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Encyclopedia > Tide
The Bay of Fundy at high tide
The Bay of Fundy at high tide
The Bay of Fundy at low tide
The Bay of Fundy at low tide
Spring tide at Wimereux (France)
Spring tide at Wimereux (France)

Tides are the rising and falling of Earth's ocean surface caused by the tidal forces of the Moon and the Sun acting on the oceans. Tidal phenomena can occur in any object that is subjected to a gravitational field that varies in time and space, such as the Earth's land masses. (see Other tides). A tide is the regular rising and falling of the oceans surface Tide may also mean: Tide (detergent), a laundry detergent Tidal force, a celestial mechanics effect Tidal (album), album by Fiona Apple album This is a disambiguation page—a list of articles associated with the same title. ... Ebb Tide is a popular song, written in 1953 by lyricist Carl Sigman and musicwriter Robert Maxwell. ... The bay of Fundy at high tide This picture was taken in about 1972 by me. ... The bay of Fundy at high tide This picture was taken in about 1972 by me. ... The Bay of Fundy (French: ) is a bay located on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. ... The Bay of Fundy at low tide taken in 1972 File links The following pages link to this file: Tide Bay of Fundy Categories: GFDL images ... The Bay of Fundy at low tide taken in 1972 File links The following pages link to this file: Tide Bay of Fundy Categories: GFDL images ... The Bay of Fundy (French: ) is a bay located on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. ... Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution (3072 × 2304 pixel, file size: 2. ... Image File history File links Metadata Size of this preview: 800 × 600 pixelsFull resolution (3072 × 2304 pixel, file size: 2. ... This article is about Earth as a planet. ... Animated map exhibiting the worlds oceanic waters. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... This article is about Earths moon. ... Sol redirects here. ... A landmass is a large extent of land. ... This article is about tides in the Earths oceans. ...

Tides noticeably affect the depth of marine and estuarine water bodies and produce oscillating currents known as tidal streams, making prediction of tides very important for coastal navigation (see Tides and navigation). 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). For other meanings, see Estuary (disambiguation) Río de la Plata estuary An estuary is a semi-enclosed coastal body of water with one or more rivers or streams flowing into it, and with a free connection to the open sea. ... This article is about tides in the Earths oceans. ... A rock, seen at low tide, exhibiting typical intertidal zonation. ... This article is about tides in the Earths oceans. ...

The changing tide produced at a given location is the result of the changing positions of the Moon and Sun relative to the Earth coupled with the effects of Earth rotation and the local shape of the sea floor.[1] Sea level measured by coastal tide gauges may also be strongly affected by wind. In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ... Bathymetry is the underwater equivalent to topography. ... This tidal gauge is ready to be installed underwater in a marina. ...


Introduction and tidal terminology

Types of tides.

A tide is a repeated cycle of sea level changes in the following stages: Image File history File links Size of this preview: 433 × 600 pixel Image in higher resolution (621 × 860 pixel, file size: 18 KB, MIME type: image/gif) page: OUR RESTLESS TIDES National Ocean Service NOAA http://co-ops. ... Image File history File links Size of this preview: 433 × 600 pixel Image in higher resolution (621 × 860 pixel, file size: 18 KB, MIME type: image/gif) page: OUR RESTLESS TIDES National Ocean Service NOAA http://co-ops. ...

  • Over several hours the water rises or advances up a beach in the flood tide.
  • The water reaches its highest level and stops at high tide. Because tidal currents cease this is also called slack water or slack tide. The tide reverses direction and is said to be turning.
  • The sea level recedes or falls over several hours during the ebb tide.
  • The level stops falling at low tide. This point is also described as slack or turning.

Tides may be semidiurnal (two high tides and two low tides each day), or diurnal (one tidal cycle per day). In most locations, tides are semidiurnal. Because of the diurnal contribution, there is a difference in height (the daily inequality) between the two high tides on a given day; these are differentiated as the higher high water and the lower high water in tide tables. Similarly, the two low tides each day are referred to as the higher low water and the lower low water. The daily inequality changes with time and is generally small when the Moon is over the equator.[2] Slack water is the time during which no appreciable current in flowing in a body of water. ... A tide table is used for tidal prediction and shows the daily times and height of high water and low water for a particular location. ...

The various frequencies of astronomical forcing which contribute to tidal variations are called constituents. In most locations, the largest is the "principal lunar semidiurnal" constituent, also known as the M2 (or M2) tidal constituent. Its period is about 12 hours and 24 minutes, exactly half a tidal lunar day, the average time separating one lunar zenith from the next, and thus the time required for the Earth to rotate once relative to the Moon. This is the constituent tracked by simple tide clocks.[3] In broad terms, the zenith is the direction pointing directly above a particular location (perpendicular, orthogonal). ... Tide clock A tide clock is a specially-designed clock that keeps track of the Moons apparent motion around the Earth. ...

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. These data are compared to the reference (or datum) level usually called mean sea level.[4] This tidal gauge is ready to be installed underwater in a marina. ... For considerations of sea level change, in particular rise associated with possible global warming, see sea level rise. ...

Constituents other than M2 arise from factors such as the gravitational influence of the Sun, the tilt of the Earth's rotation axis, the inclination of the lunar orbit and the ellipticity of the orbits of the Moon about the Earth and the Earth about the Sun. Variations with periods of less than half a day are called harmonic constituents. Long period constituents have periods of days, months, or years.

Tidal range variation: springs and neaps

An artist's conception of spring tide
An artist's conception of neap tide

The semidiurnal tidal range (the difference in height between high and low tides over about a half day) varies in a two-week or fortnightly cycle. 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. The tide's range is then maximum: this is called the spring tide, or just springs and is derived not from the season of spring but rather from the verb meaning "to jump" or "to leap up". 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. At these points in the lunar cycle, the tide's range is minimum: this is called the neap tide, or neaps. Spring tides result in high waters that are higher than average, low waters that are lower than average, slack water time that is shorter than average and stronger tidal currents than average. Neaps result in less extreme tidal conditions. There is about a seven day interval between springs and neaps. Image File history File linksMetadata Spingtide. ... Image File history File linksMetadata Spingtide. ... Image File history File linksMetadata Neaptide. ... Image File history File linksMetadata Neaptide. ... The lunar phase depends on the Moons position in orbit around Earth. ... For other uses, see Full Moon. ... Look up Syzygy in Wiktionary, the free dictionary. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...

The changing distance of the Moon from the Earth also affects tide heights. When the Moon is at perigee the range is increased and when it is at apogee the range is reduced. Every 7½ lunations, perigee coincides with either a new or full moon causing perigean tides with the largest tidal range. If a storm happens to be moving onshore at this time, the consequences (in the form of property damage, etc.) can be especially severe. Perigee is the point at which an object in orbit around the Earth makes its closest approach to the Earth. ... This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms. ... Lunation is the mean time for one lunar phase cycle (i. ...

