Geocentric Datum of Australia (GDA)

• Introduction
• What is a Coordinate System?
• Projections
• Mathematical Figures of the Earth
• Ellipsoids used in Australia
• What is a Datum?
• Why change to a Geocentric Datum?

• Australia's old coordinate systems
• Geoscience Australia GDA Implementation Statement

• GDA Technical Manual
• Visit ICSM GDA Home Page

Australia has changed the way it references geographic positions on its maps to accord with a the global coordinate reference system that is directly compatable with the Global Positioning System (GPS). This page looks at what a datum change actually means and why we have adopted a new datum. In order to fully understand the changes, it is necessary to first look at the concepts behind the geographic positions of features on a map including coordinate systems and projections.

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For map reading purposes, an infinite combination of lines can be used to divide Australia up into equal portions. A common example of a division of this kind is the local street directory. Street directories use sets of evenly spaced lines, known as a coordinate system, to break large areas of land into parcels. By giving each portion a reference marker in the north-south and east-west direction as well as a unique page number, features in the directory can be identified more efficiently as the area in which the feature exists is much smaller.

Street Directory Reference System	In the above map, the Blue Lake is located by the reference Page 10, D8. This kind of system is used in street directories and defines only the grid square in which the feature exists. Though the coordinate system is repeated on each page, by specifying the page number each grid is uniquely identified.
Topographic Map Reference System	In the above map, the Blue Lake is located by the reference 472 500E, 5 802 500N. Though the system is more complex it allows features to be located more exactly by interpolating coordinate values in both directions. Like a street directory, the coordinate system is repeated but instead of on each page, it is only between zones.

Feature referencing on Geoscience Australia's mapping products work on a similar principle to a street directory but there are two main differences:

 

1. Geoscience Australia's mapping products do not use page numbers to divide the country into portions. Instead, maps are divided into zones. Zones cover a much larger area than a single page in a Street Directory and are numbered according to a world wide convention. Australia is covered by zones 49 to 56, each zone covers 6 degrees of longitude. Zones are related to the Universal Transverse Mercator projectionand used by many countries to map the earth.
   
2. The coordinate system used on Geoscience Australia's mapping products enables features to be pinpointed to a greater degree of accuracy than a Street Directory where a grid area, in which the feature exists, is defined rather than the feature itself. Street directories generally use a letter and a number, topotgraphic maps use a consecutive range of numbers in both directions. The range of numbers, allows the position of features to be interpolated to much greater degree of accuracy.

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The type of coordinates found in a street directory and on Geoscience Australia's topographic maps are known as Cartesian Coordinates. Cartesian Coordinates are related to a line that represents zero in the east-west direction, known as the X axis, and a line that represents zero in the north-south direction, known as the Y axis.
Movements by a point away from the axes are recorded as a set of two values, known as coordinates. Coordinates tell you how far away from the origin of the axes, 0 on X and 0 on Y, that you are. By convention, the point's position is identified by quoting the distance along the X axis first, and distance along the Y axis second, thus each point has a unique name.

These are the mathematical coordinates you find on a map. In cartography and surveying, the X axis coordinates are known as Eastings, and the Y axis coordinates as Northings.

Cartesian Coordinates can define a point in space, that is, in three dimensions. To do this, another axis must be introduced. This axis will represent a height above the surface defined by the x and y axes. This new axis is known as the Z axis. For local 3D cartesian coordinate systems, the Z axis represents "up".

This diagram shows the earth with two local coordinate systems defined on either side of the earth. The Z axis points directly up into the sky.

These coordinates are read like the 2D Cartesian System only there is now an extra coordinate in the direction of z; instead of (X,Y) it is (X,Y,Z).

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The new cartesian coordinate system that will be used in Australia will be known as the Map Grid of Australia 1994 (MGA94).The cartesian system that is being phased out is called the Australian Map Grid, there are two versions of the coordinates from this system, the originals from 1966 and their subsequent update in 1984. For the purposes of this document they will be considered as the same (they differ only by a few metres) and will be refered to as the AMG66/84.

Where street directory coordinates are arbitrary, the values assigned in Geoscience Australia's maps are derived from the position's longitude and latitude. Longitude and latitude are coordinates that relate to the feature's positions on the spherical earth.

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Lines of longitude intersect both the North and South poles. They are numbered using degrees beginning at the Royal Greenwich Observatory in England, which is designated as 0°, and continue both East and West until they meet at 180°.

Lines of latitude are measured as an angle from the equator (0°) to either Pole, 90° South and 90° North. The equator is a line of latitude.

Latitude and longitude are collectively known as geographic coordinates.

As with cartesian coordinates, one point on the earth can have many different geographic coordinates assigned to it, depending on how the reference system was defined. The GDA94 will have longitude and latitude values that relate to a reference surface called the Geodetic Reference System 1980 [GRS80].

