AUSGeoid2020 combined gravimetric–geometric model: location-specific uncertainties and baseline-length-dependent error decorrelation

Abstract

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.

Using AUSGeoid2020 and its error grids in surveying computations

“…The computation of AGQG2017 delivered a gravimetric-only quasigeoid model, but this was subsequently tilted (cf. Featherstone and Filmer, 2012) and surface-fitted to GPS-AHD heights across the continent using least squares prediction (Brown et al, 2018a). As such, its physical-geodetic definition in terms of the Earth's gravity field is somewhat nebulous; instead, it gives a model of the separation between the AHD and GRS80 ellipsoid (cf.…”

“…However, the simple use of AUSGeoid2020 values at each end of the GNSS baseline neglects the benefit of using relative GNSS so that common-mode errors cancel, not only in the GNSS baseline processing, but also in the AUSGeoid2020 separation difference, thus making the derived height difference more precise (Kearsley, 1986(Kearsley, , 1988. Brown et al (2018a) thus devised an exponential decorrelation function from ~8,000 GPS-AHD stations not used in the production of AUSGeoid2020 to account for this. The error propagation when using Eq.…”

“…(3) for relative GNSS heighting becomes Eq. (11) from Brown et al (2018a), noting the change in symbology for the present manuscript:…”

“…63,151 am  (Brown et al, 2018a). By GNSSsoftware-provided, we mean the values delivered directly by the GNSS processing software, taken at face value, but acknowledging they may be overoptimistic (e.g., Rothacher, 2002).…”

“…Unlike all its predecessors that used a "one size fits all" uncertainty estimate for the entire continent, AUSGeoid2020 GDA2020-AHD separations are now accompanied by a location-specific error grid at a 1'x1' spacing (Brown et al, 2018a). AUSGeoid2020 is public-domain and available at https://s3ap-southeast-2.amazonaws.com/geoid/.…”