Editing Geoid (section)

==Formulation{{anchor|Shape|Undulation}}==
[[File:Geoundnsrp.png|thumb|Meridional profile of geoid undulation (red) relative to the reference ellipsoid (black), greatly exaggerated; see also: [[Earth's pear shape]].]]

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]]. 
<math display="block">N=h-H</math>
The undulation 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]]:
<math display="block">H=h-N</math>
(An analogous relationship exists between [[normal height]]s and the ''[[quasigeoid]]'', which disregards local density variations.)
In practice, many handheld GPS receivers [[spatial interpolation|interpolate]] ''N'' in a pre-computed ''geoid map'' (a [[lookup table]]).<ref>{{cite web|last1=Wormley|first1=Sam|title=GPS Orthometric Height|url=http://www.edu-observatory.org/gps/height.html|website=edu-observatory.org|access-date=15 June 2016|url-status=dead|archive-url=https://web.archive.org/web/20160620102914/http://www.edu-observatory.org/gps/height.html|archive-date=20 June 2016}}</ref>

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 [[satellite]]s, orbiting about 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 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.

[[File:Geoundaequrp.png|thumb|Equatorial profile of geoid undulation (red) relative to the reference ellipsoid (black), greatly exaggerated; see also: [[triaxial Earth]].]]