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In this case, the calculation is adjusted with the Gaussian least squares method. A numerical value for the accuracy of the transformation parameters is obtained by calculating the values at the reference points, and weighting the results relative to the centroid of the points.
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 ...
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. N = h − H {\displaystyle N=h-H} The undulation is not standardized, as different countries use different mean sea levels as reference, but most commonly refers to the EGM96 geoid.
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.
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.
Since the Sea Level Datum of 1929 was a hybrid model, it was not a pure model of mean sea level, the geoid, or any other equipotential surface. Therefore, it was renamed the National Geodetic Vertical Datum of 1929 (NGVD 29) May 10, 1973, by the National Geodetic Survey , a part of the National Oceanic and Atmospheric Administration .
The separation between the geoid and the reference ellipsoid is called the undulation of the geoid, symbol . The geoid, or mathematical mean sea surface, is defined not only on the seas, but also under land; it is the equilibrium water surface that would result, would sea water be allowed to move freely (e.g., through tunnels) under the land.
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.