Since the rise of the global positioning system (GPS), 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 (whether horizontal, vertical, or 3D) 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 (often monumented) location on or inside Earth (not necessarily at 0 latitude 0 longitude); 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.[3] However, as the benefits of a global system outweigh the greater accuracy, the global WGS84 datum has become widely adopted.[4]
The Great Trigonometrical Survey of India, one of the first surveys comprehensive enough to establish a geodetic datum.
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 (wider at the equator), while the early surveys of Jacques Cassini (1720) led him to believe Earth was prolate (wider at the poles). The subsequent French geodesic missions (1735-1739) 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 (1718) and the Anglo-French Survey (1784–1790), 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 (1816-1855) and the Great Trigonometrical Survey of India (1802-1871) 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 (horizontal) of 1927 (NAD27) and the Vertical Datum of 1929 (NAVD29), 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 (WGS84) used in the U.S. global positioning system (GPS), and the International Terrestrial Reference System and Frame (ITRF) 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.[citation needed]
An approximate definition of sea level is the datum WGS 84, an ellipsoid, whereas a more accurate definition is Earth Gravitational Model 2008 (EGM2008), 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.
The same position on a spheroid has a different angle for latitude depending on whether the angle is measured from the normal line segment CP of the ellipsoid (angle α) or the line segment OP from the center (angle β). The "flatness" of the spheroid (orange) in the image is greater than that of Earth; as a result, the corresponding difference between the "geodetic" and "geocentric" latitudes is also exaggerated.
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 (or several kilometers for some remote islands). 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 (reference ellipsoids). For example, in Sydney there is a 200 metres (700feet) difference between GPS coordinates configured in GDA (based on global standard WGS84) and AGD (used for most local maps), which is an unacceptably large error for some applications, such as surveying or site location for scuba diving.[7]
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 (later improved as HARN), 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.
A geodetic reference datum is a known and constant surface which is used to describe the location of unknown points on Earth. Since reference datums can have different radii and different center points, a specific point on Earth can have substantially different coordinates depending on the datum used to make the measurement. There are hundreds of locally developed reference 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 most common reference Datums in use in North America are NAD27, NAD83, and WGS 84.
The North American Datum of 1927 (NAD27) is "the horizontal control datum for the United States that was defined by a location and azimuth on the Clarke spheroid of 1866, with origin at (the survey station) Meades Ranch (Kansas)." ... The geoidal height at Meades Ranch was assumed to be zero, as sufficient gravity data was not available, and this was needed to relate surface measurements to the datum. "Geodetic positions on the North American Datum of 1927 were derived from the (coordinates of and an azimuth at Meades Ranch) through a readjustment of the triangulation of the entire network in which Laplace azimuths were introduced, and the Bowie method was used."[8] NAD27 is a local referencing system covering North America.
The North American Datum of 1983 (NAD 83) is "The horizontal control datum for the United States, Canada, Mexico, and Central America, based on a geocentric origin and the Geodetic Reference System 1980 (GRS 80). "This datum, designated as NAD83…is based on the adjustment of 250,000 points including 600 satellite Doppler stations which constrain the system to a geocentric origin." NAD83 may be considered a local referencing system.
WGS84 is the World Geodetic System of 1984. It is the reference frame used by the U.S. Department of Defense (DoD) and is defined by the National Geospatial-Intelligence Agency (NGA) (formerly the Defense Mapping Agency, then the National Imagery and Mapping Agency). WGS84 is used by the DoD for all its mapping, charting, surveying, and navigation needs, including its GPS "broadcast" and "precise" orbits. WGS84 was defined in January 1987 using Doppler satellite surveying techniques. It was used as the reference frame for broadcast GPS Ephemerides (orbits) beginning January 23, 1987. At 0000 GMT January 2, 1994, WGS84 was upgraded in accuracy using GPS measurements. The formal name then became WGS84 (G730), since the upgrade date coincided with the start of GPS Week 730. It became the reference frame for broadcast orbits on June 28, 1994. At 0000 GMT September 30, 1996 (the start of GPS Week 873), WGS84 was redefined again and was more closely aligned with International Earth Rotation Service (IERS) frame ITRF 94. It was then formally called WGS84 (G873). WGS84 (G873) was adopted as the reference frame for broadcast orbits on January 29, 1997.[9] Another update brought it to WGS84 (G1674).
The WGS84 datum, within two meters of the NAD83 datum used in North America, is the only world referencing system in place today. WGS84 is the default standard datum for coordinates stored in recreational and commercial GPS units.
Users of GPS are cautioned that they must always check the datum of the maps they are using. To correctly enter, display, and to store map related map coordinates, the datum of the map must be entered into the GPS map datum field.
The Earth's tectonic plates move relative to one another in different directions at speeds on the order of 50 to 100mm (2.0 to 3.9in) per year.[24] Therefore, locations on different plates are in motion relative to one another. For example, the longitudinal difference between a point on the equator in Uganda, on the African Plate, and a point on the equator in Ecuador, on the South American Plate, increases by about 0.0014 arcseconds per year.[citation needed] These tectonic movements likewise affect latitude.
