Introduction to Earth Systems: Lesson 6 The UTM System   Reading Assignment: David Greenhood, Mapping, Chapter 6 Internet link:  Description of UTM   NAVIGATION (To return, use back button) Reading Key Concepts Discussion More Links Exercises
Side Notes	Key Concepts	Links
Lat-lon vs. rectangular coordinates	These are the key concepts in this lesson. You should be able to define or describe them after you have read this lesson, finished the assigned reading and explored the links. You should also be able to do the exercises and answer the questions at the end of the lesson. transverse Mercator UTM zone easting, northing UTM coordinates The Universal Transverse Mercator (UTM) coordinate system Since the development of Mercator's projection in the 16th century, there have been dozens of attempts at representing Earth's spherical surface on a flat surface. All such projections sacrifice accuracy in some attributes, e.g. distance, shape. But most preserve the latitude-longitude coordinate system. In those cases. meridians and parallels are transformed to lines and curves in the planar images. The relationship between longitude and distance varies with latitude because the meridians intersect at the poles and are thus closer to each other near the poles than at the equator. For example, the equator and the parallels each have arc measure 360 degrees. But as latitude increases, the circumferences of the parallels decrease. The circumference of the Arctic Circle is less than the circumference of the Equator. Although one degree of arc occupies 60 nautical miles at the Equator, one degree occupies substantially less than that on the Arctic Circle. In contrast with the longitude-distance relationship, the relationship between latitude and distance along a meridian line is constant. Regarding Earth as approximately spherical, one minute of latitude occupies approximately (very close approximation) one nautical mile everywhere on the planet. Thus the relationship between longitude measure and distance varies with latitude, but the relationship between between latitude measure and distance does not vary with longitude. Compared to calculation within the latitude-longitude system, calculation of distance within a rectangular coordinate system is relatively simple. Units for coordinates are the same as those for distance. The use of coordinates to calculate distance between two points is actually an application of the Pythagorean Theorem. Because of the consistency of relationship between distance and location throughout a rectangular coordinate system, estimation of distances is much easier than is the case with a latitude-longitude system.	Relationship between lat-lon and UTM.
Projection to a plane	The Universal Transverse Mercator system is an attempt to replicate some advantages of a rectangular coordinate system on a plane model of Earth. Recall that a Mercator projection is more accurate near the Equator than is the case farther north or south. Since the Mercator projection is a projection of Earth to a cylinder and the cylinder is tangent to Earth at the Equator, portions of the meridians that are very near the Equator are nearly parallel to the cylinder. Since the cylinder can be unrolled to a plane, the region near the Equator, e.g. within 2°or 3° of the Equator, can be accurately, but not perfectly, represented on a plane. Near the equator on a Mercator projection, latitude is proportional to distance from the Equator, and longitude is nearly proportional to east-west distance. Distortion of the relationship between longitude and distance increases as distance from the Equator increases. The UTM system uses portions of many cylindrical projections, each to a cylinder that is tangent to Earth at a meridian rather than at the Equator; the axis of the cylinder is perpendicular to Earth's axis. The meridians tangent to cylinders have longitudes that are midway between multiplies of six, i.e. 3°, 9°, 15°, . . . , 177° both east and west. Each projection of a cylinder tangent at one of these meridians accounts for a band on the sphere that is 6° wide. Since each zone, or band, is 6° wide, there are 60 zones. Thus the surface of Earth is projected to portions of 30 cylinders, each accounting for two meridians. For example, one cylinder is tangent to the Earth along the meridians at 177° W and at 3° E., another is tangent along the meridians at 171° W and at 9° E, etc. The boundaries of the UTM zones are along meridians whose longitudes are multiples of six, i.e. 6°, 12°, 18°, … , 174° east and west, 0° and 180°. The zones are numbered as follows: Zone 1 is between 180°and 174° W, zone 2 is between 174° W and 168° W, ... etc., and zone 60 is between 174° E and 180°. The International Date Line is, with some deviation, the boundary between zone 60 and zone 1. The Greenwich meridian is the boundary between zone 30 and zone 31. Near the poles, the UTM system creates an image with relatively small areas segmented into 60 narrow zones, making UTM representation impractical. To avoid this, while accommodating land mass separation, UTM zones have northern boundaries at 84°N and southern boundaries at 80° S. So the length of a UTM zone occupies 164°. Since the width of a zone is 6°, the ratio of length to width is (164/6). The length of a zone is approximately 27 times its width at the equator.	Map of UTM zones.
