Geoid

geodetic sea levelundulation of the geoidgeoid heightgeoid undulationgeoidal undulationgravitational potential of the sea surfaceGravityshape of the Earthundulations of the geoidvaries slightly
The geoid is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent.wikipedia
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Figure of the Earth

curvature of the Earthshape of the EarthEarth's curvature
According to Gauss, who first described it, it 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.
Better approximations can be had by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoids.

Satellite geodesy

satellite altimetrygeodeticAltimetry
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 the late 20th century.
These missions led to the accurate determination of the leading spherical harmonic coefficients of the geopotential, the general shape of the geoid, and linked the world's geodetic datums.

Geophysics

geophysicistgeophysicalgeophysicists
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 the late 20th century.
The geopotential surface called the geoid is one definition of the shape of the Earth.

Earth

Earth's surfaceterrestrialworld
The geoid is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent.
In geodesy, the exact shape that Earth's oceans would adopt in the absence of land and perturbations such as tides and winds is called the geoid.

Tide

tidalhigh tidelow tide
The geoid is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent.
The ocean's surface is closely approximated by an equipotential surface, (ignoring ocean currents) commonly referred to as the geoid.

Mount Everest

EverestMt. EverestMt Everest
Although the physical Earth has excursions of +8,848 m (Mount Everest) and −11,034 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.
Geoid uncertainty casts doubt upon the accuracy claimed by both the 1999 and 2005 [See below] surveys.

Geodesy

geodeticgeodesistgeodetic survey
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 the late 20th century.
The geoid is essentially the figure of Earth abstracted from its topographical features.

Ocean surface topography

sea surface heightdynamic sea surface topographysea surface topography
The permanent deviation between the geoid and mean sea level is called ocean surface topography.
These variations are expressed in terms of average sea surface height (SSH) relative to the Earth's geoid.

Reference ellipsoid

ellipsoidexact size and shapeAiry ellipsoid
The geoid surface is irregular, unlike the reference ellipsoid (which is a mathematical idealized representation of the physical Earth), but is considerably smoother than Earth's physical surface.
In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, the truer figure of the Earth, or other planetary body.

Orthometric height

In maps and common use the height over the mean sea level (such as orthometric height) is used to indicate the height of elevations while the ellipsoidal height results from the GPS system and similar GNSS.
When the reference height is a geoid model, orthometric height is for practical purposes "height above sea level".

Sea level

mean sea levelMSLAMSL
The permanent deviation between the geoid and mean sea level is called ocean surface topography.
The alternative is to use a geoid-based vertical datum such as NAVD88 and the global EGM96 (part of WGS84).

Earth Gravitational Model

EGM96WGS84 EGM96 Geoid vertical datumEarth Gravitational Model 1996
The undulation is not standardised, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid.
EGM96 from 1996 is used as the geoid reference of the World Geodetic System.

Spherical harmonics

spherical harmonicspherical functionsLaplace series
Spherical harmonics are often used to approximate the shape of the geoid.
Spherical harmonics are important in many theoretical and practical applications, e.g., the representation of multipole electrostatic and electromagnetic fields, computation of atomic orbital electron configurations, representation of gravitational fields, geoids, fiber reconstruction for estimation of the path and location of neural axons based on the properties of water diffusion from diffusion-weighted MRI imaging for streamline tractography, and the magnetic fields of planetary bodies and stars, and characterization of the cosmic microwave background radiation.

Gravity anomaly

gravity anomaliesgravity techniquesgravitational anomalies
The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit).

World Geodetic System

WGS84WGS 84GPS coordinates
Modern GPS receivers have a grid implemented in the source of the geoid (e.g. EGM-96) height over the World Geodetic System (WGS) ellipsoid from the current position.
As a result, the elevations in the data are referenced to the geoid, a surface that is not readily found using satellite geodesy.

Petr Vaníček

Peter VaníčekVaníček
The precise geoid solution by Vaníček and co-workers improved on the Stokesian approach to geoid computation.
Petr Vaníček (born 1935 in Sušice, Czechoslovakia, today in Czech Republic) is a Czech Canadian geodesist and theoretical geophysicist who has made important breakthroughs in theory of spectral analysis and geoid computation.

Global Positioning System

GPSglobal positioning systemsGlobal Positioning System (GPS)
In maps and common use the height over the mean sea level (such as orthometric height) is used to indicate the height of elevations while the ellipsoidal height results from the GPS system and similar GNSS.
The height may then be further converted to height relative to the geoid, which is essentially mean sea level.

Gravity Field and Steady-State Ocean Circulation Explorer

GOCEGoce satellite
Recent satellite missions, such as the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and
The low orbit and high accuracy of the system greatly improved the known accuracy and spatial resolution of the geoid (the theoretical surface of equal gravitational potential on the Earth).

GRACE and GRACE-FO

GRACEGravity Recovery and Climate ExperimentGRACE-FO
For example, many of the authors of EGM96 are working on an updated model that should incorporate much of the new satellite gravity data (e.g., the Gravity Recovery and Climate Experiment), and should support up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients).
These geopotential coefficients may be used to compute geoid height, gravity anomalies, and changes in the distribution of mass on Earth's surface.

Normal height

Likewise, the deviation \zeta between the ellipsoidal height h and the normal height H_N can be calculated by
The reference surface that normal heights are measured from is called the quasi-geoid, a representation of "mean sea level" similar to the geoid and close to it, but lacking the physical interpretation of an equipotential surface.

Geodetic datum

datumGeodetic systemgeodetic
OSGB36, for example, is a better approximation to the geoid covering the British Isles than the global WGS 84 ellipsoid.

Geopotential

Geopotential functiongeopotential numbergeopotential numbers
The global mean sea surface is close to one of the equipotential surfaces of the geopotential of gravity W. This equipotential surface, or surface of constant geopotential, is called the geoid.

Physical geodesy

gravity fieldGeodesyPhysikalische Geodäsie
Due to the irregularity of the Earth's true gravity field, the equilibrium figure of sea water, or the geoid, will also be of irregular form.

Gravity of Mars

areoidGravity on mars
The analogous to the geoid for Marks is called areoid.
The areoid represents the gravitational and rotational equipotential figure of Mars, analogous to the concept of geoid ("sea level") on Earth.

Ocean

marineoceansmaritime
The geoid is the shape that the ocean surface would take under the influence of the gravity and rotation of Earth alone, if other influences such as winds and tides were absent.