Understanding Map Projections
By: Rajesh Sigdel
Tags: Mapping, Projection System, Maps, Geospatial, Data Visualization

Have you ever seen two maps of a place that looked alike but also different? Have you wondered which map is the correct visualization of the geographic data? In Figure 1, I illustrate this phenomenon using two side-by-side maps. Each map portrays the same data. However, map (b) is slightly elongated from East to West and compressed from North to South compared to map (a). The labels “Canada” clearly shows these differences. Which one is the correct representation of the United States? The answer is not simple.

In order to answer this question, you need to understand what coordinate systems and map projections are, and why they are important when visualizing geographic data.

Geographic Coordinate Systems

Figure 2: Latitude and Longitude of the Geographic Coordinate System. Source: Encyclopedia Britannica.

Location on the earth’s surface is defined by its coordinates. Coordinates are arranged using reference lines or curves which are referred to as coordinate systems. There are two different coordinate systems: Geographic Coordinate System and Projected Coordinate System.

The Geographic Coordinate System (GCS) defines the angular measurements on the Earth. It has two values: longitude and latitude. Longitude is an angular distance of a place (East or West) from the Prime Meridian. The latitude, on the other hand, represents the angular distance of a place (North or South) from the Equator. Together longitude and latitude uniquely describe points or places on the Earth.

Projected Coordinate Systems

When making a traditional cartographic visualization, the three-dimensional GCS needs to be projected and flattened into a two-dimensional surface, and this is where Projected Coordinate Systems come into play. Projected Coordinate Systems are also known as Cartesian Coordinate Systems (CGS). There are four properties to consider when converting from three to two dimensions: (1) shape, (2) area, (3) distance, and (4) direction. At least one of these properties will have to be compromised during the flattening process, since it is impossible to make a two-dimensional visualization that maintains all four properties.

There are three families of projection systems: cylindrical, conical, and planar. In a simplistic model, you can imagine a light bulb in the center of the Earth or globe (Figure 3). Then a cylinder, a cone, or a plane surface is placed around or on the globe. The shadow cast by the light bulb from each point of the globe on the surface is recorded. The surface is then cut and made flat. There are innumerable projection systems in use. Some projections like the Gall-Peter projection preserve areas, the Mercator projection preserves shapes, and the Robinson projection compromises between shape and area. Other projections, such as the State Plane Coordinate System, are designed to achieve minimal distortions in area and shape. The State Plane Coordinate System, however, can only be used for specific locations (i.e., a state or region), but if this system is used for other then the defined place, you can expect errors in your calculations. For expediency, I will discuss two of the most commonly used projection systems in the US: the Mercator projection and the State Plane Coordinate System.