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Geodesy
Published in Basudeb Bhatta, Global Navigation Satellite Systems, 2021
The ellipsoidal (h) and orthometric (H) heights are closely related by the geoid height (N) (Figure 9.7). Geoidal height is the separation between ellipsoid and geoid—height of geoid above the ellipsoid (it may have a negative value if the geoid is under the ellipsoid). A network of benchmark observations, gravity observations, and elevation models are used to develop a geoid model from which geoidal heights can be estimated (RMITU 2006; Zilkoski et al. 2005). The accuracy of these geoid heights is dependent upon the accuracies of the various measurements used to construct the model. Surveyors must apply the geoidal height to GNSS derived height values to obtain orthometric heights (which are related to mean sea level). GNSS derived ellipsoidal height, when combined with geoidal height, can give usable orthometric height. The following height equation is used: h=H+N
Satellite positioning
Published in W. Schofield, M. Breach, Engineering Surveying, 2007
The orthometric height H of a point is the linear distance from that point, measured along the gravity vector, to the equipotential surface of the Earth that approximates to MSL. The difference between the two heights is called the geoid-ellipsoid separation, or the geoid height and is denoted by N, thus: h=N+H In relatively small areas, generally encountered in construction, GPS heights can be obtained on several benchmarks surrounding and within the area, provided the benchmarks are known to be stable. The difference between the two sets of values gives the value of N at each benchmark. The geoid can be regarded as a plane between these points or a contouring program could be used, thus providing corrections for further GPS heighting within the area. Accuracies relative to tertiary levelling are achievable.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
The vertical distance referenced to the geoid is called an orthometric height (elevation), H. Orthometric height is measured along the plumb line. A height referenced to the ellipsoid is called an ellipsoidal height, h. Ellipsoidal height is measured along the normal to the ellipsoid. Geoid height, N, is the distance between the geoid and the ellipsoid measured along the normal to the ellipsoid. Neglecting the deviation between the plumb line and the ellipsoidal normal, the geoid height is related to the orthometric and ellipsoidal heights by the following equation: h=H+N
Vertical accuracy evaluation of freely available latest high-resolution (30 m) global digital elevation models over Cameroon (Central Africa) with GPS/leveling ground control points.
Published in International Journal of Digital Earth, 2019
Loudi Yap, Ludovic Houetchak Kandé, Robert Nouayou, Joseph Kamguia, Nasser Abdou Ngouh, Marie Brigitte Makuate
Orthometric heights at the 555 GCPs used in this study refer to mean sea level. The latitude and longitude coordinates are referenced to WGS84. All the DEMs tested here provide elevation data in regularly spaced grids of geographical coordinates, also referenced to the WGS84 datum. The vertical datum of SRTM 1 and ASTER GDEM 2 is EGM96 geoid and mean sea level for AW3D30 DEM. As the EGM96 surface is very close approximation to mean sea level (Pavlis, Rapp, and Olson 1998; Sun et al. 2003; Mukherjee et al. 2013; Jain et al. 2017), matching vertical datum is not necessary in this study. Details about each of the three DEMs tested in this study are indicated in the following Table 2.