Tidal phase and amplitude

The M2 tidal constituent. Amplitude is indicated by color, and the white lines are cotidal differing by 1 hr. The curved arcs around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period.[5]

Because the M2 tidal constituent dominates in most locations, the stage or phase of a tide, denoted by the time in hours after high tide, is a useful concept. It is also measured in degrees, with 360° per tidal cycle. Lines of constant tidal phase are called cotidal lines. High tide 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.[6] If one thinks of the ocean as a circular basin enclosed by a coastline, the cotidal lines point radially inward and must eventually meet at a common point, the amphidromic point. An amphidromic point is at once cotidal with high and low tides, which is satisfied by zero tidal motion. (The rare exception occurs when the tide circles around an island, as it does around New Zealand.) 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 tide) which decrease to zero at the amphidromic point. For a 12 hour semidiurnal tide the amphidromic point behaves roughly like a clock face,[7] with the hour hand pointing in the direction of the high tide cotidal line, which is directly opposite the low tide cotidal line. High tide rotates about once every 12 hours in the direction of rising cotidal lines, and away from ebbing cotidal lines. The difference of cotidal phase from the phase of a reference tide is the epoch.[8] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... An amphidromic point is a point within a tidal system where the tidal range is almost zero. ... An amphidromic point is a point within a tidal system where the tidal range is almost zero. ...

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 tide from the position of the Moon in the sky. 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.

Tidal physics

See also: Tidal force
The Earth and Moon, looking at the North Pole

Isaac Newton laid the foundations for the mathematical explanation of tides in the Philosophiae Naturalis Principia Mathematica (1687). In 1740, the Académie Royale des Sciences in Paris offered a prize for the best theoretical essay on tides. Daniel Bernoulli, Antoine Cavalleri, Leonhard Euler, and Colin Maclaurin shared the prize. 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. Maclaurin was also the first to write about the Earth's rotational effects on motion. Euler realized that the horizontal component of the tidal force (more than the vertical) drives the tide. In 1744 D'Alembert studied tidal equations for the atmosphere which did not include rotation. 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. The Laplace tidal equations are still in use today. William Thomson rewrote Laplace's equations in terms of vorticity which allowed for solutions describing tidally driven coastally trapped waves, which are known as Kelvin waves.[9] Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... Diagram of lunar phases, created by Minesweeper and donated to Wikipedia. ... Diagram of lunar phases, created by Minesweeper and donated to Wikipedia. ... For other uses, see North Pole (disambiguation). ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Newtons own copy of his Principia, with handwritten corrections for the second edition. ... Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ... The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... Daniel Bernoulli Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland where he died. ... Leonhard Paul Euler (pronounced Oiler; IPA ) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. ... Colin Maclaurin Colin Maclaurin (February, 1698 - June 14, 1746) was a Scottish mathematician. ... A spheroid is a quadric surface in three dimensions obtained by rotating an ellipse about one of its principal axes. ... In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ... Pierre-Simon, marquis de Laplace (March 23, 1749 - March 5, 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy. ... For other persons named William Thomson, see William Thomson (disambiguation). ... Vorticity is a mathematical concept used in fluid dynamics. ... A Kelvin wave is a wave in the ocean or atmosphere that balances the Earths Coriolis force against a topographic boundary such as a coastline. ...

Tidal forces

A schematic of the Earth-Moon system (not to scale), showing the entire Earth following the motion of its center of gravity.
A schematic of the Earth-Moon system (not to scale), showing the entire Earth following the motion of its center of gravity.

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 center of mass of the Earth. Thus, the tidal force depends not on the strength of the gravitational field of the Moon, but on its gradient. 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. The tidal force produced by the Sun is therefore only 46% as large as that produced by the Moon. Image File history File links Two bodies with a major difference in mass orbiting around a common barycenter (red cross) with circular orbits. ... Image File history File links Two bodies with a major difference in mass orbiting around a common barycenter (red cross) with circular orbits. ... This article or section may contain original research or unverified claims. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... This article covers the physics of gravitation. ...

Tidal forces can also be analyzed from the point of view of a reference frame that translates with the center of mass of the Earth. Consider the tide due to the Moon (the Sun is similar). First observe that the Earth and Moon rotate around a common orbital center of mass, as determined by their relative masses. The orbital center of mass is 3/4 of the way from the Earth's center to its surface. The second observation is that the Earth's centripetal motion is the averaged response of the entire Earth to the Moon's gravity and is exactly the correct motion to balance the Moon's gravity only at the center of the Earth; but every part of the Earth moves along with the center of mass and all parts have the same centripetal motion, since the Earth is rigid.[10] On the other hand each point of the Earth experiences the Moon's radially decreasing gravity differently; the near parts of the Earth are more strongly attracted than is compensated by inertia and experience a net tidal force toward the Moon; the far parts have more inertia than is necessary for the reduced attraction, and thus feel a net force away from the Moon. Finally only the horizontal components of the tidal forces actually contribute tidal acceleration to the water particles since there is small resistance. The actual tidal force on a particle is only about a ten millionth of the force caused by the Earth's gravity. In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ... A centripetal force is a force pulling an object toward the center of a circular path as the object goes around the circle. ...

The Moon's (or Sun's) gravity differential field at the surface of the earth is known as the tide generating force. This is the primary mechanism that drives tidal action and explains two tidal equipotential bulges, accounting for two high tides per day.
The Moon's (or Sun's) gravity differential field at the surface of the earth is known as the tide generating force. This is the primary mechanism that drives tidal action and explains two tidal equipotential bulges, accounting for two high tides per day.

The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) which is commonly referred to as the geoid. 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. Now consider the effect of external, massive bodies such as the Moon and Sun. 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. 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. 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. When the tidal equipotential changes, the ocean surface is no longer aligned with it, so that the apparent direction of the vertical shifts. The surface then experiences a down slope, in the direction that the equipotential has risen. Image File history File links Field_tidal. ... Image File history File links Field_tidal. ... Gravity is a force of attraction that acts between bodies that have mass. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ... The GOCE project will measure high-accuracy gravity gradients and provide an accurate geoid model based on the Earths gravity field. ... For other uses, see Gradient (disambiguation). ... This diagram shows how the law works. ... In algebra, the square of a number is that number multiplied by itself. ... In arithmetic and algebra, the cube of a number n is its third power — the result of multiplying it by itself two times: n3 = n × n × n. ...

Laplace tidal equation

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: (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 rate of change of the surface height is proportional to the negative divergence of velocity multiplied by the depth. The last means that as the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively. The boundary conditions dictate no flow across the coastline, and free slip at the bottom. The Coriolis effect steers waves to the right in the northern hemisphere and to the left in the southern allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity. [11] An abstract model (or conceptual model) is a theoretical construct that represents something, with a set of variables and a set of logical and quantitative relationships between them. ... For the Marvel Comics character, see Windshear (comics). ... In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ...

