Georeferencing, Coordinates
and Projections – EB/ES/GE 351

James S. Aber

What is a map?

A map is a graphical representation or scale model of all or part of the Earth's surface or the surface of any other celestial body or spatial phenomenon. It is a means for conveying geographic information, namely selected physical, biological, and cultural phenomena. Maps are a universal medium for communication, easily understood and appreciated by most people, regardless of language or culture.

Incorporated in a map is the understanding that it is a “snapshot” of an idea, a single picture, a selection of concepts from a constantly changing database of geographic information (Merriam 1996). GIS represents a major shift in the cartographic paradigm. In traditional (paper) cartography, the map was both the database and the display of geographic information. For GIS, however, data storage, analysis, and display are physically and conceptually separate aspects of handling geographic information.

Maps are usually made flat according to a projection of the curved surface onto the map plane. Globes are maps displayed on a sphere, which approximates the true shape of the Earth. Georeferencing refers to the manner by which locations in raster and vector GIS files are related to actual earth-surface positions (IDRISI manual).

Latitude and longitude

The coordinates for any point on the Earth's surface can be specified by latitude and longitude, the most commonly used global reference system. In GIS useage, latitude and longitude are treated as an x-y grid. Northern latitudes are given positive (x) values, and southern latitudes are negative. Longitude (y) is counted in positive direction eastward (0-360°), or east longitude may be positive while west longitude is negative.

Latitude-longitude grid centered on the
equator (W-E) and prime meridian (N-S).
Image obtained from NASA/JPL.

The ground spacing of latitude lines is nearly constant at about 111 km per degree. However, longitude lines converge toward the poles, so spacing of longitude varies according to latitude. Each degree of latitude or longitude is divided into 60 minutes, and each minute is subdivided into 60 seconds. The standard USGS 1:24,000 scale topographic map covers an area defined by 7½ minutes in latitude and longitude. The Topeka, Kansas quadrangle, for example, is bounded by north latitudes 39° and 39°7'30", and by west longitudes 95°37'30" and 95°45'.

Minutes and seconds are awkward units for GIS applications, so decimal degrees are employed instead. One decimal minute is 1/60, or 0.016667°; one decimal second is 1/3600, or 0.00027778°. North latitudes and east longitudes are given positive values, whereas south latitudes and west longitudes are negative. For example, the boundaries of the Topeka quadrangle become, in decimal degrees: 39.0°, 39.125°, -95.625°, and -95.75°.

Map projections

Maps of the Earth are two-dimensional graphical displays of a curved surface. Any means for flattening the curved surface of the Earth onto a map involve some kind of distortion of angles, sizes, or shapes of the features shown on the map. Maps may be geometrically projected onto three kinds of developable surfaces: cylinder, cone, and plane. These surfaces can be transformed to a plane without further distortion. A great many map projections have been devised for various purposes. Two basic categories of map projections are:

  1. Equal-area — Maps on which area (size) is conserved, so that a given object would appear as the same size no matter where it is located on the map. Angles and shapes of objects and map scale are usually distorted over most of the map, but some parts of the map may display these features correctly.

  2. Conformal — Maps on which shape is conserved, so that a given object would appear as the same shape no matter where it is located on the map. Relative angles are correct at any point on the map, so that meridians and parallels intersect at right angles. Areas of objects are distorted over most of the map, although area may be correct along certain lines. Conformal projections are widely used.

Mercator projection and UTM grid

Mercator projection – cylindrical and conformal. Most famous of all map projections, first developed in 1569 by Gerardus Mercator of Flanders. Meridians are equally spaced and parallel; latitudes are unequally spaced and parallel. All rhumb lines (lines of constant angle or bearing) are straight lines. Image obtained from NASA/JPL.

This map is used primarily for navigation and for display of relatively small regions of the globe. High latitudes are greatly distorted in area; poles cannot be shown. For these reasons the Mercator projection is not suitable for showing the entire world. Prior to global positioning system (GPS), navigation on the high seas as well as aeronautical navigation were difficult tasks accomplished with Mercator maps, magnetic compass, star sightings, and landmarks. Often "dead reckoning" was involved based on a best guess of travel direction and distance.

See early navigation.

The Universal Transverse Mercator (UTM) grid system is one of the most important map grids in common use today. The UTM is based on a transverse Mercator projection—see Shawnee County map (on campus). This projection and grid were adopted by the U.S. Army for large-scale military maps of the entire world. Between 84°N and 80°S latitudes the Earth is divided into zones that are generally 6° wide in longitude. The bounding longitudes are evenly divisible by 6, and the zones are numbered from west to east beginning at longitude 180°.

