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GeographicLib provides a utility GeoidEval (with source code) to evaluate the geoid height for the EGM84, EGM96, and EGM2008 Earth gravity models. Here is an online version of GeoidEval . The Tracker Component Library from the United States Naval Research Laboratory is a free Matlab library with a number of gravitational synthesis routines.
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 orthometric height (symbol H) is the vertical distance along the plumb line from a point of interest to a reference surface known as the geoid, the vertical datum that approximates mean sea level. [1] [2] Orthometric height is one of the scientific formalizations of a layman's "height above sea level", along with other types of heights in ...
where = and the coordinates are relative to the standard geodetic reference system extended into space with origin in the center of the reference ellipsoid and with z-axis in the direction of the polar axis.
For the geoid determination (mean sea level) and for exact transformation of elevations. The global geoidal undulations amount to 50–100 m, and their regional values to 10–50 m. They are adequate to the integrals of VD components ξ,η and therefore can be calculated with cm accuracy over distances of many kilometers.
Here we have assumed that measurements are made relatively close to the surface so that R does not vary significantly. The value of the free-air correction is positive when measured above the geoid, and negative when measured below. There is the assumption that no mass exists between the observation point and the reference level.
The geometrical separation between it and the reference ellipsoid is called the geoidal undulation, or more usually the geoid-ellipsoid separation, N. It varies globally between ±110 m. A reference ellipsoid, customarily chosen to be the same size (volume) as the geoid, is described by its semi-major axis (equatorial radius) a and flattening f.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS.The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM).