2.6.2 Reference system

From Geostandards

For spatial information, data is linked to locations on earth. Of course, the shape of the earth is the basis for the co-ordinate systems. All the points are located on the curved surface of the earth. With all its mountains and valleys, it is impossible to describe this shape in a perfectly mathematical way.

A three-dimensional representation of the geoid with undulations indicated in colour. Red means places where the geoid is higher, blue where it is lower than a perfect ellipsoid.

At first view it appears to be a sphere, but because the earth is flattened at the poles, a better approach is to call it a three dimensional ellipse, a so-called ellipsoid. The purpose of an ellipsoid is to describe the total surface of the earth in as good a way as is possible, for worldwide use. However, ellipsoids can also be defined with somewhat different centre points, a different orientation and a different shape that fits as closely as possible to a specific part of the earth’s surface. In the nineteenth century the Bessel-ellipsoid was defined for the Netherlands. An example of an ellipsoid is the WGS84 ellipsoid, the reference system of the GPS system. Co-ordinates on a geographic body such as this are geographic co-ordinates. A point on the earth is thus described by a longitude ϕ and a latitude λ and referenced to the centre point of the sphere or the ellipsoid.

Longitude and latitude may be represented on a flat plain with a perpendicular co-ordinate axis. The x-axis mostly contains length, the y-axis width. Each little cube of the figure above is then represented as a small square. Reality is a deformed version of this, because the vertical lines (the meridians) near the poles become closer to each other. In the plain on the map the distance between, for example, the fifth and the sixth longitude at 52o N (the height of Arnhem) seems to be the same length as the distance between the fifth and the sixth longitude at 53o N (the height of Assen). However, in reality, these distances differ by more than one and a half kilometres from each other. In conclusion: on a map are no measurements that can be taken for corners, distances and surfaces that conform to reality. The larger the represented area is, the larger the deformations on the map plain are.

Over the past years, many clever methods have been developed to try to convert geographic co-ordinates to co-ordinates in a flat plain and keep the deformations as small as possible. These mathematical methods are called projections on the map; the map projection which is the most suitable depends on the application, the largeness of the form and the position on earth of the area which is to be represented. However map projections which contain no deformations do not exist.

So co-ordinates can be given on an ellipsoid (mostly length and width), or in a map plain (mostly x and y). The conversion from ellipsoid to map plain is called projection on the map; the conversion between different ellipsoids is called date transformation.

In the Dutch situation, the systems RD (projected) WGS84/ETRS89 (ellipsoïdisch) and UTM (projected from ED or from WGS84/ETRS89) are most frequently used. RD-co-ordinates are, in principle, only applicable in the Netherlands.

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