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101-445: The geoid ( / ˈ dʒ iː . ɔɪ d / JEE -oyd ) is the shape that the ocean surface would take under the influence of the gravity of Earth , including gravitational attraction and Earth's rotation , if other influences such as winds and tides were absent. This surface is extended through the continents (such as might be approximated with very narrow hypothetical canals ). According to Gauss , who first described it, it

202-410: A halocline . If a zone undergoes a strong, vertical chemistry gradient with depth, it contains a chemocline . Temperature and salinity control ocean water density. Colder and saltier water is denser, and this density plays a crucial role in regulating the global water circulation within the ocean. The halocline often coincides with the thermocline, and the combination produces a pronounced pycnocline ,

303-493: A mid-ocean ridge , which creates a long mountain range beneath the ocean. Together they form the global mid-oceanic ridge system that features the longest mountain range in the world. The longest continuous mountain range is 65,000 km (40,000 mi). This underwater mountain range is several times longer than the longest continental mountain range – the Andes . Oceanographers state that less than 20% of

404-444: A boundary between less dense surface water and dense deep water. Tangential component More generally, given a submanifold N of a manifold M , and a vector in the tangent space to M at a point of N , it can be decomposed into the component tangent to N and the component normal to N . More formally, let S {\displaystyle S} be a surface, and x {\displaystyle x} be

505-595: A gentle breeze on a pond causes ripples to form. A stronger gust blowing over the ocean causes larger waves as the moving air pushes against the raised ridges of water. The waves reach their maximum height when the rate at which they are travelling nearly matches the speed of the wind. In open water, when the wind blows continuously as happens in the Southern Hemisphere in the Roaring Forties , long, organized masses of water called swell roll across

606-474: A given distance, causing the geoid to move towards the mass deficit. The presence of a localized inclusion in the background medium will rotate the gravity acceleration vectors slightly towards or away from a denser or lighter body, respectively, causing a bump or dimple in the equipotential surface. The largest absolute deviation can be found in the Indian Ocean Geoid Low , 106 meters below

707-508: A point p ∈ N {\displaystyle p\in N} , we get a short exact sequence involving the tangent spaces : T p N → T p M → T p M / T p N {\displaystyle T_{p}N\to T_{p}M\to T_{p}M/T_{p}N} The quotient space T p M / T p N {\displaystyle T_{p}M/T_{p}N}

808-433: A point on the surface. Let v {\displaystyle \mathbf {v} } be a vector at x {\displaystyle x} . Then one can write uniquely v {\displaystyle \mathbf {v} } as a sum v = v ∥ + v ⊥ {\displaystyle \mathbf {v} =\mathbf {v} _{\parallel }+\mathbf {v} _{\perp }} where

909-433: A reference coordinate surface for various vertical coordinates , such as orthometric heights , geopotential heights , and dynamic heights (see Geodesy#Heights ). All points on a geoid surface have the same geopotential (the sum of gravitational potential energy and centrifugal potential energy). At this surface, apart from temporary tidal fluctuations, the force of gravity acts everywhere perpendicular to

1010-455: A result, the photic zone is the most biodiverse and the source of the food supply which sustains most of the ocean ecosystem . Ocean photosynthesis also produces half of the oxygen in the Earth's atmosphere. Light can only penetrate a few hundred more meters; the rest of the deeper ocean is cold and dark (these zones are called mesopelagic and aphotic zones). The continental shelf is where

1111-496: A shallow area and this, coupled with a low pressure system, can raise the surface of the ocean dramatically above a typical high tide. The average depth of the oceans is about 4 km. More precisely the average depth is 3,688 meters (12,100 ft). Nearly half of the world's marine waters are over 3,000 meters (9,800 ft) deep. "Deep ocean," which is anything below 200 meters (660 ft), covers about 66% of Earth's surface. This figure does not include seas not connected to

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1212-634: A specific value of n {\displaystyle n} there are two coefficients for every value of m {\displaystyle m} except for m = 0 {\displaystyle m=0} . There is only one coefficient when m = 0 {\displaystyle m=0} since sin ⁡ ( 0 λ ) = 0 {\displaystyle \sin(0\lambda )=0} . There are thus ( 2 n + 1 ) {\displaystyle (2n+1)} coefficients for every value of n {\displaystyle n} . Using these facts and

1313-403: A wave-cut platform develops at the foot of the cliff and this has a protective effect, reducing further wave-erosion. Material worn from the margins of the land eventually ends up in the sea. Here it is subject to attrition as currents flowing parallel to the coast scour out channels and transport sand and pebbles away from their place of origin. Sediment carried to the sea by rivers settles on