Location         Easting	Portions of Earth represented in a UTM transformation resemble orange peel that has been scored sixty times from top to bottom. Flattening of the UTM image produces a row of sixty narrow north-south bands, convex on the eastern and western boundaries, each band (zone) tangent to its adjacent zones approximately at midpoints of its eastern and western boundaries. Within each zone, there is a grid comprised of lines, approximately east-west, that are parallel to the equator and lines, approximately north-south, that are parallel to the center meridian. The east-west lines are slightly different from the parallels of the latitude-longitude system. On a UTM grid, the latter would appear as arcs. Except for the center meridian, the north-south lines, since they are parallel in a plane, are not meridians. Since the eastern and western boundaries are meridians and their images in the plane are curved, they are not parallel to the north-south grid lines. Each north-south coordinate line intersects at least one boundary. With each zone covered by a rectangular grid, we now need a system for naming the coordinate lines, and therefore each point. Note that the circumference of Earth at the equator is approximately 40,123 kilometers. So the width of each UTM zone at the equator is approximately (40,123)/60 kilometers, i.e. approximately 669 kilometers. To take advantage of the grid, and because the boundaries of the zone are curved, the center meridian is assigned an east-west coordinate. To avoid negative coordinates and keep reference numbers relatively simple, each central meridian is assigned a coordinate within its zone, called an "easting", of 500,000. Coordinates of this magnitude will represent numbers of meters. East-west coordinates increase from west to east and are based on metric distances. So, for example using more digits in approximating the circumference of Earth, Circumference of Earth is approximately 40,123.648 kilometers or 40,123,648 meters Therefore, the width of each UTM zone at the Equator is approximately (40,123,648)/60 meters, or approximately 668,727 meters Since the center of the grad line has an easting coordinate 500,000 , the end points on the equator within the zone are 500,000 - (668,727)/2 and 500,000 + (668,727)/2 So the easting coordinates at the equator of the east and west boundaries of the zone at the Equator are 165636 and 834364, respectively.
Northing	In this development, North-South coordinates are also distances in meters. They are called the "northing" components. Except for the central meridian, the distances are measured along north-south grid lines, not on meridians. The central meridian is a grid line. Coordinates northward begin at the equator with zero and increase to approximately 10,000,000. By definition of the meter, the distance along the Greenwich meridian, which is not a central meridian, from the equator to the north pole is exactly 10,000,000 meters. For points in the Southern Hemisphere, the Equator is given a northing value 10,000,000. Travel southward on a grid line produces coordinate values decreasing toward zero. The essential components of a UTM grid name for a location are the zone number, an easting component, and a northing component. There are some variations on the strategy described, but all versions include the essential features of UTM that are described here. Some applications identify grids in terms of kilometers, others in terms of squares 10 kilometers on a side, still others assign letters to bands of northing. Following is an example of notation as described above: UTM name for a location has the form zone number easting coordinate northing coordinate The point whose coordinates are 10 565000 4151000N is in zone 10, i.e. between 126° W and 120° W longitude. Within zone 10, the central meridian (123° W longitude) is at easting 500,000, so the point is on a grid line that intersects the equator 65,000 meters east of the central meridian. On the grid line, the distance north from the equator to the point is 4,151,000 meters. In some contexts, the coordinates are shown to the nearest kilometer, i.e. in this case as 10 565 4151N A point in the Southern Hemisphere symmetric in the equator to the point above would have northing component, in meters, 10,000,000 - 4151000, i.e 5849000. So the UTM designation for the point is 10 565000 5849000S or, using kilometers, 10 565 5849S Links Links for Global Positioning System, UTM Reading UTM coordinates from a USGS map   TOP   Discussion Exercises Describe the variation of the relationship between latitude and east-west distance between longitude lines.   Determine equivalent UTM representations for each of the following lat-lon specifications:   3° W 22°30' N   3° E 22°30' S   122°20' W 0° N   Determine equivalent lat-lon representations for each of the following UTM specifications:   5 500 5000N   20 500 2750S   60 600 0N Note: Exercises 2 and 3 above, while illustrating the concepts, are for rather special cases. In general, conversion between UTM and lat-lon is more complicated than is the case for these exercises.