Universal Transverse Mercator (UTM) Projection System
As the name suggests, the Universal Transverse Mercator projection is based on the cylindrical Transverse Mercator projection. The cylinder in the Transverse Mercator projection is tangent along a meridian (line of longitude) or it is secant, in which case it cuts through the earth at two standard meridians.
In the UTM projection the transverse cylinder rotates by 6° increments, thus creating 60 (360° / 6°) strips or projection zones. In such a projection, instead of projecting the complete globe into a flat surface, each of the 60 strips or zones gets projected onto a plane separately, therefore minimizing scale distortion within each zone. The meridian at the center of each zone is called the central meridian. The cylinder is secant in the UTM projection; it intersects the globe creating two standard meridians that are 180 km to each side of the central meridian. Also since a Transverse Mercator projection results in extreme distortion in polar areas, the UTM zones are limited to 80°S and 84°N latitudes. Polar regions (below 80°S and above 84°N) use the UPS – Universal Polar Stereographic coordinate system based on the Polar Stereographic projection.
The narrow width (6° of longitude) of each zone ensures minimal scale distortion within a zone. Also a map derived from a secant cylinder has less overall distortion than a map from a tangent cylinder. The scale is true (scale factor = 1) on each of the standard meridians meaning that there is no distortion along these lines. Between the secant lines, where the cylinder is inside the globe, features appear smaller than in reality and scale factor is less than 1. The central meridian has a scale factor of 0.9996. At places on map where the cylinder is outside the globe, features appear larger than in reality and scale factor is greater than 1. The scale error within each UTM projection zone remains less than 0.1 percent, or in other words scale distortion is kept to less than 1 part in 1000. Naturally for areas that span more than one UTM zone, the distortion and error increase.
The Mercator and Transverse Mercator projections are conformal projections. In a conformal projection local angles are preserved and shapes are represented accurately and without distortion for small areas. As a result of preserving angles and shapes, area or size of features are distorted in these maps. As mentioned, choosing a secant projection and a narrow zone minimizes the distortions in a map generated from UTM projection.
UTM Coordinate System: Grid
By means of a map projection, the earth’s curved surface is transformed to a flat two-dimensional surface. A coordinate system or grid is superimposed on the resulting flat surface. Such a coordinate system provides a referencing frame in order to define the position of objects.
Universal Transverse Mercator is a projected coordinate system, which is a type of plane rectangular coordinate system (also called Cartesian coordinate system). In the two-dimensional surface, two straight lines intersect each other at right angles. These lines are called the axes, and their point of intersection is defined as the origin (0, 0) of the coordinate system. The horizontal axis (east-west) is labeled as x-axis and the vertical axis (north-south) as y-axis. The position of a point in the rectangular coordinate system is defined by its distance from the x and y axes. The two distance values are the x and y coordinates of the point, and use a measurement unit such as meters, feet, etc.
The intersection of the x and y axes in the rectangular coordinate system divides the space into four quadrants. Points along a vertical grid line to the right of y-axis have a positive x coordinate value while those to the left of y-axis have a negative x coordinate value. Points on a horizontal line above the x-axis have positive y coordinate value while those below x-axis are given negative y value. Therefore a point lying in the first quadrant, to the right of y-axis and above x-axis, has positive x and y coordinate values.
In contrast to the projected coordinate system, the geographic coordinate system uses curved grids in order to accommodate the curved surface of the earth; and the geographic latitude, longitude coordinates are measured in degrees, minutes and seconds of arc. These geographic coordinates are converted to plane coordinates by means of map projections.
The UTM coordinate system is a universally used plane coordinate system (except for polar regions). UTM zones are “flattened” using the Transverse Mercator projection, and a rectangular grid network of straight horizontal and vertical lines is superimposed on each zone. Although meridians inside the zone and on zone boundaries converge towards the poles, vertical grid lines are oriented parallel to the central meridian of each zone (and make an angle to the other meridians). Horizontal lines in turn are parallel to the equator. As a result the grid squares stay the same size and shape throughout the map.