1414-406: A zone undergoes dramatic changes in temperature with depth, it contains a thermocline , a distinct boundary between warmer surface water and colder deep water. In tropical regions, the thermocline is typically deeper compared to higher latitudes. Unlike polar waters , where solar energy input is limited, temperature stratification is less pronounced, and a distinct thermocline is often absent. This

1515-439: Is a bay , a small bay with a narrow inlet is a cove and a large bay may be referred to as a gulf . Coastlines are influenced by several factors including the strength of the waves arriving on the shore, the gradient of the land margin, the composition and hardness of the coastal rock, the inclination of the off-shore slope and the changes of the level of the land due to local uplift or submergence. Normally, waves roll towards

1616-1267: Is a generalized space of normal vectors. If M is a Riemannian manifold , the above sequence splits , and the tangent space of M at p decomposes as a direct sum of the component tangent to N and the component normal to N : T p M = T p N ⊕ N p N := ( T p N ) ⊥ {\displaystyle T_{p}M=T_{p}N\oplus N_{p}N:=(T_{p}N)^{\perp }} Thus every tangent vector v ∈ T p M {\displaystyle v\in T_{p}M} splits as v = v ∥ + v ⊥ {\displaystyle v=v_{\parallel }+v_{\perp }} , where v ∥ ∈ T p N {\displaystyle v_{\parallel }\in T_{p}N} and v ⊥ ∈ N p N := ( T p N ) ⊥ {\displaystyle v_{\perp }\in N_{p}N:=(T_{p}N)^{\perp }} . Suppose N

1717-743: Is about −2 °C (28 °F). In all parts of the ocean, deep ocean temperatures range between −2 °C (28 °F) and 5 °C (41 °F). Constant circulation of water in the ocean creates ocean currents . Those currents are caused by forces operating on the water, such as temperature and salinity differences, atmospheric circulation (wind), and the Coriolis effect . Tides create tidal currents, while wind and waves cause surface currents. The Gulf Stream , Kuroshio Current , Agulhas Current and Antarctic Circumpolar Current are all major ocean currents. Such currents transport massive amounts of water, gases, pollutants and heat to different parts of

1818-444: Is an important reference point for oceanography and geography, particularly as mean sea level . The ocean surface has globally little, but measurable topography , depending on the ocean's volumes. The ocean surface is a crucial interface for oceanic and atmospheric processes. Allowing interchange of particles, enriching the air and water, as well as grounds by some particles becoming sediments . This interchange has fertilized life in

1919-411: Is customarily divided into five principal oceans – listed below in descending order of area and volume: The ocean fills Earth's oceanic basins . Earth's oceanic basins cover different geologic provinces of Earth's oceanic crust as well as continental crust . As such it covers mainly Earth's structural basins , but also continental shelfs . In mid-ocean, magma is constantly being thrust through

2020-411: Is defined so that it has negative values and is inversely proportional to distance from the body. So, while a mass excess will strengthen the gravity acceleration, it will decrease the gravity potential. As a consequence, the geoid's defining equipotential surface will be found displaced away from the mass excess. Analogously, a mass deficit will weaken the gravity pull but will increase the geopotential at

2121-399: Is due to the fact that surface waters in polar latitudes are nearly as cold as deeper waters. Below the thermocline, water everywhere in the ocean is very cold, ranging from −1 °C to 3 °C. Because this deep and cold layer contains the bulk of ocean water, the average temperature of the world ocean is 3.9 °C. If a zone undergoes dramatic changes in salinity with depth, it contains

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2222-463: Is further divided into zones based on depth and the amount of light present. The photic zone starts at the surface and is defined to be "the depth at which light intensity is only 1% of the surface value" (approximately 200 m in the open ocean). This is the zone where photosynthesis can occur. In this process plants and microscopic algae (free floating phytoplankton ) use light, water, carbon dioxide, and nutrients to produce organic matter. As

2323-503: Is given by non-degenerate equations. If N is given explicitly, via parametric equations (such as a parametric curve ), then the derivative gives a spanning set for the tangent bundle (it is a basis if and only if the parametrization is an immersion ). If N is given implicitly (as in the above description of a surface, (or more generally as) a hypersurface ) as a level set or intersection of level surfaces for g i {\displaystyle g_{i}} , then

2424-456: Is irregular, unevenly dominating the Earth's surface . This leads to the distinction of the Earth's surface into a water and land hemisphere , as well as the division of the ocean into different oceans. Seawater covers about 361,000,000 km (139,000,000 sq mi) and the ocean's furthest pole of inaccessibility , known as " Point Nemo ", in a region known as spacecraft cemetery of

2525-602: Is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid. In maps and common use, the height over the mean sea level (such as orthometric height , H ) is used to indicate the height of elevations while the ellipsoidal height , h , results from the GPS system and similar GNSS : H = h − N {\displaystyle H=h-N} (An analogous relationship exists between normal heights and

