The implementation of the Geocentric Datum of Australia (GDA) is proceeding, with its nation-wide implementation recommended by the year 2000. This involves an approximate 200-metre change from existing Australian Geodetic Datum (AGD) coordinates. The definitions of regional and geocentric datums, and the history of datums in Australia are reviewed. The benefits and effects of the GDA upon the users and producers of spatial information are outlined. The method of updating maps and spatial databases, using a seven-parameter transformation, is explained.
PREFACE
Following a suggestion by Mr Frank Bryant, this is a composite version of two tutorial papers published in Cartography (Featherstone, 1994 and 1995), with further amendments made in consultation with the Inter-governmental Committee on Surveying and Mapping (ICSM). Since writing the original version in early-1994, the ICSM resolved to adopt the Geocentric Datum of Australia 1994 (GDA94) at its November 1994 meeting, necessitating that these revisions be made. This revised explanation has been prepared in order to avoid the perception that ambiguities exist with some of these issues, which is not the case.
INTRODUCTION
Current national mapping in Australia uses the Australian Map Grid 1966 (AMG66) and 1984 (AMG84), which are projections of geographical coordinates from the Australian Geodetic Datum 1966 (AGD66) and 1984 (AGD84) respectively, see NMC (1986). A change from the AGD66 and AGD84 to the Geocentric Datum of Australia (GDA) was recommended at the inaugural meeting of the Inter-governmental Committee on Surveying and Mapping in July 1988 (ICSM, 1990, 1991a, 1991b). This new earth-centred datum will be used for future mapping and nautical charting of Australia and its offshore islands.
The establishment of the GDA is now proceeding, with its nation-wide adoption recommended at the turn of the century (Manning and Harvey, 1994). As such, there will be a transition from current AGD geographical coordinates to GDA geographical coordinates, and likewise for easting and northing. This will manifest as a horizontal difference between AGD and GDA ground coordinates of approximately 200-metres over continental Australia. The implementation of the GDA will be progressive from 1994, with a varying pace of transition depending upon user demand.
The adoption of the GDA will enable the production of a homogeneous series of Australian maps and nautical charts which will meet international navigation requirements. However, this change will also have far-reaching implications for the users and producers of maps and spatial information systems in Australia. These people will need to become conversant with the respective datums, acronyms, and their transformation, in order to deal with the coordinate sets that they will inevitably encounter. Appendix A lists the acronyms used in association with Australian datums.
This discussion reviews the spheroids and datums that are used for national and international mapping, the definition of the GDA and its associated geometrical parameters, and presents a rigorous method to update current Australian maps and spatial information systems from the AGD to the GDA.
OVERVIEW OF REFERENCE SPHEROIDS AND DATUMS
The Figure of the Earth
The figure of the earth is defined, in geodetic terms, as that of the geoid. The geoid is the equipotential surface of the earth's gravity field, which corresponds most closely with mean sea level and extends continuously through the continents (Figure 1).
Figure 1. The relation between the geoid, spheroid and the earth's surface
However, the geoid is a geometrically and mathematically complicated surface, which is impractical to use for mapping purposes. Instead, a simplified figure of the earth is used as the fundamental reference surface for horizontal coordinates. This figure is a spheroid or an oblate biaxial ellipsoid of revolution about its minor axis, flattened towards the earth's poles (Figure 2). The size of the spheroid is defined by its semi-major axis (a) and its geometrical shape defined by the flattening (f=1-b/a).
Figure 2. An oblate spheroid, flattened towards the poles, with semi-major axis a and semi-minor axis b
The distinction is made between a spheroid and an ellipsoid because these terms are often used interchangeably in geodesy texts. According to the Oxford English Dictionary (OED, 1989), a spheroid is:
"Spheroid. A body approaching in shape to a sphere, especially one formed by the revolution of an ellipse about one of its axes. oblate, prolate spheroid"
whereas an ellipsoid is (ibid.):
"Ellipsoid. A solid of which all the plane sections through one of the axes are ellipses, and all other sections are ellipses or circles. Formerly in narrower sense: A solid generated by the revolution of an ellipse about one of its axes; now called ellipsoid of revolution".
Evidently, there is some ambiguity in the exact name which should be used to describe this approximation of the figure of the earth. In accordance with the revised OED definition of the ellipsoid, the term spheroid is deemed more appropriate in this instance, and will be used hereafter.
