# 2.3: Datums, Coordinate Systems, and Map Projections

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All map users and viewers have certain expectations about what is contained on a map. Such expectations are formed and learned from previous experience by working with maps. However, it is essential to note that such expectations also change with increased exposure to maps. Understanding and meeting the expectations of map viewers is a challenging but necessary task because such expectations provide a starting point for creating any map.

The central purpose is to provide relevant and valuable information to the map user. For a map to be of value, it must convey information effectively and efficiently. Mapping conventions facilitate the delivery of information in such a manner by recognizing and managing the expectations of map users. Mapping or cartographic conventions refer to the accepted rules, norms, and practices behind the making of maps. For example, one of the most recognized mapping conventions is that “north is up” on most maps. Though this may not always be the case, many map users expect the north to be oriented or coincide with the top edge of a map or viewing device like a computer monitor.

Several other formal and informal mapping conventions and characteristics can be identified, many of which are taken for granted. The essential cartographic considerations are map scale, coordinate systems, and map projections. Map scale is concerned with reducing geographical features of interest to manageable proportions. Coordinate systems help us define the positions of features on the earth’s surface. Moreover, map projections are concerned with moving from the three-dimensional world to the two dimensions of a flat map or display.

# Map Scale

One of the most significant challenges behind mapping the world and its resident features, patterns, and processes is reducing it to a manageable size. What exactly is meant by “manageable” is open to discussion and depends on the purpose and needs of the map at hand. Nonetheless, all maps reduce or shrink the world and its geographic features of interest by some factor. Map scale refers to the factor of reduction of the world so it fits on a map.

Map scale can be represented by text, a graphic, or some combination of the two. For example, it is common to see “one inch represents one kilometer” or something similar written on a map to give map users an idea of its scale. Map scale can also be portrayed graphically with a scale bar. Scale bars are usually used on reference maps and allow map users to approximate distances between locations and features on a map and get an overall idea of the map’s scale.

The representative fraction (RF) describes scale as a simple ratio. The numerator, which is always set to one (i.e., 1), denotes map distance, and the denominator denotes ground or “real-world” distance. One of the benefits of using a representative fraction to describe scale is unit neutral. In other words, any unit of measure can be used to interpret the map scale. For example, consider a map with an RF of 1:10,000. This means that one unit on the map represents 10,000 units on the ground. Such units could be inches, centimeters, or even pencil lengths; it does not matter.

Map scales can also be described as “small” or “large.” Such descriptions are usually made about representative fractions and the amount of detail represented on a map. For instance, a map with an RF of 1:1,000 is considered a large-scale map when compared to a map with an RF of 1:1,000,000 (i.e., 1:1,000 > 1:1,000,000). Furthermore, while the large-scale map shows more detail and less area, the small-scale map shows more area but less detail. Determining the thresholds for small- or large-scale maps is a judgment call.

All maps possess a scale, whether it is formally expressed or not. Though some say that online maps and GIS are “scaleless” because we can zoom in and out at will, it is more accurate to say that GIS and related mapping technology are multiscale. Therefore, understanding map scale and its overall impact on how the earth and its features are represented is critical for map-making and GIS.

# Coordinate Systems

Just as all maps have a map scale, all maps have locations, too. Coordinate systems are frameworks that are used to define unique positions. For instance, in geometry, we use x (horizontal) and y (vertical) coordinates to define points on a two-dimensional plane. The coordinate system used to define locations on the three-dimensional earth is the geographic coordinate system (GCS), based on a sphere or spheroid. A spheroid (a.k.a. ellipsoid) is simply a slightly wider sphere than it is tall and approximates the actual shape of the earth more closely. Spheres are commonly used as models of the earth for simplicity.

The unit of measure in the GCS is degrees, and their respective latitude and longitude define locations within the GCS. Latitude is measured relative to the equator at zero degrees, with a maximum of ninety degrees north at the North Pole or ninety degrees south. Longitude is measured relative to the prime meridian at zero degrees, with a maximum of 180 degrees west or 180 degrees east.

Note that latitude and longitude can be expressed in degrees-minutes-seconds (DMS) or decimal degrees (DD). When using decimal degrees, latitudes above the equator and longitudes east of the prime meridian are positive, and latitudes below the equator and longitudes west of the prime meridian are negative (see the following table for examples).

Converting from DMS to DD is a straightforward exercise. For example, since there are sixty minutes in one degree, we can convert 118° 15 minutes to 118.25 (118 + 15/60). An online search of the term “coordinate conversion” will return several coordinate conversion tools.

When we want to map things like mountains, rivers, streets, and buildings, we need to define how the lines of latitude and longitude will be oriented and positioned on the sphere. A datum serves this purpose and specifies precisely the orientation and origins of the lines of latitude and longitude relative to the center of the earth or spheroid.

Depending on the need, situation, and location, there are several datums to choose from. For instance, local datums try to match the spheroid closely to the earth’s surface in a local area and return accurate local coordinates. A typical local datum used in the United States is NAD83 (i.e., North American Datum of 1983). For locations in the United States and Canada, NAD83 returns relatively accurate positions, but positional accuracy deteriorates when outside of North America.

