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## Geoid undulation model - MAPGEO2015

### Description

Digital model obtained from geodetic surveyings decribing the variation between the ellipsoid surface and the geoid surface.

### About the publication - Geoid Undulation Model

**What is the Geoid?**

In 1828, C.F. Gauss introduced an improved model of the figure of the Earth, but the term ‘geoid’ was created in 1873 by J.F. Listing. The Geoid is the equipotential surface of the Earth’s gravitational field, which coincides with the mean undisturbed sea level. Every point of this surface is at right angles to the gravity vector. The Geoid surface can be imagined as extended through the continents. It has a slightly irregular undulating shape that accompanies the structure variations of the Earth’s mass distribution. This undulation is about ±30 m, the maximum level is ±100m, in relation to the reference ellipsoid.

**Why are geoid undulation models necessary?**

Heights determined by a GNSS receiver are not related to the mean sea level, but to a reference ellipsoid with specific dimensions. Therefore, it is necessary to know the geoid model (difference between geoid and ellipsoid surfaces) so that the height above mean sea level can be obtained.

**Introduction**

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:

### More on the product - Geoid Undulation Model

### MAPGEO2015

MAPGEO2015 is available for download either through a desktop Microsoft Windows application or online.

In both applications, the coordinates of the points for which the geoid undulation should be obtained can be entered either through a keyboard or file, according to the available formatting options of the entry and output.

### Concepts and methods - Geoid Undulation Model

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