The AUSGeoid09 model of the Australian Height Datum

Abstract

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.

The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates

“…Compute two 1 × 1 grids of residual quasigeoid heights for both the above residual gravity anomaly grids. So as to replicate the approach taken in Featherstone et al (2011), the computation used the Featherstone et al (1998) The difference between these two regional RCR quasigeoid models is shown in Fig. 13.…”

“…All previous Australian geoid or quasigeoid models (cited in Featherstone et al 2001Featherstone et al , 2011 have focussed only on the Australian mainland and Tasmania. However, Australia administers several offshore territories and a 200-nauticalmile maritime boundary around each.…”

Deterministic, stochastic, hybrid and band-limited modifications of Hotine’s integral

“…Therefore, it is important to consider the kernel modification not only as means to reduce the truncation error, but also as a filter to reduce leakage of any low-frequency errors from the terrestrial data (cf. Omang and Forsberg 2002;Featherstone et al 2011;Wang et al 2011). …”

“…In Australia, for instance, the vertical datum contains a confirmed tilt with respect to the geoid (Featherstone and Filmer 2012), regional distortions [e.g., Featherstone et al (2011) and the citations therein], and uses a height system that is not compatible with the geoid (Filmer et al 2010). These will cause errors in the computed terrestrial gravity anomalies (cf .…”

“…Heck 1990) that can propagate into the combined geoid solution unless modelled and/or filtered out (cf. Vaníček and Featherstone 1998;Wang et al 2011;Featherstone et al 2011).…”