Universal Transverse Mercator (UTM) Explained

The Universal Transverse Mercator (UTM) coordinate system is a globally consistent plane coordinate system, convenient for GIS work over large areas, and is a standard set of map projections, which covers the world along with the Universal Polar Stereographic system. It is a horizontal position representation that treats the earth surface as an oblate ellipsoid, ignoring altitude. The system divides Earth into 60 zones and projects each to the plane as a basis for its coordinates. This article delves into the intricacies of the UTM system, exploring its origins, structure, application, and importance in various fields.

Origins and Development

Prior to UTM, allies found that their differing systems hindered the synchronization of military operations. The UTM system wasn't born overnight. Conferences were held on the subject from 1945 to 1951, with representatives from Belgium, Portugal, France, and Britain, and the outlines of the present UTM system were developed. The UTM system was conceived to provide a consistent coordinate system that could promote cooperation between the military organizations of several nations. It was probably carried out by the Abteilung für Luftbildwesen (Department for Aerial Photography). Army introduced a system that was very similar to that currently used. Army; but several nations, and the North Atlantic Treaty Organization (NATO), played roles in its creation after World War II. At that time, the goal was to design a consistent coordinate system that could promote cooperation between the military organizations of several nations. Before the introduction of UTM, allies found that their differing systems hindered the synchronization of military operations. Conferences were held on the subject from 1945 to 1951, with representatives from Belgium, Portugal, France, and Britain, and the outlines of the present UTM system were developed. Army introduced a system that was very similar to that currently used.

Before the introduction 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 possible using the trigonometric formulas required under the graticule-based system of latitude and longitude.

The Transverse Mercator Projection

The foundation of the UTM system lies in the transverse Mercator projection, a variant of the Mercator projection originally developed in 1570. The transverse Mercator projection is an adaptation of the standard Mercator projection which flips the cylinder 90 degrees (transverse). The transverse Mercator projection, also known as the Gauss-Krüger projection, is similar to Mercator except that the cylinder touches the sphere or ellipsoid along a meridian instead of the equator. The result is a conformal projection that does not maintain true directions. The central meridian is placed in the center of the region of interest. This centering minimizes distortion of all properties in that region. This projection is best suited for north-south oriented areas. The Universal Transverse Mercator (UTM) coordinate system and Gauss-Krüger coordinate systems are based on the transverse Mercator projection and the State Plane Coordinate System uses it for all north-south zones. Various countries use this projection for their topographic maps and large-scale coordinate systems. The spherical version of the projection was presented by Johann H. Lambert in 1772. First formulas with ellipsoidal correction were developed by Carl F. Gauss in 1822. The Gauss-Krüger name refers to the ellipsoidal form reevaluated by Louis Krüger in 1912. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later. The transverse Mercator projection is shown centered on Greenwich.

This projection is conformal, which means it preserves angles and therefore shapes across small regions.

UTM Zone System

The UTM system divides the Earth into 60 zones, each 6° of longitude in width. The UTM projection divides the world into 60 zones that begin at longitude 180º, the International Date Line. Zone 1 is from 180° to the 174° W longitude. Zone 1 covers longitude 180° to 174° W; zone numbering increases eastward to zone 60, which covers longitude 174°E to 180°. The zones are numbered consecutively beginning with Zone 1, which includes the westernmost point of Alaska, and progress eastward to Zone 19, which includes Maine. The conterminous United States is within UTM zones 10 to 19.

From north to south, the zones extend from 84° N latitude to 80° S latitude. Originally the northern limit was at 80° N latitude and the southern 80° S latitude. On the south, the latitude is a small circle that conveniently traverses the ocean well south of Africa, Australia, and South America. However, 80° N latitude was found to exclude parts of Russia and Greenland and was extended to 84° N latitude.

Here is a convenient way to find the zone number for a particular longitude. Consider west longitude negative and east longitude positive, add 180° and divide by 6. Any answer greater than an integer is rounded to the next highest integer, and you have the zone. For example, Denver, Colorado is near 105° W.

Exceptions to the Uniform Zone System

The UTM zones are uniform across the globe, except in two areas. On the southwest coast of Norway, zone 32 is extended 3° further west, and zone 31 is correspondingly shrunk to cover only open water. Universal Transverse Mercator (UTM) Grid Zones 31N through 37N differ from the standard 6° wide by 84° zone for the northern hemisphere, in part to accommodate the western part of the Kingdom of Norway. For more on its history, see Clifford J.