Tidal amplitude and cycle time

The theoretical amplitude of oceanic tides due to 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. 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. 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. Since the orbits of the Earth about the Sun, and the Moon about the Earth, are elliptical, the amplitudes of the tides change somewhat as a result of the varying Earth-Sun and Earth-Moon distances. This causes a variation in the tidal force and theoretical amplitude of about ±18% for the Moon and ±5% for the Sun. If both the Sun and Moon were at their closest positions and aligned at new moon, the theoretical amplitude would reach 93 cm.

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. 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).

Tidal dissipation

See also: Tidal acceleration

The tidal forcing is essentially driven by orbital energy of the Earth Moon system at a rate of about 3.75 Terawatts. The dissipation arises as the basin scale tidal flow drives smaller scale flows which experience turbulent dissipation. This tidal drag gives rise to a torque on the Moon that results in the gradual transfer of angular momentum to its orbit, and a gradual increase in the Earth-Moon separation. As a result of the principle of conservation of angular momentum, the rotational velocity of the Earth is correspondingly slowed. 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 less day per 100 million years. See tidal acceleration for further details.[12] It has been suggested that Tidal friction be merged into this article or section. ... In physics, angular momentum intuitively measures how much the linear momentum is directed around a certain point called the origin; the moment of momentum. ... It has been suggested that Tidal friction be merged into this article or section. ...

Tidal observation and prediction

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. Pytheas travelled to the British Isles and seems to be the first to have related spring tides to the phase of the moon. 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. 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. 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. In Europe the Venerable Bede around 730 A.D. 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 tide along the Northumbrian coast. Pytheas (Πυθέας(Pitheas), ca. ... Naturalis Historia, 1669 edition, title page. ... Pliny the Elder: an imaginative 19th Century portrait. ... The Greek geographer Strabo in a 16th century engraving. ... The Euripus Strait (Greek: Ευριπος), is a narrow channel of water separating the Greek island of Euboea in the Aegean Sea from Boeotia in mainland Greece. ... For other uses, see Aristotle (disambiguation). ... For other uses, see Bede (disambiguation). ...

Eventually 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.The first known tide-table is thought to be that of John, Abbott of Wallingford (d. 1213), based on high water occurring 48 minutes later each day, and three hours later upriver at London than at the mouth of the Thames. William Thomson led the first systematic harmonic analysis to tidal records starting in 1867. The main result was the building of a tide-predicting machine (TPM) on using a system of pulleys to add together six harmonic functions of time. It was "programmed" by resetting gears and chains to adjust phasing and amplitudes. Similar machines were used until the 1960s. The tidal bore in Upper Cook Inlet, Alaska A tidal bore (or just bore, or eagre) is a tidal phenomenon in which the leading edge of the incoming tide forms a wave (or waves) of water that travel up a river or narrow bay against the direction of the current. ... -1...

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 gages 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. These points of no tide were confirmed by measurement in 1840 by Captain Hewett, RN, from careful soundings in the North Sea.[9]


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. Springs and neaps in the North Sea, for example, are two days behind the new/full Moon and first/third quarter. This is called the age of the tide.[13] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The North Sea is a sea of the Atlantic Ocean, located between the coasts of Norway and Denmark in the east, the coast of the British Isles in the west, and the German, Dutch, Belgian and French coasts in the south. ...

The exact time and height of the tide at a particular coastal point is also greatly influenced by the local bathymetry. 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 metres (53 ft), because of the shape of the bay.[14] Southampton in the United Kingdom has a double high tide caused by the interaction between the different tidal harmonics within the region. This is contrary to the popular belief that the flow of water around the Isle of Wight creates two high waters. The Isle of Wight is important, however, as it is responsible for the 'Young Flood Stand', which describes the pause of the incoming tide about three hours after low water. Ungava Bay in Northern Quebec, north eastern Canada, is believed by some experts to have higher tidal ranges than the Bay of Fundy (about 17 metres or 56 ft)[citation needed], but it is free of pack ice for only about four months every year, whereas the Bay of Fundy rarely freezes. For other uses, see Coast (disambiguation). ... Bathymetry is the underwater equivalent to topography. ... The Bay of Fundy (French: ) is a bay located on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. ... For other uses, see Southampton (disambiguation). ... For other uses, see Isle of Wight (disambiguation). ... Ungava Bay. ... This article is about the Canadian province. ... The Bay of Fundy (French: ) is a bay located on the Atlantic coast of North America, on the northeast end of the Gulf of Maine between the Canadian provinces of New Brunswick and Nova Scotia, with a small portion touching the U.S. state of Maine. ... An icebreaker navigates some through young (1 year) sea ice Sea ice is formed from ocean water that freezes. ...

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. Extremely small tides also occur for the same reason in the Gulf of Mexico and Sea of Japan. On the southern coast of Australia, because the coast is extremely straight (partly due to the tiny quantities of runoff flowing from rivers), tidal ranges are equally small. Mediterranean redirects here. ... For other uses, see Baltic (disambiguation). ... Gulf of Mexico in 3D perspective. ... The Sea of Japan is a marginal sea of the western Pacific Ocean, bordered by Japan, Korea and Russia. ... Run-off, composed of a mixture of water and soil along with any other organic or inorganic substances that may exist in the land, is the product of precipitation, snowmelt, over-irrigation, or other water coming in contact with the earth and carrying matter to streams, rivers, lakes, and other...

Tidal analysis

It was the universal theory of gravitation due to Isaac Newton 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. When confronted by a periodically varying function, the standard approach is to employ Fourier series, a form of orthogonal analysis that uses trigonometrical functions as its basis set, specifically a collection of sinusoidal functions having frequencies (the number of cycles per day, or other convenient unit) that are zero, one, two, three, etc. times the frequency of a particular fundamental cycle; these are called harmonics of the fundamental frequency, and the process is termed Harmonic Analysis. If sinusoidal functions are well-suited to the behaviour being modelled, relatively few harmonic terms need to be carried in the analysis, and fortunately, because orbital paths are circular, sinusoidal variations are very suitable. Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ...

For the analysis of tide heights, the Fourier Series approach is best made more elaborate. 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. A much better (i.e. more compact) decomposition for this case involves a basis set having more than one fundamental frequency: specifically, the periods of one revolution of the earth, and one orbit of the moon about the earth are incommensurable (for simplicity in phrasing, this discussion is entirely geocentric, but is informed by the heliocentric model) so to represent both influences via one frequency would require many harmonic terms. 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 one fundamental frequency and its (integer) multiples would require many terms. For tides then, although the process is still termed Harmonic Analysis, it does not limit itself to harmonics of a single frequency. To demonstrate this, http://www.arachnoid.com/tides/index.html offers a tidal height pattern converted into a .mp3 sound file, and the rich sound is quite different from a pure tone. In still other words, the harmonies are multiples of many fundamental frequencies, not just of the one fundamental frequency of the common Fourier series approach.