2626-536: Is positive, opposite to what should be expected if the thickening affects the entire lithosphere . Mantle convection also changes the shape of the geoid over time. The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly or negative disturbing potential (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly or positive disturbing potential (mass deficit). This relationship can be understood by recalling that gravity potential

2727-454: Is produced and magma is forced up creating underwater mountains, some of which may form chains of volcanic islands near to deep trenches. Near some of the boundaries between the land and sea, the slightly denser oceanic plates slide beneath the continental plates and more subduction trenches are formed. As they grate together, the continental plates are deformed and buckle causing mountain building and seismic activity. Every ocean basin has

2828-407: Is pushed across the surface of the ocean by the wind, but this represents a transfer of energy and not horizontal movement of water. As waves approach land and move into shallow water , they change their behavior. If approaching at an angle, waves may bend ( refraction ) or wrap around rocks and headlands ( diffraction ). When the wave reaches a point where its deepest oscillations of the water contact

2929-423: Is reflected back out of the water. Red light is most easily absorbed and thus does not reach great depths, usually to less than 50 meters (164 ft). Blue light, in comparison, can penetrate up to 200 meters (656 ft). Second, water molecules and very tiny particles in ocean water preferentially scatter blue light more than light of other colors. Blue light scattering by water and tiny particles happens even in

3030-480: Is sometimes referred to as the World Ocean, global ocean or the great ocean . The concept of a continuous body of water with relatively unrestricted exchange between its components is critical in oceanography . The word ocean comes from the figure in classical antiquity , Oceanus ( / oʊ ˈ s iː ə n ə s / ; ‹See Tfd› Greek : Ὠκεανός Ōkeanós , pronounced [ɔːkeanós] ),

3131-440: Is the "mathematical figure of the Earth ", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics , it has been defined to high precision only since advances in satellite geodesy in

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3232-442: Is the body of salt water that covers approximately 70.8% of Earth . In English , the term ocean also refers to any of the large bodies of water into which the world ocean is conventionally divided. The following names describe five different areas of the ocean: Pacific , Atlantic , Indian , Antarctic/Southern , and Arctic . The ocean contains 97% of Earth's water and is the primary component of Earth's hydrosphere and

3333-400: Is thereby essential to life on Earth. The ocean influences climate and weather patterns, the carbon cycle , and the water cycle by acting as a huge heat reservoir . Ocean scientists split the ocean into vertical and horizontal zones based on physical and biological conditions. The pelagic zone is the open ocean's water column from the surface to the ocean floor. The water column

3434-514: Is thus non-uniform over the geoid. The geoid surface is irregular, unlike the reference ellipsoid (which is a mathematical idealized representation of the physical Earth as an ellipsoid ), but is considerably smoother than Earth's physical surface. Although the "ground" of the Earth has excursions on the order of +8,800 m ( Mount Everest ) and −11,000 m ( Marianas Trench ), the geoid's deviation from an ellipsoid ranges from +85 m (Iceland) to −106 m (southern India), less than 200 m total. If

3535-406: The quasigeoid , which disregards local density variations.) In practice, many handheld GPS receivers interpolate N in a pre-computed geoid map (a lookup table ). So a GPS receiver on a ship may, during the course of a long voyage, indicate height variations, even though the ship will always be at sea level (neglecting the effects of tides). That is because GPS satellites , orbiting about

3636-485: The Gravity Recovery and Climate Experiment ), and supports up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients), with additional coefficients extending to degree 2190 and order 2159. EGM2020 is the international follow-up that was originally scheduled for 2020 (still unreleased in 2024), containing the same number of harmonics generated with better data. Ocean The ocean

3737-635: The International Association of Geodesy (IAG), e.g., through the International Gravity Bureau (BGI, Bureau Gravimétrique International). Another approach for geoid determination is to combine multiple information sources: not just terrestrial gravimetry, but also satellite geodetic data on the figure of the Earth, from analysis of satellite orbital perturbations, and lately from satellite gravity missions such as GOCE and GRACE . In such combination solutions,

3838-691: The North Sea or the Red Sea . There is no sharp distinction between seas and oceans, though generally seas are smaller, and are often partly (as marginal seas ) or wholly (as inland seas ) bordered by land. The contemporary concept of the World Ocean was coined in the early 20th century by the Russian oceanographer Yuly Shokalsky to refer to the continuous ocean that covers and encircles most of Earth. The global, interconnected body of salt water

3939-481: The South Pacific Ocean , at 48°52.6′S 123°23.6′W  /  48.8767°S 123.3933°W  / -48.8767; -123.3933  ( Point Nemo ) . This point is roughly 2,688 km (1,670 mi) from the nearest land. There are different customs to subdivide the ocean and are adjourned by smaller bodies of water such as, seas , gulfs , bays , bights , and straits . The ocean

