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 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.
 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
Relationship to mass density 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), 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.
 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.
 Studies using the time-variable geoid computed from GRACE data have provided information on global hydrologic cycles, mass balances of ice sheets, 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
 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.
 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.
[‘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.
2. ^ 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.
3. ^ “Earth’s Gravity Definition”. GRACE – Gravity
Recovery and Climate Experiment. Center for Space Research (University of Texas at Austin) / Texas Space Grant Consortium. 11 February 2004. Retrieved 22 January 2018.
4. ^ “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.
5. ^ Fowler, C.M.R. (2005). The Solid Earth; An Introduction to Global Geophysics. United Kingdom: Cambridge University Press. p. 214. ISBN
6. ^ Lowrie, W. (1997). Fundamentals of Geophysics. Cambridge University Press. p. 50. ISBN 978-0-521-46728-5. Retrieved 2 May 2022.
7. ^ Raman, Spoorthy (16 October 2017). “The missing mass — what is causing a geoid low in the
Indian Ocean?”. GeoSpace. Retrieved 2 May 2022.
8. ^ Richards, M. A.; Hager, B. H. (1984). “Geoid anomalies in a dynamic Earth”. Journal of Geophysical Research. 89 (B7): 5987–6002. Bibcode:1984JGR….89.5987R. doi:10.1029/JB089iB07p05987.
Sideris, Michael G. (2011). “Geoid Determination, Theory and Principles”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. pp. 356–362. doi:10.1007/978-90-481-8702-7_154. ISBN 978-90-481-8701-0. S2CID 241396148.
Sideris, Michael G. (2011). “Geoid, Computational Method”. Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. pp. 366–371. doi:10.1007/978-90-481-8702-7_225. ISBN 978-90-481-8701-0.
11. ^ Wormley, Sam. “GPS Orthometric
Height”. edu-observatory.org. Archived from the original on 20 June 2016. Retrieved 15 June 2016.
12. ^ “UNB Precise Geoid Determination Package”. Retrieved 2 October 2007.
13. ^ Vaníček, P.; Kleusberg, A. (1987). “The Canadian geoid-Stokesian
approach”. Manuscripta Geodaetica. 12 (2): 86–98.
14. ^ Vaníček, P.; Martinec, Z. (1994). “Compilation of a precise regional geoid” (PDF). Manuscripta Geodaetica. 19: 119–128.
15. ^ P., Vaníček; A., Kleusberg; Z., Martinec; W., Sun; P., Ong; M.,
Najafi; P., Vajda; L., Harrie; P., Tomasek; B., ter Horst. Compilation of a Precise Regional Geoid (PDF) (Report). Department of Geodesy and Geomatics Engineering, University of New Brunswick. 184. Retrieved 22 December 2016.
16. ^ Kopeikin, Sergei;
Efroimsky, Michael; Kaplan, George (2009). Relativistic celestial mechanics of the solar system. Weinheim: Wiley-VCH. p. 704. ISBN 9783527408566.
17. ^ Chicaiza, E.G.; Leiva, C.A.; Arranz, J.J.; Buenańo, X.E. (14 June 2017). “Spatial uncertainty
of a geoid undulation model in Guayaquil, Ecuador”. Open Geosciences. 9 (1): 255–265. Bibcode:2017OGeo….9…21C. doi:10.1515/geo-2017-0021. ISSN 2391-5447.
18. ^ “ESA makes first GOCE dataset available”. GOCE. European Space Agency. 9 June 2010.
Retrieved 22 December 2016.
19. ^ “GOCE giving new insights into Earth’s gravity”. GOCE. European Space Agency. 29 June 2010. Archived from the original on 2 July 2010. Retrieved 22 December 2016.
20. ^ “Earth’s gravity revealed in unprecedented
detail”. GOCE. European Space Agency. 31 March 2011. Retrieved 22 December 2016.
21. ^ Schmidt, R.; Schwintzer, P.; Flechtner, F.; Reigber, C.; Guntner, A.; Doll, P.; Ramillien, G.; Cazenave, A.; et al. (2006). “GRACE observations of changes in
continental water storage”. Global and Planetary Change. 50 (1–2): 112–126. Bibcode:2006GPC….50..112S. doi:10.1016/j.gloplacha.2004.11.018.
22. ^ Ramillien, G.; Lombard, A.; Cazenave, A.; Ivins, E.; Llubes, M.; Remy, F.; Biancale, R. (2006). “Interannual
variations of the mass balance of the Antarctica and Greenland ice sheets from GRACE”. Global and Planetary Change. 53 (3): 198. Bibcode:2006GPC….53..198R. doi:10.1016/j.gloplacha.2006.06.003.
23. ^ Vanderwal, W.; Wu, P.; Sideris, M.; Shum, C.
(2008). “Use of GRACE determined secular gravity rates for glacial isostatic adjustment studies in North-America”. Journal of Geodynamics. 46 (3–5): 144. Bibcode:2008JGeo…46..144V. doi:10.1016/j.jog.2008.03.007.
24. ^ Paulson, Archie; Zhong, Shijie;
Wahr, John (2007). “Inference of mantle viscosity from GRACE and relative sea level data”. Geophysical Journal International. 171 (2): 497. Bibcode:2007GeoJI.171..497P. doi:10.1111/j.1365-246X.2007.03556.x.
25. ^ Jump up to:a b Smith, Dru A. (1998).
“There is no such thing as ‘The’ EGM96 geoid: Subtle points on the use of a global geopotential model”. IGeS Bulletin No. 8. Milan, Italy: International Geoid Service. pp. 17–28. Retrieved 16 December 2016.
26. ^ Pavlis, N. K.; Holmes, S. A.;
Kenyon, S.; Schmit, D.; Trimmer, R. “Gravitational potential expansion to degree 2160”. IAG International Symposium, gravity, geoid and Space Mission GGSM2004. Porto, Portugal, 2004.
27. ^ “Earth Gravitational Model 2008 (EGM2008)”. National Geospatial-Intelligence
Agency. Archived from the original on 8 May 2010. Retrieved 9 September 2008.
28. ^ Barnes, D.; Factor, J. K.; Holmes, S. A.; Ingalls, S.; Presicci, M. R.; Beale, J.; Fecher, T. (2015). “Earth Gravitational Model 2020”. AGU Fall Meeting Abstracts.
2015: G34A–03. Bibcode:2015AGUFM.G34A..03B.
Photo credit: https://www.flickr.com/photos/clairity/3065719996/’]