The study of tide height by Harmonic Analysis was begun by Laplace, Lord Kelvin and George Darwin, then rigorously extended by A.T. Doodson who introduced the Doodson Number notation to organise the hundreds of terms that result. This approach has been the international standard ever since, and the complications arise as follows: so far, the tide-raising force is notionally given by A.cos(w.t + p) where A is the amplitude, w the angular frequency (usually given in degrees per hour) and p the phase offset with regard to the astronomical state at time t = 0; there is a term for the moon and a second term for the sun. If the orbits were circular, that would be the end of the matter, but of course they're not. Accordingly, the value of A is itself varying with time, slightly, about some average figure. Replace it then by A(t), but, what functional form? It turns out that another sinusoid gives an excellent approximation, rather like the cycles and epicycles of Ptolemaic theory. 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. Thus the simple term is now a compound term, the product of two cosine terms: A.[1 + Aa.cos(wa + pa)].cos(w.t + p) Pierre-Simon Laplace Pierre-Simon Laplace (March 23, 1749 – March 5, 1827) was a French mathematician and astronomer, the discoverer of the Laplace transform and Laplaces equation. ... William Thomson, 1st Baron Kelvin (26 June 1824–17 December 1907) was an Scotch-Irish mathematical physicist and engineer, an outstanding leader in the physical sciences of the 19th century. ... George Howard Darwin (1845-1912) Sir George Howard Darwin, F.R.S. (July 9, 1845 – December 7, 1912) was a British astronomer and mathematician, the second son and fifth child of Charles and Emma Darwin. ... Dr. Arthur Thomas Doodson (1890-1968) spent much of his life developing the analysis of tidal motions mainly in the oceans but also in lakes, and was the first to devise methods for shallow water as in estuaries. ... This article is about the geographer, mathematician and astronomer Ptolemy. ...

Now, given that cos(a).cos(b) = [cos(a + b) + cos(a - b)]/2, it is clear that a compound term involving the product of two cosine terms each with their own frequency is the same as three (not two: it is (1 + cos).cos) 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. Consider further that the tidal force on a location depends also on whether the moon (or the sun) is above or below the plane of the equator, and that these attributes have their own periods also incommensurable with a day and a month, and it is clear that many combinations result. With a careful choice of the basic astronomical frequencies, the Doodson Number annotates the particular additions and differences of them to form the frequency of each simple cosine term.

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 over a period of many days and to calculate this requires a detailed knowledge of the shape of all the ocean basins. Instead, the procedure is pragmatic. At each location of interest, measure the tide heights over at least a lunar cycle (to capture the spring - neap tidal response) and then analyse the differences from mean sea level with respect to the known astronomical frequencies and phases of the tide-raising forces on the expectation that the tide height behaviour will follow the behaviour of the tide force. Then, because astronomical states can be calculated with certainty, the tide height at other times can be predicted. The main patterns are the twice-daily tide, the difference between the first and second tide of a day (due to the moon and sun being north or south of the equator), the spring-neap cycle in amplitude (due to the relative positions of the moon and sun), and the adjustment of spring tide heights due to the perigees of the moon and sun. The Highest Astronomical Tide is the perigean spring tide. Remember always that the astronomical tides do not include the effect of weather, and, changes to local conditions (sandbank movement, dredging harbour mouths, etc.) away from those prevailing at the time of measurement can affect the timing and magnitude of the actual tide. 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. If the size of a "weather surge" is assessed by subtracting the astronomical tide from the observed tide at the time, care is needed.

Tidal prediction summing constituent.
Tidal prediction summing constituent.

Careful Fourier data analysis over a nineteen-year period (the National Tidal Datum Epoch in the US) uses frequencies called the tidal harmonic constituents. 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. This analysis can be done using only the knowledge of the period of forcing, but without detailed understanding of the physical mathematics, which means that useful tidal tables have been constructed for centuries.[15] The resulting amplitudes and phases can then be used to predict the expected tides. These are usually dominated by the constituents near 12 hours (the semidiurnal constituents), but there are major constituents near 24 hours (diurnal) as well. Longer term constituents are 14 day or fortnightly, monthly, and semiannual. 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. 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 (fourteen day period).[16] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Fourier analysis, named after Joseph Fouriers introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. ... Data analysis is the act of transforming data with the aim of extracting useful information and facilitating conclusions. ... Meton of Athens was a mathematician, astronomer and engineer who lived in Athens in the 5th century BCE. He is best known for the 19-year Metonic Cycle which he introduced into the Athenian luni-solar calendar as a method of calculating dates. ... Filipino name Tagalog: Luzon Sea Portuguese name Portuguese: Mar da China Meridional Vietnamese name Vietnamese: The South China Sea is a marginal sea south of China. ... Gulf of Mexico in 3D perspective. ...

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. 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. In the southern hemisphere this direction is clockwise. On the other hand M2 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. But the tides do propagate northward on the east side and southward on the west coast, as predicted by theory. The exception is the Cook Strait where the tidal currents periodically link high to low tide. This is because cotidal lines 180° around the amphidromes are in opposite phase, for example high tide across from low tide. Each tidal constituent has a different pattern of amplitudes, phases, and amphidromic points, so the M2 patterns cannot be used for other tide components. An amphidromic point is a point within a tidal system where the tidal range is almost zero. ... A view of from the summit of Mount Victoria, Wellington - Cook Strait stretches to the right (west). ...


This is adapted from a script for the MatLab system, and its main merit is that it actually does generate a suitable curve. In more general work, times and phases are usually referenced to GMT, and the prediction would be annotated with actual dates and times.

