Module 3. Coordinate Systems, Projections, and Datums
Learning Objectives
Select appropriate projections suited to specific map purposes and phenomena.
Diagnose an inappropriate projection choice for a given map and suggest an alternative.
Identify the map projections commonly used for certain types of maps.
Explain why certain map projection properties have been associated with specific map types.
Lecture Slides
Assignments
Overview
In order for geospatial data to be accurate, it is necessary to locate it on the earth’s surface. The process of converting a 3D surface to a 2D surface, such as conversion from the earth’s surface to a planar map, is called projection. To understand how this process, you must become familiar with four components of mapping features on the earth’s surface- coordinate systems, datums, projections, and map scale.
Coordinate Systems
A coordinate system is a numerical framework for identifying a location on a planar surface. You are probably familiar with the Cartesian coordinate system, developed in the 17th century by René Descartes. This system uses two (x,y) or three axes (x,y,z) to define a location. An alternative is the Polar coordinate system, which is based on direction, or angle (𝜃) and distance(r) in the form (𝜃,r). While these are sufficient for planar spaces, the earth’s shape demands a spherical coordinate system.
The geographic coordinate system (GCS) is a spherical coordinate system based on the spheroid (ellipsoid) shape, a sphere slightly wider than tall and approximates more closely the true shape of the earth. You may hear the term WGS84, which stands for World Geodetic System of 1984, which defines its origin at the center of the earth, Greenwich as the starting point (prime meridian) for the longitude and the equator for latitude. Locations are the surface represented by latitude (x) and longitude (y) using degrees.
Another type of coordinate system used by geographers is the projected coordinate system (PCS). A projected coordinate system is comprised of the geographic coordinate system as well as projection parameters that relate the 3D coordinates to planar 2D ones. Projected coordinate systems use linear units of measure for coordinates instead of degrees.
In addition to horizontal coordinate systems, like the GCS and PCS types, there are also vertical coordinate systems that are used to measure the height and depth of features. Such coordinate systems are important when rendering virtual environments. We will not discuss vertical coordinate systems in depth in this module.
Geospatial Surfaces
The earth’s surface is complex, made up of soaring peaks and deep oceanic trenches. Additionally, the earth itself is not a perfect sphere. Instead, we characterize the earth’s shape as a spheroid. In order to simplify the shape for the projection process, we approximate the surface using a datum. A datum is an abstract coordinate system with a reference surface (such as sea level) providing known locations to create maps. There is no single perfect datum, and it is important to understand that different models exist, and this can cause differences in plotting locations on a map. Global datums are generalized to approximate the entire earth's surface, and local datums are established to provide high-accuracy representations of local regions on the earth’s surface.
Map Projections
The map projection defines how to distort a 3D surface to a 2D surface. There are many different map projections that serve multiple purposes. A PCS is a GCS that has been flattened using a map projection. Every map you map requires a projection of the GCS. Every map you create will also contain some distortion due to the translation of the GCS to the PCS. It is important to know what your map goal is and choose a map projection that minimizes distortion that would impact that goal. For example, the Mercator projection was developed to aid in world navigation and exploration. Because of the innate properties of this projection, it distorts the appearance and size of regions, such as countries. You may have read articles about this type of distortion in popular news media. It would be important not to use the Mercator projection in cases where a comparison of region size is important.
To make it easier to understand the differences between different map projections and the distortions they cause, cartographers have developed groups of projections based on their ability to preserve different properties.
Table 3.1. Families of map projections, their properties, examples, and intended uses.
Conformal
Local angles/Shape
Mercator
Navigation
Equivalent/ Equal Area
Area
Albers Conic
Choropleths
Equidistant
preserves distances from one or two points to all other points
Plate carrée
Measuring traveled distance
Azimuthal
Direction to a fixed location B
Azimuthal Equidistant
Polar mapping
Compromise
No attribute is preserved
Robinson
World maps
Another method for organizing map projections is based on the projection surface, the shape of the surface that the 3D surface is projected onto. There are three main types of projection surfaces. First, the cone shape is used in the case of conic projections. A conic projection surface is identifiable by its straight lines of longitude and curved lines of latitude. Second, a cylinder can be used, leading to a conic projection surface with straight lines of latitude and longitude that meet at 90-degree angles. Finally, a plane can be used. A planar projection surface is often associated with azimuthal projections.
Identifying your Map Projection
To identify what type of coordinate system and projection your map is using, you should begin by determining if the map projection is a geographic (GCS), projected (PCS), or local system first. a global projection system will use latitude and longitude for their coordinates and the intersection of the equator and prime meridian as the origin. Projected coordinate systems come in many more flavors than GCS. A projected coordinate system will use some linear unit of measure and identify a datum. There are many different combinations of linear units and datums that make up Projected Coordinate Systems. Finally, the local coordinate system sets its origin to a location other than the intersection of the prime meridian and equator.
Conclusion
When precise location is key, it is imperative to select the most appropriate datum, coordinate system, and projection for your intended goals. The difference in coordinate positions between one reference ellipsoid and another can have serious consequences when trying to precisely measure the earth's surface. When dealing with different reference systems, it is necessary to transform all of the data sources to the same reference system to avoid misalignment of your data. There are resources available to help you pick which coordinate system is best for your given analysis. For example, ESRI's Geographic and Vertical Coordinate System Tables.
Choosing the right projection is also important when mapping data. Because all map projections introduce some distortion, it is necessary to choose a map projection that preserves the map properties that are most important to your mapping purpose.
Readings
You may need to obtain these from the University of Illinois Library.
Battersby, S. (2017). Map Projections. The Geographic Information Science & Technology Body of Knowledge (2nd Quarter 2017 Edition), John P. Wilson (ed.). DOI: 10.22224/gistbok/2017.2.7
Šavrič, Bojan, Tom Patterson, and Bernhard Jenny. "The equal earth map projection." International Journal of Geographical Information Science 33.3 (2019): 454-465. https://doi.org/10.1080/13658816.2018.1504949
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