Geographic Coordinate Systems and Projections

Nick Eubank

September 2, 2015

Two of the most challenging concepts in GIS are geographic coordinate systems, projections, and therelationship between the two. This handout provides a brief overview of these two concepts, how theyrelate to one another, and how they are operationalized in ArcGIS and other GIS programs.

1 Geographic Coordinate Systems

Surprisingly, when two people provide a latitude and longitude of a location, they may not always be thesame. The reason for this is the location of a real-world point in terms of latitude and longitude dependson the model of the earth someone is using to computer latitudes and longitudes, and these models varyin their degree of simplification. Some assume that the earth is a perfect sphere; some assume it’s aalmost a sphere, but is a little fat in the middle (an ellipsoid); and some try to capture every hill andvalley on the earth.

Geographic coordinate system is the name for this model of the Earth. You can think of the differencesbetween geographic coordinate systems as being analogous to differences in globes you’ve seen in yourlife – some are perfect balls, while others are spheres with elevations, while others capture the fullweirdness of the earth’s shape.

Different Geographic Coordinate Systems

Smooth sphere Sphere with elevations Satellite-based model of earth1

So when you see “Geographic Coordinate System”, think “which globe is this?”.

There are two important things to keep in mind about Geographic Coordinate Systems:

1. For any given dataset, there is always a correct geographic coordinate system! The data youget was created using a model of the Earth – the correct geographic coordinate system is the oneused to create the data.

1Note that elevation differences in this figure are exaggerated for visualization.

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2. ArcGIS calls these models of the Earth “Geographic Coordinate Systems”, but in other settingsyou may find the model characterized by two different parameters – an “ellps” and a “datum”.What this mean is not important, just be aware that a “Geographic Coordinate System” in ArcGISis the same as this pair of parameters in other contexts.2

2 Projections

The Earth is round, but our computer screens are not. As a result, before working with spatial data, wehave to find a way of taking points on a three-dimensional surface (the Earth) and projecting them ontoa two-dimensional surface (our screens).3 A “Map Projection” is a specific way of smooshing points onEarth onto a two-dimensional surface.

The thing to remember about projections is that all projections are distortions, and unlike GeographicCoordinate Systems, there is no such thing as the “correct” projection – different projections justdistort things in different ways.4 In particular, no projection can ever preserve all of the following prop-erties, so you have to pick a projection that strikes the balance between the various properties you careabout most:

• Shape5

• Area• Distances between points• Directions

A few examples of projections are presented in Figure 1 below, along with a little commentary fromXKCD.

3 Geographic Coordinate Systems & Projections

Working with spatial data requires both a Geographic Coordinate System (so you know where yourpoints are on Earth) and a Projection (a way of putting points in 2 dimensions). Full stop. Both. Always.

ArcGIS, however, can make this very confusing in a couple ways:

• In ArcGIS, it is possible to select a “Geographic Coordinate System” and not a “Projected Coordi-nate System” and work with data. This creates the illusion that projections are not always required,but what Arc is actually doing is using latitudes and longitudes as x-y coordinates, which is es-sentially a Plate Carree projection. In other words, if you only select a “Geographic CoordinateSystem”, you are implicitly choosing a projection.• A “Projected Coordinate System” in Arc includes a geographic coordinate system. For example,

if you pick a “UTM” projection for a shapefile, when you look at the shapefile’s information youwill see that the “Geographic Coordinate System” has been set to “WGS84”.

2For the interested party: the “ellps” defines the perfect geometric shape that is used as a baseline – usually either a perfectsphere or an ellipsoid that’s like a sphere but a little fatter around the equator – and the “datum” defines the deviations from thisperfect shape (like a mountain or valley) at each point.

3A careful reader may ask why this is necessary – after all, computers can work with 3-D models, why not do everythingin three dimensions? The answer is that (a) three dimensions is much harder computationally, and (b) some properties aren’twell defined in three dimensions. For example, consider the distance between Sydney, Australia and San Francisco – in threedimensions, the shortest distance is actually right through the middle of the Earth. But of course that’s not what we want– we want the distance along the surface of the Earth, which means we’re basically back to working on a surface, which isfundamentally two dimensional.

4OK, so some projections are more “right” than others – you wouldn’t want to use a projection designed to minimizedistortions when mapping the United States to project data from Indonesia. But you get the idea.

5Or more specifically, the angle at which lines intersect.

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Figure 1:

What's that? You think I don't like the Peters map because I'm uncomfortable with having my cultural assumptions challenged? Are you sure you're not… ::puts on sunglasses:: … projecting? http://xkcd.com/977/ - http://bit.ly/explainxkcd-977

4 Recap

1. Geographic coordinate systems are like globes.2. Projections convert globes to flat surfaces.3. There is always an objectively correct geographic coordinate system.4. There is never an objectively correct projection.5. You always need both.

• If it seems like you’re working with spatial data and only have one, the other has been setwithout your knowledge.

6. What ArcGIS calls a “Geographic Coordinate Systems” corresponds to a pair of parameters insome other systems (like R) – “ellps” and “datum”.

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