• 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.

  • Being an equigeopotential means the geoid corresponds to the free surface of water at rest (if only 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.

  • 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 the center of the Earth to that

  • Relationship to GPS/GNSS[edit] 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.

  • [17] Temporal change 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.

  • Relationship to mass density[edit] 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).

  • In reality, the geoid does not have a physical meaning under the continents, but geodesists are able to derive the heights of continental points above this imaginary, yet
    physically defined, surface by spirit leveling.

  • 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.

  • The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid.

  • It incorporates much of the new satellite gravity data (e.g., the Gravity Recovery and Climate Experiment), and supports up to degree and order 2160 (1/6 of a degree, requiring
    over 4 million coefficients),[26] with additional coefficients extending to degree 2190 and order 2159.

  • The geoid (/ˈdʒiː.ɔɪd/) 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.

  • The permanent deviation between the geoid and mean sea level is called ocean surface topography.

  • As a consequence, the geoid’s defining equipotential surface will be found displaced away from the mass excess.

  • [13][14][15][16] Geoid undulations display uncertainties which can be estimated by using several methods, e.g.

  • Geoid measures thus help understanding the internal structure of the planet.

  • Conversely, height determined by spirit leveling from a tide gauge, as in traditional land surveying, is closer to orthometric height.

  • [20] Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles,[21] mass balances of ice sheets,[22] and postglacial

  • 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

  • [7] Gravity anomalies Variations in the height of the geoidal surface are related to anomalous density distributions within the Earth.

  • Generally the geoid rises where the earth material is locally more dense, which is where the Earth exerts greater gravitational pull.

  • [23] From postglacial rebound measurements, time-variable GRACE data can be used to deduce the viscosity of Earth’s mantle.

  • ), describing details in the global geoid as small as 55 km (or 110 km, depending on your definition of resolution).

  • 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.

  • Note that the above equation describes the Earth’s gravitational potential , not the geoid itself, at location the co-ordinate being the geocentric radius, i.e., distance
    from the Earth’s centre.

  • Description 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.


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