The art and science of map making is not standing still; it has enjoyed a long tradition of innovation and incremental improvement. With this comes a raft of ideas, best practices, and terminology, some of which can occasionally be confusing. I was reminded of this recently by an interesting thread on the gislist mailing list (sign-up required) which discussed some of the words around modeling and mapping our world: geoid, ellipsoid, datum, coordinate system, projection, etc. Without going into the same detail as the excellent discussion there, I’d like to give you a whirlwind tour of what it takes to turn real-world locations into coordinates and then into maps.
The high level goal – starting with locations and ending up with coordinates you can plot on a map or visa-versa – is addressed with a coordinate system (also called a coordinate reference system). A coordinate system along with coordinates is enough to uniquely identify a spot on earth. For example, Safe Software is near (510359E, 5442815N) in the UTM10N/WGS84 coordinate system. There’s a lot packed into this concept; let’s look closer:
First Concept: Modeling the Earth
If you start with the assumption that the world is flat and try to make maps over a large area, it doesn’t work. The curvature of the earth gets in the way and prevents the measured angles and lengths from adding up. The typical strategy is to approximate the earth as an ellipsoid (flattened sphere) that fits your data well (be it a country, continent, or the whole world). In my example above, the WGS84 ellipsoid is 6,378,137m “wide” and 6,356,752.3142m “tall”. A more accurate strategy is to use the geoid, which is a smooth surface over the earth that roughly corresponds to the idea of “sea level”.
Second Concept: Tying the Model to the Earth
The next challenge is to associate coordinates (typically latitude, longitude, and height above the chosen ellipsoid) with real locations. There are lots of ways to do that (e.g. by consulting a GPS receiver or looking for nearby survey monuments). A datum extends a model of the earth with whatever else is needed to do this. Again going back to the example, the WGS84 datum is defined by the locations of US Department of Defense GPS stations located around the world, and is typically what GPS devices report by default.
Third Concept: Flattening it Out
The last (optional) concept is to flatten the map out. Again, there are many choices (called projections) that allow you to map between e.g. lat/long in degrees and northings/eastings in meters. Flattening the map adds distortion, but you can choose projections which preserve important properties to a greater or lesser extent, including area, distance, direction, shape, and scale. Our example uses the UTM10N projection, part of the family of oft-used “Universal Transverse Mercator” projections.
If you’re interested in more detail, the OGC and ISO standards bodies have done a good job of summarizing these concepts in Spatial Referencing by Coordinates (see especially Section 6).