Learning Objectives

After completing this lesson, you’ll be able to:

• Define a geographic coordinate system.
• Define a projected coordinate system.
• Explain the difference between geographic and projected coordinate systems.
• Understand why local coordinate systems exist.

Introduction

Thinking back to my classroom days, when I spun a globe to determine my future, I realize I could have played this same game with similar results with the flat hanging map on the chalkboard. Could my friends and I not have chosen to spin ourselves dizzy, then stumble-walked towards the map and pointed out a location that way?

Yes, we could have, if our teacher hadn’t rolled his eyes and called us disruptive, threatening to take away recess.

We would have been able to do this because a projected coordinate system had been utilized to translate the 3D reality of our world (aka. A globe that uses a geographic coordinate system) to a flat 2D depiction. Handy for human interaction and classroom mischief (or learning).

Geographic Coordinate Systems

Now that you know that a geographic coordinate system (GCS) comprises a datum, angular units, and a prime meridian, let’s see how it works. It’s a lot easier to understand if you look at a picture.

1. In this diagram, we start with an ellipsoid. This loosely represents the surface of the Earth.
2. We locate a centerpoint where the X-, Y-, and Z-axis cross.
3. We define a prime meridian, the vertical measure of 0 degrees. This can be in a different location in different coordinate systems.
4. We define Up, North, East, South, and West cardinal directions.
5. Now that orientations are set, you can see how the Earth is divided into quadrants. Moving away from the Equator and prime meridian gives you negative or positive values. These values are coordinates and can be used to locate anything on the Earth.

One of the most commonly used GCS is the WGS 1984 (World Geodetic System 1984). This system is commonly used for sharing global locations, particularly with GPS.

While the information gained from a GPS can be beneficial, solely relying on a geographic coordinate system won't solve all your coordinate system problems.

We’ve all seen and managed that “Location” setting on our mobile devices, which enables your phone to measure GPS coordinates. That’s great, but imagine just being given a string of numbers from a GPS and nothing else. You’d know exactly where you were, but how would you ever make it to dinner in rush hour traffic without all of those super-secret side street route options being revealed? That’s why Google and Apple Maps are ubiquitous these days for navigating.

Coordinate data becomes much more accessible and meaningful when it’s moved from a GCS to a Projected Coordinate System (PCS). Using a projection method, a PCS takes the coordinates identified in a GCS and tells us how to draw that information to a flat surface (like your phone screen). I know that I would be lost without projected coordinate systems in my life.

Projected Coordinate Systems

When it comes to a projected coordinate system (PCS), we first need to understand what a “projection” is.

There’s more than one way to peel an orange. You’ve got a lovely, spherical orange, just asking to be eaten. You peel off the skin and pop a slice into your mouth. Yum. Once wrapped around your orange, the orange peel can now lie flat on the table because of how you ripped through the peel. That first orange was so darn good you gotta have another one. Another orange peel lies flat on the table, with a different pattern of tears. Projection is the method by which we “peel” the Earth and lay it out flat.

A peeled orange. By Shunichi Kouroki, licensed CC-BY-2.0. 

However, regarding maps, we aren’t just “peeling and laying the Earth flat.” We’re trying to represent something spherical in 2D, such as a rectangle (or other shape), consistently without tears to break up the image. Many different projection methods are used because moving from 3D to 2D space will always result in distortion of some kind. Different projection algorithms are selected to preserve as many of the following qualities as possible to varying degrees, but note all four can never be preserved in 2D:

• Area – how accurate are the size of the landmasses compared to their reality?
• Shape – how accurate are the shapes of features compared to their reality?
• Distance – how accurate are the measurements between two points?
• Direction – how accurately are two locations portrayed relative to each other?

Check out how the Mercator projection works. To put everything on a flat, rectangular surface, countries closest to the poles see a distortion of the area, and they end up being displayed larger than they are as they are stretched to fill the rectangle space.

Take Greenland vs. Brazil for an extreme example of the Mercator projection. While Greenland appears to be larger than Brazil in the Mercator projection, in reality, Greenland's area is 2,166,086 km², and Brazil's is 8,515,767 km².

The Mercator projection has chosen to prioritize direction and conformality over area (it was initially designed for marine navigation to help ships sail using compass directions).  (Wikimedia, CC-BY-SA)

This screenshot was taken from The True Size , which allows you to experience how the Mercator projection prioritizes direction and conformality over area (it was originally designed for marine navigation to help ships sail using compass directions).

One additional key difference between a GCS and a PCS is that since a PCS is a flat, 2D representation of the Earth’s surface, it will use linear units to measure distances instead of angular units. Units like feet, meters, links, or chains are all commonly used with projected coordinate systems. Therefore, spatial analysis, e.g., measuring area or distance, should only be conducted with data using a projected coordinate system.

What About Local Coordinate Systems?

A local coordinate system optimizes for accuracy for a specific location. These are most often used by local governments, construction teams, and surveyors because the narrower the area a coordinate system needs to cover, the less distortion you need to account for globally when projecting.

This is why we have thousands of coordinate systems—they have been created and optimized to reduce distortion of the area, distance, shape, direction, or any combination of those within a certain location.

For example, Canada's federal government depends on NAD83 (North American Datum 1983), while the province of British Columbia, Canada, uses NAD 1983 BC Albers, which defines a projection method specific to the provincial boundaries.

This lesson was adapted from a post on the Safe Software blog.