Instituto Brasileiro de Geografia e Estatística

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Geoid Undulation Model


Due to its speed and precision obtaining coordinates, the Global Navigation Satellite Systems (GNSS) have revolutionized the activities which demand positioning. However, the height established using a GNSS receptor is not related to the mean sea level (or, more rigorously, to the geoid, which is the equipotential surface of the gravity field of the Earth that coincides with the mean still water level) but  to an ellipsoidal reference with specific dimensions. As a result, it is necessary to tell the difference between the geoid surfaces and the ellipsoidal ones, i. e., the geoid height or undulation, in order to obtain the orthometric height (above the mean sea level). Thus, there is a great need for a more and more accurate Brazilian undulation model for applications in mapping and engineering. MAPGEO2015, as well as the previous models, (MAPGEO2010, MAPGEO2004, MAPGEO92), was designed to meet these demands. It was conceived in a partenership between the Brazilian Institute of Geography and Statistics (IBGE), through the Department of Geodetics (CGED), and the Polytechnic School of the University of São Paulo – EPUSP. The new model was estimated with a 5’-of-arc resolution, and the Geoid Undulation Interpolation System was updated. Via this system, users can obtain the geoid undulation at one point or a set of points, whose coordinates refer to SIRGAS2000 and are found between the latitudes 6°N and 35°S and between the longitudes 75°W and 30°W, inside the Brazilian territory.

In order to convert the ellipsoidal height (h), obtained by GNSS receptors, into orthometric height (H), it is necessary to use the value of the geoid height (N) obtained in a geoid undulation model, using the following expression:

H = h – N


Reports (in pdf format - in Portuguese)