A Comparison of Existing Co-ordinate Transformation Models and Parameters in Australia

Abstract

Four standard procedures to transform curvilinear co-ordinates from the Australian Geodetic Datum 1984 to the World Geodetic System 1984 are compared. These comprise the Bursa-Wolf model with the national set of seven parameters currently used by Federal and State surveying and mapping authorities, the standard Molodensky model with the five parameters used by the United States Defense Mapping Agency, the simple three-parameter model with the origin shifts taken from the Bursa-Wolf and standard Molodensky models, and the multiple regression equations as determined by the Defense Mapping Agency. The differences between the resulting co-ordinates can reach 4.2 metres over continental Australia, which has implications for the final approach adopted to transform to the Geocentric Datum of Australia. The arguments are presented in favour of more suitable transformation strategies using projective transformation models, which are able to simultaneously correct any known errors existing in the Australian Geodetic Datum. These models also allow the direct transformation of both Australian Geodetic Datum 1966 and Australian Geodetic Datum 1984 coordinates in a single procedure, which will be of benefit to those States which rely upon older geodetic datums. INTRODUCTION Australia’s transition to the use of the Geocentric Datum of Australia (GDA) for surveying and mapping by the 1st January, 2000 will require that existing spatial data are transformed to this new co-ordinate datum (Featherstone, 1994 and 1996; Steed, 1995; Inter-governmental Committee on Surveying and Mapping, 1994; Higgins, 1994; Manning and Harvey, 1994). Featherstone (1994 and 1996), among other authors, only presents the seven-parameter conformal transformation model using the Higgins (1987) constants. However, there are several alternative transformation models and parameters currently available for Australia which can also be employed for this purpose. This paper compares four mathematical models and their associated parameters for the transformation of curvilinear co-ordinates from the Australian Geodetic Datum 1984 (AGD84) to the World Geodetic System 1984 (WGS84), which can be assumed compatible with the GDA for many practical purposes. These are: 1. A seven-parameter conformal transformation using the Bursa-Wolf model (Bursa, 1962; Wolf, 1963), where the transformation is staged via Cartesian co-ordinates and uses the parameters of Higgins (1987). 2. A five-parameter conformal transformation based on a curvilinear version of the Molodensky-Badekas model (Molodensky et al., 1962; Badekas, 1969) with the Defense Mapping Agency’s (1991) parameters. 3. The multiple regression equation approach of the Defense Mapping Agency (1991), which is a spatially varying or projective transformation. (The latter two approaches are designed to operate directly on the curvilinear co-ordinates, and thus provide a conceptually more direct transformation.)