So any point on the earth's surface can have a set of geographic coordinates and a corresponding set of cartesian coordinates. The next section explains how the two are related.

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World globes are a good estimation of the earth's surface but their scale is too small to allow you to plan trips across town. A flat map of the region that we can fold up and put in our pocket is more functional.

To convert the round earth to flat map is complicated. The best way to illustrate the difficulty in doing this is by thinking of the earth as a rubber ball with the land and water painted on it. To flatten the rubber ball into a flat square we need to cut it up and stretch it.

Because the rubber ball is being stretched, the land shown on it will be distorted from its original shape.

This same, cutting and stretching process is used to make maps through mathematical formulae called 'Projections'. Projection formulae take the geographic coordinates from the spherical earth (longitude and latitude) and convert them to cartesian coordinates (X & Y).

There are many projection formulae that can be used and consequently maps can look very different.

A 'Universal Transverse Mercator' (UTM) projection of the GDA94 geographic coordinates produces cartesian coordinates known as Map Grid of Australia 1994 (MGA94). This UTM projection was also used for the Australian Map Grid, 1966 and 1984 [AMG66/84] - the coordinate system of maps that are being superceeded by the MGA94.

You may wonder why the AMG66/84 and MGA94 are different if they are both projections of geographic coordinates to cartesian coordinates. It is because the geographic coordinates are different. The AMG66/84 cartesian coordinates are based on the geographic coordinates derived from the Australian National Spheroid [ANS] and the MGA94 cartesian coordinates come from the geographic coordinates defined by the Geodetic Reference System 1980 [GRS80]. They are from different models of the earth, more about this next section.

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Some earth models relevant to Australia are the World Geodetic System 1984 [WGS84] and the Geodetic Reference System 1980 [GRS80]. The WGS84 is used for the Global Positioning System and is very similar to the GRS80. They have a small difference in the definition of their ellipsoid parameters and generally may be treated as the same.

  

The GRS80 (and hence the WGS84) is a geocentric system. This means that the origin of its coordinate systems corresponds with the centre of mass of the earth.The GRS80 is important to Australia as it is the ellipsoid used to define the GDA94.

The Australian Map Grid [AMG66/84], the system being updated, was based on the Australian National Spheroid [ANS] which was an ellipsoid designed to be the best estimate of the earth's shape around the Australian continent rather than the world. As a result, the origin of the ellipsoid used in its definition did not correspond with the centre of the earth - it was about 200m away from it. Consequently the shift to the new datum will mean that all coordinates will shift by approximately 200m to the north east.The width of an ellipsoid at the equator is called the semi major axis and is conventionally named the letter 'a'. The flattening of the ellipsoid is refered to by the letter 'f' and is a measure of how much the ellipsoid differs from a sphere.

The Map Grid of Australia MGA94, the new system, uses the GRS80 ellipsoid. It was designed to be a best estimate of the earth's shape globally. Its centre corresponds with the centre of the earth.

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A datum is a framework that enables us to define coordinate systems. The framework includes the ellipsoid and other parameters not discussed here, for information about these see the ICSM GDA Home Page.The way a datum is defined has changed with the improvement of measurment techniques through technology. The AGD66/84 was defined differently to the GDA94, the two methods are outlined briefly below.

Traditional Geodetic Datums - The AGD66/84

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Today's technology means that a new datum can be based on several well determined points. The 8 points used to define the GDA94 are known as the Australian Fiducial Network [AFN]. The adopted coordinates of the AFN were computed in terms of the International Terrestrial Reference Frame (ITRF) and from these AFN coordinates the geodetic network that covers the whole continent was recomputed. The ITRF is based on a number of very accurate observations all over the earth, including Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Lunar Laser Ranging (LLR) and the Global Positioning Sytem (GPS)"

The measurements relate to a 3D earth-centered cartesian coordinate system, shown above. This system could be considered a 'global' 3D cartesian coordinate system in contrast to the 2D system previously described.

Though the AFN provides coordinates in three dimensions, only the horizontal components have been adopted. Heights in Australia remain those of the AHD.

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The main reason was so that we can use the Global Positioning System [GPS] more easily. The Global Positioning System is becoming more and more widely used for navigation by both the spatial sciences and the general public world-wide. Geocentric datums have been adopted for most aeronautical and shipping applications due to its international capabilities. As GPS is based on a geocentric datum, to use the coordinates here in Australia means we have to convert the coordinates to our datum, the AGD66/84. With the introduction of the GDA94, the datums will both be based on the same ellipsoid and this will eliminate the need for a complex conversion as the coordinates read from the GPS will be the same as those of the GDA94.

For further Technical Knowledge on this topic, visit the ICSM GDA Home Page For information on what stage Geoscience Australia is at Geoscience Australia GDA Implementation Statement

This page was copied from
http://www.auslig.gov.au/geodesy/datums/ on the 19/12/02