Coordinates

Within each zone, coordinates are measured as northings and eastings in meters. Coordinates are given as easting, then northing.

Eastings

Each zone has a central meridian that is assigned an easting value of 500,000 meters. UTM easting coordinates are referenced to the center line of the zone known as the central meridian. The central meridian is assigned an easting value of 500,000 meters East. This arbitrary value is chosen to avoid negative easting coordinates within the zone. A point that has an easting of 400000 meters is about 100 km west of the central meridian. For most such points, the true distance would be slightly more than 100 km as measured on the surface of the Earth because of the distortion of the projection.

Northings

The northing values are measured from zero at the equator in a northerly direction. UTM northing coordinates are measured relative to the equator. The equator is assigned the northing value of 0 meters North. In the Northern Hemisphere positions are measured northward from zero at the equator. The maximum "northing" value is about 9300000 meters at latitude 84 degrees North, the north end of the UTM zones. The Southern Hemisphere's northing at the equator is set at 10000000 meters. Northings decrease southward from these 10000000 meters to about 1100000 meters at 80 degrees South, the south end of the UTM zones. Some UTM northing values are valid both north and south of the equator. The full coordinate needs to specify if the location is north or south of the equator.

Grid Lock

The UTM projection flattens the sphere 60 times by shifting the cylinder central meridian 6° for each zone. This gives cartographers a map to work with always in meters.

Latitude Bands and MGRS

Latitude bands are not a part of UTM, but rather a part of the military grid reference system (MGRS). They are however sometimes included in UTM notation. Each zone is divided into horizontal bands spanning 8 degrees of latitude. From south to north, beginning at 80° S with the letter C and ending with the letter X at 84° N. I and O are skipped to avoid confusion with the numbers one and zero. You will notice letters of the alphabet along the right edge of the illustration. There are a few letters missing. You see C,D,E, F, G,H -but there is no I, because it's too close to the number 1 and could be confused- J,K, L, M, N -but there is no O, it could be confused for the number zero- P,Q, R, S,T U, V, W, X, there is no Y, - and finally there is Z. I point this out because there are GPS/GNSS systems that use these letter designations along with the number of the UTM zone to identify a particular quadrangle. For example, C21 would be the square that you see just immediately above 21 in the Southern Hemisphere. This is a useful method of referring to a particular quadrangle in a particular UTM zone.

Origins

Unlike any of the systems previously discussed, every coordinate in a UTM zone occurs twice, once in the Northern Hemisphere and once in the Southern Hemisphere. This is a consequence of the fact that there are two origins in each UTM zone. The origin for the portion of the zone north of the equator is moved 500 km west of the intersection of the zone’s central meridian and the equator. This arrangement ensures that all of the coordinates for that zone in the Northern Hemisphere will be positive. The origin for the coordinates in the Southern Hemisphere for the same zone is 500 km west of the central meridian, as well. But in the Southern Hemisphere, the origin is not on the equator, it is 10,000 km south of it, close to the South Pole. This orientation of the origin guarantees that all of the coordinates in the Southern Hemisphere are in the first quadrant and are positive. In other words, the intersection of each zone’s central meridian with the equator defines its origin of coordinates.

Scale Factor

In each zone, the scale factor at the central meridian is specified to be 0.9996 of true scale (for most UTM systems in use). The UTM secant projection gives approximately 180 kilometers between the lines of exact scale where the cylinder intersects the ellipsoid. The scale factor grows from 0.9996 along the central meridian of a UTM zone to 1.00000 at 180 km to the east and west. In State Plane coordinates, the scale factor is usually no more than 1 part in 10,000. In UTM coordinates, it can be as large as 1 part in 2500.

By using narrow zones of 6° of longitude (up to 668 km) in width, and reducing the scale factor along the central meridian to 0.9996 (a reduction of 1:2500), the amount of distortion is held below 1 part in 1,000 inside each zone. In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator).

Datum

The reference ellipsoids for UTM coordinates vary. While historically UTM has been used with a range of geodetic datums, since the proliferation of civilian GPS usage, the World Geodetic System WGS84 ellipsoid has become the default for specifying a point's longitude and latitude. The WGS84 datum has therefore become the implicit default for UTM coordinates as well, if no alternate datum is specified. In North America, WGS84 UTM coordinates of a given point can differ up to 200 meters from older ones based on NAD27, for instance.

