Datum and Projection

Mapping is a process of:

determining geographic location (latitude/longitude) of features on the earth,

transforming features from the surface of the earth (globe) onto a flat map, and

graphically symbolizing the features (cartography).

Our understanding of the shape of the earth and the projection of surface features onto a flat map has implications for location accuracy and distortion (area, distance, shape and direction).

Datum

Datum is a reference surface used to generate coordinates (i.e. latitude and longitude). Latitudes and longitude are angular measures, given in degrees. Imagine yourself in the centre of the world and look out at the equator. You would be looking straight out (i.e. flat), therefore your angle would be zero. Now imagine looking at Malaspina University-College (in B.C. Canada). You would be looking up at an angle of about 49 degrees (latitude) from the equator. For longitude you start by looking out at Greenwich, England. That is your zero degree mark. As you turn towards the Atlantic Ocean you are turning west. Central America has longitudes around 90 degrees west. Note that 90 degrees East Longitude would run through Asia. So Longitudes go off in both directions from Greenwich and meet in the Pacific at 180 degrees (the international dateline). If the world was perfectly round we could stop here.

Unfortunately the world is not a perfect sphere. It’s more of an ellipsoid. This is because the earth is not a hardened rock (centre is molten, also surface is about 75% water). Since the earth spins, centrifugal force pulls out the earth at the equator. But wait, it gets uglier yet. The surface of the earth, and therefore the shape of the earth, is essentially mean sea level (m.s.l.). M.S.L. is determined not only by centrifugal force (pushing out at the equator) but also by earth’s gravity (that force that makes apples fall down instead of up). Here’s the kicker … m.s.l. is not a smooth, perfect ellipsoid. It is essentially a dented ellipsoid (more properly known as a geoid). This is because gravity is not constant. Mass and density of an object determine gravity. The density and mass of the earth’s crust varies,

therefore, gravity varies,

therefore, m.s.l. varies,

therefore, the earth’s surface is an ellipsoid with slight undulations.

It is easy to determine the latitudes and longitudes (a.k.a. the graticule) for a sphere. Figuring out the graticule on an ellipsoid is a manageable task. But determining the graticule on the irregular geoid is very complicated. In the end it was decided that for medium and large scale maps (1:250,000 to 1:5,000) using an ellipse would be more accurate than a sphere. (The math for the geoid is just too complicated to bother with).

The only complications are:

1. An ellipse that best approximates Central America is not the best ellipse for Europe. Thus each part of the world uses it’s own ellipse. The ellipse used is what is known as datum.

2. Our understanding of the earth’s true shape continues to change as technology changes.

For example, the datum (i.e. ellipse) used for North (and Central) America in 1927 was based on an ellipse developed in 1866. This was known as NAD27 (for North America Datum 1927). After satellites were deployed and provided better measures of the earth, a new ellipse was developed in 1980 (GRS80). In 1983 it was decided to use this new ellipse for mapping in North and Central America. The new datum is known as NAD83. Belize City did not move between 1927 and 1983. However, Belize City has different latitude and longitude under NAD83 than it did under NAD27. Indeed, some places in North America had a difference equivalent to 300 metres.

Datums have nothing to do with distortions. Datums have everything to do with location (more precisely, the coordinates assigned to any given location). Datum is the choice of ellipsoid to use. As the graticule (latitude/longitude) varies from ellipsoid to ellipsoid, changing datums will change the coordinates of a feature on the earth’s surface. Kinda complicated huh? Hey, I never said you’d like it.

Projections

We transfer features on the earth’s surface (i.e. the roads, rivers and cities of Belize) onto flat maps. Intuitively, transferring shapes (i.e. rivers, country boundaries) from a curved surface to a flat surface involves some sort of distortion. Parameters that can get distorted are shape, area, distance and/or direction. Different methods of projections can preserve one of these parameters.

1. Conformal projections preserve shape on a local basis and preserve direction. Examples are Mercator and Lambert Conformal Conic.

2. Equal-area projections preserve areas. An example is Albers Equal Area.

3. Equidistant preserves distance from the centre out (usually only on radial lines). This one is not normally used in GIS.

Shapes used for projections include a cone, a cylinder and a flat plane. It is actually done mathematically but is easier understood with pictures.

Conic projections work well for mid-latitude areas (Canada, USA, Europe). The cylinder projection (Mercator) shown above is perhaps the best known projection. It was originally used for navigation, as it was conformal (maintained direction). This projection also works well for areas close to the equator. It does however greatly enlarge areas further from the equator (Greenland is greatly enlarged compared to equatorial areas).

Datum, Projection & GIS

So what has this to do with GIS? Well, GIS projects often combine data from several different sources.

If the maps from different sources have different datums then the same locations will have different coordinates. When GIS combines different maps it uses the coordinates to align features. Thus a soils map based on NAD27 will not properly line up with a vegetation map based on NAD83. The soils map would have to be converted to NAD83. Luckily the GIS can do this for us.

The second factor is projection. Different projections distort surface features in different ways (i.e. area, shape, direction and/or distance). Because of this we can only combine maps with the same projection. Again the GIS can do the conversion.

For the GIS project manager it is important to note the datums and projections of each map included in the project and to convert all maps to a common datum and projection.