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# Map Projections

Map projection is the process whereby positional information related to the earth is transferred onto a workable surface such as a paper map or computer screen. All maps and geographically referenced datasets are affected by map projection, even though this may not be apparent to the casual user. As shown in the figure, the process involves approximating the shape of the earth using a three-dimensional (3D) mathematical model and decomposing the 3D coordinates onto a horizontal surface. Through the process of map projection, every position on the 3-dimenional earth’s surface can be transformed onto a 2-dimensional mapping surface. There are a range of different map projection types, of which three major ones are illustrated in the figure. The figure shows how the representation of geographical features is affected by the choice of map projection. For example, there are slight differences in the apparent outline of Africa between the (i) conformal and (ii) equidistant maps, but the continent is much elongated in the (iii) equivalence map.

Depending on the scale of the mapping products, the 3D model can be a sphere or a spheroid. The latter does not have a constant radius like a sphere but is a 3D model formed by rotating an ellipse about its principal axis. It is a suitable representation of the earth and provides the necessary mathematical basis for scientists to establish coordinate systems such as the World Geodetic System defined in 1984 (WGS84) used by the Global Positioning System (GPS).

### Geographical Coordinates and Datum

While it is convenient to give a geographical position in terms of latitude and longitude, e.g. the geographical coordinates of Christchurch in the UK and New Zealand are (50.44 N, 1.47 W) and (43.33 S, 172.47 E) respectively, many computer programs and processing algorithms require the input data to be in a rectangular format such as (X, Y). Unlike latitude and longitude whereby the equator and the Greenwich Meridian are the agreed reference lines, the initial points of a rectangular coordinate system can only be determined after the map datum has been established. A map datum is the reference surface upon which the mapping and surveying of a country or a region is based. It defines the origin from which all geographical measurements within a region are taken. While there are global datums such as WGS84, most developed countries establish their own nationwide horizontal and vertical datums for historical and practical reasons. Mean sea level, for example, has long been used by many national mapping agencies as a vertical datum for height measurement and levelling. A horizontal datum will normally consist of the definition of a map origin and orientation as well as a scale factor in order to minimise the distortion introduced by map projection.

### Local Coordinate Systems and National Grids

The consideration of map datums is particularly important in large scale mapping where geographical positions are often captured and represented in a plane coordinate system, sometimes known as a grid. In order to maintain continuity and minimize the numerical complexity of coordinate transformation, many countries elect to adopt a single reference system which is often referred to as a national grid. A typical example is the British National Grid, used by Ordnance Survey (Great Britain). Within the British National Grid, locations are expressed by rectangular coordinates commonly known as Eastings and Northings which are measured in metric units from a false origin in the extreme southwest. Grid references of varying precision can be specified by varying the numbers of digits used. Users therefore need to be particularly aware that they may need to convert geographical coordinates obtained in latitude and longitude to local coordinates before it is possible to link or map their data.

It is important that the datum and coordinate systems chosen in field measurement or data linkage are appropriate to the intended use of the geographical data. Should data derived from two different systems be used, GIS software provides functions for re-projection. This type of processing facility is not usually available via the Web, however some sites do allow the user to convert individual coordinate pairs. It is also important to bear in mind that no matter how sophisticated GIS may appear, data manipulation can never put back geographical details that were not part of the original data collection.