4040-592: The Thames Barrier is designed to protect London from a storm surge, while the failure of the dykes and levees around New Orleans during Hurricane Katrina created a humanitarian crisis in the United States. Most of the ocean is blue in color, but in some places the ocean is blue-green, green, or even yellow to brown. Blue ocean color is a result of several factors. First, water preferentially absorbs red light, which means that blue light remains and

4141-406: The coastline and structure of the world ocean. A global ocean has existed in one form or another on Earth for eons. Since its formation the ocean has taken many conditions and shapes with many past ocean divisions and potentially at times covering the whole globe. During colder climatic periods, more ice caps and glaciers form, and enough of the global water supply accumulates as ice to lessen

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4242-407: The cross product . These formulas do not depend on the particular unit normal n ^ {\displaystyle {\hat {\mathbf {n} }}} used (there exist two unit normals to any surface at a given point, pointing in opposite directions, so one of the unit normals is the negative of the other one). More generally, given a submanifold N of a manifold M and

4343-448: The dot product . Another formula for the tangential component is v ∥ = − n ^ × ( n ^ × v ) , {\displaystyle \mathbf {v} _{\parallel }=-{\hat {\mathbf {n} }}\times ({\hat {\mathbf {n} }}\times \mathbf {v} ),} where " × {\displaystyle \times } " denotes

4444-450: The geocentric radius , i.e., distance from the Earth's centre. The geoid is a particular equipotential surface, and is somewhat involved to compute. The gradient of this potential also provides a model of the gravitational acceleration. The most commonly used EGM96 contains a full set of coefficients to degree and order 360 (i.e., n max = 360 {\displaystyle n_{\text{max}}=360} ), describing details in

4545-591: The ocean floor , they begin to slow down. This pulls the crests closer together and increases the waves' height , which is called wave shoaling . When the ratio of the wave's height to the water depth increases above a certain limit, it " breaks ", toppling over in a mass of foaming water. This rushes in a sheet up the beach before retreating into the ocean under the influence of gravity. Earthquakes , volcanic eruptions or other major geological disturbances can set off waves that can lead to tsunamis in coastal areas which can be very dangerous. The ocean's surface

4646-578: The viscosity of Earth's mantle . Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM2020 (Earth Gravitational Model 2020), determined in an international collaborative project led by the National Imagery and Mapping Agency (now the National Geospatial-Intelligence Agency , or NGA). The mathematical description of

4747-466: The EGM96 value of n max = 360 {\displaystyle n_{\text{max}}=360} . For many applications, the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms. Still, even higher resolution models have been developed. Many of the authors of EGM96 have published EGM2008. It incorporates much of the new satellite gravity data (e.g.,

4848-442: The Earth's biosphere . Oceanic evaporation , as a phase of the water cycle, is the source of most rainfall (about 90%), causing a global cloud cover of 67% and a consistent oceanic cloud cover of 72%. Ocean temperatures affect climate and wind patterns that affect life on land. One of the most dramatic forms of weather occurs over the oceans: tropical cyclones (also called "typhoons" and "hurricanes" depending upon where

4949-863: The European Space Agency. ESA launched the satellite in March 2009 on a mission to map Earth's gravity with unprecedented accuracy and spatial resolution. On 31 March 2011, a new geoid model was unveiled at the Fourth International GOCE User Workshop hosted at the Technical University of Munich , Germany. Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles, mass balances of ice sheets , and postglacial rebound . From postglacial rebound measurements, time-variable GRACE data can be used to deduce

5050-456: The Moon are 20x stronger than the Moon's tidal forces on the Earth.) The primary effect of lunar tidal forces is to bulge Earth matter towards the near and far sides of the Earth, relative to the moon. The "perpendicular" sides, from which the Moon appears in line with the local horizon, experience "tidal troughs". Since it takes nearly 25 hours for the Earth to rotate under the Moon (accounting for

5151-403: The Moon's 28 day orbit around Earth), tides thus cycle over a course of 12.5 hours. However, the rocky continents pose obstacles for the tidal bulges, so the timing of tidal maxima may not actually align with the Moon in most localities on Earth, as the oceans are forced to "dodge" the continents. Timing and magnitude of tides vary widely across the Earth as a result of the continents. Thus, knowing

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5252-471: The Moon's gravity, oceanic tides are also substantially modulated by the Sun's tidal forces, by the rotation of the Earth, and by the shape of the rocky continents blocking oceanic water flow. (Tidal forces vary more with distance than the "base" force of gravity: the Moon's tidal forces on Earth are more than double the Sun's, despite the latter's much stronger gravitational force on Earth. Earth's tidal forces upon

