3-2 Horizontal Datum Parameters

Since the geoid is not a suitable surface for defining coordinates and geometric quantities, we select a biaxial ellipsoid, which is more suitable due to its smoother shape. Depending on the domain fitting of this ellipsoid to the geoid, two types of datums can be defined: a global datum, where the ellipsoid is fitted to a global geoid (covering the entire Earth), or a local datum, where a part of the ellipsoid is fitted to a specific part of the geoid. In both cases, three sets of parameters are used to define the horizontal datum. The first set contains parameters that define the shape and size of the ellipsoid, the second set specifies the position of the ellipsoid, and the third set defines its orientation.

The shape and size of an ellipsoid are defined by the length of its semi-major axis and the first eccentricity. The position or translation parameters include the coordinates of the centre of the ellipsoid in the astronomical coordinate system for a global datum, or the astronomical latitude, longitude, and geoid height of a point on the ellipsoid and its counterpart on the geoid for a local one. Finally, three rotation angles around the ellipsoid’s geodetic coordinate system are used when the datum is global. For a local datum, the north-south and east-west components of the deflections of the vertical (representing the slopes of the ellipsoid along the meridian and local parallel), and the difference between the astronomical and geodetic azimuths (aligning the direction of the north pole and geodetic pole) are considered.

In summary, a horizontal datum—whether global or local—requires a minimum of eight constraints for definition: two related to shape and size, three to translation, and three to orientation.

In this video lecture, the geometrical concepts of these parameters are explained with figures and animations.