If you have ever dealt with spatial data you might have heard (at least once) one of these three words: datum, coordinate system and projection. What do they mean?

Datums and projections

Datums and projections are algorithms that help us represent real-world objects sitting on a 3D surface (the Earth surface with its topographic features: mountains, valleys and submarine chasms) into a plane or 2D surface (our beloved map).

Model of the Earth. Source: ESRI
Model of the Earth Source: ArcUser Online ESRI®
  • A datum is a mathematical model that fits the earth to a sphere or an ellipsoid. It is a reference from real-world to an ellipse. It provides an idealization of the earth surface that does not account for local changes in topography. It defines the surface (ex radius for a sphere, major axis and minor axis or inverse flattening for an ellipsoid) and the position of the surface relative to the center of the earth.
  • A projection is a mathematical operation that transfers the real position/shape of an object on earth from a sphere/ellipsoid to a plane, using a datum as reference of origin. It distorts and shrinks a portion of the spheroid onto flat paper.

You can find more information about the differences between the concepts of datum and projection in this StackExchange thread (I’ve already taken part of my definitions from it).

All projections cause distortion! Or, as other people put it… maps have been lying to you

Try to use a projection that minimizes distortion in the property you are interested in measuring. For example, imagine you are a herpetologist interested in evaluating the influence of the distance between waterbodies in the metapopulation dynamics of a frog species. You have a GIS layer representing the location of your waterbodies and want to calculate the edge to edge distance between them. Before figuring out the tool you need to use to estimate these distances you should check that your waterbodies layer is in a projection that minimizes distortion in distance. If the projection of your waterbodies layer doesn´t minimize distortion in distance, you need to re-project your layer into a projection that does, then, calculate the distances.

The different classes of projections that minimize distortion of a particular property receive different names:

  • Conformal projections minimize distortion in shape
  • Equidistant projections minimize distortion in distance
  • Equal-area projection minimize distortion in area
  • Azimuthal or True-direction projections minimize distortion in direction.

There are also projections that try to balance out distortions in all properties (compromise projections) but at the same time, don’t preserve any of the four spatial properties of area, shape, distance, and direction.

Public administrations provide guidance about the accepted/recommended projections for a particular area (states’ official projection). For example, if your study area is in Australia you can check the GEOSCIENCE website and there you will find information about the current Australian coordinate system.

Coordinate systems in GIS practice

I´ve found ESRI’s definition of coordinates systems very useful: A coordinate system is a reference system used to represent the locations of geographic features, imagery, and observations, such as Global Positioning System (GPS) locations, within a common geographic framework.

Each coordinate system is defined by the following:

  • Its measurement framework, which is either geographic (in which spherical coordinates are measured from the earth’s center) or planimetric (in which the Earth’s coordinates are projected onto a two-dimensional planar surface)
  • Units of measurement (typically feet or meters for projected coordinate systems or decimal degrees for latitude-longitude)
  • The definition of the map projection for projected coordinate systems
  • Other measurement system properties such as a spheroid of reference, a datum, one or more standard parallels, a central meridian, and possible shifts in the x- and y-directions

In practice, coordinate systems can be classified in two groups:

1. Geographic Coordinate Systems
Road sign from the Department of Conservation in New Zealand indicating you are crossing the Latutidue 45 South.
Road sign from the Department of Conservation in New Zealand indicating you are crossing the Latitude 45° South.

If you´ve ever used a GPS or Google maps you are familiar with the use of geographic coordinate systems.

More technically: a geographic coordinate system is a common spherical coordinate reference system for specifying location of features on the curved surface of the earth. A network of intersecting lines consisting of north-south lines of longitude and east-west lines of latitude creates an imaginary mesh around the globe. Such a network (graticule) allows for the description of the position of any point on the surface of the earth.

  • Coordinate pairs: longitude (East-West location from a reference meridian) and latitude (North-South location from a reference parallel)
  • Units: Decimal degrees, Degrees minutes seconds
  • Examples: World Geodetic System of 1984 (WGS 84), Geocentric Datum of Australia 1994 (GDA94).

 

Geographic coordinate system with lines of latitude parallel to the equator and lines of longitude with the prime meridian through Greenwich. Latitude values are measured relative to the equator and range from –90° at the south pole to +90° at the north pole. Longitude values are measured relative to the prime meridian. They range from –180° when traveling west to 180° when traveling east. If the prime meridian is at Greenwich, then Australia, which is south of the equator and east of Greenwich, has positive longitude values and negative latitude values. Note that the side of the units in the map changes from the equator (bigger and wider units) to the pole (narrower). Source: documentation QGIS® 2.0
Geographic coordinate system with lines of latitude parallel to the equator and lines of longitude with the prime meridian through Greenwich. Latitude values are measured relative to the equator and range from –90° at the south pole to +90° at the north pole. Longitude values are measured relative to the prime meridian. They range from –180° when traveling west to +180° when traveling east. If the prime meridian is at Greenwich, then Portugal, which is north of the equator and east of Greenwich, has negative longitude values and positive latitude values.
Note that the size and shape of the grid units of the map change when moving from the equator to the pole and from west to east. Source: documentation QGIS® 2.0

A geographic coordinate system doesn’t have constant lengths, angles, and areas across the two dimensions. Degrees of latitude and longitude are not consistent units of measure for area, shape, distance, and direction (have a look at the units of the above map: grid cells differ in size and shape when you move from the equator to the poles).

When do you normally use geographic coordinate systems? To explore, visualize and present continent-wide and world-wide data (small spatial scales and large spatial extents in general). Latitude-longitude is a good system for storing spatial data but not as good for viewing, querying, or analyzing maps.

2. Projected coordinate systems

A mathematical model transforms locations on the globe (3D curve surface) to locations on a two-dimensional (2D – flat) surface. In a projected coordinate system, locations are identified by X, Y coordinates on a grid, with the origin at the center of the grid. Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions.

A very famous projected coordinate system is the Universal Transverse Mercator (UTM), with effects on map distortion that you can see in the video above.

The longitude and latitude zones in the Universal Transverse Mercator system (UTM zones) Source:  Wikimedia Commons
The longitude and latitude zones in the Universal Transverse Mercator system (UTM zones)
Source: Wikimedia Commons
  • Coordinate pairs: X (Eastings) and Y (Northings)
  • Units: feet, metres, km, miles
  • Examples: Australia: Map Grid of Australia 1994 (GDA_MGA94_Zone52), Spain: ETRS89_UTM_Zone30.

Every projected coordinate system is based on a geographic coordinate system. In practice, the name of a projected coordinate system is composed of two elements, datum and projection. In the case of GDA_MGA94_Zone52:

projected coordinate systems

When do you normally use projected coordinate systems? Local and regional studies (large scales and small/intermediate spatial extents in general). When you want to make accurate measurements from your map and/or preserve one of the above mentioned properties (area, shape, distance or direction).

Do you want to learn more? Where can you find good resources?

Geokov is a great educational website where you can find a very good explanation of datums, projections, distortions, and lots of useful links related to this topic and many more things in relation to the fundamentals of mapping and cartography .

There is a lot of documentation about coordinate systems, projections, etc. in the user’s guides/manuals or online help resources of the main GIS hardware developers. Have a look for example at the online help of QGIS or ESRI.

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