# Chapter 4.  Geodetic datums

A geodetic datum is an ellipsoid (described by parameters of its size and shape) together with the data about its dislocation, and in some cases, its orientation and scale. It is very important to note that as the ellipsoid size, the dislocation and the orientation are different from a datum to another one, the geodetic coordinates in the different datums (according to different geodetic networks) are also different. We repeat: at a same field point the geodetic coordinates are different on different datums (Fig. 16). The GIS software packages are capable to make transformations between them, if the appropriate datum parameters are known. . This chapter shows the method of usage and estimation of these parameters.

Fig. 16. The ellipsoidal coordinates of a church in the city of Szeged are different in different geodetic datum. This is the case of all terrain points.

## 4.1 Parameters of the triangulation networks

As it was shown in the previous chapter, the triangulation networks are characterized by its geodetic point set and the fixed geodetic coordinates of these base-points. A triangulation network is a geodetic datum. To use it in any GIS software, we have to give these data of the network in a more compressed way that is still characteristic for the whole network. We have also to know that which data is needed for a network/datum description for our very GIS software.

The most commonly used possibilities in geodetic practices to provide data at a selected point of the network (the so-called fundamental point) are as follows:

• the geodetic coordinates

• the astronomical coordinates and

• a triangulated and astronomical azimuth to a selected neighboring network point.

As the geodetic network adjustment can be interpreted as the fit of the ellipsoid to the geoid surface, the geoid undulation at the fundamental point is usually taken as zero. If it is different by any cause, if should be given, too. For example, in the case of the Hungarian Datum 1972, the geoid undulation at the Szőlőhegy, the fundamental point, is set to 6.56 meters by the reason to fit it vertically to the unified datum of the former Warsaw Pact cartography. This value should be taken into account during our work to avoid vertical errors, if they are important.

The above set of information is considerably smaller than the one represented by the whole set of base-point coordinates in the network. It is assumed that by fitting the given ellipsoid to the fundamental point, described its own data, the coordinates of the other points can be computed. Obviously, it is not true, and the quality of a geodetic datum is given by just this accuracy of the point coordinate calculation at all points of the network. Usually, the newer the triangulation network, the better its quality is. In case of the historical Hungarian systems, the average error at the networks form the end of 19th century is 2-3 meters, 1,5-2 meters at the systems of mid-20th century, while nowadays the accuracy is as low as half a meter.

Sometimes there are other ways to giving parameters to a geodetic network: to use the three-dimensional Cartesian coordinates of the fundamental point or just giving the components of the deflection of vertical, completed by the geoid undulation.

The above parameters do not suit the GIS software needs; these programs follows a different philosophy at the datum definition. They are not using just one datum but aim to handle several ones. So, they need parameters between datums and not just for parameters of different ones. In most cases, they don’t handle all possible datum pairs to convert between them but select one datum and give the transformation parameters from any other one to this. Practically, this selected datum is an absolutely displaced, globally fit WGS84, and all other (local) datums are characterized by the transformation parameters from them to the WGS84. In this method, it is needed to define the position of the geometric center of the local datum ellipsoid and – if available – the orientation difference between the local datum and the WGS84.