Ageographic coordinate system (GCS) is aspherical orgeodetic coordinate system for measuring and communicatingpositions directly onEarth aslatitude andlongitude.[1] It is the simplest, oldest, and most widely used type of the variousspatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinatetuple like acartesian coordinate system, geographic coordinate systems are not cartesian because the measurements are angles and are not on a planar surface.[2]
A full GCS specification, such as those listed in theEPSG and ISO 19111 standards, also includes a choice ofgeodetic datum (including anEarth ellipsoid), as different datums will yield different latitude and longitude values for the same location.[3]
Thelatitudeφ of a point on Earth's surface is defined in one of three ways, depending on the type of coordinate system. In each case, the latitude is the angle formed by the plane of the equator and a line formed by the point on the surface and a second point on equatorial plane. What varies between the types of coordinate systems is how the point on the equatorial plane is determined:
In an astronomical coordinate system, the second point is found where the extension of theplumb bob vertical from the surface point intersects the equatorial plane.
In a geodetic coordinate system, the second point is found where thenormal vector from the surface of the ellipsoid at the surface point intersects the equatorial plane.
In a geocentric coordinate system, the second point is the center of Earth.
The path that joins all points of the same latitude traces a circle on the surface of Earth, as viewed from above the north or south pole, calledparallels, as they are parallel to the equator and to each other. Thenorth pole is 90° N; thesouth pole is 90° S. The 0° parallel of latitude is defined to be theequator, thefundamental plane of a geographic coordinate system. The equator divides the globe intoNorthern andSouthern Hemispheres.
Thelongitudeλ of a point on Earth's surface is the angle east or west of a referencemeridian to another meridian that passes through that point. All meridians are halves of greatellipses, which converge at the North and South Poles. The meridian of the BritishRoyal Observatory inGreenwich, in southeast London, England, is the internationalprime meridian, although some organizations—such as the FrenchInstitut national de l'information géographique et forestière—continue to use other meridians for internal purposes. Theantipodal meridian of Greenwich is both 180°W and 180°E. This is not to be conflated with theInternational Date Line, which partly overlaps with the 180° meridian but diverges from it in several places for political and convenience reasons, including between far eastern Russia and the far westernAleutian Islands.
The combination of these two components specifies the position of any location on the surface of Earth, without consideration ofaltitude or depth. The visual grid on a map formed by lines of latitude and longitude is known as agraticule.[7] The origin/zero point of this system is located in theGulf of Guinea about 625 km (390 mi) south ofTema, Ghana, a location often facetiously calledNull Island.
In order to use the theoretical definitions of latitude, longitude, and height to precisely measure actual locations on the physical earth, ageodetic datum must be used. Ahorizonal datum is used to precisely measure latitude and longitude, while avertical datum is used to measure elevation or altitude. Both types of datum bind a mathematical model of the shape of the earth (usually areference ellipsoid for a horizontal datum, and a more precisegeoid for a vertical datum) to the earth. Traditionally, this binding was created by a network ofcontrol points, surveyed locations at which monuments are installed, and were only accurate for a region of the surface of the Earth. Newer datums are based on a global network for satellite measurements (GNSS,VLBI,SLR andDORIS).
