Understanding Map Projections
Choosing the right projection when visualizing geospatial data
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
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.
The Mercator projection
There are several variations of Cartesian map projections. For example, instead of putting the cylinder vertically, we can also put it in a horizontal position. The most famous cylindrical projection is the Mercator projection, developed by the Flemish geographer Gerardus Mercator in 1569. Many online map providers such as Google, Bing, and Open Streets Maps uses a variant of Mercator projection called Web Mercator. Mercator preserves the shape and local direction, making it easy to use for navigation. The projection, however, distorts the area of the objects away from the Equator.
The farther you go from the Equator in a Mercator projection, the higher is the inflation of an area, giving the false impression that countries near the poles are bigger than they actually are. The True Size Of website provides visual information about how the sizes of countries closer to poles get exaggerated in a Mercator projection. For example, Greenland appears almost the size of Africa on the map, but in reality, Greenland is fourteen and half times smaller compared to Africa. The Mercator projection has been accused of being used to maintain European Hegemony during the colonial era, but we will leave that discussion for some other time. The projection is still widely used today, for example, in the COVID-19 dashboard by John Hopkin’s University of Medicine. If you use this projection, make sure to note that it distorts the size of the countries closer to the poles.
State Plane Coordinate System
The United States started building up a localized projection system, called the State Plane Coordinate System (SPCS), to provide a common reference system to cartographers. In SPCS, the United States is divided into 124 zones and each state may have one or more zones depending on its size. For example, let’s look into the State Plane Map of Michigan (Figure 5).
Michigan is divided into three zones. If you are calculating a parcel’s size or area in the Upper Peninsula of Michigan, the SPCS’s North Zone would help you achieve your goal with the lowest error rate (with only 1 part in 10,000) compared to other projection systems. There might be a situation where you have data points from more than one zone, and you want to interpolate the data into the whole state. In this case, the Michigan GeoRef Coordinate system, a different projection system, would be a better choice that combines all three zones into one. However, you will still need to sacrifice some accuracy, as the error rate increases to 4 parts in 10,000 (10,000 ft. distance on the ground can range from 9,996 ft. to 10,004 on the map), when combining the dataset in Michigan GeoRef coordinate system.
Choosing the right projection system
The choice of projection systems depends on the objectives of the cartography, and the scale of the illustration. Knowing whether the map is for a general purpose or for a specific thematic application will help to select the projections that preserve certain properties without compromising others.
Scale is the ratio of the distance on the map to the distance on the Earth's surface. If you are recording geospatial information of a place on a larger scale, i.e., showing a smaller amount of area with greater detail, setting up a local State Plane Coordinate System will help minimize the error rate in your statistics. For instance, if you apply geostatistics to Florida geospatial data using the Michigan State Plane Coordinate System, there will be a high degree of inaccuracy in your results.
When you work with georeferenced data at a smaller scale, that is, a larger area with fewer details, then using a projection system that represents area appropriately will help you achieve your visualization goal. For example, when showing global wind pattern movement, choosing the Robinson or Gall-Peters projection instead of the Mercator projection is better because it reduces the exaggeration of the size of countries farther from the Equator. However, if you are navigating at sea, the Mercator projection is the best because it preserves direction.
In conclusion, maps are made by converting a three-dimensional sphere into a two-dimensional surface. There are several methods to flatten a three-dimensional sphere into a two-dimensional surface, leading to many Projection Coordinate Systems, each with at least one property compromised. Maps are made to meet the specific objectives of the cartographers. A map, like any other visuals, can depict more information than intended to the audience directly or indirectly. Knowing the potential interpretations of this information will help you to become a better illustrator and alleviate negative cartographic results by choosing the right projection system. If you need to convert from one projection to another, many vendors such as ArcMap and free tools like QGIS are equipped with tools to help you.
Rajesh Sigdel (Raj) is a Ph.D. student in the Department of Geography, Environment, and Sustainability at the University of North Carolina at Greensboro. Raj enjoys wrangling and visualizing various spatial and non-spatial data. For more posts like this, you can follow him on Twitter or LinkedIn.