 %Speed in degrees per hour for various Earth-Moon-Sun astronomical attributes, as given in Tides, Surges and Mean Sea-Level, D.T. Pugh. clear EMS; EMS.T = +360/24; %+15 w0: Nominal day, ignoring the variation followed via the Equation of Time. %T + h - s =+14.492054485 w1: is the advance of the Moon's longitude, referenced to the Earth's zero longitude. EMS.s = +360/(27.3217)/24; %+0.5490141536 w2: Moon around the earth in 27.3217 mean solar days. EMS.h = +360/(365.2422)/24; %+0.0410686388 w3: Earth orbits the sun in a tropical year of 365.24219879 days, not the 365.2425 in 365 + y/4 - y/100 + y/400. Nor with - y/4000. EMS.p = +360/(365.25* 8.85)/24; %+0.0046404 w4: Precession of the moon's perigee, once in 8.85 Julian years: apsides. EMS.N = -360/(365.25*18.61)/24; %-0.00220676 w5: Precession of the plane of the moon's orbit, once in 18.61 Julian years: negative, so recession. EMS.pp= +360/(365.25*20942)/24; %+0.000001961 w6: Precession of the perihelion, once in 20942 Julian years. %T + h = 15.041068639°/h is the rotation of the Earth with respect to the fixed stars, as both are in the same sense. % Reference Angular Speed Degrees/hour Period in Days. Astronomical Values. %Sideral day Distant star ws = w0 + w3 = w1 + w2 15.041 0.9973 %Mean solar day Solar transit of meridian w0 = w1 + w2 - w3 15 1 %Mean lunar day Lunar transit of meridian w1 14.4921 1.0350 %Month Draconic Lunar ascending node w2 + w5 .5468 27.4320 %Month Sideral Distant star w2 .5490 27.3217 27d07h43m11.6s 27.32166204 %Month Anomalistic Lunar Perigee (apsides) w2 - w4 .5444 27.5546 %Month Synodic Lunar phase w2 - w3 = w0 - w1 .5079 29.5307 27d12h44m02.8s 29.53058796 %Year Tropical Solar ascending node w3 .0410686 365.2422 365d05h48m45s 365.24218967 at 2000AD. 365.24219879 at 1900AD. %Year Sideral Distant star .0410670 365.2564 365d06h09m09s 365.256363051 at 2000AD. %Year Anomalistic Solar perigee (apsides) w3 - w6 .0410667 365.2596 365d06h13m52s 365.259635864 at 2000AD. %Year nominal Calendar 365 or 366 %Year Julian 365.25 %Year Gregorian 365.2425 % Obtaining definite values is tricky: years of 365, 365.25, 365.2425 or what days? These parameters also change with time. 
 clear Tide; % w1 w2 w3 w4 w5 w6 Tide.Name{1} = 'M2'; Tide.Doodson{ 1} = [+2 0 0 0 0 0]; Tide.Title{1} = 'Principal lunar, semidiurnal'; Tide.Name{2} = 'S2'; Tide.Doodson{ 2} = [+2 +2 -2 0 0 0]; Tide.Title{2} = 'Principal solar, semidiurnal'; Tide.Name{3} = 'N2'; Tide.Doodson{ 3} = [+2 -1 0 +1 0 0]; Tide.Title{3} = 'Principal lunar elliptic, semidiurnal'; Tide.Name{4} = 'L2'; Tide.Doodson{ 4} = [+2 +1 0 -1 0 0]; Tide.Title{4} = 'Lunar semi-diurnal: with N2 for varying speed around the ellipse'; Tide.Name{5} = 'K2'; Tide.Doodson{ 5} = [+2 +2 -1 0 0 0]; Tide.Title{5} = 'Sun-Moon angle, semidiurnal'; Tide.Name{6} = 'K1'; Tide.Doodson{ 6} = [+1 +1 0 0 0 0]; Tide.Title{6} = 'Sun-Moon angle, diurnal'; Tide.Name{7} = 'O1'; Tide.Doodson{ 7} = [+1 -1 0 0 0 0]; Tide.Title{7} = 'Principal lunar declinational'; Tide.Name{8} = 'Sa'; Tide.Doodson{ 8} = [ 0 0 +1 0 0 0]; Tide.Title{8} = 'Solar, annual'; Tide.Name{9} = 'nu2'; Tide.Doodson{ 9} = [+2 -1 +2 -1 0 0]; Tide.Title{9} = 'Lunar evectional constituent: pear-shapedness due to the sun'; Tide.Name{10} = 'Mm'; Tide.Doodson{10} = [ 0 +1 0 -1 0 0]; Tide.Title{10} = 'Lunar evectional constituent: pear-shapedness due to the sun'; Tide.Name{11} = 'P1'; Tide.Doodson{11} = [+1 +1 -2 0 0 0]; Tide.Title{11} = 'Principal solar declination'; Tide.Constituents = 11; %Because w0 + w3 = w1 + w2, the basis set {w0,...,w6} is not independent. Usage of w0 (or EMS.T) can be eliminated. %For further pleasure w2 - w6 correspond to other's usage of w1 - w5. 
 %Collect the basic angular speeds into an array as per A.T. Doodson's organisation. The classic Greek letter omega is represented as w. %w(0) = EMS.T; %This should be w(0), but MatLab doesn't allow this! w(1) = EMS.T + EMS.h - EMS.s; w(2) = EMS.s; w(3) = EMS.h; w(4) = EMS.p; w(5) = EMS.N; w(6) = EMS.pp; 
 %Prepare the basis frequencies, of sums and differences. Doodson's published coefficients typically have 5 added %so that no negative signs will disrupt the layout: the scheme here does not have the offset. disp('Name °/hour Hours Days'); for i = 1:Tide.Constituents Tide.Speed(i) = sum(Tide.Doodson{i}.*w); %Sum terms such as DoodsonNumber(j)*w(j) for j = 1:6. disp([int2str(i),' ',Tide.Name{i},' ',num2str(Tide.Speed(i)),' ',num2str(360/Tide.Speed(i)),' ',num2str(15/Tide.Speed(i)),' ',Tide.Title{i}]); end; 
 clear place; %The amplitude H and phase for each constituent are determined from the tidal record by least-squares %fitting to the observations of the amplitudes of the astronomical terms with expected frequencies and phases. %The number of constituents needed for accurate prediction varies from place to place. %In making up the tide tables for Long Island Sound, the National Oceanic and Atmospheric Administration %uses 23 constituents. The eleven whose amplitude is greater than .1 foot are: Place(1).Name = 'Bridgeport, Cn'; %Counting time in hours from midnight starting 1'st September 1991. % M2 S2 N2 L2 K2 K1 O1 Sa nu2 Mm P1... Place(1).A = [ 3.185 0.538 0.696 0.277 0.144 0.295 0.212 0.192 0.159 0.108 0.102]; %Tidal heights (feet) Place(1).P = [-127.24 -343.66 263.60 -4.72 -2.55 142.02 505.93 301.5 45.70 86.82 340.11]; %Phase (degrees). %The values for these coefficients are taken from http://www.math.sunysb.edu/~tony/tides/harmonic.html %which originally came from a table published by the US. National Oceanic and Atmospheric Administration. 
 %Calculate a tidal height curve, in terms of hours since the start time. PlaceCount = 1; Colour=cellstr(strvcat('g','r','b','c','m','y','k')); %A collection. clear y; step = 0.125; LastHour = 720; %8760 hours in a year. n = LastHour/step + 1; y(1:n,1:PlaceCount) = 0; t = (0:step:LastHour)/24; for it = 1:PlaceCount i = 0; for h = 0:step:LastHour i = i + 1; y(i,it) = sum(Place(it).A.*cosd(Tide.Speed*h + Place(it).P)); %Sum terms A(j)*cos(speed(j)*h + p(j)) for j = 1:Tide.Constituents. end; %Should use cos(ix) = 2*cos([i - 1]*x)*cos(x) - cos([i - 2]*x), but, for clarity... end; 
 figure(1); clf; hold on; title('Tidal Height'); xlabel('Days'); for it = 1:PlaceCount plot(t,y(1:n,it),Colour{it}); end; legend(Place(1:PlaceCount).Name,'Location','NorthWest'); 

Tidal Current

The flow pattern due to tidal influence is much more difficult to analyse, and also, data is much more difficult to collect. A tidal height is a simple number, and applies to a wide region simultaneously (often as far as the eye can see), but a flow has both a magnitude and a direction, and can vary substantially over just a short distance due to local bathymetry, and also vary with depth. Although the centre of a channel is the most useful measuring site, mariners will not accept a current measuring installation obstructing navigation! A flexible attitude is required. A flow proceeding up a curved channel is the same flow, even though its direction varies continuously along the channel. Even the obvious expectation that the flood and ebb flows will be in reciprocal directions is not met, as the direction of a flow is determined by the shape of the channel it is coming from, not the shape where it will shortly be. Likewise, eddies can form in one direction but not the other.

