Geoid

Not to be confused with geode, a crystal-filled rock.
Not to be confused with GEOID, a geocoding scheme.
Map of the undulation of the geoid in meters (based on the EGM96 gravity model and the WGS84 reference ellipsoid).[1]
Geodesy
Fundamentals
Concepts
Technologies
Standards (history)
NGVD 29 Sea Level Datum 1929
OSGB36 Ordnance Survey Great Britain 1936
SK-42 Systema Koordinat 1942 goda
ED50 European Datum 1950
SAD69 South American Datum 1969
GRS 80 Geodetic Reference System 1980
ISO 6709 Geographic point coord. 1983
NAD 83 North American Datum 1983
WGS 84 World Geodetic System 1984
NAVD 88 N. American Vertical Datum 1988
ETRS89 European Terrestrial Ref. Sys. 1989
GCJ-02 Chinese obfuscated datum 2002
Geo URI Internet link to a point 2010

The geoid (/ˈdʒiː.ɔɪd/ 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 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.[2] 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 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 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 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) is thus non-uniform over the geoid.[3]

Geoid undulation in pseudocolor, shaded relief and vertical exaggeration (10000 vertical scaling factor).
Geoid undulation in pseudocolor, without vertical exaggeration.
  1. ^ "WGS 84, N=M=180 Earth Gravitational Model". NGA: Office of Geomatics. National Geospatial-Intelligence Agency. Archived from the original on 8 August 2020. Retrieved 17 December 2016.
  2. ^ Gauß, C.F. (1828). Bestimmung des Breitenunterschiedes zwischen den Sternwarten von Göttingen und Altona durch Beobachtungen am Ramsdenschen Zenithsector (in German). Vandenhoeck und Ruprecht. p. 73. Retrieved 6 July 2021.
  3. ^ Geodesy: The Concepts. Petr Vanicek and E.J. Krakiwsky. Amsterdam: Elsevier. 1982 (first ed.): ISBN 0-444-86149-1, ISBN 978-0-444-86149-8. 1986 (third ed.): ISBN 0-444-87777-0, ISBN 978-0-444-87777-2. ASIN 0444877770.