Geocentric Datum of Australia - GDA

Transcription

1 Geocentric Datum of Australia - GDA Supporting GDA94 ARC/INFO ArcView 3.1 An ESRI Australia White Paper September 1999 White Paper Series

2 OVERVIEW... 1 INTRODUCTION... 1 PART 1 ESRI SOLUTION... 2 ARC/INFO Transforming data to GDA94 using ARC/INFO... 2 Results... 5 Summary... 6 ARCVIEW Transforming data to GDA94 using ArcView... 7 Results... 9 Summary PART 2 DATUMS AND PROJECTIONS INTRODUCTION MODELS OF THE EARTH The Geoid Definition of a Geodetic Datum Local Geodetic Datum Geocentric Datum DATUMS IN AUSTRALIA Australian Geodetic Datum (AGD) World Geodetic System 1984 (WGS84) Geocentric Datum of Australia (GDA94) MAP PROJECTIONS Universal Transverse Mercator (UTM) Lambert s Conformal Conic Projection COORDINATE SYSTEMS Geographical Coordinates Cartesian Coordinates Australian Map Grid 1966 (AMG66) Australian Map Grid 1984 (AMG84) Map Grid of Australia 1994 (MGA94) TRANSFORMING DATA ONTO GDA Molodensky Method (3 parameters) Dimensional Similarity Transformation (7 parameters) Distortion Grids APPENDIX A APPENDIX B APPENDIX C BIBLIOGRAPHY GLOSSARY OF TERMS White Paper Series

3 Figure 1: Approximate coordinate shift from AGD to GDA94(m)... 1 Figure 2: Method of Datum Transformation in ARC/INFO... 3 Figure 3: Contour Map of the ARC/INFO 7 parameter transformation Residuals (m)... 5 Figure 4: Contour Map of the ArcView 3 parameter transformation Residuals (m)... 9 Figure 5: Contour Map of the ArcView 3 parameter transformation Residuals (m) Figure 6: Reference Ellipsoid Figure 7: Local Geodetic Datum Figure 8: Geocentric Datum Figure 9: AGD Coordinate Set Usage Figure 10: The Australian National Network (ANN) Figure 11 : Hierarchy of GDA Adjustments Figure 12: UTM Projection, Zone Figure 13: Lambert s Conformal Conic Projection Figure 14: Latitude and Longitude Definition Figure 15: 3D Cartesian Coordinates (XYZ) Definition Figure 16: Flow chart of steps in transforming data on AMG84 to MGA Table 1: ICSM National Transformation Accuracies... 2 Table 2: Comparison of Transformed AGD84 to GDA94 Coordinates... 5 Table 3: Comparison of Transformed MGA94 Coordinates... 6 Table 4: Comparison of Transformed AMG84 Coordinates... 6 Table 5: Comparison of Transformed AGD66 to GDA94 Coordinates... 9 Table 6: Comparison of Transformed AGD84 to GDA94 Coordinates Table 7: Datum Summary Table 8: The set of parameters defining the characteristics of the UTM projection Table 9 : ICSM endorsed National 3 parameters AGD66 & AGD84 to GDA Table 10: ICSM endorsed National 7 parameters - AGD84 to GDA White Paper Series

4 Australia is in the process of implementing a new datum. This datum, the Geocentric Datum of Australia (GDA) is planned to be adopted nationally by the year 2000 for all surveying, mapping and navigation applications. The purpose of this document is to provide details of transforming data to the GDA using the ESRI suite of products, such as ARC/INFO and ArcView, and a background into datums and common coordinate systems used in Australia. Note: This paper has information on ARC/INFO Rev and ArcView only. There will be ongoing amendments to this paper for other ESRI and ERDAS products as testing and documentation of GDA support is completed. In 1988, the Inter-Governmental Committee on Surveying and Mapping for Australia (ICSM) resolved to adopt an earth centred or geocentric datum in Australia by the year This new datum has been named the Geocentric Datum of Australia (GDA94). The main reasons for moving to GDA94 are to; be compatible with Global Positioning System (GPS). Return to a single coordinate system for all of Australia. provide a reference framework compatible with other international datums. The GDA94 is an earth centred datum, unlike the existing Australian Geodetic Datum (AGD) which was designed to suit only the Australian region. As a result, GDA94 coordinates reflect a 200 metre north east shift of the Australian Geodetic Datum coordinates of the same point. The precise size and orientation of the difference varies across the country. Figure 1: Approximate coordinate shift from AGD to GDA94(m) (GDA Brochure.) White Paper Series Page 1