Go to UTM Grid.

UTM zones are designated by letters from south to north, mostly at 8° intervals. Polar regions are shown on the Universal Polar Stereographic (UPS) projection. The location of any point is given in x and y coordinates in meters. UTM zone lines and meter grid tick marks are normally shown on all topographic and planimetric maps, although the map projection may not be transverse Mercator. As an example of the UTM grid, Topeka, Kansas is part of UTM zone 15S: 96-90°W, 32-40°N; the State Capitol building has coordinates of approximately: 268300mE and 4325350mN.

Other cylindrical projections

Plate Carrée projection – cylindrical, equidistant projection that is neither conformal nor equal area. The simplist of all projections to construct: all meridians and latitudes are equally spaced, straight lines that intersect at right angles. Meridians are half the length of the equator; scale is true along the equator and meridians. Image obtained from NASA/JPL.

This projection is used for simple outline maps of regions or the world or for index maps. This projection may have been devised by Eratosthenes (275?-195? B.C.); Marinus of Tyre is also credited with its invention around A.D. 100. It was widely used during the 15th and 16th centuries. This projection is ideally suited for display of GIS data in a latitude-longitude raster grid, although it has major distortions at high-latitudes.

Mollweide projection – equal area, pseudocylindrical. A good map for depicting the whole world with moderate distortion. Image obtained from NASA/JPL.

Conic and pseudoconic projections

Albers equal-area conic projection – Compare spacing of latitude lines between this projection and the next one. Both are widely utilized for mapping (national atlases) in Canada and the United States. Image obtained from NASA/JPL.
Lambert conformal conic projection – Image obtained from NASA/JPL.
Bonne projection – a heart-shaped pseudoconic projection. The central portion of this projection was utilized by Ptolemy for his "world map" during the Roman Era. The projection was expanded for the whole Earth and became quite popular for global maps during the 16-17th centuries. A novelty map today–see stamp below. Image obtained from NASA/JPL.

Polyconic projection – neither conformal nor equal-area. Central meridian is straight line; all others are complex curves, equally spaced along the equator. Equator is a straight line; other latitudes are nonconcentric circular arcs spaced at true distance along the central meridian. Scale is true along the central meridian and along each latitude. This projection was widely used for topographic and coastal mapping of the United States prior to the 1950s. It is still utilized for many large-scale topographic maps in the U.S.–see Topeka quadrangle. It was devised about 1820 by F.R. Hassler, first Director of U.S. Survey of the Coast (later U.S. Coast and Geodetic Survey).

Planar (azimuthal) projections

Orthographic projection – azimuthal and perspective, but neither conformal nor equal-area. Produces a map that resembles a globe. Excellent means to display a single continent, ocean, or hemisphere; also used to simulate the appearance of the Earth from space. Image obtained from NASA/JPL.
Stereographic projection – azimuthal and conformal. In polar aspect, all meridians are straight, radial lines (like spokes of a wheel) and latitudes are concentric circles–see title stamp at top. The basis for the Universal Polar Stereographic (UPS) grid for use in high-latitude, polar areas of the world. Image obtained from NASA/JPL.

PLSS

In the central and western United States, western Canada, and some other countries, land survey is based on the township-and-range system, also known in the U.S. as the Public Land Survey System (PLSS). Each township measures 6 miles by 6 miles and is divided into 36 square-mile sections. Each section (640 acres) may be subdivided into quarter sections (160 acres), quarter-quarter sections (40 acres), and so on. PLSS is the basis for land ownership, from large ranches to residential subdivisions as well as federal and state lands. Knowledge of the PLSS is essential for all types of professional resource and environmental assessment and evaluation.

Further explanation, see PLSS Part I and Part II
From the North Dakota Geological Survey.


Having emphasized the advantage of maps and geospatial analysis, it is wise to note some cautions. All maps are estimations, generalizations, and interpretations of true geographic conditions; no map can depict all physical, biological, and cultural features for even the smallest area. A map may display only a few selected features, which are portrayed usually in highly symbolic styles according to some kind of classification scheme. Furthermore, all maps and GIS datasets are products of human endeavor, which may lead to unwitting errors, misrepresentation, bias, or outright fraud. In spite of these limitations, maps have proven to be remarkably adaptable, and geospatial analysis is an essential part of modern society.

Reference

U.S. National Atlas—map projections
Topographic Maps for the Nation—US Topo
USGS topographic map symbols

Return to course schedule.
EB/ES/GE 351 © J.S. Aber (2014).