Nevertheless, analysis proceeds on the same basis. 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 reciprocal) direction. Take the velocities along the flood direction as positive, and along the ebb direction as negative, and proceed as if these were tide height figures. 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. In this case, analysis might proceed along two pairs of directions, the primary flow directions and the secondary directions at right angles. Alternatively, the tidal flows can be treated as complex numbers, as each value has both a magnitude and a direction.

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. The tidal flow through Cook Strait between the two main islands of New Zealand is particularly interesting, as on each side of the strait the tide is almost exactly out of phase so that high tide on one side meets low tide on the other. Strong currents result, with almost zero tidal height change in the centre of the strait. Yet, although the tidal surge should flow in one direction for six hours and then the reverse direction for six hours, etc. a particular surge might last eight or ten hours with the reverse surge enfeebled. In especially boisterous weather conditions, the reverse surge might be entirely overcome so that the flow remains in the same direction through three surge periods and longer.

Tidal Power Generation

Power can be extracted by two means: inserting a water turbine into a tidal current, or, building impoundment ponds so as to release or admit water through a turbine. In the first case, the generation is entirely determined by the timing and magnitude of the tidal currents, and the best currents may be unavailable because the turbines would obstruct navigation. In the second, the impoundment dams are expensive to construct, the natural water cycles are completely disrupted, as is navigation, but with multiple impoundment ponds power can be generated at chosen times. So far, there are few systems for tidal power generation (most famously, La Rance by Saint Malo, France) and many difficulties. Aside from environmental issues, simply withstanding sea-water corrosion and fouling by biological growths is difficult! Rance tidal power plant Other view Scale model of the tidal power plant The Rance tidal power plant is the worlds first electrical generating station powered by tidal energy. ... Categories: France geography stubs | Communes of Ille-et-Vilaine ...

Proponents of tidal power systems usually boast that unlike wind power systems, the generation pattern can be predicted years ahead, and prefer not to talk about weather effects. Another assertion is that some generation is possible for most of the tidal cycle. This may be true in principle since the time of still water is short, but in practice turbines lose efficiency at partial operating powers. 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 turn out to be rather brief. An obvious fallback then is to have a number of 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. Again, New Zealand has particularly interesting opportunities. Because the tidal pattern is such that a state of high tide orbits the country once per cycle, there is always somewhere around the coast where the tide is at its peak, and somewhere else where it is at its lowest, etc. so that via the electricity transmission network, there could always be supply from tidal generation somewhere. The most convenient situation is presented with Auckland city, which is between Manukau harbour and Waitemata harbour so that both power stations would be close to the load: nothing could be better! For other uses, see Auckland (disambiguation). ... Location of Manukau Harbour. ... Auckland Harbour Bridge crossing the harbour. ...

But, because the power available varies with the cube of the flow, even with the optimum phase difference of three hours between two stations, there are still significant amounts of time when neither tidal flow is rapid enough for significant generation, and worse, during the time of neap tides, the flow is weak all of the day, and there is no getting around this via multiple stations, because the neap tides apply to the whole earth at once. The most feeble neap tides would be when the sun's influence is maximum whilst the moon's is weakest, and as far as the sun is concerned, it is closest to the earth during the time of the southern hemisphere's summer, which is when electricity demand is the least there, a small bonus.

As a result, interest must fall on the Kaipara harbour which not only is large, but also is two-lobed in shape, and thus almost pre-designed for a tidal impoundment scheme where one lobe could be filled by high tide and the other emptied by a low tide, and then via a canal from one to the other generation would be possible at a time of choice. Location of Kaipara Harbour The Kaipara Harbour is an inlet of the Tasman Sea located near the base of the North Auckland Peninsula on the western side of the North Island of New Zealand. ...

There is scant likelihood of any such scheme proceeding, due to the disruption to natural conditions.

Tides and navigation

Tidal flows are of profound importance in navigation and very significant errors in position will occur if they are not taken into account. Tidal heights are also very important; for example many rivers and harbours have a shallow "bar" at the entrance which will prevent boats with significant draft from entering at certain states of the tide. The draft of a ships hull is the vertical distance from the bottom of the hull to the waterline. ...

The timings and velocities of tidal flow can be found by looking at a tidal chart or tidal stream atlas for the area of interest. Tidal charts come in sets, with each diagram of the set covering a single hour between one high tide and another (they ignore the extra 24 minutes) and give the average tidal flow for that one hour. An arrow on the tidal chart indicates the direction and the average flow speed (usually in knots) for spring and neap tides. If a tidal chart is not available, most nautical charts have "tidal diamonds" which relate specific points on the chart to a table of data giving direction and speed of tidal flow. A tidal atlas is used to predict the direction and speed of tadal currents. ... A knot is a unit of speed abbreviated kt or kn. ... A tidal diamond table Tidal diamonds are symbols on British admiralty charts that indicate the direction and speed of tidal streams. ...

Standard procedure to counteract the effects of tides on navigation is to (1) calculate a "dead reckoning" position (or DR) from distance and direction of travel, (2) mark this on the chart (with a vertical cross like a plus sign) and (3) draw a line from the DR in the direction of the tide. The distance the tide will have moved 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). Dead reckoning (DR) is the process of estimating ones current position based upon a previously determined position, or fix, and advancing that position based upon measured velocity, time, heading, as well as the effect of currents or wind. ...

Civil and maritime uses of tidal data

Nautical charts display the "charted depth" of the water at specific locations with "soundings" and the use of bathymetric contour lines to depict the shape of the submerged surface. These depths are relative to a "chart datum", which is typically the level of water at the lowest possible astronomical tide (tides may be lower or higher for meteorological reasons) and are therefore the minimum water depth possible 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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A 1976 United States NOAA chart of part of Puerto Rico A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. ... Sounding - The historical nautical term for measuring depth. ... The seafloor topography near the Puerto Rico Trench Bathymetry is the underwater equivalent to topography. ... Contour map A contour line (also isopleth, level set, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a particular value. ... The chart datum is the level of water that charted depths displayed on nautical charts are measured from. ... The seabed (also sea floor, seafloor, or ocean floor) is the bottom of the ocean. ...

Heights and times of low and high tide on each day are published in tide tables. The actual depth of water at the given points at high or low water can easily be calculated by adding the charted depth to the published height of the tide. The water depth for times other than high or low water can be derived from tidal curves published for major ports. If an accurate curve is not available, the rule of twelfths can be used. This approximation works on the basis that the increase in depth in the six hours between low and high tide will follow this simple rule: first hour - 1/12, second - 2/12, third - 3/12, fourth - 3/12, fifth - 2/12, sixth - 1/12. A tide table is used for tidal prediction and shows the daily times and height of high water and low water for a particular location. ... The rule of twelfths is a rule of thumb for estimating the level of the sea at any time, given only the time and height of high and low water. ...