The global WGS84 datum (i.e., World Geodetic System of 1984) uses the center of the earth as the origin of the GCS and is used for defining locations across the globe. Because the datum uses the earth’s center as its origin, locational measurements tend to be more consistent regardless of where they are obtained. However, they may be less accurate than those returned by a local datum. Note that switching between datums will alter the coordinates (i.e., latitude and longitude) for all locations of interest.

# Map Projections

The earth is not flat or round but has a spherical shape called a spheroid. A globe is an excellent representation of the three-dimensional, spheroid earth. However, one of the problems with globes is that they are not very portable (i.e., you cannot fold a globe and put it in your pocket), and their small scale makes them of limited practical use (i.e., geographic detail is sacrificed). To overcome these issues, it is necessary to transform the three-dimensional shape of the earth into a two-dimensional surface like a flat piece of paper, computer screen, or mobile device display to obtain more helpful map forms and map scales. Enter the map projection.

Map projections refer to the methods and procedures used to transform the spherical three-dimensional earth into two-dimensional planar surfaces. Specifically, map projections are mathematical formulas used to translate latitude and longitude on the earth’s surface to x and y coordinates on a plane. Since there is an infinite number of ways this translation can be performed, there is an infinite number of map projections.

To illustrate the concept of a map projection, imagine that we place a light bulb in the center of a translucent globe. On the globe are outlines of the continents and the lines of longitude and latitude called the graticule. When we turn the light bulb on, the outline of the continents and the graticule will be “projected” as shadows on the wall, ceiling, or any other nearby surface. This is what is meant by map “projection.”

Within the realm of maps and mapping, there are three surfaces used for map projections (i.e., surfaces on which we project the shadows of the graticule). These surfaces are the plane, the cylinder, and the cone. Referring again to the previous example of a light bulb in the center of a globe, note that we can situate each surface in many ways during the projection process. For example, surfaces can be tangential to the globe along the equator or poles, and they can pass through or intersect the surface and be oriented at any number of angles.

Naming conventions for many map projections include the surface and its orientation. For example, as the name suggests, “planar” projections use the plane, “cylindrical” projections use cylinders, and “conic” projections use the cone. For cylindrical projections, the “normal” or “standard” aspect refers to when the cylinder is tangential to the equator (i.e., the axis of the cylinder is oriented north-south). When the cylinder’s axis is perfectly oriented east-west, the aspect is called “transverse,” All other orientations are called “oblique.” Regardless of the orientation or the surface on which a projection is based, several distortions will be introduced that will influence the choice of map projection.

When moving from the three-dimensional surface of the earth to a two-dimensional plane, distortions are not only introduced but also inevitable. For example, map projections introduce distance, angles, and area distortions. Depending on the map’s purpose, trade-offs will need to be made concerning such distortions.

Map projections that accurately represent distances are referred to as equidistant projections. Note that distances are only correct in one direction, usually running north-south, and are not correct everywhere across the map. Equidistant maps are frequently used for small-scale maps that cover large areas because they do an excellent job of preserving the shape of geographic features such as continents.

Maps that represent angles between locations, also referred to as bearings are called conformal. Conformal map projections maintain a bearing or head when traveling great distances. However, the cost of preserving bearings is that areas tend to be quite distorted in conformal map projections. Though shapes are preserved over small areas, areas become wildly distorted at small scales. The Mercator projection is an example of a conformal projection and is famous for distorting Greenland.

As the name indicates, equal area or equivalent projections preserve the area’s quality. Such projections are of particular use when accurate measures or comparisons of geographical distributions are necessary (e.g., deforestation, wetlands). However, to maintain accurate proportions on the earth’s surface, features sometimes become compressed or stretched depending on the orientation of the projection. Moreover, such projections distort distances as well as angular relationships.

As noted earlier, there is theoretically an infinite number of map projections to choose from. One of the key considerations behind the choice of map projection is to reduce the amount of distortion. The geographical object being mapped and the respective scale at which the map will be constructed are essential factors. For instance, maps of the North and South Poles usually use planar or azimuthal projections, and conical projections are best suited for the middle latitude areas of the earth. Features that stretch east-west, such as the country of Russia, are represented well with the standard cylindrical projection. In contrast, countries-oriented north-south (e.g., Chile, Norway) are better represented using a transverse projection.

If a map projection is unknown, sometimes it can be identified by working backward and carefully examining the nature and orientation of the graticule (i.e., grid of latitude and longitude) and the varying degrees of distortion. There are trade-offs made concerning distortion on every map. There are no fixed rules as to which distortions are more preferred over others. Therefore, the selection of map projection depends on the map’s purpose.

Within the scope of GIS, knowing and understanding map projections are critical. For instance, to perform an overlay analysis like the earlier one, all map layers need to be in the same projection. If they are not, geographical features will not be appropriately aligned, and any analyses performed will be inaccurate. Most GIS include functions to assist in the identification of map projections, as well as to transform between projections to synchronize spatial data. Awareness of the potential pitfalls surrounding map projections is essential despite the technology capabilities.

This page titled 2.3: Datums, Coordinate Systems, and Map Projections is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Adam Dastrup.