tides.htm, accessed April 24, 2008
  40. ^ To demonstrate this Tides Home Page offers a tidal height pattern converted into an .mp3 sound file, and the rich sound is quite different from a pure tone.
  41. ^ Center for Operational Oceanographic Products and Services, National Ocean Service, National Oceanic and Atmospheric Administration (January 2000). "Tide and Current Glossary". Silver Spring, MD. 
  42. ^ Harmonic Constituents,NOAA.
  43. ^ Society for Nautical Research (1958). The Mariner's Mirror. http://books.google.com/books?id=lagPAAAAIAAJ&q=%22shift+his+tides%22&dq=%22shift+his+tides%22&lr=&pgis=1. Retrieved 2009-04-28. 
  44. ^ The Descent of Man, and Selection in Relation to Sex. London: John Murray. 1871. 
  45. ^ "Do the Great Lakes have tides?". Great Lakes Information Network. October 1, 2000. http://www.great-lakes.net/teach/chat/answers/100100_tides.html. Retrieved 2010-02-10. 
  46. ^ "Tides on Lake Michigan". Argonne National Laboratory. http://www.newton.dep.anl.gov/askasci/phy00/phy00330.htm. Retrieved 2010-02-10. 
  47. ^ Duane Dunkerson. "Moon and Tides". Astronomy Briefly. http://www.thespaceguy.com/moontides.htm. Retrieved 2010-02-10. 
  48. ^ "Linac". Stanford. http://news-service.stanford.edu/news/2000/march29/linac-329.html. 
  49. ^ "Effects of Tidal Forces on the Beam Energy in LEP". IEEE. 1993. http://accelconf.web.cern.ch/accelconf/e00/PAPERS/MOP5A04.pdf. 
  50. ^ "Long term variation of the circumference of the spring-8 storage ring". Proceedings of EPAC. 2000 Location=Vienna, Austria. http://accelconf.web.cern.ch/accelconf/p93/PDF/PAC1993_0044.PDF. 
  51. ^ Tanaka, Sachiko (2010). Geophys. Res. Lett.. doi:10.1029/2009GL041581. 
  52. ^ 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: 1367–1376. doi:10.1046/j.1365-8711.2001.04854.x+. http://adsabs.harvard.edu/abs/2001MNRAS.327.1367N. 

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Tide predictions


1911 encyclopedia

Up to date as of January 14, 2010
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From LoveToKnow 1911

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Wiktionary

Up to date as of January 15, 2010

Definition from Wiktionary, a free dictionary

See also tide

German

Noun

Tide f. (genitive Tide, plural Tiden)
  1. Tide.

Simple English

File:Bay of Fundy High
The Bay of Fundy at high tide
File:Bay of Fundy Low
The Bay of Fundy at low tide

A tide is the periodic rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. Tides cause changes in the depth of marine (sea) and estuarine (river mouth) waters. Tides also make oscillating currents known as tidal streams. This means that being able to predict the tide is important for coastal navigation. The strip of seashore that is under water at high tide and exposed at low tide, called the intertidal zone, is an important ecological product of ocean tides.

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Tide predictions

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Citable sentences

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