Known geographical coordinates, namely latitude and longitude, comprise the datum and are referenced to
the surface of the spheroid. In Figure 3, the geographical latitude (
) is the angle, measured in the meridional
plane, between the spheroidal surface normal and the equatorial plane of the spheroid. Note that the
projection of the surface normal through the equatorial plane does not necessarily pass through the
geometrical centre of the spheroid. The geographical longitude (
) is the angle, measured in the equatorial
plane, from the Greenwich meridian to the meridian through the point of interest.
Figure 3. Geographical latitude () and longitude () on the spheroid
Two classes of spheroid are used at either regional or global scales. A regional spheroid corresponds to a best fit to the geoid in a particular region or country, whereas a global spheroid is a best fit to the geoid over the whole earth. As such, a number of different reference spheroids have been defined both locally and globally, see Bretreger (1991), Chovitz (1981) or Smith (1988).
The geographical coordinates of known points in the region to be mapped comprise the datum. Therefore, there is a distinction between the spheroid and the datum: The spheroid is a geometrical reference surface, whereas the datum is the adopted coordinate set, which is based on a particular spheroid. Therefore, not all geographical latitudes and longitudes of the same surface location are equal, but depend upon the spheroid and coordinate datum to which they are referenced. This is of particular importance when dealing with the AGD and GDA.
Regional Spheroids and Datums
As stated, a regional reference spheroid is chosen so as to fit the geoid, as closely as possible, over the area to be mapped. This approach enables subsequent geodetic data, which are collected on the physical surface of the earth, to be reduced to the surface of this spheroid without the introduction of significant horizontal scale error.
As the geoid is an undulating surface, the best-fitting spheroid in one region is not necessarily the best fit in another (Smith, 1988). Consequently, different reference spheroids have been defined in different regions. For example, the Australian National Spheroid (ANS) is used in Australia (Bomford, 1967), whereas the Airy 1830 spheroid is used in Great Britain (HMSO, 1950).
Regional spheroids have generally been established using astronomical observations to define the deflection of the vertical (difference between geoidal and spheroidal normals) to be zero at an origin point. The orientation and scale of the spheroid is defined using further geodetic observations, see Smith (1988).
Once the best fitting regional spheroid has been defined, it is adopted as the reference surface for geodetic positions in that region. The available geodetic observations are then adjusted, in a least squares sense, to form the regional datum based on that reference spheroid. For example, in Australia the AGD84 and AGD66 datums are based on the ANS, whereas in Great Britain, the OSGB36 and OS(SN)80 datums are based on the Airy 1830 spheroid.
Global Spheroids and Datums
A global spheroid corresponds to a best fit to the geoid over the entire earth. Early attempts to define the global spheroid used both gravity and arc measurements (Chovitz, 1981). The first internationally recognised global spheroid was the 1924 International Ellipsoid.
The advent of satellite-derived geodetic data in the 1960's enabled improved determinations of the global spheroid. Furthermore, such spheroids are geocentric, which means that their geometrical centre corresponds with the earth's centre of mass or geocentre. The orientation of this spheroid is achieved by aligning its minor axis with the earth's mean spin axis at a particular time.
The next internationally recognised global geocentric spheroid, which was derived with the inclusion of satellite observations, was the Geodetic Reference System 1967 or GRS67 (IAG, 1971). This was soon refined and superseded by the Geodetic Reference System 1980 or GRS80, which is also geocentric, with a=6378137 metres and f=1/298.257222101 (Moritz, 1980).
In addition to defining the geometrical size and shape of the earth, physical parameters are associated with
global spheroids. These are the product of the Newtonian gravitational constant and the mass of the earth
(GM), the angular velocity of the earth's rotation (
), and the dynamical form factor (J2). This factor is used
to derive the flattening of the spheroid (Heiskanen and Moritz, 1967; Moritz, 1980). These additional physical
parameters allow a model gravity field to be computed.
The most recent global geocentric spheroid that is widely used is the World Geodetic System 1984 or WGS84 (DMA, 1987, Kumar, 1993). The WGS84 spheroid is based on the GRS80 spheroid, but with f=1/298.257223563. This slight difference in flattening is due to rounding errors. However, the effect on three-dimensional coordinates is less than a millimetre and can therefore be neglected.
The Global Positioning System (GPS) provides positions that are referenced to the WGS84 spheroid. It is envisaged that GPS will be used for the majority of positioning and navigation applications in the future. For example, the International Maritime Organisation uses WGS84 for its navigational charts.
