Word of the Month - Geographic Coordinate System

For the December installment of Word of the Month, we will tackle one of the cornerstones of modern mapping, the Geographic Coordinate System. I'm sure all of you can appreciate the challenges of accurately depicting a round world on a flat paper map or computer screen; and it is the geographic coordinate system that allows us to make this transition.

While the geographic coordinate system may seem like a rather simple concept, the deeper you dig, the more complexities you will uncover. As such, this article is meant to provide a high-level overview of a complex topic written in easy-to-digest terminology. By no means do we purport that this summary covers every nuance of the concept; it will however give you a leg up on many other geospatial users and will also serve as a starting point for your own deeper analysis of the topic.

With that said, the basic point of a geographic coordinate system is to provide a data user with an accurate X,Y coordinate (and sometimes Z, or elevation above sea level) no matter where the point is located on our planet. Most people are familiar with X,Y coordinates that are given in decimal degrees or degrees minutes second for your Longitude and Latitude (e.g. -105.0, 39.7 or 39 degrees 42' 0" N, 105 degrees 0' 0" W for Denver, CO); but there are many other ways to communicate the same information using different coordinate systems. As such, a geographic coordinate system establishes a language for people to talk about the same location in a standardized manner as well as a way to translate between different languages (i.e. between different coordinate systems).

Rene Descartes (1596-1650) introduced geographic coordinate systems based on orthogonal (right angle) coordinates. Traditional Latitude and Longitude is an example of an orthogonal coordinate system as they form right angles with each other anywhere on the surface of our planet. We often call these Cartesian coordinate systems. They can be contrasted with polar coordinate systems which are based on angles and distance from a fixed baseline and centerpoint origin. We will not cover polar systems in this article.

Every geographic coordinate system as four basic components that are crucial in determining the X,Y coordinate of your point accurately. Here is a summary of these four components:

• Reference Datum - this is a known and constant surface which can be used to describe the location of unknown points. One common way to define a datum is through a series of known control points laid across the surface of the planet, for instance as is done with NAD27 and NAD83 (NAD stands for North American Datum). Locations of unknown points are described by their geometric relationships to the known surface.
• Geiod - this can be described as the modeled surface of our planet whereby the force of gravity would be perpendicular to every surface of our planet. You can imagine it as if you could sail across the surface of our planet (and through mountains) without feeling any undulations, it would be a completely smooth ride. This does not mean the geiod is flat; it does have peaks and valleys but it varies less than 200 meters in elevation across the entire planet. Simply stated, the geiod is a reference point for elevation.
• Reference Ellipsoid - this is a mathematical model of a very generalized shape of the planet. Different geographic coordinate systems will use different shapes for the ellipsoid but a common shape is one with a slightly flat and fattened center of the globe due to the rotational force of the Earth.
• Projection - this is the mathematical function that is used to fit a round world on a flat surface. The projection utilizes the datum, geiod and ellipsoid to come up with a final answer. The ultimate goal of a projection is minimize the amount of distortion that takes place during the transformation. Depending on the scale, location and use of your dataset, different projections may work better than others for you. For instance, an Albers Equal-Area Conic Projection will maintain area along the same longitude but it will distort shape; whereas Equirectangular Projection (this is the common flat square map of the world we are very familiar with) distorts both area and shape but maintains equally spaced and perpendicular latitude and longitude meridians.

When these four components are taken together, they allow us to accurately determine our X,Y coordinate on the planet as well as translate this coordinate among the other Cartesian coordinate systems.

Tips on Working with Geographic Coordinate Systems

A Word of the Month would not be complete without several tips for working with geographic coordinate systems. First, eMap recommends that all raster and vector products you work with are defined with the same coordinate system. In ArcGIS, a coordinate system is defined by a projection and datum. If you cannot match up the coordinate systems of all your datasets, not to worry as most geospatial packages, such as ArcGIS, have on-the-fly reprojection abilities so datasets should match up even if they are in a different projection-datum combination.

Second, we always recommend clients work with raster and vector datasets in Universal Transverse Mercator (UTM) with a WGS84 datum. UTM WGS84 is widely recognized as the most accurate projection-datum combination for raster and vector datasets (except perhaps in the polar regions) given its consideration of regional zone numbers in the mathematical projection process for reduced distortion during transformation (see JPEG below); and for the exactness of the WGS84 datum. Furthermore, if you plan on ordering satellite imagery from GeoEye (i.e. IKONOS and/or GeoEye-1 data) and then utilizing the RPC files for orthorectification, you must order the data in UTM WGS84 to have valid RPC files delivered.

A final word to the wise is related to working with projections and datum inside ArcGIS. An often missed fact is that any shapefile must have a PRJ file for ArcGIS to recognize its native projection and datum. If this is not present, the file will have an undefined coordinate system. Here are three useful tips for working with shapefiles and coordinate systems in ArcGIS

• You can easily determine if your shapefile has an undefined coordinate system by checking on the "Properties > Source" tab
• If you have a shapefile that is undefined, you can define the projection by using the toolbox "Data Management Tools > Projections and Transformations > Define Projection" option.
• If you need to reproject a shapefile from a defined coordinate system to a new one, then you want to use the toolbox "Data Management Tools > Projections and Transformations > Feature > Project" option.

The Project and Define Projection options are commonly confused so always be mindful of how you are working with your data when moving between various coordinate systems.

A numbered UTM grid overlain on a map of the world.

Brock Adam McCarty
Vice President
Map Wizard