Comparison of ITRF to GDA94 coordinate transformations by Dawson & Woods (2010) to AUSGeoid09: a more direct and more accurate model for converting ellipsoidal heights to AHD heights by Brown, Featherstone, Hu and Johnston (2011)

In their work, John Dawson and Alex Woods aimed to improve and extend the GDA94 to ITRF coordinate transformations presented by Dawson and Steed in 2004. In addition, they review the effect of dealing incorrectly with inconsistencies that arise between satellite trajectories and references station coordinates in the reduction of differential GNSS observations in GDA94 based geodetic networks. Lastly, they investigate the alternative to station coordinate transformations, ITRF-to-GDA94 satellite trajectory transformations, and their limitations then highlight the limitations of GDA94 (Dawson & Woods 2010, p. 189). On the other hand, Brown, Featherstone, Hu & Johnston (2011) objective is to provide a ‘product’ that allows users of GNSS to recover AHD heights more accurately because AHD is the official national vertical datum in Australia. This is possible through provision a model of the base of the AHD (Brown et al. 2011).

Datasets used by Dawson & Woods (2010) were obtained from the ITRF product center of the International Earth Rotation and References System Services (IERS) using the software INdependent EXchange (SINEX) format. For consistency, all solutions were first projected using the station velocity estimates to the reference epoch of GDA94 (Dawson & Woods 2010, p. 190). For the GDA94 coordinates, datasets were obtained from the gazette positions of the AFN which include seven AFN stations. On the other hand, Brown et al. (2011) used both gravitational and geometric datasets. The gravitational dataset used the degree-2190 spherical harmonic expansion of the EGM2008 global gravity model, the 9” by 9” GEODATA-DEM9S digital elevation model of Australia, about 1.4 million land gravity anomalies from the Australian national gravity database, and altimeter-derived marine gravity anomalies from the DNSC2008GRA grid. A readjustment of the Australian National Leveling Network (ANLN) was done with reference to the CARS2006 dynamic ocean topography model so as to reduce the effect of the north-south slope and regional distortions in the AHD. About 1000 GNSS heights were used in datasets for this report. For the geometric datasets, spatial variable offsets were obtained through comparison of AHD-ellipsoid separations to the AGQG2009-ellipsoid separations. This was done through the use of two datasets; primary dataset of 2626 co-located GNSS-AHD heights and secondary datasets of 4233 leveling junction points from the ANLN used t provide higher resolution definitions of the offset between AGOG2009 and AHD (Brown et al. 2011, p.3-4).

The methodology used in Dawson & Woods (2010) involved the use of a 14 parameter relation to transforming station coordinates and velocity from ITRF to GDA94. The relational method used had three translations, t_x,t_y,t_z, three rotations, r_x,r_y,r_z, one scale factor, s_c, and their first-time derivates t_x,t_y,t_z,r_x,r_y,r_z and s_c (Dawson & Woods 2010, p. 191)_. On the other hand, the Brown et al. (2011) study used a model that combined gravimetric-geometric AUSGeoid09 model that was developed in two stages; the gravimetric component of the 1’ by 1’ model was developed, and a cross-validated LSC used to develop the geometric component that models the spatiality varying offset between gravimetric quasigeoid and the AHD then ‘draped’ over the gravimetric geoid (Brown et al. 2011, p. 4).

Findings by Dawson & Woods (2010) showed the root-mean-square (RMS) residual differences between GDA94 and the ITRF2005 and ITRF2008 less than 10 and 30 mm in the horizontal and vertical components respectively after transformation. The RMS for ITRF2000 was slightly worse, but less than 10 and 60mm but the maximum residual for ITRF2000, ITRF2005, and ITRF2008 occasionally exceed 10 and 60 mm in the horizontal and vertical components respectively (Dawson & Woods 2010, p. 192). Brown et al. (2011) on the other hand showed that  the RMS of the relative difference between AUSGeoid09 and the GNSS-AHD data points is related to results of the cross-validation testing with an RMS value of approximately 0.03m in all baselines and those shorter than 100 km (Brown et al. 2011, p. 8).

Based on the new and improved ITRF-to-GDA94 transformations for a range of realizations, Dawson and Wood (2010) conclude that the Geosciences Australia is to adopt them in its capacity as the Verifying Authority of Position Measurements in line with the National Measurement Regulations 1999, National Measurement Act 1960, and the relevant requirements of the National Association of Testing Authorities (NATA), Australia.

As a result of the large residuals observed in Western Australia, mainly in Perth Metropolitan, the report recommends future development of time-dependent deformation modeling to aid geodetic positioning (Dawson & Wood 2010, p.196).  On the other hand, based on the findings that the combined gravimetric-geometric AUSGeoid09 model is more accurate than AUSGeoid98 for the recovery of AHD heights for GNSS with an uncertainty of 0.030 m, Brown et al. (2011) concludes GNSS users can compute accurate AHD heights in near-real-time or through post processing (p. 9).

References

Brown N, Featherstone W, Hu G & Johnston G, (2011). AUSGeoid09: a more direct and more accurate model for converting ellipsoidal heights to AHD heights, Journal of Spatial Science 56 (1): pp. 27-37.

Dawson J & Woods A, (2010). ITRF to GDA94 coordinate transformations, Journal of Applied Geodesy 4, 189–199