5353-400: The Moon's position does not allow a local to predict tide timings, instead requiring precomputed tide tables which account for the continents and the Sun, among others. During each tidal cycle, at any given place the tidal waters rise to maximum height, high tide, before ebbing away again to the minimum level, low tide. As the water recedes, it gradually reveals the foreshore , also known as

5454-648: The Okeanos is represented with a dragon-tail on some early Greek vases. Scientists believe that a sizable quantity of water would have been in the material that formed Earth. Water molecules would have escaped Earth's gravity more easily when it was less massive during its formation. This is called atmospheric escape . During planetary formation , Earth possibly had magma oceans . Subsequently, outgassing , volcanic activity and meteorite impacts , produced an early atmosphere of carbon dioxide , nitrogen and water vapor , according to current theories. The gases and

5555-741: The World Ocean, such as the Caspian Sea . The deepest region of the ocean is at the Mariana Trench , located in the Pacific Ocean near the Northern Mariana Islands . The maximum depth has been estimated to be 10,971 meters (35,994 ft). The British naval vessel Challenger II surveyed the trench in 1951 and named the deepest part of the trench the " Challenger Deep ". In 1960, the Trieste successfully reached

5656-421: The amounts in other parts of the water cycle. The reverse is true during warm periods. During the last ice age, glaciers covered almost one-third of Earth's land mass with the result being that the oceans were about 122 m (400 ft) lower than today. During the last global "warm spell," about 125,000 years ago, the seas were about 5.5 m (18 ft) higher than they are now. About three million years ago

5757-479: The atmosphere are thought to have accumulated over millions of years. After Earth's surface had significantly cooled, the water vapor over time would have condensed, forming Earth's first oceans. The early oceans might have been significantly hotter than today and appeared green due to high iron content. Geological evidence helps constrain the time frame for liquid water existing on Earth. A sample of pillow basalt (a type of rock formed during an underwater eruption)

5858-758: The average sea level. Another large feature is the North Atlantic Geoid High (or North Atlantic Geoid Swell), caused in part by the weight of ice cover over North America and northern Europe in the Late Cenozoic Ice Age . Recent satellite missions, such as the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and GRACE , have enabled the study of time-variable geoid signals. The first products based on GOCE satellite data became available online in June 2010, through

5959-407: The bottom of the trench, manned by a crew of two men. Oceanographers classify the ocean into vertical and horizontal zones based on physical and biological conditions. The pelagic zone consists of the water column of the open ocean, and can be divided into further regions categorized by light abundance and by depth. The ocean zones can be grouped by light penetration into (from top to bottom):

6060-408: The center of gravity of the Earth, can measure heights only relative to a geocentric reference ellipsoid. To obtain one's orthometric height , a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tide gauge , as in traditional land surveying, is closer to orthometric height. Modern GPS receivers have a grid implemented in their software by which they obtain, from

6161-505: The center of the Earth to that location. The geoid level coincides with where the water would be. Generally the geoid rises where the Earth's material is locally more dense, exerts greater gravitational force, and pulls more water from the surrounding area. The geoid undulation (also known as geoid height or geoid anomaly ), N , is the height of the geoid relative to a given ellipsoid of reference . N = h − H {\displaystyle N=h-H} The undulation

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6262-570: The current position, the height of the geoid (e.g., the EGM96 geoid) over the World Geodetic System (WGS) ellipsoid. They are then able to correct the height above the WGS ellipsoid to the height above the EGM96 geoid. When height is not zero on a ship, the discrepancy is due to other factors such as ocean tides, atmospheric pressure (meteorological effects), local sea surface topography , and measurement uncertainties. The undulation of

6363-402: The density and weight of different geological compositions in the Earth's crust , mountain ranges, deep sea trenches, crust compaction due to glaciers, and so on. If that sphere were then covered in water, the water would not be the same height everywhere. Instead, the water level would be higher or lower with respect to Earth's center, depending on the integral of the strength of gravity from

6464-509: The elder of the Titans in classical Greek mythology . Oceanus was believed by the ancient Greeks and Romans to be the divine personification of an enormous river encircling the world. The concept of Ōkeanós has an Indo-European connection. Greek Ōkeanós has been compared to the Vedic epithet ā-śáyāna-, predicated of the dragon Vṛtra-, who captured the cows/rivers. Related to this notion,

6565-1060: The first vector in the sum is the tangential component and the second one is the normal component. It follows immediately that these two vectors are perpendicular to each other. To calculate the tangential and normal components, consider a unit normal to the surface, that is, a unit vector n ^ {\displaystyle {\hat {\mathbf {n} }}} perpendicular to S {\displaystyle S} at x {\displaystyle x} . Then, v ⊥ = ( v ⋅ n ^ ) n ^ {\displaystyle \mathbf {v} _{\perp }=\left(\mathbf {v} \cdot {\hat {\mathbf {n} }}\right){\hat {\mathbf {n} }}} and thus v ∥ = v − v ⊥ {\displaystyle \mathbf {v} _{\parallel }=\mathbf {v} -\mathbf {v} _{\perp }} where " ⋅ {\displaystyle \cdot } " denotes