Precision and Measurement

UTM with the Universal Polar Stereographic system covers the world in one consistent system. It is four times less precise than typical State Plane Coordinate systems, with a scale factor that reaches 0.9996. A Universal Transverse Mercator zone embraces a much larger portion of the earth than does a state plane coordinate zone. When you get a larger bite, a larger portion of the earth, the scale factor is less attractive. Yet, the ease of using UTM and its worldwide coverage makes it very attractive for work that would otherwise have to cross many different SPCS zones.

Almost all USGS topographic maps produced after 1977 show UTM tick marks on the sides of the map (or a full-line grid) every 1,000 meters. Some maps, including all those produced after 2009 (US Topo maps) include full UTM grid lines. To make UTM measurements, subdivide the 1,000-meter grid squares into tenths or hundredths. This narrows down the coordinate to a 100 meter or 10 meter square. Measurements can be made using a gridded mylar overlay, a paper scale, or a coordinate reader.

Note that the large numbers adjacent to the tick marks around the perimeter of the map represent tens of thousands and thousands of meters. The millions and hundreds of thousands of meters are shown with small numbers and are sometimes dropped when giving UTM coordinate positions. The military implementation of UTM (Military Grid Reference System or MGRS) drops the small digits and indicates the 100,000 meter square by a two letter identifier.

Truncated Coordinates

In most land navigation situations the area of interest is much smaller than a zone. 100,000m are dropped. The 1m, 10m and 100m digits are used only to the extent of accuracy desired. the smaller digits that are dropped in the notation used by the USGS on the edges of their maps. mN.

Distortion

Distortion of scale increases in each UTM zone as the boundaries between the UTM 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. Distortion is small near the central meridian, and as you move away it worsens. Just like every map projection, the Universal Transverse Mercator has its strengths and weaknesses.

Conventions

There are different conventions how to write UTM.

Convention 1

Zone Number -- Band Letter (eg. In this convention, a Zone Number is followed by a Band Letter and is used to identify each 6 x 8 grid.

Convention 2

Zone Number followed by 'N' or 'S' (eg. In this convention, a Zone Number is followed by an 'N' for the Northern Hemisphere or 'S' for Southern Hemisphere.

Applications

Geological Survey (USGS) quad sheets, and many aeronautical charts show the UTM grid lines. The UTM system is used for designating rectangular coordinates on large scale military maps. NATO armed forces.

Formulas for Advanced Use

The WGS 84 spatial reference system describes Earth as an oblate spheroid along north-south axis with an equatorial radius of km and an inverse flattening of . Taking a point of latitude and of longitude and computing its UTM coordinates as well as point scale factor and meridian convergence using a reference meridian of longitude . By convention, in the Northern Hemisphere km and in the Southern Hemisphere km. In the following formulas, the distances are in kilometers and angles are in radians. Since transverse Mercator projections are conformal, maps in UTM coordinates do not distort subtended angles or local shapes, and scale distortion is isotropic. More specifically, on a UTM map, meridians other than the central one are slightly curved, their rotation (tangent line at any point) given by the grid convergence angle there. The scale factor increases from at the central meridian. The value of each depends on the latitude and the deviation in longitude . The quadratic dependence for scale factor makes it fairly constant around the central meridian, increasing more rapidly when closer to a zone's edge. At zone edges, °, the scale factor is approximately 1.0010 at the equator and 1.0005 at latitude 45°. These formulas for and are particularly relevant for converting paths described by ground distances and astronomic (true) bearings, for instance land surveyors' measurements, to UTM coordinates. For a small-scale survey (extent <1 km), and are both essentially constant for the whole area covered. However, for conversion of ground distance to grid, correcting the scale factor for elevation is also necessary (projecting down to the reference geoid at elevation zero). For medium-scale surveys (a few km in east-west extent), the change in over the area represented may be material, as shown by the part of the formula using . However, the variation of over the area will be negligible. In practice, surveyors will usually use one combined scale factor (covering average distance from central meridian and elevation) and one grid convergence angle in digitizing and coordinate-parametrizing any one cadastral survey, though may be forced to vary when integrating with neighboring surveys along a long east-west traverse.

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