Homework 5: Projections in ArcGIS

Equal Area Projections

Distance between Washington D.C., USA and Kabul, Afghanistan
Sinusoidal
Planar: 8,098 miles
Great Elliptic: 6,934 miles

Cylindrical Equal Area
Planar: 10,108 miles
Great Elliptic: 6,934 miles

Equidistant Projections

Distance between Washington D.C., USA and Kabul, Afghanistan
Azimuthal Equidistant
Planar: 8,341 miles
Great Elliptic: 6,934 miles

Two-Point Equidistant
Planar: 6,648 miles
Great Elliptic: 6,934 miles

Conformal Projections

Distance between Washington D.C., USA and Kabul, Afghanistan
Mercator
Planar: 10,112 miles
Great Elliptic: 6,934 miles

Stereographic
Planar: 9,878 miles
Great Elliptic: 6,934 miles

Because the Earth is a 3D object, a 2D map of the world is guaranteed to be distorted in some way. In  cartography and its applications to geographic information systems, map projections describe the process of this mathematical conversion from ellipsoid to plane. We can categorize these projections by the shape of the developable surface (e.g., planar/azimuthal, cylindrical, conical) and by their preserved properties (e.g., equal area, equidistant, and conformal). Every projection preserves particular surface aspects at the expense of another (or even several others), so the most appropriate map projection varies depending on the purpose of the map.

As indicated in the name, equal area projections (also called equivalent projections) preserve the area. That is, the areas on the map are proportional to the areas on the Earth that they correspond to. However, as we can see from the Sinusoidal and Equal Area Cylindrical projections above, the shapes of the land masses can get significantly distorted, especially as we move away from the center of the Sinusoidal projection or the equator of the Equal Area Cylindrical projection.

Equidistant map projections preserve distance from some standard point or line (generally in the center of the projection). Here these projections are exemplified by the Azimuthal Equidistant and Two-Point Equidistant. The former preserves distances along the great circles extending from the center of the projection, and the latter preserves distances from any point on the map to either of two chosen points. Although the Azimuthal Equidistant projection conserves distances, it compromises on the shape and area, distorting more and more in both aspects as we move away from the center. The same goes for the Two-Point Equidistant projection, but instead the shape and area become more distorted as we move away from the two chosen points.

Conformal projections preserve local shapes and angles. This means that the parallels and the meridians must intersect at the correct angles. The most common conformal map is the Mercator projection, which is shown above along with a Stereographic projection. Looking at these, we can see that the areas are completely misrepresented on the maps. For example, in the Mercator projection, Africa is shown to be only slightly larger than the United States, but in reality, Africa is large enough to fit the United States, China, India, and many other countries. The Stereographic map indicates that Africa is actually smaller than the United States.

Although it is impossible to have a map projection that is 100% accurate in every aspect, map projections are still a very useful and informative way of visualizing the world. What's important is that map viewers ask themselves, "What map projection is being used here? What surface properties have been preserved, and what properties have been distorted?" Those who do not employ this kind of critical thinking can be easily misled by textbooks or news information sources, further perpetuating poor geographical knowledge. In some cases, however, the type of projection used is not of critical importance because the map exists solely for illustration purposes. In addition, the type of projection is not important for large-scale maps because the distortions from projections are not really apparent.