L2.03: Locating Things on the Earth

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I begin this lesson with a brief introduction of the concepts of locating points on the Earth, scale, and the representation of geographic features in a digital form. With these fundamentals, the lesson then discusses GEOINT data.

Coordinate Systems

Essential to creating geospatial data is locating something on the Earth. The following discussion of coordinate systems was drawn from the Penn State course, GEOG 482, The Nature of Geographic Information.

A Cartesian coordinate system
Figure 2.1: A Cartesian coordinate system.
Source: Bacastow

As you might know, locations on the Earth's surface are measured and represented in terms of coordinates. A coordinate is a set of two or more numbers that specifies the position of a point, line, or other geometric figure in relation to some reference system. The simplest system of this kind is a Cartesian coordinate system (named for the 17th century mathematician and philosopher René Descartes). A Cartesian coordinate system is simply a grid formed by juxtaposing two measurement scales—one horizontal (x) and one vertical (y). The point at which both x and y equal zero is called the origin of the coordinate system. In Figure 2.1, above, the origin (0,0) is located at the center of the grid. All other positions are specified relative to the origin. The coordinate of the upper right-hand corner of the grid is (6,3). The lower left-hand corner is (-6,-3).

Cartesian and other two-dimensional (plane) coordinate systems are handy due to their simplicity. For obvious reasons, they are not perfectly suited to specifying geospatial positions, however. The geographic coordinate system is designed specifically to define positions on the Earth's roughly-spherical surface. Instead of the two linear measurement scales, x and y, the geographic coordinate system juxtaposes two curved measurement scales termed longitude and latitude. This is a geographic coordinate system.

Longitude specifies positions east and west as the angle between the prime meridian and a second meridian that intersects the point of interest. Longitude ranges from +180° (or 180° E) to -180° (or 180° W). 180° East and West longitude together form the International Date Line.

Latitude specifies positions north and south in terms of the angle subtended at the center of the Earth between two imaginary lines, one that intersects the equator and another that intersects the point of interest. Latitude ranges from +90° (or 90° N) at the North pole to -90° (or 90° S) at the South pole. A line of latitude is also known as a parallel.

At higher latitudes, the length of parallels decreases to zero at 90° North and South. Lines of longitude are not parallel, but converge toward the poles. Thus, while a degree of longitude at the equator is equal to a distance of about 111 kilometers, that distance decreases to zero at the poles.

Geodetic coordinate system
Figure 2.2: The geographic (or "geodetic") coordinate system.
Source: Bacastow
Geographic coordinate system
Figure 2.3: The geographic coordinate system.
Source: Bacastow

Try This!

Geographic Coordinate System Practice Application

Nearly everyone learned latitude and longitude as a kid. But how well do you understand the geographic coordinate system, really? My experience is that while everyone who enters this class has heard of latitude and longitude, only about half can point to the location on a map that is specified by a pair of geographic coordinates. The Flash application linked below lets you test your knowledge. The application asks you to click locations on a globe as specified by randomly generated geographic coordinates.

You will notice that the application lets you choose between "easy problems" and "hard problems." Easy problems are those in which latitude and longitude coordinates are specified in 30° increments. Since the resolution of the graticule (the geographic coordinate system grid) used in the application is also 30°, the solution to every "easy" problem occurs at the intersection of a parallel and a meridian. The "easy" problems are good warm-ups.

"Hard" problems specify coordinates in 1° increments. You have to interpolate positions between grid lines. You can consider yourself to have a good working knowledge of the geographic coordinate system if you can solve at least six "hard" problems consecutively and on the first click.

Click here to download and launch the Geographic Coordinate System practice application (5.7 Mb). (If the globe doesn't appear after the Flash application has loaded, right-click and select "Play" from the pop-up menu.)

Screenshot of the Geographic Coordinate System practice application
Figure 2.4: Geographic Coordinate Practice Tool.
Note: You will need to have the Adobe Flash player installed in order to complete this exercise. If you do not already have it, you can download the Flash Player for free at the adobe website.
 

Datums

We said that all of our positions on the Earth are specified relative to the origin. So, how is the origin established? A geodetic datum is a spatial reference system that describes the shape and size of the Earth and establishes an origin for coordinate systems. Two main types of datums include horizontal datums and vertical datums. Horizontal datums are used to describe what we typically think of as x and y coordinates. Vertical datums describe position in the vertical direction and are often based on height above sea level.

People have created hundreds of datums that are in use around the world today. The main reason that people have developed different datums for different places is so that they can choose an ellipsoid that best matches the shape of the Earth at an area of local interest (usually a country). There are two main types of datums: local datums and geocentric datums. In local datums, a point of the ellipsoid is matched to a point on the Earth’s surface (e.g., the North American Datum of 1927 intersects the surface of the Earth at Meades Ranch in Kansas, while the Australian Geodetic Datum intersects with the Johnston Geodetic Station in the Northern Territory). Geocentric datums, on the other hand, are based on the Earth’s center of mass. Our knowledge of where that center of mass is located has improved with modern satellite data. Many countries are now shifting to geocentric datums because GPS measurements are based on a geocentric datum. This switch avoids the need for transforming GPS-collected data from one coordinate system to another. It is important to understand which datum was used when your data were created, because the position of features may be different depending on which datum was used. In some cases, there may be a positional discrepancy of up to one kilometer! These shifts are especially important in large-scale mapping applications, as these discrepancies will be much larger than any projection-induced error.