6 How is spatial data located in coordinate space?
6.1 Once the geographic phenomena to be portrayed and the model to be used to store the spatial data have been decided, it is necessary to determine the framework to use to locate the spatial data in space.
6.2 A map (and a typical GIS theme) is a flat two-dimensional media that shows graphically the location and interrelationships of geographic phenomena on or near the Earth’s surface. However, the Earth’s surface is actually a three dimensional shape approximating an ellipsoid (a slightly squashed spheroid[1]). Therefore as a map is flat and the surface of the earth is curved, no map can be made without some distortion of the geographic phenomena portrayed (Davis, Foote, Anderson and Mikhail, 1981, pp9, 564).
6.3 The accepted method of overcoming this problem is to use a map projection. Map Projections are designed to depict with varying degrees of accuracy the ellipsoidal earth in two-dimensional media. There are many different types of map projection. Each projection is suited to a particular use and minimises one or more of the distortions inherent in portraying a three-dimensional surface in a two-dimensional media, including: distortions in length, distortions in azimuth and angle and distortions in area (Davis, Foote, Anderson and Mikhail, 1981, p10). The distortion remaining in the data increases from the origin of the projection towards its edges (Maling 1991, p144).
6.4 A map projection uses a mathematical model to represent the complexity of the earth’s surface when performing calculations to project geographic phenomena onto a two-dimensional medium. This mathematical model is usually referred to as an ellipsoid and sometimes as a spheroid. Traditionally an ellipsoid is chosen that best approximates the surface of the earth over the area of interest, the Geoid[2]. The shape of the Geoid is determined by Geodetic Surveyors, after the conduct of precise, high order surveys (Huxhold 1991 and Hunter 1991). Typically the ellipsoid chosen may be suitable for a continental region, e.g. the Australian National Spheroid or for the entire earth, e.g. the Geodetic Reference System 1980.
6.5 The ellipsoid is further constrained by the use of a datum, allowing geographical coordinates[3] to be assigned to projected features. A datum is defined by parameters describing the origin, size, shape, position and orientation of the ellipsoid (NMC 1972 and Hunter 1991).
6.6 As geographical coordinates are not always suited for use with the phenomena that has been projected, it is often necessary to define a Cartesian Coordinate System[4] for use with the projection, usually by reference to the origin of the projection.
6.7 Two examples of commonly used frameworks used to locate geographic phenomena in Australia are:
6.7.1 AMG 1966 The Australian Map Grid 1966 (AMG66) is the name of the Cartesian coordinate system that has been in use within Australia for over thirty years. It uses:
6.7.1.1 The Australian National Spheroid as its ellipsoid, constrained by the Australian Geodetic Datum 1966. This ellipsoid is one that best approximated the shape of the Geoid over continental Australia, as it was understood in 1966.
6.7.1.2 A series of zones, six degrees of Longitude in width, utilising a Universal Transverse Mercator Projection for each zone.
6.7.1.3 A metric Cartesian coordinate system defined in relation to the origin of the UTM Projection for each zone. The origin is the junction of the Equator and the Central Meridian. A False Origin with the coordinates of 0,0 is defined 500,000 meters to the West and 10,000,000 meters to the South of the origin. All coordinates for a particular zone relate to that zone’s False Origin.
6.7.1.4 A repeating range of coordinate values. That is, the range of coordinates used by one AMG Zone, are also used by all other AMG Zones.
6.7.2 MGA 1994 The Map Grid of Australia 1994 (MGA94) is the name of the Cartesian coordinate system that is to supercede AMG66 and also AMG84 for use within Australia. It is directly compatible with the Global Positioning System (ICSM, 1999). It uses:
6.7.2.1 The Geodetic Reference System 1980 as its ellipsoid, constrained by the Geodetic Datum of Australia. This ellipsoid is an earth centric one that best approximated the shape of the Geoid over the entire Earth, as it was understood in 1994.
6.7.2.2 A series of zones, six degrees of longitude in width, utilising a Universal Transverse Mercator Projection for each zone.
6.7.2.3 A metric Cartesian coordinate system defined in relation to the origin of the UTM Projection for each zone. The origin is the junction of the Equator and the Central Meridian. A False Origin with the coordinates of 0,0 is defined 500,000 meters to the West and 10,000,000 meters to the South of the origin.
6.7.2.4 A repeating range of coordinate values. That is, the range of coordinates used by one MGA Zone, are also used by all other MGA Zones.
6.8 At a cursory glance, both AMG66 and MGA94 appear very similar. However a single geographic phenomenon on the earth’s surface will have totally different coordinates on both grids. The MGA94 coordinates will be in the vicinity of 200 meters to the North East of the AMG66 coordinates. The difference is caused by the different datum and ellipsoids used by both grids (ICSM, 1999). It is extremely difficult to determine which framework has been used to produce a set of coordinates, unless the datum is explicitly stated.
6.9 In addition to the requirement to use a datum to determine the horizontal coordinates of geographic phenomena, there is also a need to use a separate datum to determine the vertical coordinate (the height) of the same features. In Australia, the Australian Height Datum (AHD) is used. It equates approximately to (though is different from) Mean Sea Level (ICSM, 1999). AHD may be used with both GDA and AMG coordinates.
6.10 In Summary A framework is necessary to locate geographic phenomena in space. This includes:
6.10.1 An ellipsoid that most closely represents the surface of the earth over the region of interest.
6.10.2 A datum to orient the ellipsoid so that geographical coordinates may be determined.
6.10.3 A projection selected for a particular use that minimises the distortion inherent in portraying a curved three-dimensional surface on a two-dimensional media.
6.10.4 A grid to provide metric Cartesian coordinates.
[1] A spheroid is a three dimensional spherical surface.
[2] “The Geoid is the shape of the earth as a three dimensional spheroid that coincides with the surface of the earth at sea level and extends in an imaginary surface through the continents with a direction of gravity that is perpendicular at every point” (Huxhold 1991 and Hunter 1991).
[3] Latitude and Longitude, using degrees, minutes and seconds or decimal degrees.
[4] A rectangular grid, defined by an origin and a distance in the X and Y direction from that origin (from DeMers, 1997, p 462).
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