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Aprojected coordinate system – also called aprojected coordinate reference system,planar coordinate system, orgrid reference system – is a type ofspatial reference system that represents locations onEarth usingCartesian coordinates (x,y) on a planar surface created by a particularmap projection.[1] Each projected coordinate system, such as "Universal Transverse Mercator WGS 84 Zone 26N," is defined by a choice of map projection (with specific parameters), a choice ofgeodetic datum to bind the coordinate system to real locations on the earth, an origin point, and a choice of unit of measure.[2] Hundreds of projected coordinate systems have been specified for various purposes in various regions.
When the first standardized coordinate systems were created during the 20th century, such as theUniversal Transverse Mercator,State Plane Coordinate System, andBritish National Grid, they were commonly calledgrid systems; the term is still common in some domains such as the military that encode coordinates as alphanumericgrid references. However, the termprojected coordinate system has recently become predominant to clearly differentiate it from other types ofspatial reference system. The term is used in international standards such as theEPSG and ISO 19111 (also published by theOpen Geospatial Consortium as Abstract Specification 2), and in mostgeographic information system software.[3][2]
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Themap projection and thegeographic coordinate system (GCS, latitude and longitude) date to theHellenistic period, proliferating during theEnlightenment Era of the 18th century. However, their use as the basis for specifying precise locations, rather than latitude and longitude, is a 20th century innovation.
Among the earliest was theState Plane Coordinate System (SPCS), which was developed in the United States during the 1930s for surveying and engineering, because calculations such as distance are much simpler in aCartesian coordinate system than the three-dimensional trigonometry of GCS. In theUnited Kingdom, the first version of theBritish National Grid was released in 1938, based on earlier experiments duringWorld War I by theArmy and theOrdnance Survey.[4]
DuringWorld War II, modern warfare practices required soldiers to quickly and accurately measure and report their location, leading to the printing of grids on maps by the U.S.Army Map Service (AMS) and other combatants.[5] Initially, eachtheater of war was mapped in a custom projection with its own grid and coding system, but this resulted in confusion. This led to the development of theUniversal Transverse Mercator coordinate system, possibly adopted from a system originally developed by the GermanWehrmacht.[6] To facilitate unambiguous reporting, the alphanumericMilitary Grid Reference System (MGRS) was then created as an encoding scheme for UTM coordinates to make them easier to communicate.[5]
After the War, UTM gradually gained users, especially in the scientific community. Because UTM zones do not align with political boundaries, several countries followed the United Kingdom in creating their own national or regional grid systems based on custom projections. The use and invention of such systems especially proliferated during the 1980s with the emergence ofgeographic information systems. GIS requires locations to be specified as precise coordinates and performs numerous calculations on them, making Cartesian geometry preferable to spherical trigonometry when computing power was at a premium. In recent years, the rise of global GIS datasets andsatellite navigation, along with an abundance of processing speed in personal computers, have led to a resurgence in the use of GCS. That said, projected coordinate systems are still very common in the GIS data stored in thespatial data infrastructures (SDI) of local areas, such as cities, counties, states and provinces, and small countries.
Because the purpose of any coordinate system is to accurately and unambiguously measure, communicate, and perform calculations on locations, it must be defined precisely. TheEPSG Geodetic Parameter Dataset is the most common mechanism for publishing such definitions in a machine-readable form, and forms the basis for many GIS and other location-aware software programs.[3] A projected SRS specification consists of three parts:
To establish the position of a geographic location on amap, a map projection is used to convert geodetic coordinates to plane coordinates on a map; it projects the datum ellipsoidal coordinates and height onto a flat surface of a map. The datum, along with a map projection applied to a grid of reference locations, establishes agrid system for plotting locations.Conformal projections are generally preferred. Common map projections include thetransverse Mercator (used inUniversal Transverse Mercator, theBritish National Grid, theState Plane Coordinate System for some states),Lambert conformal conic (some states in theSPCS), andMercator (Swiss coordinate system).
Map projection formulas depend on the geometry of the projection as well as parameters dependent on the particular location at which the map is projected. The set of parameters can vary based on the type of project and the conventions chosen for the projection. For thetransverse Mercator projection used in UTM, the parameters associated are the latitude and longitude of the natural origin, the false northing and false easting, and an overall scale factor.[7] Given the parameters associated with particular location or grin, the projection formulas for the transverse Mercator are a complex mix of algebraic and trigonometric functions.[7]: 45–54
Every map projection has anatural origin, e.g., at which the ellipsoid and flat map surfaces coincide, at which point the projection formulas generate a coordinate of (0,0).[7] To ensure that the northing and easting coordinates on a map are not negative (thus making measurement, communication, and computation easier), map projections may set up afalse origin, specified in terms offalse northing andfalse easting values, that offset the true origin. For example, in UTM, the origin of each northern zone is a point on the equator 500 km west of the central meridian of the zone (the edge of the zone itself is just under 400 km to the west). This has the desirable effect of making all coordinates within the zone positive values, being east and north of the origin. Because of this, they are often referred to as theeasting andnorthing.
Grid north (GN) is anavigational term referring to the direction northwards along the grid lines of amap projection. It is contrasted withtrue north (the direction of theNorth Pole) andmagnetic north (the direction in which a compass needle points). Manytopographic maps, including those of theUnited States Geological Survey and Great Britain'sOrdnance Survey, indicate the difference between grid north, true north, and magnetic north.[8]
The grid lines on Ordnance Survey maps divide the UK into one-kilometre squares, east of an imaginary zero point in the Atlantic Ocean, west of Cornwall. The grid lines point to a Grid North, varying slightly from True North. This variation is zero on the central meridian (north-south line) of the map, which is at two degrees west of thePrime Meridian, and greatest at the map edges. The difference between grid north and true north is very small and can be ignored for most navigation purposes. The difference exists because the correspondence between a flat map and the round Earth is necessarily imperfect.
At theSouth Pole, grid north conventionally points northwards along thePrime Meridian.[9] Since the meridians converge at the poles, true east and west directions change rapidly in a condition similar togimbal lock. Grid north solves this problem.
Locations in a projected coordinate system, like any cartesian coordinate system, are measured and reported as easting/northing or (x,y) pairs. The pair is usually represented conventionally with easting first, northing second. For example, the peak ofMount Assiniboine (at50°52′10″N115°39′03″W / 50.86944°N 115.65083°W /50.86944; -115.65083 on theBritish Columbia/Alberta border inCanada) in UTM Zone 11 is at(0594934mE, 5636174mN), meaning that is almost 600km east of the false origin for Zone 11 (95km east of the true central meridian at 117°W) and 5.6 million meters north of theequator.
While such precise numbers are easy to store and calculate inGIS and other computer databases, they can be difficult for humans to remember and communicate. Thus, since the mid 20th century, there have been alternative encodings that shorten the numbers or convert the numbers into some form of alphanumeric string.
For example, atruncated grid reference may be used where the general location is already known to participants and may be assumed.[10] Because the (leading)most significant digits specify the part of the world and the (trailing)least significant digits provide a precision that is not needed in most circumstances, they may be unnecessary for some uses. This permits users to shorten the example coordinates to949-361 by concealing05nnn34 56nnn74, assuming the significant digits (3,4, and 5 in this case) are known to both parties.[11]
Alphanumeric encodings typically use codes to replace the most significant digits by partitioning the world up into large grid squares. For example, in theMilitary Grid Reference System, the above coordinate is in grid 11U (representing UTM Zone 11 5xxxxxx mN), and grid cell NS within that (representing the second digit 5xxxxxmE x6xxxxxm N), and as many remaining digits as are needed are reported, yielding an MGRS grid reference of 11U NS 949 361 (or 11U NS 9493 3617 or 11U NS 94934 36174).
TheOrdnance Survey National Grid (United Kingdom) and other national grid systems use similar approaches. InOrdnance Survey maps, each Easting and Northing grid line is given a two-digit code, based on theBritish national grid reference system with an origin point just off the southwest coast of theUnited Kingdom. The area is divided into 100 km squares, each of which is denoted by a two-letter code. Within each 100 km square, a numerical grid reference is used. Since the Eastings and Northings are one kilometre apart, a combination of a Northing and an Easting will give a four-digit grid reference describing a one-kilometre square on the ground. The convention is the grid reference numbers call out the lower-left corner of the desired square. In the example map above, the town Little Plumpton lies in the square 6901, even though the writing which labels the town is in 6802 and 6902, most of the buildings (the orange boxed symbols) are in square 6901.
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The more digits added to a grid reference, the more precise the reference becomes. To locate a specific building in Little Plumpton, a further two digits are added to the four-digit reference to create a six-digit reference. The extra two digits describe a position within the 1-kilometre square. Imagine (or draw or superimpose aRomer) a further 10x10 grid within the current grid square. Any of the 100 squares in the superimposed 10×10 grid can be accurately described using a digit from 0 to 9 (with 0 0 being the bottom left square and 9 9 being the top right square).
For the church in Little Plumpton, this gives the digits 6 and 7 (6 on the left to right axis (Eastings) and 7 on the bottom to top axis (Northings). These are added to the four-figure grid reference after the two digits describing the samecoordinate axis, and thus our six-figure grid reference for the church becomes 696017. This reference describes a 100-metre by 100-metre square, and not a single point, but this precision is usually sufficient for navigation purposes. The symbols on the map are not precise in any case, for example the church in the example above would be approximately 100x200 metres if the symbol was to scale, so in fact, the middle of the black square represents the map position of the real church, independently of the actual size of the church.
Grid references comprising larger numbers for greater precision could be determined using large-scale maps and an accurateRomer. This might be used insurveying but is not generally used for land navigating for walkers or cyclists, etc. The growing availability and decreasing cost of handheldGPS receivers enables determination of accurate grid references without needing a map, but it is important to know how many digits the GPS displays to avoid reading off just the first six digits. A GPS unit commonly gives a ten-digit grid reference, based on two groups of five numbers for the Easting and Northing values. Each successive increase in precision (from 6 digit to 8 digit to 10 digit) pinpoints the location more precisely by a factor of 10. Since, in the UK at least, a 6-figure grid reference identifies a square of 100-metre sides, an 8-figure reference would identify a 10-metre square, and a 10-digit reference a 1-metre square. In order to give a standard 6-figure grid reference from a 10-figure GPS readout, the 4th, 5th, 9th and 10th digits must be omitted, so it is important not to read just the first 6 digits.
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