## Wednesday, July 22, 2009

### Map basics: datum, coordinate system, projection

Map projections, coordinate systems and geodetic datums are not the most exciting topics to discuss in reference to maps but any user of geographic information should have at least a basic understanding of the concepts.

In a nutshell, Earth is an oblate spheroid an in order to represent its surface as a flat map, complex mathematical transformations are required.

[oblate spheroid - image courtesy of Wikipedia]

Geodetic datum defines reference points on the Earth's surface against which position measurements are made. Central to this concept is an associated model of the shape of the Earth (that is, reference spheroid) to define a coordinate system.

Map coordinates are usually shown in one of two ways, as geographical coordinates (ie latitude and longitude values, in degrees) or grid coordinates, (as easting and northing values, in metres).

Map projection is a method of representing the surface of a sphere on a plane. By definition, all map projections show a distorted representation of the Earth surface therefore different map projections exist in order to preserve some properties of the sphere-like body (ie. either area, shape, direction, bearing, distance and/or scale) at the expense of other properties.

What does it all mean? The key point is that commonly quoted “geographic coordinates” (eg Sydney Opera House: lat, lng) are only meaningful in reference to a specific datum (eg. that point is shifted approximately 200m on AGD66 datum as compared to GDA94 datum). And to represent that point properly on a map you will also need to know projection of the map, otherwise the point may be depicted in a wrong place.

[example of mismatch resulting from source data being in geographic projection and the underlying map in Mercator projection]

More examples to illustrate the point. Satellite based navigation systems (the Global Positioning System or GPS) are becoming more and more popular in Australia so users should be aware that GPS coordinates are based on WGS84 datum, which is different from official Australian datum GDA94 (different spheroid definitions were used). All current official maps and data in Australia are based on GDA94. However, luckily, the difference between WGS84 and GDA94 is negligible and for most common uses both datums can be used interchangeably.

As to map projections, when you have a map showing just a few streets, projections don’t really matter. Similarly, if you view small scale maps in atlases or on wall posters, projection rarely comes to mind simply because it has already been determined by the author to best represent the phenomenon and also to “look nice”. However, when you deal with raw geographic data (whether vector – points, lines and polygons, or raster - images) and need to compile them into a map, projections of source data and final map are of outmost importance. Similarly, if you need to take a reliable measure of distance or area on the map you have to know which projections preserve those properties and therefore are the most appropriate to use.

The following is an illustration of the “distortions” in representation of shapes on a map due to different projections. The first image was generated by applying a common projection to input data and the second shows the result of not applying any projection at all.

Projections that you are most likely to encounter in Australia are:

1. Geographic/Equirectangular projection: a de-facto standard for computer applications because of the connection between an image pixel and its geographic position.

The following are the international reference codes to precise definitions of the transformation: EPSG:4326 (WGS84 datum) and Australian specific EPSG:4283 (GDA94 datum) – for all common purposes, they are interchangeable, unless you require a sub-meter accuracy.

[image courtesy of spatialreference.org]

2. Transverse Mercator projection used with Universal Transverse Mercator coordination system (UTM zones 49 to 56) - suitable for measuring distances and areas; mostly used for medium scale printed maps.

3. Lambert Conformal Conic projection (EPSG:3112) - well approximates distance between two points; often used for aeronautical charts, small scale maps or road maps.

[image courtesy of spatialreference.org]

4. Mercator projection (EPSG:3395) - used for Google Map, Virtual Earth/ Bing Map, and all tile based online maps – distance between two points on the map is distorted, the more the further you move from the equator.

Individual States in Australia also define their own local projections for variety of purposes so it is always wise to check metadata before putting the data to any use.

Anonymous said...

Thanks for a clear explanation.

I want to plot lat/lon pairs to a world map using mercator projection WGS84. Could you recommend a source of SVG maps to use with this datum?

thanks
Jon

All Things Spatial said...

Hi Jon,

Unfortunately there aren't many svg maps around, although you my try this link: http://www.mappetizer.de/en/examples/oilspill/index.html and I always find this site very useful http://www.carto.net/.

You would probably have to recompute each point - lon is easy but lat is a bit more complex. If you need I can try to dig out some references.

Cheers
Arek

Kevin said...

Thanks for the explanation of datum in mapping coordinate.
I was looking for a video that would explain this, do you have any recommendations. It is for a college course in AutoDesk Mapping.
Thank you,
Kevin

All Things Spatial said...

Hi Kevin and thanks for your comment.

Nothing specific comes to mind but youtube is an obvious place to have a look. I know ESRI created quite a few videos so, chances are, you will be able to find something suitable for your purposes.

Cheers

Arek