6666-412: The formation of unusually high rogue waves . Most waves are less than 3 m (10 ft) high and it is not unusual for strong storms to double or triple that height. Rogue waves, however, have been documented at heights above 25 meters (82 ft). The top of a wave is known as the crest, the lowest point between waves is the trough and the distance between the crests is the wavelength. The wave

6767-603: The formula, ∑ I = 1 L I = 1 2 L ( L + 1 ) {\textstyle \sum _{I=1}^{L}I={\frac {1}{2}}L(L+1)} , it follows that the total number of coefficients is given by ∑ n = 2 n max ( 2 n + 1 ) = n max ( n max + 1 ) + n max − 3 = 130317 {\displaystyle \sum _{n=2}^{n_{\text{max}}}(2n+1)=n_{\text{max}}(n_{\text{max}}+1)+n_{\text{max}}-3=130317} using

6868-411: The fully normalized associated Legendre polynomials of degree n   {\displaystyle n\ } and order m   {\displaystyle m\ } , and C ¯ n m {\displaystyle {\overline {C}}_{nm}} and S ¯ n m {\displaystyle {\overline {S}}_{nm}} are

6969-666: The geoid N is closely related to the disturbing potential T according to Bruns' formula (named after Heinrich Bruns ): where γ {\displaystyle \gamma } is the force of normal gravity , computed from the normal field potential U {\displaystyle U} . Another way of determining N is using values of gravity anomaly Δ g {\displaystyle \Delta g} , differences between true and normal reference gravity, as per Stokes formula (or Stokes' integral ), published in 1849 by George Gabriel Stokes : The integral kernel S , called Stokes function ,

7070-418: The geoid and the local horizon tangential to it. Likewise, spirit levels will always be parallel to the geoid. Earth's gravitational field is not uniform. An oblate spheroid is typically used as the idealized Earth, but even if the Earth were spherical and did not rotate, the strength of gravity would not be the same everywhere because density varies throughout the planet. This is due to magma distributions,

7171-445: The geoid, meaning that plumb lines point perpendicular and bubble levels are parallel to the geoid. Being an equigeopotential means the geoid corresponds to the free surface of water at rest (if only the Earth's gravity and rotational acceleration were at work); this is also a sufficient condition for a ball to remain at rest instead of rolling over the geoid. Earth's gravity acceleration (the vertical derivative of geopotential)

7272-453: The global geoid as small as 55 km (or 110 km, depending on the definition of resolution). The number of coefficients, C ¯ n m {\displaystyle {\overline {C}}_{nm}} and S ¯ n m {\displaystyle {\overline {S}}_{nm}} , can be determined by first observing in the equation for V {\displaystyle V} that for

7373-416: The heights of continental points above the geoid by spirit leveling . Being an equipotential surface , the geoid is, by definition, a surface upon which the force of gravity is perpendicular everywhere, apart from temporary tidal fluctuations. This means that when traveling by ship, one does not notice the undulation of the geoid ; neglecting tides, the local vertical (plumb line) is always perpendicular to

7474-421: The interface between water and air is called swell – a term used in sailing , surfing and navigation . These motions profoundly affect ships on the surface of the ocean and the well-being of people on those ships who might suffer from sea sickness . Wind blowing over the surface of a body of water forms waves that are perpendicular to the direction of the wind. The friction between air and water caused by

7575-482: The intertidal zone. The difference in height between the high tide and low tide is known as the tidal range or tidal amplitude. When the sun and moon are aligned (full moon or new moon), the combined effect results in the higher "spring tides", while the sun and moon misaligning (half moons) result in lesser tidal ranges. In the open ocean tidal ranges are less than 1 meter, but in coastal areas these tidal ranges increase to more than 10 meters in some areas. Some of

7676-739: The largest tidal ranges in the world occur in the Bay of Fundy and Ungava Bay in Canada, reaching up to 16 meters. Other locations with record high tidal ranges include the Bristol Channel between England and Wales, Cook Inlet in Alaska, and the Río Gallegos in Argentina. Tides are not to be confused with storm surges , which can occur when high winds pile water up against the coast in

7777-411: The late 20th century. The geoid is often expressed as a geoid undulation or geoidal height above a given reference ellipsoid , which is a slightly flattened sphere whose equatorial bulge is caused by the planet's rotation. Generally the geoidal height rises where the Earth's material is locally more dense and exerts greater gravitational force than the surrounding areas. The geoid in turn serves as