Furthermore, a global network of accurately positioned ground stations comprises a global datum, called the IERS's (International Earth Rotation Service's) Terrestrial Reference Frame (ITRF). The ITRF is positioned relative to the geocentre using a variety of space-based techniques, such as Satellite Laser Ranging (SLR), Very Long Baseline Interferometry (VLBI), and GPS; see Seeber (1993) for a description of these methods.
The ITRF92 is a more recent datum than the WGS84 datum and is considered to be an improvement upon WGS84. Also, the ITRF92 is internationally recognised and endorsed through the International Association of Geodesy (IAG). As such, it has been chosen to form the backbone of the GDA (Manning and Harvey, 1994). In fact, the WGS84 datum was modified in early 1994 and is now coincident with the ITRF92 at the 10cm level (Malays and Slater, 1994). Therefore, for all practical purposes, the GDA is fully compatible with GPS in terms of spheroid and datum.
To summarise, a regional or geocentric datum comprises geographical coordinates that are referenced to the surface of a particular reference spheroid. Therefore, a single ground point can have different geographical coordinates by virtue of the datum and spheroid used.
HISTORY OF AUSTRALIAN DATUMS, SPHEROIDS AND MAPS
Before 1966, mapping and charting in Australia was heterogeneous by virtue of the use of several different datums and spheroids. Coordinate discrepancies arose because fixed points in the same area were defined by several different coordinate sets, depending upon the datum used (Steed, 1990, annex A).
This problem was rectified in 1966 by the introduction of the continent-wide Australian Geodetic Datum (AGD66). This involved an adjustment of the then-available geodetic observations to produce the AGD66 set of geographical coordinates (Bomford, 1967).
The AGD66 datum is based upon the regional Australian National Spheroid (ANS), for which a=6378160
metres and f=1/298.25 exactly. The origin point of the ANS and AGD is fixed at the Johnson Geodetic
Station in the Northern Territory (=25o 56' 54.5515" S, =133o 12' 30.0771" E, and spheroidal height
h=571.2 metres). The ANS was oriented by defining its minor axis parallel to the earth's mean axis of rotation
at the beginning of 1962, and zero AGD longitude to be 149o 00' 18.855" west of the Mount Stromlo
observatory (ibid.).
The Australian Map Grid 1966 (AMG66) is used by National and State/Territory authorities to map coordinates from the AGD66. The AMG66 is synonymous with a Universal Transverse Mercator (UTM) projection (Snyder, 1987) and uses geometrical constants of the ANS (NMC, 1986).
As more accurate, notably satellite-derived, geodetic data became available, deficiencies in the AGD66 coordinates were revealed (Lambert, 1981). A re-adjustment was performed using these additional data to produce the Geodetic Model of Australia 1982 (Allman and Veenstra, 1984). This was subsequently adopted as the Australian Geodetic Datum 1984 (AGD84), which is also based on the ANS and Johnson origin.
AGD84 geographical coordinates differ from the previous AGD66 coordinates by up to six metres, as a consequence of this re-adjustment (Allman and Veenstra, 1984). A similar situation occurred in North America, for example, when NAD27 was updated to NAD83 (Olsen, 1993).
The Australian Map Grid 1984 (AMG84) easting and northing are derived from AGD84 geographical coordinates using a UTM projection from the ANS (NMC, 1986).
However, despite the availability of the improved AGD84 datum, AGD66 and AMG66 coordinates are still used for surveying and mapping in Victoria, New South Wales, the Northern Territory, the Australian Capital Territory and Tasmania. Only Western Australia, South Australia and Queensland implemented the AGD84 and AMG84 (Manning and Harvey, 1992). Obviously, this resulted in a regression to the heterogeneous national use of coordinate datums for mapping.
The Geocentric Datum of Australia
For some time, Australia has intended to use a geocentric datum for national mapping. For example, page 3 of NMC (1986) states:
"Recognising the need for Australia to eventually convert to a geocentric datum, the National Mapping Council, at its forty-second meeting in October 1984, resolved that the GMA82 [Geodetic Model of Australia 1982 (Allman and Veenstra, 1984)] adjustment would be adopted as the first step in the conversion process. However, the Council also resolved that members could use their discretion in the timing of the conversion process."