Biological aspects

Intertidal ecology

A rock, seen at low tide, exhibiting typical intertidal zonation.
A rock, seen at low tide, exhibiting typical intertidal zonation.
Main article: Intertidal ecology

Intertidal ecology is the study of intertidal ecosystems, where organisms live between the low and high tide lines. At low tide, the intertidal is exposed (or ‘emersed’) whereas at high tide, the intertidal is underwater (or ‘immersed’). Intertidal ecologists therefore study the interactions between intertidal organisms and their environment, as well as between different species of intertidal organisms within a particular intertidal community. The most important environmental and species interactions may vary based on the type of intertidal community being studied, the broadest of classifications being based on substrates - rocky shore and soft bottom communities. Image File history File linksMetadata Download high resolution version (1131x1820, 637 KB) Summary A rock on a beach near Kalaloch, Washington. ... Image File history File linksMetadata Download high resolution version (1131x1820, 637 KB) Summary A rock on a beach near Kalaloch, Washington. ... Intertidal habitats occur on shorelines between the low and high tide lines. ... A rock, seen at low tide, exhibiting typical intertidal zonation. ... A coral reef near the Hawaiian islands is an example of a complex marine ecosystem. ... An ecologist studies the distribution and abundance of living organisms and how the distribution and abundance are affected by interactions between the organisms and their environment. ... Biological interactions result from the fact that organisms in an ecosystem interact with each other, in the natural world, no organism is an autonomous entity isolated from its surroundings. ... Anjajavy Forest on Tsingy rocks jutting into the Indian Ocean Rocky shore RENECK!!!!!!!is an intertidal area on seacoasts where solid rock predominates. ...

Organisms living in this zone have a highly variable and often hostile environment, and have evolved various adaptations to cope with and even exploit these conditions. One easily visible feature of intertidal communities is vertical zonation, where the community is divided into distinct vertical bands of specific species going up the shore. Species ability to cope with desiccation determines their upper limits, while competition with other species sets their lower limits. For other uses, see Adaptation (disambiguation). ... A rock, seen at low tide, exhibiting typical intertidal zonation. ... Desiccation is the state of extreme dryness, or the process of extreme drying. ... Trees in this Bangladesh forest are in competition for light. ...

Intertidal regions are utilized by humans for food and recreation, but anthropogenic actions also have major impacts, with overexploitation, invasive species and climate change being among the problems faced by intertidal communities. In some places Marine Protected Areas have been established to protect these areas and aid in scientific research. Timber Exploitation of natural resources is an essential condition of the human existence. ... Lantana invasion of abandoned citrus plantation; Moshav Sdey Hemed, Israel The term invasive species refers to a subset of introduced species or non-indigenous species that are rapidly expanding outside of their native range. ... Global warming refers to the increase in the average temperature of the Earths near-surface air and oceans in recent decades and its projected continuation. ... The term Marine Protected Area is often used as an umbrella term covering a wide range of marine areas with some level of restriction to protect living, non-living, cultural, and/or historic resources. ... A scientific method or process is considered fundamental to the scientific investigation and acquisition of new knowledge based upon physical evidence. ...

Biological rhythms and the tides

Intertidal organisms are greatly affected by the approximately fortnightly cycle of the tides, and hence their biological rhythms tend to occur in rough multiples of this period. This is seen not only in the intertidal organisms however, but also in many other terrestrial animals, such as the vertebrates. Examples include gestation and the hatching of eggs. In humans, for example, the menstrual cycle lasts roughly a month, an even multiple of the period of the tidal cycle. This may be evidence of the common descent of all animals from a marine ancestor.[17] A biorhythm (or biological rhythm) is a cyclic pattern of alterations in physiology, emotions, and/or intellect. ... This article does not cite any references or sources. ... Gestation is the carrying of an embryo or fetus inside a female viviparous animal. ... Menstrual cycle The menstrual cycle is a recurring cycle of physiologic changes that occurs in the females of several mammals, including human beings and other apes. ... A group of organisms is said to have common descent if they have a common ancestor. ...

Other tides

In addition to oceanic tides, there are atmospheric tides as well as earth tides. All of these are continuum mechanical phenomena, the first two being fluids and the third solid (with various modifications). Atmospheric tides (sometimes known as air tides or atmospheric oscillations) are global-scale periodic atmospheric oscillations. ... It has been suggested that this article or section be merged into Tide. ... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... This box:      Fluid mechanics is the study of how fluids move and the forces on them. ... Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ...

Atmospheric tides are negligible from ground level and aviation altitudes, drowned by the much more important effects of weather. Atmospheric tides are both gravitational and thermal in origin, and are the dominant dynamics from about 80 km to 120 km where the molecular density becomes too small to behave as a fluid. For the geological process, see Weathering or Erosion. ...

Earth tides or terrestrial tides affect the entire rocky mass of the Earth. The Earth's crust shifts (up/down, east/west, north/south) in response to the Moon's and Sun's gravitation, ocean tides, and atmospheric loading. While negligible for most human activities, the semidiurnal amplitude of terrestrial tides can reach about 55 cm at the equator (15 cm is due to the Sun) which is important in GPS calibration and VLBI measurements. 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. The semi-diurnal M2 Earth tides are nearly in phase with the Moon with tidal lag of about two hours.[18] Terrestrial tides also need to be taken in account in the case of some particle physics experiments.[19] For instance, at the CERN or SLAC, the very large particle accelerators were designed while taking terrestrial tides into account for proper operation. Among the effects that need to be taken into account are for circular accelerators and particle beam energy[20] Since tidal forces generate currents of conducting fluids within the interior of the Earth, they affect in turn the Earth's magnetic field itself. Over fifty GPS satellites such as this NAVSTAR have been launched since 1978. ... This article needs cleanup. ... Rotation (green), Precession (blue) and Nutation (red) of the Earth Nutation is a slight irregular motion (etymologically a nodding) in the axis of rotation of a largely axially symmetric object, such as a gyroscope or a planet. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... CERN logo The European Organization for Nuclear Research (French: ), commonly known as CERN (see Naming), pronounced (or in French), is the worlds largest particle physics laboratory, situated just northwest of Geneva on the border between France and Switzerland. ... The Stanford Linear Accelerator Center (SLAC) is a U.S. national laboratory operated by Stanford University for the U.S. Department of Energy. ... For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ... The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ...

When oscillating tidal currents in the stratified ocean flow over uneven bottom topography, they generate internal waves with tidal frequencies. Such waves are called internal tides. Internal waves are gravity waves that oscillate due to the buoyancy force. ...