7878-940: The low-resolution part of the geoid solution is provided by the satellite data, while a 'tuned' version of the above Stokes equation is used to calculate the high-resolution part, from terrestrial gravimetric data from a neighbourhood of the evaluation point only. Calculating the undulation is mathematically challenging. The precise geoid solution by Petr Vaníček and co-workers improved on the Stokesian approach to geoid computation. Their solution enables millimetre-to-centimetre accuracy in geoid computation , an order-of-magnitude improvement from previous classical solutions. Geoid undulations display uncertainties which can be estimated by using several methods, e.g., least-squares collocation (LSC), fuzzy logic , artificial neural networks , radial basis functions (RBF), and geostatistical techniques. Geostatistical approach has been defined as

7979-471: The majority of Earth's surface. It includes the Pacific , Atlantic , Indian , Southern/Antarctic , and Arctic oceans. As a general term, "the ocean" and "the sea" are often interchangeable. Strictly speaking, a "sea" is a body of water (generally a division of the world ocean) partly or fully enclosed by land. The word "sea" can also be used for many specific, much smaller bodies of seawater, such as

8080-401: The most-improved technique in prediction of geoid undulation. Variations in the height of the geoidal surface are related to anomalous density distributions within the Earth. Geoid measures thus help understanding the internal structure of the planet. Synthetic calculations show that the geoidal signature of a thickened crust (for example, in orogenic belts produced by continental collision )

8181-1163: The non-rotating part of the potential function in this model is: V = G M r ( 1 + ∑ n = 2 n max ( a r ) n ∑ m = 0 n P ¯ n m ( sin ⁡ ϕ ) [ C ¯ n m cos ⁡ m λ + S ¯ n m sin ⁡ m λ ] ) , {\displaystyle V={\frac {GM}{r}}\left(1+{\sum _{n=2}^{n_{\text{max}}}}\left({\frac {a}{r}}\right)^{n}{\sum _{m=0}^{n}}{\overline {P}}_{nm}(\sin \phi )\left[{\overline {C}}_{nm}\cos m\lambda +{\overline {S}}_{nm}\sin m\lambda \right]\right),} where ϕ   {\displaystyle \phi \ } and λ   {\displaystyle \lambda \ } are geocentric (spherical) latitude and longitude respectively, P ¯ n m {\displaystyle {\overline {P}}_{nm}} are

8282-414: The numerical coefficients of the model based on measured data. The above equation describes the Earth's gravitational potential V {\displaystyle V} , not the geoid itself, at location ϕ , λ , r ,   {\displaystyle \phi ,\;\lambda ,\;r,\ } the co-ordinate r   {\displaystyle r\ } being

8383-408: The ocean faces many environmental threats, such as marine pollution , overfishing , and the effects of climate change . Those effects include ocean warming , ocean acidification and sea level rise . The continental shelf and coastal waters are most affected by human activity. The terms "the ocean" or "the sea" used without specification refer to the interconnected body of salt water covering

8484-423: The ocean meets dry land. It is more shallow, with a depth of a few hundred meters or less. Human activity often has negative impacts on marine life within the continental shelf. Ocean temperatures depend on the amount of solar radiation reaching the ocean surface. In the tropics, surface temperatures can rise to over 30 °C (86 °F). Near the poles where sea ice forms, the temperature in equilibrium

8585-413: The ocean were of constant density and undisturbed by tides, currents or weather, its surface would resemble the geoid. The permanent deviation between the geoid and mean sea level is called ocean surface topography . If the continental land masses were crisscrossed by a series of tunnels or canals, the sea level in those canals would also very nearly coincide with the geoid. Geodesists are able to derive

8686-508: The ocean, on land and air. All these processes and components together make up ocean surface ecosystems . Tides are the regular rise and fall in water level experienced by oceans, primarily driven by the Moon 's gravitational tidal forces upon the Earth. Tidal forces affect all matter on Earth, but only fluids like the ocean demonstrate the effects on human timescales. (For example, tidal forces acting on rock may produce tidal locking between two planetary bodies.) Though primarily driven by

8787-469: The ocean. If the wind dies down, the wave formation is reduced, but already-formed waves continue to travel in their original direction until they meet land. The size of the waves depends on the fetch , the distance that the wind has blown over the water and the strength and duration of that wind. When waves meet others coming from different directions, interference between the two can produce broken, irregular seas. Constructive interference can lead to

8888-419: The oceans absorb CO 2 from the atmosphere , a higher concentration leads to ocean acidification (a drop in pH value ). The ocean provides many benefits to humans such as ecosystem services , access to seafood and other marine resources , and a means of transport . The ocean is known to be the habitat of over 230,000 species , but may hold considerably more – perhaps over two million species. Yet,