If a global reference frame (such as WGS 84) is used, the coordinates of a place on the surface generally will change from year to year. Most mapping, such as within a single country, does not span plates. To minimize coordinate changes for that case, a different reference frame can be used, one whose coordinates are fixed to that particular plate. Examples of these reference frames are "NAD 83" for North America and "ETRS89" for Europe.
Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets or circumplanetary systems. Geodesy is an earth science and many consider the study of Earth's shape and gravity to be central to that science. It is also a discipline of applied mathematics.
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from −90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude and longitude are used together as a coordinate pair to specify a location on the surface of the Earth.
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. It is the simplest, oldest and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface.
Earth radius is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378 km (3,963 mi) to a minimum of nearly 6,357 km (3,950 mi).
The geoid is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is extended through the continents. According to Gauss, who first described it, it is the "mathematical figure of the Earth", a smooth but irregular surface whose shape results from the uneven distribution of mass within and on the surface of Earth. It can be known only through extensive gravitational measurements and calculations. Despite being an important concept for almost 200 years in the history of geodesy and geophysics, it has been defined to high precision only since advances in satellite geodesy in the late 20th century.
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also describes the associated Earth Gravitational Model (EGM) and World Magnetic Model (WMM). The standard is published and maintained by the United States National Geospatial-Intelligence Agency.
In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems.
The Geodetic Reference System 1980 (GRS80) consists of a global reference ellipsoid and a normal gravity model. The GRS80 gravity model has been followed by the newer more accurate Earth Gravitational Models, but the GRS80 reference ellipsoid is still the most accurate in use for coordinate reference systems, e.g. for the international ITRS, the European ETRS89 and for WGS 84 used for the American Global Navigation Satellite System (GPS).
The National Geodetic Survey (NGS) is a United States federal agency based in Washington, D.C. that defines and manages a national coordinate system, providing the foundation for transportation and communication, mapping and charting, and a large number of science and engineering applications. Since its founding in 1970, it has been part of the National Oceanic and Atmospheric Administration (NOAA), a division within the Department of Commerce.
The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes.
The European Terrestrial Reference System 1989 (ETRS89) is an ECEF geodetic Cartesian reference frame, in which the Eurasian Plate as a whole is static. The coordinates and maps in Europe based on ETRS89 are not subject to change due to the continental drift.
A spatial reference system (SRS) or coordinate reference system (CRS) is a framework used to precisely measure locations on the surface of Earth as coordinates. It is thus the application of the abstract mathematics of coordinate systems and analytic geometry to geographic space. A particular SRS specification comprises a choice of Earth ellipsoid, horizontal datum, map projection, origin point, and unit of measure. Thousands of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between different SRS.
The North American Datum (NAD) is the horizontal datum now used to define the geodetic network in North America. A datum is a formal description of the shape of the Earth along with an "anchor" point for the coordinate system. In surveying, cartography, and land-use planning, two North American Datums are in use for making lateral or "horizontal" measurements: the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). Both are geodetic reference systems based on slightly different assumptions and measurements.
The Earth-centered, Earth-fixed coordinate system, also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth as X, Y, and Z measurements from its center of mass. Its most common use is in tracking the orbits of satellites and in satellite navigation systems for measuring locations on the surface of the Earth, but it is also used in applications such as tracking crustal motion.
The North American Vertical Datum of 1988 is the vertical datum for orthometric heights established for vertical control surveying in the United States based upon the General Adjustment of the North American Datum of 1988.
The Bessel ellipsoid is an important reference ellipsoid of geodesy. It is currently used by several countries for their national geodetic surveys, but will be replaced in the next decades by modern ellipsoids of satellite geodesy.
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations.
In geodesy, surveying, hydrography and navigation, vertical datum or altimetric datum is a reference coordinate surface used for vertical positions, such as the elevations of Earth-bound features and altitudes of satellite orbits and in aviation. In planetary science, vertical datums are also known as zero-elevation surface or zero-level reference.
The National Spatial Reference System (NSRS), managed by the National Geodetic Survey (NGS), is a coordinate system that includes latitude, longitude, elevation, and other values. The NSRS consists of a National Shoreline, the NOAA CORS Network, a network of permanently marked points, and a set of models that describe dynamic geophysical processes affecting spatial measurements. The system is based on the datums NAD 83 and NAVD 88.
Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a reference ellipsoid. They include geodetic latitude (north/south) ϕ, longitude (east/west) λ, and ellipsoidal heighth. The triad is also known as Earth ellipsoidal coordinates.
References
↑ Jensen, John R.; Jensen, Ryan R. (2013). Introductory Geographic Information Systems. Pearson. p.25.
↑ Yang, H.; Lee, Y.; Choi, Y.; Kwon, J.; Lee, H.; Jeong, K. (2007). "The Korean Datum Change to a World Geodetic System". AGU Spring Meeting Abstracts. 2007: G33B–03. Bibcode:2007AGUSM.G33B..03Y.
GeographicLib includes a utility CartConvert which converts between geodetic and geocentric (ECEF) or local Cartesian (ENU) coordinates. This provides accurate results for all inputs including points close to the center of Earth.
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