Projections & Coordinate Reference Systems
Basic Terminology Overview
Map projections are mathematical transformations used to represent a three-dimensional shape of the Earth on a flat surface. Every time we display a geospatial dataset on a computer screen, a map projection is involved.
In a GIS environment, we often (mistakenly) use the terms projection and coordinate reference system (CRS) interchangeably because a) setting a CSR — projected or geographic — within a GIS software will inevitably involve using a projection, and b) this terminology can be genuinely confusing for many GIS users and educators. This post is intended to briefly overview the basic terms and methods of working with map projections and coordinate reference systems.
Approximating Earth’s Shape
Earth is not a sphere but a lumpy object with topography, bathymetry, and changing ocean heights. The science of studying its shape, size, gravity, and orientation in space is called Geodesy.
GGeodesists use Geoid as an idealized model of the Earth abstracted from its topographical features. It approximates the global mean sea level, but across which gravity is equal. If we imagine the Earth as one big ocean — a geoid would be the figure that this earth/ocean would take under its gravity and rotation. Geoids are also lumpy because gravity varies in response to local differences in topography and variations in the density of materials in the Earth’s interior.
EEllipsoids are commonly used as surrogates for geoids to simplify projection mathematics. They are 3D approximations that define Earth’s shape and size. Most of them are oblate spheroids, which means they bulge at the equator and are somewhat squashed at the poles. Many different ellipsoids are used worldwide: local ellipsoids minimize differences between the geoid and the ellipsoid for individual countries or continents, while global ellipsoids approximate the geoid as a mean Earth ellipsoid.
DDatums are models of the Earth consisting of a reference ellipsoid and information about its position relative to the Earth’s surface. In other words, datums ‘fix’ ellipsoids to the Earth. They rely on a network of physical control points, also known as benchmarks, precisely placed and measured by terrestrial surveying or satellite geodesy techniques.
Geographic coordinate systems are reference frameworks that assign coordinate values to locations on the Earth. They have three primary parameters: a datum, a prime meridian (location of 0° longitude), and an angular unit specification (usually degrees).
Projections
Projections are methods involved in transforming a three-dimensional model of the Earth into a two-dimensional flat surface. They are just one parameter used in creating projected coordinate systems. All projections involve distorting one or more geometric map properties, such as shape, size, or distance, which makes them political and/or politicized.
Based on the spatial property they preserve, projections can be categorized as:
- Conformal: they preserve local shape and angles (e.g., Mercator, Lambert Conformal Conic)
- Equal Area: they preserve the area of displayed features (e.g., Gall-Peters)
- Equidistant: they preserve distances between certain points (e.g., Polar Azimuthal Equidistant)
- Compromise: they try to balance all kinds of distortions aiming for something that “looks right,” and are often used for visualizations on world maps (e.g., Robinson, Winkel tripel)
Projected coordinate systems are reference frameworks that contain a full definition of how a specific model of the Earth is projected onto a flat map. They consist of a geographic coordinate system, a projection method (and a set of projection-associated parameters, such as false easting and false northing), and a linear unit specification (usually meters or feet).
In QGIS, the default CRS is a geographic coordinate system called the “World Geodetic System of 1984 (WGS 84).” WGS 84 coordinate system is based on the WGS 84 datum. The WGS 84 datum uses the ellipsoid also named WGS 84. The WGS 84 ellipsoid currently uses the Earth Gravitational Model 2008 geoid.
Coordinate Reference System Formats
There are numerous different ways to define and store CRS information. The three most common are:
- Well-Known Text (WKT) formats
- proj.4 strings
- EPSG codes
Well-Known Text (WKT) is a string containing all necessary coordinate system parameters using a combination of brackets [] and elements separated by commas. (If you open a .prj file of a shapefile in a text editor, you would see it as a WKT.)
Here is an example of WKT for WGS 84 CRS:
GEOGCRS["WGS 84",
ENSEMBLE["World Geodetic System 1984 ensemble",
MEMBER["World Geodetic System 1984 (Transit)"],
MEMBER["World Geodetic System 1984 (G730)"],
MEMBER["World Geodetic System 1984 (G873)"],
MEMBER["World Geodetic System 1984 (G1150)"],
MEMBER["World Geodetic System 1984 (G1674)"],
MEMBER["World Geodetic System 1984 (G1762)"],
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ENSEMBLEACCURACY[2.0]],
PRIMEM["Greenwich",0,
ANGLEUNIT["degree",0.0174532925199433]],
CS[ellipsoidal,2],
AXIS["geodetic latitude (Lat)",north,
ORDER[1],
ANGLEUNIT["degree",0.0174532925199433]],
AXIS["geodetic longitude (Lon)",east,
ORDER[2],
ANGLEUNIT["degree",0.0174532925199433]],
USAGE[
SCOPE["Horizontal component of 3D system."],
AREA["World."],
BBOX[-90,-180,90,180]],
ID["EPSG",4326]]Proj.4 strings are more compact ways of storing CRS information. Here is an example of proj.4 string for WGS 84 CRS:
+proj=longlat +datum=WGS84 +no_defsEPSG codes are 4–5 digit numbers that represent CRS definitions (the EPSG acronym stands for now-defunct European Petroleum Survey Group). The WGS 84 CRS code is EPSG:4326.
You can explore the EPSG codes on spatialreference.org