The vertical direction of grid lines is referred to as grid north on maps, as opposed to true north which is associated with the direction of meridians or lines of longitude. The angular difference between grid north and true north is referred to as grid declination, and is sometimes indicated on the map margin along with magnetic declination. For large scale maps this difference is small and is usually not taken into account in map reading.
In the UTM grid layout, the unit of measurement is meters, and the coordinates of a point are designated as easting (determine east-west position) and northing (determine north-south position). Vertical grid lines on map are used to find easting while horizontal grid lines are used to find northing of a point; similarly grid lines can be used to help locate a point with known coordinates.
Designation of the central meridian as the reference y-axis (i.e. easting = 0) of the coordinate system within each zone would result in negative easting values for points to the west of the central meridian. For this reason, the central meridian is assigned an arbitrary value of 500000 meters, thus avoiding any negative easting coordinates; points lying to the east of it would have an easting value greater than 500000m and points lying to the west would have a value less than 500000m. This assignment would place the origin outside the zone at 500000m west of the central meridian, as a result the origin is called a false origin and the easting coordinates are referred to as false easting.
The equator is designated as the horizontal reference axis for UTM northing coordinates and is assigned a value of 0 meters North for zones in northern hemisphere. To avoid negative numbers, the equator is assigned a false northing of 10,000,000 meters South for referencing northing coordinates in the southern hemisphere.
UTM Coordinates : Easting & Northing
The easting coordinate of a point is measured from the false origin 500000 meters to the west of the central meridian of the UTM zone. Within a zone, easting values increase towards east. A point lying 8 meters east of central meridian has an easting of 500000 + 8 = 500008mE. The easting of a point 350m west of central meridian would be 500000 – 350 = 499650mE. The east-west distance between two points is obtained by the difference of their easting values. The distance between the above points is 500008 – 499650 = 358m.
Longitude lines are furthest apart at the equator, where latitude is zero. Therefore the maximum width of a UTM zone occurs on the equator. Depending on the datum and the chosen ellipsoid, an approximate range for the easting values can be calculated. In general the easting values can not be larger than 834000m and smaller than 166000m. As a result, an easting coordinate is always a six digit number. Sometimes in GPS systems and GIS software, the easting values are preceded with a 0 in order to represent them as 7 digit numbers.
A northing value in northern hemisphere specifies the number of meters a point is located north of the equator. The northing of a point south of the equator is equal to 10,000,000m minus its distance from the equator. In both northern and southern hemispheres, northing values increase from south to north.
A point south of equator with a northing of 7587834mN is 10,000,000 – 7587834 = 2412166m south of the equator. A point located 34m south of the equator has a northing of 9999966mN, while a point 34m north of the equator has a northing of 0000034mN. The north-south distance between two points north of equator with northings of 4867834mN and 4812382mN is 4867834 – 4812382 = 55452m.
Depending on the datum and the chosen ellipsoid, an approximate range for the northing values can be calculated. In the southern hemisphere the northing values range from 10,000,000m at the equator to approximately 1100000m at the 80th south parallel. In the northern hemisphere the northing values stretch from 0m at the equator to around 9350000m at the 84th north parallel. If the northing values are less than 7 digits, they will usually be preceded with 0(s) to represent them as 7 digit numbers.
UTM easting and northing coordinates specify the position of a point on Earth. UTM coordinate of a point is stated by writing the zone, easting and then northing values. When finding a position on a map, it is helpful to “read right up“, that is to read west to east to find the easting and then south to north to find the northing of the location. An example of a complete UTM coordinate: 11U 358657mE 5885532mN.
Since there are coordinate values that occur in both northern and southern hemispheres within a UTM zone, it is important to specify the hemisphere or the latitude band where the point is located. Usually GPS receivers can use both ways to distinguish the hemisphere. Care should be taken so that stating the hemisphere by the use of N (north) or S (south) after the zone number not to be confused with interpretation of N or S as latitude band letters.