In 1988, the Inter-governmental Committee on Surveying and Mapping (ICSM), which was established following the cessation of the National Mapping Council (NMC), initiated this conversion from the regional AGD66 and AGD84 datums to a geocentric datum (ICSM 1990, 1991a, 1991b). The ICSM resolved to adopt the Geocentric Datum of Australia 1994 (GDA94) at its November 1994 meeting. ICSM has recommended the gradual implementation of this datum Australia-wide by 1st January, 2000. The GDA is intended to supersede the AGD66 and AGD84, and lead to a homogeneous national coordinate datum for future mapping (Manning and Harvey, 1994).
A global sub-network of accurately positioned ground stations, tied to the International Terrestrial Reference Frame (ITRF), has been established using GPS, and is called the International GPS Service for Geodynamics or IGS (Morgan and Manning, 1992). In 1992, the Australian Surveying and Land Information Group (AUSLIG) took the opportunity to simultaneously establish the Australian Fiducial Network (AFN). This is a continent-wide GPS network of eight accurately positioned geocentric stations, which is, in turn, tied geodetically to the IGS and ITRF (Manning and Harvey, 1992).
The Australian National Network (ANN) is a further sub-network of the AFN, and uses GPS-derived positions at approximately 500-kilometre intervals over the continent (Manning and Harvey, 1994; ICSM, 1994). The AFN and ANN coordinates will form the backbone of the new Geocentric Datum of Australia.
TERMINOLOGY OF THE GDA
New nomenclature and acronyms (Appendix A) have been introduced to accompany the geocentric datum. These should help avoid confusion between the different horizontal coordinate sets that will inevitably be encountered in the future. The defining parameters associated with the new datum are:
Geodetic Reference System 1980 (GRS80)
The geocentric GRS80 spheroid will replace the Australian National Spheroid (ANS). Thus, the regional reference spheroid will be replaced by a global geocentric reference spheroid.
GRS80 was recommended and adopted for international geodetic use by the International Association of Geodesy (IAG) during its XVII General Assembly in Canberra in 1979 (Moritz, 1980). Its defining geometrical parameters are a=6378137 metres and f=1/298.257222101.
The World Geodetic System 1984 (WGS84) spheroid is based upon the GRS80 spheroid and the two are identical for all practical purposes. Therefore, GPS-derived coordinates are fully compatible with the GDA.
spheroid a 1/f
(metres)
ANS 6371160 298.25
(exact)
GRS80 6378137 298.257222101
Table 1. Defining geometrical constants of reference spheroids used in Australia post-1966
Geocentric Datum of Australia (GDA)
The Geocentric Datum of Australia (GDA) will form the new earth-centred Australian coordinate datum that, in time, will replace the Australian Geodetic Datum (AGD). This will ensure that Australian coordinates are compatible with GPS and international mapping and charting (ICSM, 1994). The GDA is based upon the GRS80 spheroid and the Australian Fiducial GPS Network (AFN), which is tied to the ITRF (Manning and Harvey, 1994). The AFN is a network of eight fixed geodetic stations with accurately known coordinates with respect to the geocentre that defines the GDA. This was proclaimed in the Commonwealth of Australia Gazette (GN 35, 6 September 1995, p. 3369).
Map Grid of Australia (MGA)
The Map Grid of Australia (MGA) will be used to display GDA geographical coordinates and will eventually supersede the AMG84 and AMG66. The MGA is a UTM projection of GDA geographical coordinates from the GRS80 spheroid. Therefore, Redfearn's (1948) formulae must use the geometrical parameters of GRS80 (Table 1).
The datum change corresponds to a north-easterly horizontal shift of ground coordinates by approximately 200-metres depending upon location, see ICSM (1994). This horizontal difference will affect maps according to their scale as indicated in Table 3. It is these differences that will have the most significant implications for Australian users and producers of spatial information.
GDA94 and MGA94
In the interim period before the recommended Australia-wide implementation of the GDA in the year 2000, GDA94 coordinates can be used, but this decision depends ultimately on the user's preference. The coordinate datum of the GDA94 is the AFN, which is tied to the IERS Terrestrial Reference Frame 1992 (ITRF92), epoch 1994.0. An epoch is specified for the ITRF92 because these coordinates change slowly in time due to the effects of plate tectonics. Fortunately, these coordinate changes are so slow that they would not affect Australian mapping for 20-30 years. As stated earlier, the ITRF92 datum is equivalent to the WGS84 datum for all practical purposes. Therefore, GPS is fully compatible with the GDA.
GDA94 coordinates can be derived from existing AGD coordinates (described later) using the interim transformation parameters of Higgins (1987). However, a set of rigorously computed transformation parameters will be released in 1996. These will be derived using AFN and ANN stations whose coordinates are known in both the AGD84 and GDA94 (Manning and Harvey, 1994). It is therefore worthwhile to wait for the rigorous transformation parameters to be released. However, the exact time of transition to the GDA is left to the discretion of the user.
Finally, the MGA94 is simply a UTM projection of GDA94 geographical coordinates using the GRS80 spheroidal constants.
National and State/Territory Implementation of the GDA
The implementation of the GDA throughout the States and Territories could be achieved by using a national coordinate transformation from AGD84 (and AGD66, where necessary). However, a complete re-adjustment of now-available geodetic data (including GPS) is the preferable scenario. AUSLIG is currently undertaking a joint cooperative project for a combined State/Territory geodetic adjustment using the AFN and ANN. The decision to transform or re-adjust at the State/Territory level will be left to the discretion of each. New South Wales and Queensland have reported that they are taking the opportunity to re-adjust their respective AGD66 and AGD84 coordinate sets, during the transition (Kinlyside, 1994; Higgins, 1994). Other State and Territory mapping authorities are also expected to readjust their geodetic networks. As far as the user and producer of spatial data is concerned, it is more practical to transform geographical data to the GDA using the methods described later in conjunction with published National or State/Territory transformation parameters.
At this time, it is expected that the GDA94 coordinate set will be in use in the year 2000 and the final adoption of these coordinates will be affected on 1st January, 2000. Essentially, it is envisaged that after the turn of the century, Australian geographical coordinates will be on the homogeneous GDA, as opposed to the AGD66 or AGD84 in all States and Territories.
datum spheroid map grid AGD66 ANS AMG66 AGD84 ANS AMG84 GDA94 GRS80 MGA94 Table 2. Horizontal datums, spheroids and map projection grids used in Australia post-1966
Australian Height Datum (AHD)
The use of the Australian Height Datum (AHD) for topographic elevations (NMC, 1986) will continue, and the move to the GDA will not affect heights in Australia.
IMPLICATIONS FOR SPATIAL SCIENTISTS, SPATIAL SYSTEMS USERS AND CARTOGRAPHERS
The change to the GDA will affect all Australian users and producers of coordinate-related information, in whatever form (maps, charts, GIS, etcetera). Therefore, there is now a need for a more general awareness of the different datums that will exist in Australia.
It is envisaged that this datum change will cause some confusion in the interim, but this is outweighed by the long-term benefits of the GDA. Nevertheless, a 200-metre coordinate change is quite noticeable, which should avoid most confusion between coordinate sets. Some of the benefits associated with the use of the GDA are:
The GDA will ensure a geocentric, homogeneous, GPS-compatible datum to all users, irrespective of their understanding of coordinate datums.
All Australian geographical information will be referenced to a single, homogeneous, geodetic datum. The GDA will not suffer from edge- or boundary-related discontinuities. This is considered an ideal situation, especially by spatial information system (SIS) users, who require a "seamless" datum. Furthermore, it will facilitate the exchange of compatible data at local, State/Territory, National and international levels.
Future Australian map users will inevitably become more dependent upon satellite-based positioning. The GDA will be compatible with GPS and other similar positioning systems (ICSM, 1994). Therefore, the GPS user will be able to determine positions directly on Australian maps, without the need for a series of coordinate transformations.
The International Maritime Organisation and Royal Australian Navy use a geocentric datum for hydrographic charting. Therefore, the boundary of hydrographic charts and Australian topographic maps will be compatible, thereby aiding near-coast navigation. This will also apply to aircraft navigation.
Essentially, the GDA will simplify all future surveying, mapping and navigation tasks. It will also ease the integration of GPS-derived positions into various digital and hard-copy cartographic products.
Maps
One of the major implications to the cartographer is the revision of current AMG84 and AMG66 maps. MGA ground coordinates will differ from their predecessors by approximately 200-metres in a north-easterly direction. This change in ground coordinates will affect the nation's map series by the approximate amounts indicated in Table 3. However, these changes are regional so relative spatial relationships will generally be preserved, especially for small-scale maps.
map scale shift on map (mm) 1:250000 0.8 1:100000 2.0 1:50000 4.0 1:25000 8.0 1:10000 20 1:5000 40 1:2500 80 1:1000 200 Table 3. The effect of a 200-metre coordinate change on Australian maps
One option to manage the datum change is for maps to retain the same geographical borders, but these will contain different ground positions and hence features. As such, these maps can not be joined with existing maps (ICSM, 1994). The ICSM (1991a, 1991b) proposes that this coordinate offset could be accommodated by overlapping maps by the same amount as the respective shift on the map (cf. Table 3). This can be achieved either by extending the northern and eastern boundaries, or by providing overlaps on all boundaries.
The current use of two sets of graticules/grids for small-scale maps could be extended to all maps (one AGD/AMG, and one GDA/MGA). A simple solution is to add GDA/MGA tick-marks along the map boundaries of existing maps. Of most importance when taking such an approach is that a clear explanation of the difference between the two grid/graticule sets is given so that the map user is not confused.
To update Australia's map series at all scales 'overnight' is a massive and costly undertaking. A more realistic approach is for this process to coincide with scheduled revisions of the map series. Obviously, the cost will be included as part of this process and possibly spread over a number of years. ICSM (1994) suggests that map makers employ the datum on a basis of user demand.
Spatial Information Systems (SISs)
Land and geographical information systems, which use coordinates (map or geographical) for georeferencing, will also be affected by the change, because:
Attributes with AGD/AMG coordinates must be transformed to the GDA/MGA;
SISs generally contain large amounts of georeferenced data, which must be transformed in order to preserve spatial relationships;
SISs that are not georeferenced must take into consideration the different datums when integrating data from other sources.
Fortunately, the process of updating SISs is simpler than for hard-copy maps, as these data are already stored in digital form. Nevertheless, it is imperative to clearly document the datum on which the data are given.
UPDATING SPATIAL INFORMATION USING A SEVEN-PARAMETER TRANSFORMATION
The cartographer or spatial information scientist can convert coordinates from the AGD to GDA94 immediately by using the interim transformation parameters of Higgins (1987). However, this process could be delayed until the rigorously computed transformation parameters are released in 1996.
The process of updating hard-copy maps is more involved than for a SIS because some form of graphical or grid-on-grid approach is required. However, if the conversion coincides with a digital revision process, the existing map can be converted to digital form, thereby making the transformation simple with the use of a computer.
Once the data are in digital form, the following transformation scheme from AMG to MGA coordinates can be employed (Steed, 1990):
1. Convert AMG66 to AMG84 coordinates (where applicable) using a regional block shift. The exact methods for this transformation are currently under refinement by the respective State and Territory mapping authorities.
2. Transform the AMG84 easting and northing, for each particular AMG zone, to AGD84 latitude (AGD)
and longitude (AGD). In Australia, Redfearn's (1948) formulae, with ANS geometrical constants, are used
for this conversion (NMC, 1986).
3. Transform these AGD84 coordinates to three-dimensional AGD84 Cartesian coordinates (X, Y, Z)AGD', referenced to the geometrical centre of the ANS, using (Heiskanen and Moritz, 1967, p. 182):
where a=6378160m and f=1/298.25 for the ANS.
Equations (1) describe a three-dimensional transformation. Therefore, the spheroidal height (hAGD) of the point above the ANS must be included. If the height is neglected, errors of up to 80mm will occur in Australia (the maximum is h=2200m at the summit of Mount Kosciusko). However, for millimetre-level transformation accuracy, it is sufficient to use only the AHD height, because the geoid-ANS separation (refer to Figure 1) over mainland Australia is at most +25 metres (NMC, 1986). However, if the ANS spheroidal height is available, it should be used in preference as it is more rigorous.
4. Transform the AGD84 Cartesian coordinates (X, Y, Z)AGD to GDA Cartesian coordinates (X, Y, Z)GDA', using a seven-parameter transformation (Harvey, 1986).
The seven-parameter transformation is a rigorous option for converting three-dimensional Cartesian coordinates from one datum to another. It comprises an origin shift, rotation of coordinate axes and a scale change in three-dimensional space.
A rigorous set of the seven parameters is currently being derived using the AFN and ANN networks (Higgins, 1994) for use in equation (2). However, interim AGD84 to WGS84 parameters, determined by Higgins (1987) as: Xo=-116.00m, Yo=-50.47m, Zo=+141.69m, rx=-0.23", ry=-0.39", rz=-0.344", and ds=+0.0983 parts per million, have been adopted as these are sufficiently accurate (few metres) to use as an interim transformation to the GDA. Figure 4 illustrates the difference in metres between AGD84 and GDA94 geographical coordinates when using Higgins's parameters. These parameters may be refined, and possibly expressed as a function of geographical location, once the rigorous parameters are published.
Figure 4. The difference between AGD84 and GDA94 coordinates over Australia derived from Higgins's (1987) parameters (contours in metres, Mercator projection)
5. Transform the GDA Cartesian coordinates (X, Y, Z)GDA to GDA geographical coordinates (GDA and
GDA) using the inverse of equations (1):
where a=6378137m and f=1/298.257222101 are GRS80 constants. If the incorrect constants are used mistakenly, ANS instead of GRS80 for example, this can create a 5mm horizontal error.
In equations (3), the geographical latitude is used on both sides of the second equation, which necessitates that some form of iteration be used. By using the AGD84 latitude as a first approximation on the right hand side, the number of iterations per point are reduced to less than 10.
6. Finally, convert the GDA geographical coordinates ( GDA and GDA) to MGA easting and northing
using Redfearn's (1948) UTM formulae. The geometrical constants required here are also those of the
GRS80 spheroid.
Table 4 gives a flow chart of these procedures required to update maps and SISs to the MGA. A FORTRAN77 computer program to undertake the geographical component of this coordinate transformation is available from the author.
Table 4. Flow chart for the conversion of AMG84 to MGA coordinates
Worked Example
Given the AMG84 easting 345000.000m and northing of 6345000.000m in zone 50, the intermediate values
are: AGD84 geographical = -33 01' 20.4314", =115 20' 25.5658"; AGD84 Cartesian
X=-2291123.212m Y=4838068.642m Z=-3456048.452m; GDA94 Cartesian (using Higgins's parameters)
X=-2291254.041m Y=4838018.680m Z=-3455897.375m; GDA94 geographical =-33 01' 16.1102",
=115 20' 30.9457"; MGA94 E=345138.054m ,N=6345147.974m, zone 50.
SPECULATION FOR THE FUTURE
It is evident that the move to the GDA and MGA will require major changes to almost all maps and spatial information systems in Australia. Both the users and producers of spatial information must be aware of the multiple coordinate systems. This extends to the ability to transform between datums, especially during the revision and data integration processes.
The implications for future mapping and spatial information systems are wider ranging than this introductory discussion. However, education and general awareness of the different datums, should simplify this process.
Overall, the biggest issue facing map and SIS users and producers is knowing which coordinate datum is being used. Fortunately, the approximate 200-metre difference is sufficiently large to avoid major confusion. However, this is no substitute for careful labelling of geographical data which clearly shows the datum used.
Finally, it should be stressed that the time of conversion to the GDA is predominantly user-dependent and left to their discretion.
ACKNOWLEDGEMENTS
I would like to thank the ICSM and its Geodesy Group, especially Ken Alexander and Bob Irwin, for their contributions to this revised version. I would also like to thank the two anonymous reviewers for their comments on the first edition of this paper and the Editor of Cartography, Graeme Wright, for agreeing to distribute this revised paper. Finally, thanks to Frank Bryant, whose kind comments were the catalyst for this updated version.
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APPENDIX A: Acronyms used
AFN Australian Fiducial Network
AGD Australian Geodetic Datum
AGD66 Coordinates from the 1966 adjustment of the AGD
AGD84 Coordinates from the 1984 adjustment of the AGD
AHD Australian Height Datum
AMG Australian Map Grid
AMG66 Map grid coordinates from the AGD66
AMG84 Map grid coordinates from the AGD84
ANN Australian National Network
ANS Australian National Spheroid
AUSLIG Australian Surveying and Land Information Group
DMA United States' Defense Mapping Agency
GDA Geocentric Datum of Australia
GDA94 Coordinates from the 1994 adjustment/transformation
GPS Global Positioning System
GRS67 Geodetic Reference System 1967
GRS80 Geodetic Reference System 1980
IAG International Association of Geodesy
ICSM Inter-governmental Committee on Surveying and Mapping
IERS International Earth Rotation Service
ITRF IERS's Terrestrial Reference Frame
MGA Map Grid of Australia
MGA94 Map grid coordinates from the GDA94
NMC National Mapping Council, now ICSM
SIS Spatial Information System
SLR Satellite Laser Ranging
UTM Universal Transverse Mercator
VLBI Very Long Baseline Interferometry
WGS84 World Geodetic System 1984