8989-425: The oceans could have been up to 50 m (165 ft) higher. The entire ocean, containing 97% of Earth's water, spans 70.8% of Earth 's surface, making it Earth's global ocean or world ocean . This makes Earth, along with its vibrant hydrosphere a "water world" or " ocean world ", particularly in Earth's early history when the ocean is thought to have possibly covered Earth completely. The ocean's shape

9090-434: The oceans have been mapped. The zone where land meets sea is known as the coast , and the part between the lowest spring tides and the upper limit reached by splashing waves is the shore . A beach is the accumulation of sand or shingle on the shore. A headland is a point of land jutting out into the sea and a larger promontory is known as a cape . The indentation of a coastline, especially between two headlands,

9191-537: The oceans may have always been on the Earth since the beginning of the planet's formation. In this model, atmospheric greenhouse gases kept the oceans from freezing when the newly forming Sun had only 70% of its current luminosity . The origin of Earth's oceans is unknown. Oceans are thought to have formed in the Hadean eon and may have been the cause for the emergence of life . Plate tectonics , post-glacial rebound , and sea level rise continually change

9292-451: The photic zone, the mesopelagic zone and the aphotic deep ocean zone: The pelagic part of the aphotic zone can be further divided into vertical regions according to depth and temperature: Distinct boundaries between ocean surface waters and deep waters can be drawn based on the properties of the water. These boundaries are called thermoclines (temperature), haloclines (salinity), chemoclines (chemistry), and pycnoclines (density). If

9393-418: The power of a storm wave impacting on the foot of a cliff has a shattering effect as air in cracks and crevices is compressed and then expands rapidly with release of pressure. At the same time, sand and pebbles have an erosive effect as they are thrown against the rocks. This tends to undercut the cliff, and normal weathering processes such as the action of frost follows, causing further destruction. Gradually,

9494-455: The seabed between adjoining plates to form mid-oceanic ridges and here convection currents within the mantle tend to drive the two plates apart. Parallel to these ridges and nearer the coasts, one oceanic plate may slide beneath another oceanic plate in a process known as subduction . Deep trenches are formed here and the process is accompanied by friction as the plates grind together. The movement proceeds in jerks which cause earthquakes, heat

9595-407: The seabed causing deltas to form in estuaries. All these materials move back and forth under the influence of waves, tides and currents. Dredging removes material and deepens channels but may have unexpected effects elsewhere on the coastline. Governments make efforts to prevent flooding of the land by the building of breakwaters , seawalls , dykes and levees and other sea defences. For instance,

9696-401: The shore at the rate of six to eight per minute and these are known as constructive waves as they tend to move material up the beach and have little erosive effect. Storm waves arrive on shore in rapid succession and are known as destructive waves as the swash moves beach material seawards. Under their influence, the sand and shingle on the beach is ground together and abraded. Around high tide,

9797-456: The system forms). As the world's ocean is the principal component of Earth's hydrosphere , it is integral to life on Earth, forms part of the carbon cycle and water cycle , and – as a huge heat reservoir – influences climate and weather patterns. The motions of the ocean surface, known as undulations or wind waves , are the partial and alternate rising and falling of the ocean surface. The series of mechanical waves that propagate along

9898-434: The very clearest ocean water, and is similar to blue light scattering in the sky . Ocean water represents the largest body of water within the global water cycle (oceans contain 97% of Earth's water ). Evaporation from the ocean moves water into the atmosphere to later rain back down onto land and the ocean. Oceans have a significant effect on the biosphere . The ocean as a whole is thought to cover approximately 90% of

9999-476: The world, and from the surface into the deep ocean. All this has impacts on the global climate system . Ocean water contains dissolved gases, including oxygen , carbon dioxide and nitrogen . An exchange of these gases occurs at the ocean's surface. The solubility of these gases depends on the temperature and salinity of the water. The carbon dioxide concentration in the atmosphere is rising due to CO 2 emissions , mainly from fossil fuel combustion. As

10100-427: Was derived by Stokes in closed analytical form. Note that determining N {\displaystyle N} anywhere on Earth by this formula requires Δ g {\displaystyle \Delta g} to be known everywhere on Earth , including oceans, polar areas, and deserts. For terrestrial gravimetric measurements this is a near-impossibility, in spite of close international co-operation within

10201-775: Was recovered from the Isua Greenstone Belt and provides evidence that water existed on Earth 3.8 billion years ago. In the Nuvvuagittuq Greenstone Belt , Quebec , Canada, rocks dated at 3.8 billion years old by one study and 4.28 billion years old by another show evidence of the presence of water at these ages. If oceans existed earlier than this, any geological evidence either has yet to be discovered, or has since been destroyed by geological processes like crustal recycling . However, in August 2020, researchers reported that sufficient water to fill

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