5 ARC/INFO supports two types of datum transformation methods. One type uses grids to calculate the coordinate differences between datums. The most widely used methods in North America, NADCON and CNT, are of this type. This is based on NTv1 format grids. The second type uses equations to model the differences between the coordinate systems. Any datum whose relationship to WGS84 is known can be transformed in ARC/INFO. There are two equation-based transformations available. They are based upon the Molodensky and Bursa- Wolf transformations, referred to as three- and seven- parameter transformations, respectively. These transformations use parameters published by the United States National Imagery and Mapping Agency, NIMA, formerly Defense Mapping Agency. (ARC/INFO Command reference) ARC/INFO currently supports the Australian Geodetic Datum 1966 (AGD66) and the Australian Geodetic Datum 1984 (AGD84) using transformation parameters published by the US NIMA and the 3 parameter Molodensky transformation formulae (See Appendix A). GDA94 is currently not incorporated in ARC/INFO. However there is the facility to easily add support for GDA94. Transformation parameters are located in an ASCII file, $ARCHOME/datum/datums.par and additional transformations can be added to this file so they become available in ARC/INFO for use with the Arc: PROJECT command. Visit our WEB page for the latest updated files. ESRI Australia have adopted the ICSM published transformation parameters. Method of Transformation in ARC/INFO 7 Parameter - ( Bursa-Wolf) Between AGD84 and GDA94 3 Parameter - (Molodensky) Between AGD66 and GDA94 Estimated Accuracy (GDA Technical Manual v1.02) 1 metre 5 metres Table 1: ICSM National Transformation Accuracies Because of the inconsistent nature of the AGD66 coordinate set, it is not possible to compute a set of Bursa-Wolf national AGD66/GDA94 parameters with acceptable accuracy, but they can be computed for local regions. Some authorities have computed regional AGD66/GDA94 parameters. (GDA Technical Manual v1.02) Changing from one coordinate system to another is accomplished with the PROJECT command, this is a two step process performed by one command. The first step transforms the data to latitude and longitude coordinates on WGS84, known as inverting the projection. The next step transforms the latitude and longitude coordinates to the desired output datum, the forward transformation. White Paper Series Page 2

6 Inverting Forward Transformation Latitude / Longitude WGS84 Original Coordinate system Latitude/Longitude On DATUM A New Coordinate system Latitude/Longitude On DATUM B Transforming data between different datums, ARC/INFO uses WGS84 as the intermediate datum, in this example data is transformed from Datum A to Datum B. The use of WGS84 is invisible to the user. Figure 2: Method of Datum Transformation in ARC/INFO. Although the ARC/INFO transformation parameters are from the local datum to WGS84 it is still possible to use the ICSM endorsed seven parameters. The process would be to apply the transformation parameters from AGD84 to GDA94 in the inversion process and then apply a zero transformation in the forward process to GDA94. This is an extract from the datums.par ASCII file with two extra datums added, AGD84 and GDA94, last two lines. The first three datums, WGS84, AUA and AUG are existing datums in ARC/INFO. WGS "WGS 84" AUA "AUSTRALIAN GEODETIC 1966" AUG "AUSTRALIAN GEODETIC 1984" AGD "AGD66 - ICSM" AGD "AGD84 - ICSM" GDA "GDA94 - ICSM" ARC/INFO Datum Keyword Ellipsoid Definition Semi-Major Axis & Inverse Flattening 7 transformation parameters X Y Z R X R y R z Scale Datum Description White Paper Series Page 3

7 In order to use the ICSM endorsed 7 parameters, data must be transformed using the DATUM keywords, AGD84 and GDA94. Within ARC/INFO the procedure to transform data from AGD84 to GDA94 is simple, involves using one command, PROJECT and a projection file. The projection file provides the definition of the input and output coordinate systems. This example is for transforming AMG84, Zone 54 to MGA94, Zone 54. Arc: project cover <input coverage> <output coverage> {projection file} Arc: project cover data-amg84 data-gda94 amg84mga94.prj where the projection file, amg84mga94.prj would be; /* AGD84 to GDA94 using the 7 parameter transformation INPUT PROJECTION TRANSVERSE UNITS METERS DATUM AGD84 SEVEN PARAMETERS /* scale factor /* longitude of the central meridian /* latitude of the origin /* false easting /* false northing OUTPUT PROJECTION TRANSVERSE UNITS METERS DATUM GDA94 SEVEN PARAMETERS /* scale factor /* longitude of the central meridian /* latitude of the origin /* false easting /* false northing END Although elevation models and surface analysis is a strength of ARC/INFO it does not treat the Z coordinate the same as the X,Y coordinates, the Z coordinate is usually treated as an attribute of an X,Y location. As a result the ellipsoidal height is ignored for the transformation, the effect increases as the height above the ellipsoid increases but in Australia a large error in ellipsoidal height (hundreds of metres) has negligible effect on the transformed horizontal position (millimetres). (GDA Technical Manual v1.01) White Paper Series Page 4

8 2.00 ESRI Australia Pty Ltd Test data was supplied by AUSLIG, this consisted of a number of highly accurate survey stations which had both AGD84 and GDA94 geographical coordinates. The process was to use the ARC/INFO projection command with the ICSM 7 parameter transformation and transform the AGD84 coordinates into GDA94 coordinates. The ARC/INFO transformed coordinates were then compared against the true values of the GDA94 test data. The comparison was based on determining the absolute difference in distance between the true GDA94 coordinate and the transformed coordinate for each point. A total of 1561 points distributed across Australia were used in the test. Differences between the true GDA94 and ARC/INFO transformed data were computed and summarised. This represents the residuals or distortions introduced by using a national set of parameters Figure 3: Contour Map of the ARC/INFO 7 parameter transformation Residuals (m) AGD84 to GDA94 Using the 7 parameters in ARC/INFO Mean Difference Standard Deviation Maximum Difference 0.47 metres 0.37 metres 2.75 metres Table 2: Comparison of Transformed AGD84 to GDA94 Coordinates White Paper Series Page 5

9 A second test compared the results from ARC/INFO with those computed by the South Australian Department of Environment, Heritage and Aboriginal Affairs (DEHAA). DEHAA supplied two ARC/INFO coverages of Kangaroo Island, one in AMG84 and the other in MGA94, was produced using the ICSM 7 parameter transformation with software written by DEHAA. The aim was to compare the method and transformation formulae in ARC/INFO with a 3 rd party. Using ARC/INFO the DEHAA AMG84 coverage was transformed to MGA94 and the DEHAA MGA94 coverage transformed back to AMG84. The average difference was metres, this would be mainly due to the DEHAA process including the ellipsoidal height and ARC/INFO assuming this is zero. AMG84 to MGA94 Using the 7 parameters in ARC/INFO Mean Difference Standard Deviation Maximum Difference metres metres metres Table 3: Comparison of Transformed MGA94 Coordinates MGA94 to AMG84 Using the 7 parameters in ARC/INFO Mean Difference Standard Deviation Maximum Difference metres metres metres Table 4: Comparison of Transformed AMG84 Coordinates According to the GDA Technical Manual, v1.01, National parameters to convert between AGD84 and GDA94 have been developed and have an estimated accuracy of about 1 metre. This accuracy is achieved using these parameters with ARC/INFO The majority of GIS datasets currently in use across Australia would have been captured by digitising existing mapping at various scales. For example if data was captured using 1:250,000 maps the approximate accuracy would be 125 metres, based on +/- 0.5mm at the scale of capture according to cartographic standards. The distortion introduced by the transformation would generally be negligible in comparison to the accuracy of the dataset. Very few existing GIS datasets would not be suitable for use with the 7 parameter transformation. White Paper Series Page 6

10 ArcView 3.1 has the facility to perform datum transformations via the sample extension, Datum Conversion. This extension contains two buttons on the view GUI. One allows you to enter a point and then based on a from and to datum, it returns the transformed coordinates. The other button transforms the shapes of all active themes from one datum to another. ArcView uses WGS84 as the intermediate datum, the use of WGS84 is invisible to the user. The original shapefile coordinates are updated and no new shapefile is created. If the original shapefile is still required, transform a copy of the original shapefile. ArcView 3.1 uses the Molodensky transformation (3 parameters) method. Currently ArcView supports the AGD66 and AGD84 using transformation parameters published by the US NIMA and the 3 parameters transformation formulae. See Appendix A Coordinates in these themes must be in decimal degrees. Although the GDA94 is currently not incorporated in ArcView 3.1, there is the facility to add support for GDA94. Transformation parameters are located in an ASCII file, $HOME/datums.par and additional transformations can be added to this file so they become available in ArcView for use with the Datum Conversion extension. Visit our WEB page for the latest updated files. If you have defined HOME through your operating system, ArcView uses that value. If you have not specified HOME, ArcView attempts to establish HOME in its startup script. ArcView looks for a writable directory searching for environment variables TEMP, CWD and AVHOME. If ArcView cannot find a writable directory in one of these three options, you will get a warning message when you start ArcView instructing you to define HOME. Note: Shapefile coordinates must be in decimal degrees for use with the Datum Conversion extension. This is an extract from the datums.par ASCII file with three extra datums added, AGD66, AGD84 and GDA94. The first three datums, AUA, AUG and WGS84 are existing datums in ArcView. AUA "AUSTRALIAN GEODETIC 1966" AUG "AUSTRALIAN GEODETIC 1984" WGS "WGS 84" AGD " AGD ICSM" AGD " AGD ICSM" GDA "GDA ICSM" Datum Keyword Ellipsoid Definition Semi-Major Axis & Inverse Flattening 7 transformation parameters X Y Z R X R y R z Scale Only X Y Z are used by ArcView (3 parameters) Datum Description Used to select the Datum in ArcView White Paper Series Page 7

11 Within ArcView the procedure to transform data from AGD84 or AGD66 to GDA94 is simple. Load the sample Datum Conversion extension. (See Appendix B) Copy the updated datum.par ASCII file in your $HOME or $TEMP For a PC, this is usually c:\temp Make the AGD66/84 theme in decimal degrees active AGD66 in this example. Select the theme Datum button Theme Datum Button Select the Input Datum AGD ICSM, uses the ICSM defined parameters. Select the Output Datum GDA ICSM. The active shapefile will now have been transformed into the selected output datum, in this example GDA94. Test data was supplied by AUSLIG, this consisted of a number of highly accurate survey stations which had both AGD84 and GDA94 geographical coordinates. The process was to use the ArcView Datum Conversion extension with the ICSM 3 parameter transformation and transform the AGD coordinates into GDA94 coordinates. The ArcView transformed coordinates were then compared against the true values of the GDA94 test data. The comparison was based on determining the absolute difference in distance between the true GDA94 coordinate and the transformed coordinate for each point. A total of 1561 points distributed across Australia were used in the test. White Paper Series Page 8

12 ESRI Australia Pty Ltd Differences between the true GDA94 and ArcView transformed data were computed and summarised. This represents the residuals or distortions introduced by using a national set of parameters for both AGD66 and AGD Figure 4: Contour Map of the ArcView 3 parameter transformation Residuals (m) Contour Interval: 0.5m AGD66 to GDA94 Using the 3 parameters in ArcView Mean Difference Standard Deviation Maximum Difference 1.45 metres 0.76 metres 6.20 metres Table 5: Comparison of Transformed AGD66 to GDA94 Coordinates White Paper Series Page 9

13 ESRI Australia Pty Ltd Figure 5: Contour Map of the ArcView 3 parameter transformation Residuals (m) Contour Interval: 0.25m AGD84 to GDA94 Using the 3 parameters in ArcView Mean Difference Standard Deviation Maximum Difference 0.80 metres 0.43 metres 3.2 metres Table 6: Comparison of Transformed AGD84 to GDA94 Coordinates According to the GDA Technical Manual, v1.01, The AGD66/84 to GDA94 parameters have an estimated accuracy of 5 metres. This accuracy is achieved using the ICSM published parameters with the ArcView 3.1 sample Datum Extension. White Paper Series Page 10

14 Technical Support Division The 3 and 7 parameter transformations are suitable for the majority of GIS datasets with accuracies of approximately 3-5 metres and 1 metre respectively. However this is not suitable for transforming survey data which have accuracies at the centimetre level. This is an extract from the GDA Technical Manual, version 1.10, for High accuracy transformations. The approach adopted for Australia by ICSM, is similar to that adopted in Canada in that it uses files of coordinate shifts which can compensate for distortions in the original data. All the complex mathematical processing, based on many common points, is done prior to the production of the files of coordinate shifts (Collier, 1997). A simple interpolation by the user then provides the required shifts and a simple addition performs the transformation. State and Territory authorities will produce these files for their area and when all State and Territory files are complete, they will be merged to produce a single file for Australia. This national grid file will then be freely available from the ICSM web site. Where there is appropriate common data, this transformation method is expected to have an accuracy of better than 10cm. The Australian Approach In November 1997, ICSM adopted the concept of a unique and standard grid of coordinate differences to model the AGD/GDA94 transformation and existing AGD network distortions. Subsequently, the Canadian NTv2 data format was adopted. The grid spacing is still subject to evolution according to the particular circumstances of each State and Territory and the relative control network density, but will probably range from 2.5 minutes for heavily controlled urban areas to 5-10 minutes for more sparsely controlled rural areas. Initially, each State and Territory will be responsible for producing a grid file(s) for their area. These grid files will transform from either AGD66 or AGD84, depending on which version of AGD was previously adopted by that jurisdiction. These grid files, when complete, will be combined to form a single national grid that will allow the transformation of national or interstate data sets. For further information and details on the current status of the National and State distortion grids please refer to the GDA Technical Manual, viewed at; ARC/INFO currently supports NTv1 format grids for the transformation of data in Northern America and Canada. The use of custom NTv2 distortion grids is not directly supported in ARC/INFO. ESRI Australia are working with ESRI USA and strategic clients to include support for NTv2 grids in ARC/INFO. For further details please contact the ESRI Australia Support Centre, support@esriau.com.au White Paper Series Page 11

15 The move towards the Geocentric Datum of Australia (GDA) results from an international trend to adopt a geocentric datum to make spatial data compatible with satellite based (GPS) coordinates. The GDA will provide a single reference framework for collecting, storing and applying spatial data at local, national and international levels. Prior to the GDA, multiple coordinate sets and datums, AGD66, AGD84 and WGS84 have been used across Australia creating major problems particularly when collating data on a national level. With the implementation of the GDA comes the major issue of how this is being addressed by your GIS software vendor. ESRI Australia are continually researching support for the GDA across the ESRI suite of software products. This white paper will be expanded as more products are tested for GDA compliance and accepted by ESRI Australia. This document demonstrates how you can enable your existing ESRI software to become GDA94 enabled in a few quick and easy steps. Please contact your local ESRI Australia Office for any further queries relating to the support of the GDA94 across the ESRI and ERDAS suite of products. White Paper Series Page 12

16 This second part of this paper provides information on the theory of datums and projections. A background on the GDA94 and history of Australian datums and common coordinate systems is discussed. In order to locate information on the earth a model needs to be established which represents it s shape and size. This section provides an overview of the models used to reference features on the earth. The geoid is a surface approximated by mean sea level. It's shape is affected by the earth's mass, rotation and gravity anomalies resulting in an irregular surface. All surveying observations performed using a theodolite are referenced to the geoid. It is this surface to which elevations, for instance on maps or orthometric heights are referred. Due to the irregularities in the geoid it is highly complicated to mathematically map and thus impractical to use as a reference. A datum provides a frame of reference for measuring locations on the surface of the earth. The definition of a geodetic datum comprises two parts; definition of a reference ellipsoid. the ellipsoid's position and orientation in 3D space. An ellipsoid is a mathematical shape that approximates the size and shape of the earth. The earth is actually squashed, flattened at the poles and an ellipse best represents this shape. The ellipsoid, often referred to as a spheroid, is created by rotating an ellipse about it's minor axis. Ellipsoid Semi Minor Axis Semi Major Axis Figure 6: Reference Ellipsoid White Paper Series Page 13

17 An ellipsoid is usually defined by specifying the semi - major axis (a) and the amount of flattening (f). Semi major Axis: (a) Semi minor axis: (b) Flattening: (f) = (a - b) / a Once the ellipsoid definition has been defined, the position and orientation of the ellipsoid with reference to the earth is required. The position of the ellipsoid s centre is defined and the orientation of the ellipsoid is determined by aligning it s axis with the earth s. This is a datum which best fits a local area of the geoid. Usually the datum fits the local area extremely well but may be a poor approximation of the geoid in other parts of the world. The Australian Geodetic Datum (AGD) is a local or regional datum as it was designed to best fit the geoid in the region of Australia. (Jones 1998) A point on the surface of the ellipsoid is matched to a particular position on the surface of the earth, this point is known as the origin point. The coordinates of the origin point are held fixed and all other points are calculated from it. (ESRI 1997) Poor Fit Ellipsoid Centre of mass Geoid Mean Sea level Geoid Ellipsoid separation Figure 7: Local Geodetic Datum Excellent Fit A geocentric datum best fits the whole earth. This datum does not favour any particular area of the earth. The centre of the ellipsoid coincides with the earth s centre of mass. The Global Positioning System (GPS) is based on a geocentric datum as it is designed to be used anywhere around the globe.(jones 1998) Ellipsoid Centre of mass = centre of the ellipsoid Geoid Mean Sea level Figure 8: Geocentric Datum Average Fit for the entire earth White Paper Series Page 14

18 The Australian Geodetic Datum (AGD) was proclaimed in the Australian Commonwealth Gazette of 6 October This proclamation included the parameters of the local ellipsoid, known as the Australian National Spheroid (ANS), which defines the adopted size and shape of the earth, and the position of the origin point - Johnston Geodetic Station. The definition of the datum, reference ellipsoid, the position and orientation are; Reference Ellipsoid The AGD is based upon the regional Australian National Spheroid (ANS) which at the time was recommended for use by the International Astronomical Union. The semi major axis (a) = metres The flattening (f) = 1/ Position The ANS was fixed at the origin point, Johnston geodetic Station in the Northern Territory. Latitude = Longitude = Spheroidal Height = metres The adoption of this origin and the best fitting local spheroid means that the centre of the AGD did not coincide with the centre of mass of the earth but differs by approximately 190 metres from it. (Steed 1990) Orientation The minor axis was parallel to the earth s mean axis of rotation at the beginning of 1962 and zero longitude should be parallel to Bureau International de l Heure near Greenwich (Collier et al 1996) An adjustment of the Australian Geodetic Network was computed on the AGD. (Bomford 1967) This set of coordinates, in latitude and longitude, was referred to as the Australian Geodetic Datum Finally Australia had it s first continent wide coordinate set.(collier et al 1996) The computation of the AGD66 coordinate set assumed the geoid - ellipsoid separation (N) was zero at all survey stations. Combined with this assumption, the limitations of the adjustment model used and the then unknown systematic trends in some observations meant the AGD66 was non-homogeneous, with the scale and orientation changing across Australia. (Steed 1990) With the increase of more accurate data, notably satellite derived, deficiencies were revealed with the AGD66. In 1982 a re-computation of all the data used for AGD66 and additional observations using modern technologies and satellite based was performed. This is referred to as the Geodetic Model of Australia The coordinate set from this adjustment was adopted as the Australian Geodetic Datum 1984.(Featherstone 1996) White Paper Series Page 15

19 The AGD84 is still based on the ANS and the Johnston Origin, however unlike the 1966 adjustment all observations were corrected for the geoid-ellipsoid separation (N) and systematic errors were not ignored. (Steed 1990) For AGD66 the Johnston Origin had an N value of 0 and following the 1982 readjustment, AGD84 had an N value of 4.9 metres. The use of modern computational techniques combined with additional modern survey observations resulted in a coordinate set that is generally homogeneous, with scale and orientation being relatively consistent across the continent. (Steed 1990) Effectively, AGD84 is an updated, but distinctly different version of AGD66. (Jones 1998) Despite the improvements made with the AGD84 over the AGD66, only three states moved to AGD84, WA, SA and QLD. NSW, VIC, ACT, NT and TAS remained with AGD66 and two different coordinate sets were now in use at the national level. (Manning, Harvey 1992) Northern Territory AGD66 Queensland Western Australia AGD84 AGD84 South Australia AGD84 New South Wales & ACT AGD66 Victoria AGD66 Tasmania AGD66 Figure 9: AGD Coordinate Set Usage WGS84 was developed by the US Department of Defense and is the datum the Global Positioning System (GPS) is currently based on. The WGS84 is geocentric, and is designed to best fit the whole earth, it s spheroid is based on the GRS80 ellipsoid but with a flattening that is very slightly different due to rounding errors. The effect of this is less than a millimetre. (Featherstone 1996) White Paper Series Page 16

20 Datum Australian Geodetic Datum World Geodetic System Geocentric Datum of Australia (AGD) (WGS84) (GDA) Australian Geodetic Geodetic Ellipsoid National Spheroid Reference System Reference System (ANS) 1980 (GRS80) 1980 (GRS80) Semi-Major Axis (a) 6,378,160 metres 6, metres 6,378,137 metres Flattening (f) 1 / / / Semi-Minor Axis (b) 6,356, metres - 6,356, metres Table 7: Datum Summary White Paper Series Page 17

21 Australia has commenced the introduction of a geocentric datum as the basis of all geographic data. The major driving factors of this resolution were; Compatible with the Global Positioning System (GPS) Return to a single datum for Australia. The national adoption of a new datum would lead to a single datum providing a homogenous coordinate set across Australia Using a compatible datum with the Defence forces The GDA94 will also provide an international coordinate reference for Australia. The International Terrestrial Reference Frame (ITRF) is a world wide reference frame recommended by the International Association of Geodesy (IAG). It is geocentric and maintained from observations at a number of sites around the world. The ITRF is continually monitored. It could be considered to be a dynamic datum. Australia has ten highly accurate coordinated survey marks across the country which contribute and monitor the ITRF. These ten survey marks form the Australian Fiducial Network (AFN). These were supplemented by further observations in 1993 and 1994, producing a network of about 70 well determined GPS sites, with a nominal 500 km spacing across Australia. These sites are collectively known as the Australian National Network (ANN). The GPS observations at both the AFN and ANN sites were combined in a single regional GPS solution in terms of the International Terrestrial Reference Frame 1992 (ITRF92) and the resulting coordinates were mapped to a common epoch of The positions of both the AFN and ANN sites were used to constrain a readjustment of the Australian geodetic networks, which included all observations from the previous AGD66 and AGD84 adjustments, conventional observations added since that time, and the extensive GPS networks established by the State and Territory authorities at about 100 km spacing between the ANN sites. This resulted in a data set of more than 70,000 observations and produced GDA94 coordinates at almost 8,000 stations. These GDA94 coordinates are now used by the State and Territory authorities to adjust their subsidiary survey networks onto GDA (GDA Technical Manual, version 1.10). Figure 10: The Australian National Network (ANN) This network of sites forms the framework for the GDA (AUSLIG WEB Page). White Paper Series Page 18

22 Figure 11 : Hierarchy of GDA Adjustments (Burbidge et al 1998) The definition of the GDA94 reference ellipsoid, the position and orientation are; Reference Ellipsoid The GDA is based upon the Geodetic Reference System 1980 (GRS80) ellipsoid. Semi-major axis 6,378,137.0 metres Flattening 1/ Position and Orientation The position of the GRS80 ellipsoid is based on the Australian Fiducial Network (AFN). The AFN Coordinates are based on the ITRF92 at epoch , hence the name GDA94. An epoch (point in time) is specified for the ITRF92 because these coordinates slowly change in time due to the effects of tectonic plate movement. (Featherstone 1996). These ten survey marks for the AFN fix the position and orientation of the GRS80 ellipsoid and define the coordinate set for GDA94. All GDA94 coordinates emanate from the AFN. The GDA94 and WGS84 reference frame for GPS are coincident at a 10 cm level. (Malys and Slater, 1994). Thus for all data other than survey accurate the GDA94 is effectively equivalent to WGS84. White Paper Series Page 19

23 A map projection is the process in transforming a 3D curved surface, such as an ellipsoid, onto a 2D surface, such as a flat piece of paper. This transformation usually comprises a series of mathematical formulae. Map projection coordinates are 2D Cartesian coordinates, they are referenced to two perpendicular axis, more commonly known as Eastings and Northings. Projected coordinates are usually expressed in metres or feet. A map projection introduces some distortions to the data, as it is impossible to make a curved surface flat, for example an orange peel would tear if it was flattened. The Transverse Mercator projection uses a horizontal cylinder which is tangent to the equator and makes contact along one meridian. The central meridian is placed centrally on the region of interest. This centring minimises distortion of all properties in that region. This projection is best suited for land masses that stretch north to south. The Universal Transverse Mercator (UTM) projection is a global implementation of the Transverse Mercator projection. To minimise distortion, the earth is "rotated" within the cylinder, to bring a different meridian into contact with the cylinder, for different areas. This results in north-south bands known as zones. Each UTM zone has its own central meridian and spans 3 degrees west and 3 degrees east. X (Easting) and Y (Northing) coordinates are in metres. The true origin for each zone is the intersection of the equator and its central meridian. To eliminate negative coordinates, the projection alters the coordinate values at the origin. A false easting of 500,000 meters is applied. And if in the southern hemisphere, a false northing of 10,000,000 meters is used. Redfearn s formulae are used to convert between UTM and geographical coordinates. (Collier et all 1996) The Australian Map Grid coordinates (AMG) are the UTM projected latitude and longitude s based on the Australian Geodetic Datum (AGD). To uniquely identify a location the Easting, Northing and Zone Number are required when using AMG coordinates. Longitude of initial central meridian (Zone one) 3 east longitude Longitude of the Central Meridian 6 x the zone no. 183 Zone width 6 degrees Central scale factor False easting False northing (in the southern hemisphere) 500,000 m 10,000,000 m Table 8: The set of parameters defining the characteristics of the UTM projection. White Paper Series Page 20

24 6 Wide Zone, centred on the central meridian Transverse Cylinder Central Meridian Longitude 141 E Scale factor Ellipsoid True Origin Equator Lines of intersection between the cylinder and ellipsoid. Scale factor 1.0 Figure 12: UTM Projection, Zone 54 A limitation of the UTM projection is if the area of interest covers more than one zone. This presents the dilemma of either; Using only one zone for all the data, usually the zone with the majority of the data. Use a different projection not limited by zones. If for example the data extent covered a whole state such as South Australia which is serviced by three UTM zones, a common alternative projection used is Lambert s Conformal Conic Projection. A cone is placed tangent to the ellipsoid along a line of latitude, called a standard parallel. Distortions increase north and south of the standard parallel and often two standard parallels are used to minimise the distortions. East West orientated data is best suited to this projection. Ellipsoid Central Meridian 2 Standard Parallels of Latitude Cone intersects the ellipsoid at the standard parallels Figure 13: Lambert s Conformal Conic Projection White Paper Series Page 21

25 Latitude and Longitude provide a method of referencing a point s location on the earth s surface, often referred to as geographical coordinates. The units commonly used are degrees, minutes and seconds (DMS) or decimal degrees (DD). The definitions of latitude and longitude are; Latitude (φ) is the angle between the equatorial plane and the ellipsoidal normal at the point, P. Latitude is positive north of the equator and negative to the south. Longitude (λ) is the angle between zero meridian and the meridian passing through point P. It is important to note that Latitude and Longitude are measured directly on the ellipsoid, which is a three-dimensional surface, they are not projected coordinates. Geographical coordinates have no zone limitations, unlike UTM projection and are universally applicable and understood. A major disadvantage of using geographical coordinates is the units are difficult to interpret. How long is one degree? or what is the area of the average house block in square degrees? These values are also dependant upon their location on the ellipsoid, where one degree of latitude at the equator is longer than one degree of latitude at 30 south. If the data is projected into 2D cartesian coordinates such as eastings and northings, the units are often in metres or feet, a unit of measure easily understood. Reference Ellipsoid North Pole Meridian intersecting point P Equatorial Plane 0 Latitude Longitude Latitude Point Zero Meridian 0º longitude South Pole 90 S or -90 Ellipsoidal normal Figure 14: Latitude and Longitude Definition White Paper Series Page 22

26 Cartesian coordinates enable a point s location to be referenced in X,Y,Z 3D coordinate system independent of any ellipsoid which has its origin at the centre of the earth. Z Axis Passes through North Pole Reference Ellipsoid Meridian intersecting point P Longitude Equatorial Plane X Axis 0 Longitude Y Latitude Z X Point Y Axis 90 Longitude East Ellipsoidal normal South Pole Figure 15: 3D Cartesian Coordinates (XYZ) Definition The grid coordinates derived from a Universal Transverse Mercator projection of the AGD66 geographical coordinates, using the Australian National Spheroid. The grid coordinates derived from a Universal Transverse Mercator projection of the AGD84 geographical coordinates, using the Australian National Spheroid. The only difference between AMG66 and AMG84 is a difference in coordinate set used to reference the geographical coordinates. Generally this difference is of the order of 0-5 metres. The grid coordinates derived from a Universal Transverse Mercator projection of the GDA94 geographical coordinates, using the GRS80 spheroid. The difference between AMG66/84 and MGA94 coordinates is approximately 200 metres, entirely due to the difference between the AGD and GDA.(see Figure 1.) White Paper Series Page 23

27 Data can be converted from one datum to another if the relationship between the two datums is known. This relationship is comprised of; Set of formulae describing the mathematical process used in the transformation Set of parameters, constants, used by the formulae (Jones 1998). The parameters are associated with the two datums of the transformation only. For example, if the parameters were for transforming data from AGD66 to WGS84 they can only be used for conversion between these two datums. It would be invalid to use the same parameters to transform between AGD84 and GDA94. Molodensky s transformation method uses an average origin shift (at the centre of the earth) and the change in the parameters of the two ellipsoids. The AGD66/84 to GDA94 parameters have an estimated accuracy of 5 metres (GDA Technical Manual v1.01). AGD66 to GDA94 AGD84 to GDA94 A m m 1/f X (m) Y (m) Z (m) a (m) f Table 9 : ICSM endorsed National 3 parameters AGD66 & AGD84 to GDA94 (GDA Technical Manual v1.01) Provided the rotation angles are small (a few seconds), the relationship between two consistent, three dimensional coordinate systems can be completely defined by seven parameter similarity transformation (three origin shifts, three rotations and a scale change) (Harvey, 1986). Refer to Appendix C for further explanation. The transformation is a relatively simple mathematical process, but because this technique is in terms of Earth-centred Cartesian coordinates (X Y Z), the points to be transformed must be converted to this coordinate type. This means that ellipsoidal heights are used on input and are produced on output, but in Australia a large error in ellipsoidal height (hundreds of metres) has negligible effect on the transformed horizontal position (millimetres). White Paper Series Page 24

28 Easting, Northing, Zone on AMG84 Convert from AMG coordinates to Geographical (φ,λ). Latitude(φ),Longitude(λ) on AGD84 Transform the Geographical (φ,λ) to 3D X,Y,Z Cartesian Coordinates. X,Y,Z on AGD84 Apply the 7 parameter transformation to X,Y,Z on AGD84 -> X,Y,Z on GDA94 X,Y,Z on GDA94 Transform the X,Y,Z Cartesian Coordinates to Geographical (φ,λ) Latitude(φ),Longitude(λ) on GDA94 Convert from Geographical (φ,λ) to MGA coordinates. Easting, Northing, Zone on MGA94 Figure 16: Flow chart of steps in transforming data on AMG84 to MGA94. (Featherstone 1996) National parameters to convert between AGD84 and GDA94 were endorsed by ICSM in November 1997 (see below) and have an estimated accuracy of about 1 metre. Because of the inconsistent nature of the AGD66 coordinate set, it is not possible to compute a set of national AGD66<->GDA94 parameters of similar accuracy. However, regional parameters between AGD66 and GDA94 are being developed by the appropriate local authorities. (GDA Technical Manual v1.01) White Paper Series Page 25

29 Parameter Value DX (m) DY (m) DZ (m) R X (secs) R Y (secs) R Z (secs) Sc (ppm) Table 10: ICSM endorsed National 7 parameters - AGD84 to GDA94 (GDA Technical Manual v1.01) Another method of transforming data to GDA is to provide a grid of transformation shifts. From this grid, The components of transformation ( E and N) for any given point can be determined from this grid and applied to the AGD values to determine their equivalent GDA coordinates. This same strategy has been adopted in the United States and Canada to move spatial data from North American Datum 1927(NAD27) to North American Datum 1983 (NAD83). This is an extract from the GDA Technical Manual, version 1.10, for High accuracy transformations, using distortion grids. The approach adopted for Australia by ICSM, is similar to that adopted in Canada in that it uses files of coordinate shifts which can compensate for distortions in the original data. All the complex mathematical processing, based on many common points, is done prior to the production of the files of coordinate shifts (Collier, 1997). A simple interpolation by the user then provides the required shifts and a simple addition performs the transformation. State and Territory authorities will produce these files for their area and when all State and Territory files are complete, they will be merged to produce a single file for Australia. This national grid file will then be freely available from the ICSM web site. Where there is appropriate common data, this transformation method is expected to have an accuracy of better than 10cm. The Australian Approach In November 1997, ICSM adopted the concept of a unique and standard grid of coordinate differences to model the AGD/GDA94 transformation and existing AGD network distortions. Subsequently, the Canadian NTv2 data format was adopted. The grid spacing is still subject to evolution according to the particular circumstances of each State and Territory and the relative control network density, but will probably range from 2.5 minutes for heavily controlled urban areas to 5-10 minutes for more sparsely controlled rural areas. White Paper Series Page 26

30 Initially, each State and Territory will be responsible for producing a grid file(s) for their area. These grid files will transform from either AGD66 or AGD84, depending on which version of AGD was previously adopted by that jurisdiction. These grid files, when complete, will be combined to form a single national grid that will allow the transformation of national or interstate data sets. For further information and details on the current status of the National and State distortion grids please refer to the GDA Technical Manual, viewed at; White Paper Series Page 27

31 Local Datum Keyword X (m) Y (m) Z (m) AGD66 AUA AGD84 AUG Default 3 Parameter Transformation values from AGD to WGS84 used in ARC/INFO and ArcView 3.1 as published by the United States National Imagery and Mapping Agency (NIMA). These values are used with the DATUM keywords, AUA and AUG. The updated datums.par file includes the ICSM endorsed parameters and are accessed via the keywords AGD66, AGD84 and GDA94. AUA and AUG have not changed and have been superceded by the ICSM values. White Paper Series Page 28

32 How to load a sample extension in ArcView Extensions Extensions are add-on programs to ArcView that provide additional functionality. When you load an extension, ArcView s user interface changes to reflect the functionality in the extension. For example, new menus, menu items, buttons, and tools may appear. In addition to the extensions that come with ArcView, such as the CAD Reader extension, a number of sample extensions are provided in this samples library. These sample extensions provide useful functions for your work. Examining these sample extensions will also help you learn how to create your own extensions. You can find out about each sample extension by looking at its help topic. The extensions themselves are located in the <ArcView install directory>/samples/ext directory in your ArcView installation. To load a sample extension To load extensions in ArcView you can either copy the.avx file for the extension(s) you wish to load from the <ArcView install directory>/samples/ext to the <ArcView install directory>/ext32 Once you ve done this, the sample extensions will be listed in the Extensions dialog the next time you open it. In that dialog, check the sample extension(s) you wish to load and press OK. Tip One of the sample extensions, seesmple.avx, adds a menu choice to the File menu (when the Project window is active) that makes it easy to browse and load the other sample extensions. To load this extension, first copy it to <ArcView install directory>/ext32 directory, then check it Samples Browser in the Extensions dialog. This will add an extra option to the File menu Browse Sample Extensions. White Paper Series Page 29

33 3-Dimensional Similarity Transformation (Extract from the Geocentric Datum of Australia Technical Manual Version 1.1) National parameters have been computed to transform between AGD84 and GDA94 using the similarity method. These parameters were computed from 327 points across Australia, which had both AGD84 and GDA94 coordinates, well determined AHD heights (by spirit levelling), and which were GPS points in the national GDA94 adjustment. The resulting parameters are shown in table 1. Note: These parameters can be used for projects of medium accuracy (of the order 1 m). More accurate methods must be used for projects requiring greater accuracy. Although this method transforms the height, direct transformation of the height using the geoid-ellipsoid separation is easier and generally more accurate. Because of the inconsistent nature of the AGD66 coordinate set, it is not possible to compute an accurate set of national AGD66 <-> GDA94 parameters. However, regional AGD66 parameters can be determined. Parameters Parameter Value DX (m) DY (m) DZ (m) R X (secs) R Y (secs) R Z (secs) Sc (ppm) Table 1: National parameters - AGD84 to GDA94 These parameters were tested using points additional to the initial 327, which had both AGD84 and GDA94 coordinates. A summary of these tests is shown in table 2. Average (m) Std. Dev. (m) Max (m) Min (m) Latitude Longitude Ellip. Ht Table 2: AGD84 <->GDA94 parameters, residuals from 1571 points (lat/long) and 65 points (ellip. ht.) White Paper Series Page 30

34 Formulae Once the positions have been converted to Earth-centered 3D Cartesian coordinates, the similarity transformation is performed by a simple matrix operation: Where R is the combined matrix of rotations about the X, Y and Z axes, in that order, i.e. R = R x R y R z In its full form this combined rotation matrix is: But for small rotations (a few seconds) it is closely approximated by the matrix below (where the rotations are in radians): Warning There are two different ways of applying the sign conventions for the rotations. In both cases the sign convention is the same (a positive rotation is an anti-clockwise rotation, when viewed along the positive axis towards the origin) but: 1. the International Earth Rotation Service (IERS) assumes the rotations to be of the position around the coordinate axes, while 2. the method historically used in Australia assumes the rotations to be of the coordinate axes. The only difference in the formula is a change in the signs of the angles in the rotation matrix. If the sign of the rotation parameters and the formulae used are consistent the correct results will be obtained. The only way to be absolutely sure which method or parameters are required is to test them using a known input and output for a set of parameters as shown in Table 3. If necessary the situation can be rectified by simply changing the sign of the rotation parameters. White Paper Series Page 31