Geodetic datum and geoid

The international standard ISO 19111:2007 called Geographic Information: Spatial Referencing by Coordinates defines datum as: "a set of parameters that defines the position of the origin, the scale, and the orientation of a coordinate system."

Global and regional datums

A datum can be a horizontal datum or a vertical datum, either global or local. Jekeli (2006) showed in his previous work that a traditional datum is defined by eight parameters: three to define its origin (for example, the center of mass of the Earth), three to define its orientation, and two to define the ellipsoid.

As you could see, an ellipsoid is not enough to define a global datum. We need an ellipsoid and a Terrestrial Reference System that has the defined origin and orientation with respect to the Earth, as in the following figure:

An example of global datum is the World Geodetic System 1984, known as WGS84.

A regional datum aligns the ellipsoid to a regional surface in such way to have a better match with the surface of the Earth. In this case, the origin of the datum is defined by a physical point (fundamental point) with horizontal geodetic coordinates. For example, a geodetic regional datum called Pulkovo 1942 is defined by the following:

• The latitude and longitude of an initial point (fundamental point): the Pulkovo Observatory, Latitude 59°46'18.55"N and longitude 30°19'42.09"E of Greenwich.
• The azimuth of a line from the initial point to Bugrõ is α₀= 12006'42.305" (Source: Grids&Datums. Republic of Estonia, Clifford J. Mugnier, 2007).
• Two parameters of the reference ellipsoid: Krassowsky 1940, a semi-major axis 6,378,245 meters and an inverse flattening of 298.3.

  Tip

  There are local datums that use the same ellipsoid but have different points of origin.

Another example of regional horizontal datum is the North American Datum 1927 (NAD27), which is based on the Clarke ellipsoid of 1866. (Source: North American Horizontal Datums by Jan Van Sickle.)

So you have seen how a local or global datum can be used to help determine the X and Y coordinates of features. However, how do we determine the Z or elevation? The ISO 19111: 2007 Geographic Information Spatial Referencing by Coordinates standard defines a vertical datum as the relation of the gravity-related heights to the Earth and is related to a geoid. So, a vertical coordinate reference system (1D) is then based on a vertical datum in the same way that a horizontal one is.

The geoid and heights

The international standard ISO 19111:2007 called Geographic Information Spatial Referencing by Coordinates defines a geoid as: "the equipotential surface of the Earth's gravity field that is everywhere perpendicular to the direction of gravity. The geoid best fits mean sea level either locally or globally. A geoid is considering the true shape of the Earth."

Note

For a quick introduction of the mean sea level term, please refer to the following article: Mean Sea Level, GPS, and the Geoid by Witold Fraczek, Esri Applications Prototype Lab, at http://www.esri.com/news/arcuser/0703/geoid1of3.html.

The relationship between the ellipsoid, geoid, and topographic surface in terms of height, is described in the following figure: