Universal Transverse Mercator coordinate system

The Universal Transverse Mercator (UTM) coordinate system is a grid-based method of specifying locations on the surface of the Earth. It is used to identify locations on the earth, but differs from the traditional method of latitude and longitude in several respects.

The UTM system is not a single map projection. The system instead employs a series of sixty zones, each of which is based on a specifically defined secant transverse Mercator projection.

History

The Universal Transverse Mercator coordinate system was developed by the United States Army Corps of Engineers in the 1940s. [http://www.history.noaa.gov/stories_tales/geod1.html] The system was based on an ellipsoidal model of the Earth. For areas within the conterminous United States, the Clarke 1866 ellipsoid was used. For the remaining areas of the Earth, including Hawaii, the International Ellipsoid was used. Currently, the WGS84 ellipsoid is used as the underlying model of the Earth in the UTM coordinate system.

Prior to the development of the Universal Transverse Mercator coordinate system, several European nations demonstrated the utility of grid-based conformal maps by mapping their territory during the interwar period. Calculating the distance between two points on these maps could be performed more easily in the field (using the Pythagorean theorem) than was otherwise possible using the trigonometric formulas required under the graticule-based system of latitude and longitude. In the post-war years, these concepts were extended into the Universal Transverse Mercator / Universal Polar Stereographic (UTM/UPS) coordinate system, which is a global (or universal) system of grid-based maps.

The transverse Mercator projection is a variant of the Mercator projection, which was originally developed by the Flemish geographer and cartographer Gerardus Mercator, in 1569.

It should be carefully noted that the projection defined by the projection of the Earth onto a cylinder is not conformal, and Mercator projections are invariably non-linearly scaled to provide this property. UTM involves non-linear scaling in both Eastings and Northings to ensure the projected map of the ellipsoid is conformal.

Definitions

UTM longitude zone

The UTM system divides the surface of the Earth between 80° S latitude and 84° N latitude into 60 zones, each 6° of longitude in width and centered over a meridian of longitude. Zones are numbered from 1 to 60. Zone 1 is bounded by longitude 180° to 174° W and is centered on the 177th West meridian. Zone numbering increases in an easterly direction.

Each of the 60 longitude zones in the UTM system is based on a transverse Mercator projection, which is capable of mapping a region of large north-south extent with a low amount of distortion. By using narrow zones of 6° (to 800km resp.) in width, and reducing the scale factor along the central meridian by only 0.0004 (to 0.9996, a reduction of 1:2500) the amount of distortion is held below 1 part in 1,000 inside each zone. Distortion of scale increases to 1.0010 at the outer zone boundaries along the equator.

The secant projection in each zone creates two standard lines, or lines of true scale, located approximately 180 km on either side of, and approximately parallel to, the central meridian. The scale factor is less than 1 inside these lines and greater than 1 outside of these lines, but the overall distortion of scale inside the entire zone is minimized.

UTM latitude zone

The UTM system segments each longitude zone into 20 latitude zones. Each latitude zone is 8 degrees high, and is lettered starting from "C" at 80° S, increasing up the English alphabet until "X", omitting the letters "I" and "O" (because of their similarity to the digits one and zero). The last latitude zone, "X", is extended an extra 4 degrees, so it ends at 84° N latitude, thus covering the northernmost land on Earth. Latitude zones "A" and "B" do exist, as do zones "Y" and Z". They cover the western and eastern sides of the Antarctic and Arctic regions respectively. A convenient trick to remember is that the letter "N" is the first letter in the northern hemisphere, so any letter coming before "N" in the alphabet is in the southern hemisphere, and any letter "N" or after is in the northern hemisphere.

Notation

Each grid square is referred to by the longitude zone number and the latitude zone character. The longitude zone is always written first, followed by the latitude zone. For example (see image, top right), a position in Toronto, Canada, would find itself in longitude zone 17 and latitude zone "T", thus the full reference is "17T".

Exceptions

These longitude and latitude zones are uniform over the globe, except in two areas. On the southwest coast of Norway, the UTM zone 32V is extended further west, and the zone 31V is correspondingly shrunk to cover only open water. Also, in the region around Svalbard, the four zones 31X, 33X, 35X, and 37X are extended to cover what would otherwise have been covered by the seven zones 31X to 37X. The three zones 32X, 34X and 36X are not used.Picture gallery: UTM zones in various parts of the world

Locating a position using UTM coordinates

A position on the Earth is referenced in the UTM system by the UTM longitude zone, and the easting and northing coordinate pair. The easting is the projected distance of the position from the central meridian, while the northing is the projected distance of the point from the equator. The point of origin of each UTM zone is the intersection of the equator and the zone's central meridian. In order to avoid dealing with negative numbers, the central meridian of each zone is given a "false easting" value of 500,000 meters. Thus, anything west of the central meridian will have an easting less than 500,000 meters. For example, UTM eastings range from 167,000 meters to 833,000 meters at the equator (these ranges narrow towards the poles). In the northern hemisphere, positions are measured northward from the equator, which has an initial "northing" value of 0 meters and a maximum "northing" value of approximately 9,328,000 meters at the 84th parallel — the maximum northern extent of the UTM zones. In the southern hemisphere, northings decrease as you go southward from the equator, which is given a "false northing" of 10,000,000 meters so that no point within the zone has a negative northing value.

As an example, the CN Tower is located at the geographic position coord|43|38|33.24|N|79|23|13.7|W|. This is in longitude zone 17, and the grid position is 630084m east, 4833438m north.

The latitude zone is unnecessary if the full distance from the equator is given (as above) and the hemisphere is known. It does, however, become important when further sub-division of the UTM grid is undertaken, such as in the military grid reference system.

Overlapping Grids

Distortion of scale increases in each UTM zone as the boundaries between the longitude zones are approached. However, it is often convenient or necessary to measure a series of locations on a single grid when some are located in two adjacent zones. Around the boundaries of large scale maps (1:100,000 or larger) coordinates for both adjoining UTM zones are usually printed within a minimum distance of 40 km on either side of a zone boundary. Ideally, the coordinates of each position should be measured on the grid for the zone in which they are located, but because the scale factor is still relatively small near zone boundaries, it is possible to overlap measurements into an adjoining zone for some distance when necessary.

But this overlap of grids is intended only to simplify measurements on a map. When the position of a point should be expressed in UTM coordinates, one must use the grid of the zone that contains the point.

ee also

*Military grid reference system
*Transverse Mercator projection
*Universal Polar Stereographic coordinate system

External links

* [http://www.apsalin.com/utm-zone-finder.aspx UTM zone lookup]
* [http://www.baseloc.net/home.php Free ATS/LSD + GPS + UTM mapper using Google Maps]
* [http://erg.usgs.gov/isb/pubs/factsheets/fs07701.html U.S. Geological Survey UTM Grid Fact Sheet]
* [http://www.ngs.noaa.gov/TOOLS/utm.shtml National Geodetic Survey (U.S.) UTM Utilities]
* [http://earth-info.nga.mil/GandG/publications/tm8358.1/toc.html] TM8358.1: Datums, Ellipsoids, Grids and Grid Reference Systems
* [http://earth-info.nga.mil/GandG/publications/tm8358.2/TM8358_2.pdf] TM8358.2: Defense Mapping Agency Technical Manual 8358.2 The Universal Grids: Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS)
* [http://www.gpsy.com/gpsinfo/geotoutm/ Converting Latitude/Longitude to Universal Transverse Mercator (UTM)]
* [http://www.colorado.edu/geography/gcraft/notes/coordsys/gif/utmzones.gifUTM Zones]
* [http://search.cpan.org/~grahamc/Geo-Coordinates-UTM/ UTM conversion library] written in Perl
* [http://code.google.com/p/pyproj/ Cartographic transformations library] for Python that is capable to perform UTM conversions (Proj.4 wrapper)
* [http://earth-info.nga.mil/GandG/coordsys/gislayers/gislayers.html GIS MGRS Grid Data layers and UTM zones in GIS Format]
* [http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.HTM Converting UTM to Latitude and Longitude (Or Vice Versa)] <--This Excel code produces incorrect conversions
* [http://earth-info.nga.mil/GandG/geotrans/index.html GEOTRANS] Geographic Translator software and source code from the US National Geospatial-Intelligence Agency
* [http://home.hiwaay.net/~taylorc/toolbox/geography/geoutm.html Geographic/UTM Coordinate Converter]
* [http://www.dmap.co.uk/utmworld.htm] Map of UTM Grid Zones of the World
* [http://www.cs.earlham.edu/~joshh/cgi-bin/geo/utm2ll.html] UTM to Latitude/Longitude Bulk Converter <--Checked against known values for UTM/LAT-LONG. Appears accurate.

References