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Abstract. AUSGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetricquasigeoid and AHD heights are inconsistent. Since the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree and order 2190 was used as the reference field. Other input data are: ~1.4 million land gravity anomalies from Geoscience Australia, 1'x1' DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9"x9" GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 dynamic ocean topography model. In order to determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights, showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface-fitting, the standard deviation of fit reduced to ±30 mm, one third of which is attributable to the uncertainty in the GNSS ellipsoidal heights.

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In an absolute sense, AUSGeoid09 is an order of magnitude more accurate than AUSGeoid98 at converting ellipsoidal heights to Australian Height Datum (AHD) heights and vice versa. Results of this study show AUSGeoid09 can be used to compute AHD heights from Global Navigation Satellite System (GNSS) ellipsoidal heights with an uncertainty of less than ±0.03 m (one sigma). The improvement is largely due to the inclusion of a geometric component in AUSGeoid09 that accounts for the spatially varying offset between a gravimetric quasigeoid model and the AHD. This geometric component was calculated using least squares collocation in cross validation mode and then added to the gravimetric quasigeoid. Although previous AUSGeoid models were used to convert GNSS ellipsoidal heights to the AHD and vice versa, none until now have accounted for the gravimetric quasigeoid to AHD offsets. This offset is a consequence of how the AHD was realised and has commonly resulted in misfits of ~0.5 m or more. When used with GNSS technology, AUSGeoid09 can replace the need for traditional third-order levelling (Class LC; 12 k) in many situations. Relative tests of AUSGeoid09 over a continent-wide set of over 20 million baselines showed that it can deliver better than Class LC tolerances in 99% of cases. The model accepts a user's GDA94 latitude, longitude and ellipsoidal height and returns an AHD height and deviations of the vertical. AUSGeoid09 is now available free-of-charge on the Geoscience Australia website

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