Geodetic datum
A geodetic datum or geodetic system is a global datum reference or reference frame for unambiguously representing the position of locations on Earth by means of either geodetic coordinates or geocentric coordinates.
Datums are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography.
A horizontal datum is used to measure a horizontal position, across the Earth's surface, in latitude and longitude or another related coordinate system. A vertical datum is used to measure the elevation or depth relative to a standard origin, such as mean sea level. A three-dimensional datum enables the expression of both horizontal and vertical position components in a unified form.
The concept can be generalized for other celestial bodies as in planetary datums.
Since the rise of the global positioning system, the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS84 is intended for global use, unlike most earlier datums.
Before GPS, there was no precise way to measure the position of a location that was far from reference points used in the realization of local datums, such as from the Prime Meridian at the Greenwich Observatory for longitude, from the Equator for latitude, or from the nearest coast for sea level. Astronomical and chronological methods have limited precision and accuracy, especially over long distances. Even GPS requires a predefined framework on which to base its measurements, so WGS84 essentially functions as a datum, even though it is different in some particulars from a traditional standard horizontal or vertical datum.
A standard datum specification consists of several parts: a model for Earth's shape and dimensions, such as a reference ellipsoid or a geoid; an origin at which the ellipsoid/geoid is tied to a known location on or inside Earth ; and multiple control points or reference points that have been precisely measured from the origin and physically monumented. Then the coordinates of other places are measured from the nearest control point through surveying. Because the ellipsoid or geoid differs between datums, along with their origins and orientation in space, the relationship between coordinates referred to one datum and coordinates referred to another datum is undefined and can only be approximated. Using local datums, the disparity on the ground between a point having the same horizontal coordinates in two different datums could reach kilometers if the point is far from the origin of one or both datums. This phenomenon is called datum shift or, more generally, datum transformation, as it may involve rotation and scaling, in addition to displacement.
Because Earth is an imperfect ellipsoid, local datums can give a more accurate representation of some specific area of coverage than WGS84 can. OSGB36, for example, is a better approximation to the geoid covering the British Isles than the global WGS84 ellipsoid. However, as the benefits of a global system often outweigh the greater accuracy, the global WGS84 datum has become widely adopted.
History
The spherical nature of Earth was known by the ancient Greeks, who also developed the concepts of latitude and longitude, and the first astronomical methods for measuring them. These methods, preserved and further developed by Muslim and Indian astronomers, were sufficient for the global explorations of the 15th and 16th Centuries.However, the scientific advances of the Age of Enlightenment brought a recognition of errors in these measurements, and a demand for greater precision. This led to technological innovations such as the 1735 Marine chronometer by John Harrison, but also to a reconsideration of the underlying assumptions about the shape of Earth itself. Isaac Newton postulated that the conservation of momentum should make Earth oblate, while the early surveys of Jacques Cassini led him to believe Earth was prolate. The subsequent French geodesic missions to Lapland and Peru corroborated Newton, but also discovered variations in gravity that would eventually lead to the geoid model.
A contemporary development was the use of the trigonometric survey to accurately measure distance and location over great distances. Starting with the surveys of Jacques Cassini and the Anglo-French Survey, by the end of the 18th century, survey control networks covered France and the United Kingdom. More ambitious undertakings such as the Struve Geodetic Arc across Eastern Europe and the Great Trigonometrical Survey of India took much longer, but resulted in more accurate estimations of the shape of the Earth ellipsoid. The first triangulation across the United States was not completed until 1899.
The U.S. survey resulted in the North American Datum of 1927 and the Vertical Datum of 1929, the first standard datums available for public use. This was followed by the release of national and regional datums over the next several decades. Improving measurements, including the use of early satellites, enabled more accurate datums in the later 20th century, such as NAD 83 in North America, ETRS89 in Europe, and GDA94 in Australia. At this time global datums were also first developed for use in satellite navigation systems, especially the World Geodetic System used in the U.S. global positioning system, and the International Terrestrial Reference System and Frame used in the European Galileo system.
Dimensions
Horizontal datum
A horizontal datum is a model used to precisely measure positions on Earth; it is thus a crucial component of any spatial reference system or map projection. A horizontal datum binds a specified reference ellipsoid, a mathematical model of the shape of the earth, to the physical earth. Thus, the geographic coordinate system on that ellipsoid can be used to measure the latitude and longitude of real-world locations. Regional horizontal datums, such as NAD 27 and NAD 83, usually create this binding with a series of physically monumented geodetic control points of known location. Global datums, such as WGS 84 and ITRF, are typically bound to the center of mass of the Earth (making them useful for tracking satellite orbits and thus for use in satellite navigation systems.A specific point can have substantially different coordinates, depending on the datum used to make the measurement. For example, coordinates in NAD83 can differ from NAD27 by up to several hundred feet. There are hundreds of local horizontal datums around the world, usually referenced to some convenient local reference point. Contemporary datums, based on increasingly accurate measurements of the shape of Earth, are intended to cover larger areas. The WGS 84 datum, which is almost identical to the NAD 83 datum used in North America and the ETRS89 datum used in Europe, is a common standard datum.
Vertical datum
A vertical datum is a reference surface for vertical positions, such as the elevations of Earth features including terrain, bathymetry, water level, and human-made structures.An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008, using at least 2,159 spherical harmonics. Other datums are defined for other areas or at other times; ED50 was defined in 1950 over Europe and differs from WGS84 by a few hundred meters depending on where in Europe you look.
Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there.
Geodetic coordinates
In geodetic coordinates, Earth's surface is approximated by an ellipsoid, and locations near the surface are described in terms of geodetic latitude, longitude, and ellipsoidal height.Earth reference ellipsoid
Defining and derived parameters
The ellipsoid is completely parameterised by the semi-major axis and the flattening.From and it is possible to derive the semi-minor axis, first eccentricity and second eccentricity of the ellipsoid
| Parameter | Value |
| Semi-minor axis | |
| First eccentricity squared | |
| Second eccentricity squared |
Parameters for some geodetic systems
The two main reference ellipsoids used worldwide are the GRS80and the WGS84.
A more comprehensive list of geodetic systems can be found .
World Geodetic System 1984 (WGS84)
The Global Positioning System uses the World Geodetic System 1984 to determine the location of a point near the surface of Earth.| Parameter | Notation | Value |
| Semi-major axis | ||
| Reciprocal of flattening |
| Constant | Notation | Value |
| Semi-minor axis | ||
| First eccentricity squared | ||
| Second eccentricity squared |
Datum transformation
The difference in co-ordinates between datums is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, and can be anything from zero to hundreds of meters. The North Pole, South Pole and Equator will be in different positions on different datums, so True North will be slightly different. Different datums use different interpolations for the precise shape and size of Earth. For example, in Sydney there is a 200 metres difference between GPS coordinates configured in GDA and AGD, which is an unacceptably large error for some applications, such as surveying or site location for scuba diving.Datum conversion is the process of converting the coordinates of a point from one datum system to another. Because the survey networks upon which datums were traditionally based are irregular, and the error in early surveys is not evenly distributed, datum conversion cannot be performed using a simple parametric function. For example, converting from NAD 27 to NAD 83 is performed using NADCON, a raster grid covering North America, with the value of each cell being the average adjustment distance for that area in latitude and longitude. Datum conversion may frequently be accompanied by a change of map projection.