This combination of a mathematical model and physical binding ensures that users of the same datum obtain identical coordinates for a given physical point. However, different datums typically produce different coordinates for the same location (sometimes deviating several hundred meters) not due to actual movement, but because the reference system itself is shifted. Because anyspatial reference system ormap projection is ultimately calculated from latitude and longitude, it is crucial that they clearly state the datum on which they are based. For example, aUTM coordinate based on aWGS84 realisation will be different than a UTM coordinate based onNAD27 for the same location. Transforming coordinates from one datum to another requires adatum transformation method such as aHelmert transformation, although in certain situations a simpletranslation may be sufficient.[8]
Datums may be global, meaning that they represent the whole Earth, or they may be regional,[9] meaning that they represent an ellipsoid best-fit to only a portion of the Earth. Examples of global datums include the several realizations ofWGS 84 (with the 2D datum ensemble EPSG:4326 with 2 meter accuracy as identifier)[10][11] used for theGlobal Positioning System,[note 2] and the several realizations of theInternational Terrestrial Reference System and Frame (such as ITRF2020 with subcentimeter accuracy), which takes into accountcontinental drift andcrustal deformation.[12]
Datums with a regional fit of the ellipsoid that are chosen by a national cartographical organization include theNorth American Datums, the EuropeanED50, and the BritishOSGB36. Given a location, the datum provides the latitude and longitude. In the United Kingdom there are three common latitude, longitude, and height systems in use. WGS84 differs at Greenwich from the one used on published maps OSGB36 by approximately 112m. ED50 differs from about 120m to 180m.[13]
Points on the Earth's surface move relative to each other due to continental plate motion, subsidence, and diurnalEarth tidal movement caused by theMoon and the Sun. This daily movement can be as much as a meter. Continental movement can be up to10 cm a year, or10 m in a century. Aweather system high-pressure area can cause a sinking of5 mm.Scandinavia is rising by1 cm a year as a result of the melting of the ice sheets of thelast ice age, but neighboringScotland is rising by only0.2 cm. These changes are insignificant if a regional datum is used, but are statistically significant if a global datum is used.[13]
On theGRS80 orWGS84 spheroid atsea level at the Equator, one latitudinal second measures 30.715m, one latitudinal minute is 1843 m and one latitudinal degree is 110.6 km. The circles of longitude, meridians, meet at the geographical poles, with the west–east width of a second naturally decreasing as latitude increases. On theEquator at sea level, one longitudinal second measures 30.92 m, a longitudinal minute is 1855 m and a longitudinal degree is 111.3 km. At 30° a longitudinal second is 26.76 m, at Greenwich (51°28′38″N) 19.22 m, and at 60° it is 15.42 m.
On the WGS84 spheroid, the length in meters of a degree of latitude at latitudeϕ (that is, the number of meters you would have to travel along a north–south line to move 1 degree in latitude, when at latitudeϕ), is about
(Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.)
The formulae both return units of meters per degree.
An alternative method to estimate the length of a longitudinal degree at latitude is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively):
whereEarth's average meridional radius is6,367,449 m. Since the Earth is anoblate spheroid, not spherical, that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude is
where Earth's equatorial radius equals 6,378,137 m and; for the GRS80 and WGS84 spheroids,. ( is known as thereduced (or parametric) latitude). Aside from rounding, this is the exact distance along a parallel of latitude; getting the distance along the shortest route will be more work, but those two distances are always within 0.6 m of each other if the two points are one degree of longitude apart.
Longitudinal length equivalents at selected latitudes
Like any series of multiple-digit numbers, latitude-longitude pairs can be challenging to communicate and remember. Therefore, alternative schemes have been developed for encoding GCS coordinates into alphanumeric strings or words:
Mapcode, an open-source system originally developed at TomTom.
What3words, a proprietary system that encodes GCS coordinates as pseudorandom sets of words by dividing the coordinates into three numbers and looking up words in an indexed dictionary.
These are not distinct coordinate systems, only alternative methods for expressing latitude and longitude measurements.
See also
Decimal degrees – Angular measurements, typically for latitude and longitude
Primary direction – Celestial coordinate system used to specify the positions of celestial objectsPages displaying short descriptions of redirect targets
^The pair had accurate absolute distances within the Mediterranean but underestimated thecircumference of the Earth, causing their degree measurements to overstate its length west from Rhodes or Alexandria, respectively.
^WGS 84 is the default datum used in most GPS equipment, but other datums and map projections can be selected.
References
^Chang, Kang-tsung (2016).Introduction to Geographic Information Systems (9th ed.). McGraw-Hill. p. 24.ISBN978-1-259-92964-9.
