Transformation, Datum

A datum transformation is a mathematical calculation that converts location coordinates referenced to one datum to location coordinates referenced to another datum. This calculation does not involve an actual physical relocation of the point in question, but a redefinition of its position relative to a different set of coordinate axes and a different origin point. In a general sense, a datum transformation can be done between any two n-dimensional coordinate systems. In this entry, the discussion will be limited to datum transformations in a geographic context.

Geographic coordinates are expressed in angular terms of longitude and latitude, which are referenced to a particular geodetic ellipsoid of defined size and shape. Also, the ellipsoid of reference used as a model of the earth is positioned in space relative to the actual surface of the earth so as to fit a specific area or use need. The particular size, shape, and placement in space of a geodetic ellipsoid model, upon which longitude and latitude locations are specified, composes a geographic or geodetic datum. Also, on this datum, a height above the ellipsoid surface can be specified at any longitude, latitude location.

In this geographic context, a datum transformation involves the conversion of longitude, latitude, and ellipsoid height coordinates from one geodetic datum to another. The ellipsoid heights are often ignored in most of these types of transformations, because elevations relative to the ellipsoid are often not useful in practice. There are often standards for the datum used for particular types of applications and areas of the world, so if available data are not in the datum required, a datum transformation is required.

Often, available data come in the form of one projected coordinate system, and requirement needs may dictate that these data need to be converted to another projected coordinate system. These two different projected coordinate systems may also be based on two [Page 484]differing geodetic datums. In cases such as these, a datum transformation is embedded in the conversion between the two projected coordinate systems. The general transformation process in this case is as follows:

• 1.
  Define the projected coordinate system of available data, which includes the datum.
• 2.
  Unproject the data to geographic coordinates using the same datum.
• 3.
  Transform the data to geographic coordinates referenced to the new datum.
• 4.
  Project the data to the new projected coordinate system with the new datum.

For example, NAD27 UTM Zone 10 data may need to be transformed to NAD83 UTM Zone 10. The first step in this process is to define the projected coordinate system for the data, if this has not been done already. Then, the data would be unprojected to geographic coordinates; next, the datum would be transformed from NAD27 to NAD83; and, finally, the data would be projected to UTM Zone 10.

More rarely, projection processes embed the datum transformation in the projection calculations. That is, sometimes there is no datum transformation; rather, a coordinate operation that converts directly between two projected coordinate systems is performed. For example, the National Geographic Institute of Belgium (the country's national mapping agency) uses a complex polynomial transformation that converts from ED 1950 UTM Zone 31N to Belge Lambert 1972.

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