The galactic tide is the tidal force exerted by galaxies on stars within them and satellite galaxies orbiting them. The effects of the galactic tide on the Solar System's Oort cloud are believed to be the cause of 90 percent of all observed long-period comets.[21] The Andromeda Galaxy. ... A satellite galaxy orbits a larger galaxy, due to gravitational attraction. ... This article is about the Solar System. ... This image is an artists rendering of the Oort cloud and the Kuiper Belt. ...


Tsunamis, the large waves that occur after earthquakes, are sometimes called tidal waves, but this name is due to their resemblance to the tide, rather than any actual link to the tide itself. Other phenomena unrelated to tides but using the word tide are rip tide, storm tide, hurricane tide, and black or red tides. The term tidal wave appears to be disappearing from popular usage[citation needed]. The tsunami that struck Malé in the Maldives on December 26, 2004. ... A rip current is a strong flow of water returning seaward from the shore. ... A storm tide is a tide with a high flood period caused by a storm. ... Subsequent to an Oil Spill An oil spill is the unintentional release of a liquid petroleum hydrocarbon into the environment as a result of human activity. ... A red tide off the coast of La Jolla, California. ...

See also

Workers harvest catfish from the Delta Pride Catfish farms in Mississippi Aquaculture is the cultivation of aquatic organisms. ... Many stretches of the coastline of East Anglia, England, are prone to high rates of erosion, as illustrated by this collapsed section of the cliffs at Hunstanton, Norfolk. ... The Hough functions in applied mathematics are the eigenfunctions of Laplaces tidal equations which govern fluid motion on a rotating sphere. ... Lunar phase refers to the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. ... The Lunar Laser Ranging Experiment from the Apollo 11 mission The ongoing Lunar Laser Ranging Experiment measures the distance between the Earth and the Moon using laser ranging. ... The orbit of the Moon around the Earth is completed in approximately 27. ... The primitive equations are a version of the Navier-Stokes equations that describe hydrodynamical flow on the sphere under the assumptions that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere. ... A storm tide is a tide with a high flood period caused by a storm. ... The tidal bore in Upper Cook Inlet, Alaska A tidal bore (or just bore, or eagre) is a tidal phenomenon in which the leading edge of the incoming tide forms a wave (or waves) of water that travel up a river or narrow bay against the direction of the current. ... St Michaels Mount, Cornwall at high tide in 1900. ... Tidal locking makes one side of an astronomical body always face another, like the Moon facing the Earth. ... In oceanography, tidal resonance is a phenomenon perhaps best exemplified in the Bay of Fundy. ... A rip current is a strong flow of water returning seaward from the shore. ... A tide pool on Gabriola Island, British Columbia showing ochre sea stars Tide pools (also tidal pools or rock pools) are rocky pools by oceans that are filled with seawater. ... Slack water is the time during which no appreciable current in flowing in a body of water. ... Tidal power, sometimes called tidal energy, is a form of hydropower that exploits the movement of water caused by tidal currents or the rise and fall in sea levels due to the tides. ... A red tide off the coast of La Jolla, California. ... The tidal range is the vertical difference between the highest high tide and the lowest low tide. ... A Tideline refers to where two currents in the ocean converge, driftwood, floating seaweed, foam, and other floating debris may accumulate, forming sinous lines called tidelines (even though they generally have nothing to do with the tide. ... Head of tide is the farthest point upstream where a river is affected by tidal fluctuations. ... Image File history File links No higher resolution available. ... Image File history File links Drinking_water. ... Image File history File links Commons-logo. ...

External links

Tide predictions

References and notes

  1. ^ The orientation and geometry of the coast affects the phase, direction, and amplitude of coastal Kelvin waves as well as resonant seiches in bays. In estuaries seasonal river outflows influence tidal flow.
  2. ^ 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 in the sense that they are predicted from mean data. Glossary of Coastal Terminology: H – M, Washington Department of Ecology, State of Washington (checked 5 April 2007).
  3. ^ The Moon orbits in the same direction the Earth spins. Compare this to the minute hand crossing the hour hand at 12:00 and then again at about 1:05 (not at 1:00).
  4. ^ Tidal lunar day, NOAA. Do not confuse with the astronomical lunar day on the Moon. A lunar zenith is the Moon's highest point in the sky.
  5. ^ "Solution of the Tidal Equations for the M2 and S2 Tides in the World Oceans from a Knowledge of the Tidal Potential Alone", Y. Accad, C. L. Pekeris Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 290, No. 1368 (November 28, 1978), pp. 235-266. Also Primary M2 Tide for New Zealand, animation (checked 4/4/2007).
  6. ^ Semidiurnal and long term constituents phase are measured from high tide, diurnal from maximum flood tide. This and the discussion that follows is only precisely true for a single tidal constituent.
  7. ^ Generally clockwise in the southern hemisphere, and counterclockwise in the northern hemisphere
  8. ^ The reference tide is the hypothetical constituent equilibrium tide on a landless earth that would be measured at 0° longitude, the Greenwich meridian.
  9. ^ a b "Historical Development and Use of Thousand-Year-Old Tide-Prediction Tables," Yang Zuosheng, K. O. Emery, Xui Yui, Limnology and Oceanography, Vol. 34, No. 5 (Jul., 1989), pp. 953-957. Tides: A Scientific History, David E. Cartwright, Cambridge University Press, Cambridge, UK, 1999. reviewed in "Understanding Tides—From Ancient Beliefs to Present-day Solutions to the Laplace Equations," James Case, SIAM News, Volume 33, Number 2 March 2000.
  10. ^ Compare this to passengers on a turning bus. The bus's overall motion follows the center of mass, but passengers sitting in different parts of the bus experience different forces, and so may shift within the bus. The rigid body of the bus redistributes the road traction forces through its frame and seats to the passengers, who experience the sideways traction of the seat. There is relatively small difference between the way the entire bus responds to the turn compared to individual passengers, and their movement relative to the bus is much smaller than the turning motion of the bus. Like the bus, the Earth does deform some, but the oceans still are subject to a residual forcing. ...
  11. ^ 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 height of the oceans, one facing the Moon and the other on the opposite side of the earth, facing away from the Moon. There would also be smaller, superimposed bulges on the sides facing toward and away from the Sun.
  12. ^ 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.
  13. ^ Glossary of Meteorology American Meteorological Society.
  14. ^ http://www.waterlevels.gc.ca/english/FrequentlyAskedQuestions.shtml#importantes, accessed June 23, 2007
  15. ^ Tide and Current Glossary, Center for Operational Oceanographic Products and Services, National Ocean Service, National Oceanic and Atmospheric Administration, Silver Spring, MD, January 2000.
  16. ^ Harmonic Constituents,NOAA.
  17. ^ Darwin, Charles (1871). The Descent of Man, and Selection in Relation to Sex. John Murray: London.
  18. ^ Earth tide calculator
  19. ^ Linac, Stanford online.
  20. ^ "Effects of Tidal Forces on the Beam Energy in LEP", PAC 1993, IEEE. "Long term variation of the circumference of the spring-8 storage ring", Proceedings of EPAC 2000, Vienna, Austria.
  21. ^ 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. 

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