We describe the computation of the first Australian quasigeoid model to include error estimates as a function of location that have been propagated from uncertainties in the EGM2008 global model, land and altimeterderived gravity anomalies and terrain corrections. The model has been extended to include Australia's offshore territories and maritime boundaries using newer datasets comprising an additional ∼280,000 land gravity observations, a newer altimeter-derived marine gravity anomaly grid, and terrain corrections at 1 × 1 resolution. The error propagation uses a remove-restore approach, where the EGM2008 quasigeoid and gravity anomaly error grids are augmented by errors propagated through a modified Stokes integral from the errors in the altimeter gravity anomalies, land gravity observations and terrain corrections. The gravimetric quasigeoid errors (one sigma) are 50-60 mm across most of the Australian landmass, increasing to ∼100 mm in regions of steep horizontal gravity gradients or the mountains, and are commensurate with external estimates.

A one arc-minute resolution gravimetric quasigeoid model has been computed for New Zealand, covering the region 25°S to 60°S and 160°E to 170°W. It was calculated by Wong-Gore modified Stokes integration using the removecompute-restore technique with the EIGEN-6C4 global gravity model as the reference field. The gridded gravity data used for the computation consisted of 40,677 land gravity observations, satellite-altimetry-derived marine gravity anomalies, historical shipborne marine gravity observations and, importantly, approximately one million new airborne gravity observations. The airborne data were collected with the specific intention of reinforcing the shortcomings of the existing data in areas of rough topography inaccessible to land gravimetry and in coastal areas where shipborne gravimetry cannot be collected and altimeter-derived gravity anomalies are generally poor. The new quasigeoid has a nominal precision of ±48 mm on comparison to GPS-levelling data, which is approximately 14 mm less than its predecessor NZGeoid09.

Gravity field modelling in coastal region faces challenges due to the degradation of the quality of altimeter data and poor coverage of gravimetric measurements. Airborne gravimetry can provide seamless measurements both onshore and offshore with uniform accuracies, which may alleviate the coastal zone problem. We study the role of airborne data for gravity field recovery in a coastal region, and the possibility to validate coastal gravity field model against recent altimetry data (CryoSat-2, Jason-1, and SARAL/Altika). Moreover, we combine airborne and ground-based gravity data for regional refinement, and quantify and validate the contribution introduced by airborne data. Numerical experiments in the Gippsland Basin over the southeastern coast of Australia show that the effects introduced by airborne gravity data appear as small-scale patterns on the centimetre scale in terms of quasi-geoid heights. Numerical results demonstrate that the combination of airborne data improves the coastal gravity field, and the recent altimetry data can be potentially used to validate the high-frequency signals introduced by airborne data. The validation against recent altimetry data demonstrates that the combination of airborne measurements improves the coastal quasigeoid, by ~5 mm, compared with a model computed from terrestrial and altimetry-derived gravity anomalies alone. These results show that the recently released altimetry data with relatively denser spatial resolutions and higher accuracies than older altimeter data may be beneficial for gravity field model assessment in coastal areas.

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AUSGeoid2020 is a combined gravimetric-geometric model (sometimes called a "hybrid quasigeoid model") that provides the separation between the Geocentric Datum of Australia 2020 (GDA2020) ellipsoid and Australia's national vertical datum, the Australian Height Datum (AHD). This model is also provided with a location-specific uncertainty propagated from a combination of the levelling, GPS ellipsoidal height and gravimetric quasigeoid data errors via least squares prediction. We present a method for computing the relative uncertainty (i.e. uncertainty of the height between any two points) between AUSGeoid2020-derived AHD heights based on the principle of correlated errors cancelling when used over baselines. Results demonstrate AUSGeoid2020 is more accurate than traditional third-order levelling in Australia at distances beyond 3 km, which is 12 mm of allowable misclosure per square root km of levelling. As part of the above work, we identified an error in the gravimetric quasigeoid in Port Phillip Bay (near Melbourne in SE Australia) coming from altimeter-derived gravity anomalies. This error was patched using alternative altimetry data.

We present 1 arc-minute Bouguer, Faye, free air and topography corrected gravity anomaly grids for the New Zealand region, 25°S to 60°S and 160°E to 170°W. The grids were compiled from existing terrestrial, marine and satellite altimetry-derived gravity data enhanced with new airborne gravimetry data that were acquired for improvement of the New Zealand vertical datum. The airborne data seamlessly cover onshore and offshore areas over New Zealand's North, South and Stewart islands with a uniform flight line spacing of 10 km. All data were corrected for the gravitational effect of the Geodetic Reference System 1980 (GRS80) reference ellipsoid and tied to the International Gravity Standardization Net 1971 (I.G.S.N.71) gravity datum. The gravity anomaly data from all sources were combined using the method of least squares collocation with a three dimensional logarithmic covariance function. Terrain corrections for gravity anomaly grids were calculated using an 8 m digital elevation model for topography above sea level and a 250 m seafloor topography model.

We have identified a gap in the literature on error propagation in the gravimetric terrain correction. Therefore, we have derived a mathematical framework to model the propagation of spatially correlated digital elevation model errors into gravimetric terrain corrections. As an example, we have determined how such an error model can be formulated for the planar terrain correction and then be evaluated efficiently using the 2D Fourier transform. We have computed 18.3 billion linear terrain corrections and corresponding error estimates for a 1 arc-second (∼30 m) digital elevation model covering the whole of the Australian continent.

Molodensky G terms are used in the computation of the quasigeoid. We derive error propagation formulas that take into account uncertainties in both the free air gravity anomaly and a digital elevation model. These are applied to generate G 1 terms and their errors on a 1 × 1 grid over Australia. We use these to produce Molodensky gravity anomaly and accompanying uncertainty grids. These uncertainties have average value of 2 mGal with maximum of 54 mGal. We further calculate a gravimetric quasigeoid model by the remove-compute-restore technique. These Molodensky gravity anomaly uncertainties lead to quasigeoid uncertainties with a mean of 4 mm and maximum of 80 mm when propagated through a deterministically modified Stokes's integral over an integration cap radius of 0.5°.