Journal of the Royal Society of Western Australia, 90; 143-150, 2007 
Validation of the AUSGeoid98 model in Western Australia using 
historic astrogeodetically observed deviations of the vertical 
W E Featherstone’ & L Morgan^ 
’Western Australian Centre for Geodesy & The Institute for Geoscience Research, 
Curtin University of Technology, 
" GPO Box U1987, Perth WA 6845 
S W.Featherstonc@curtin.edu.au 
-Landgate (formerly the Department of Land Information), 
PO Box 2222, Midland, WA 6936 
13 Linda.Morgan@landgate.vva.gov.au 
Manuscript received March 2007; accepted May 2007 
Abstract 
AUSGeoid98 is the national standard quasigeoid model of Australia, which is accompanied by a 
grid of vertical deviations (angular differences between the Earth's gravity vector and the surface- 
normal to the reference ellipsoid). Conventionally, co-located Global Positioning System (GPS) and 
spirit-levelling data have been used to assess the precision of quasigeoid models. Here, we instead 
use a totally independent set of 435 vertical deviations, observed at astrogeodetic stations across 
Western Australia before 1966, to assess the AUSGeoid98 gravimetrically modelled vertical 
deviations. This point-wise comparison shows that (after three-sigma rejection of 15 outliers) 
AUSGeoid98 can deliver vertical deviations with a precision (standard deviation) of around one 
arc-second, which is generally adequate for the reduction of current terrestrial-geodetic survey 
data in this State. 
Keywords: geodesy, vertical deviations, quasigeoid, geodetic surveying, geodetic astronomy 
Introduction 
Gravimetric quasigeoid models are commonly 
validated on land using co-located Global Positioning 
System (GPS) and spirit-levelling data (e.g., Featherstone 
1999, Featherstone & Guo 2001, Featherstone et al. 2001, 
Amos & Featherstone 2003). However, this approach 
suffers from correlations among the data and deficiencies 
in the local vertical datum, which is especially the case 
for the Australian Height Datum (Featherstone 1998, 
2004, 2006; Featherstone & Stewart 1998; Featherstone & 
Kuhn 2006). A better validation can be achieved by using 
deviations of the vertical (c/. Jekeli, 1999; Hirt & Seeber 
2007), which are observed using different principles and 
thus are totally independent of the vertical datum (c/. 
Featherstone, 2006). 
The deviation (or sometimes deflection) of the vertical 
is the angle between the Earth's gravity vector and the 
surface-normal to the reference ellipsoid (Bomford 1980, 
and Fig. 1). Since the plumblines (field lines) of the 
Earth's gravity field have both curvature and torsion, due 
varying mass-density distributions inside the Earth, the 
deviation of the vertical is a function of 3D position. The 
two main sub-classes of vertical deviation are (Jekeli 
1999): Pizetti deviations at the geoid (essentially the 
undulating mean sea level surface; Featherstone 1999), 
and Helmert deviations at the Earth's surface. 
The total vertical deviation (6) in Figure 1 is further 
decomposed into north-south (^) and east-west (q) 
components. These are needed in the reduction of 
© Royal Society of Western Australia 2007 
terrestrial-geodetic survey data to the reference ellipsoid 
(Featherstone & Riieger 2000) 
Vertical deviations can either be observed geodetically 
or computed from gravity data. Helmert vertical 
deviations are observed from the difference between 
astronomical latitude (O) and longitude (A) and geodetic 
latitude (ip) and longitude (X,), with the latter scaled by 
meridional convergence. Astronomical or natural 
coordinates are derived from timed angular 
measurements to the stars (e.g., Bomford 1980; Hirt & 
Seeber 2007 Hirt & Flury 2007). Geodetic coordinates are 
derived from geodetic surveying observations, e.g., 
angles, distances and GPS. Pizetti deviations can be 
computed from gravity data using Vening-Meinesz's 
integral (e.g., Heiskanen & Moritz 1967; Kearsley 1976) 
or from horizontal gradients of a geoid model (cf. Figure 
1), which is the approach taken here. All the relevant 
formulas are given in Featherstone & Riieger (2000). 
Ellipsoid Normal 
Figure 1. A generalised schematic of the deviation of the 
vertical, where the plumbline is perpendicular to the level 
surface, thus the deviation is a measure of the slope of the level 
surface with respect to the ellipsoid. 
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