Featherstone & Morgan; Validation of the AUSGeoid98 model in WA 
Vertical deviations are of practical importance in high- 
precision terrestrial-geodetic surveying (Featherstone & 
Riieger 2000), which has now become more important 
because of the introduction of the Geocentric Datum of 
Australia (GDA94) (ICSM 2002). The AUSGeoid98 
gravimetric quasigeoid model (Featherstone et al 2001) 
is accompanied by a regular two-arc-minute grid of 
vertical deviations, which were computed from 
horizontal,,quasigeoid gradients in the north-south and 
east-west directions. 
Strictly, the Pizetti vertical deviations should be 
computed from the horizontal gradients of a geoid, not 
quasigeoid, model because a quasigeoid does not model 
equipotential (level) surfaces of the Earth's gravity field 
(c/. Jekeli 1999). The differences are correlated with 
height and Bouguer gravity anomaly (e.g., Rapp 1997). 
However, AUSGeoid98 is not strictly a quasigeoid model 
because some terms were approximated, notably the 
Molodensky G1 term {e.g., Heiskanen & Moritz 1967) by 
the linear Morizian terrain correction (Featherstone et al. 
2001). Tire difference between the geoid and quasigeoid 
over Australia only reaches 15 cm and varies relatively 
smoothly (Featherstone & Kirby 1998). Therefore, this 
effect on the vertical deviations will be small, probably 
less than one arc-second (discussed later). 
Gomparing observed and computed vertical 
deviations is an independent way of validating the latter 
(cf. Featherstone 2006, 2007). In this paper, we use a 
recently released set of additional vertical deviations over 
Western Australia to validate the performance of the 
AUSGeoid98 gravimetric vertical deviations. As pointed 
out in Featherstone (2007), most of the Western 
Australian data were omitted in Featherstone (2006). Of 
the 435 vertical deviations across Western Australia, only 
96 were used by Featherstone (2006). 
Data, Methods and Results 
Observed astronomic-Helmert vertical deviations 
A set of 339 vertical deviations has recently been 
released by Landgate (formerly the Western Australian 
Department of Land Information). These are from the 
State's geodetic network at sites that have co-located 
geodetic and astronomic observations. The astronomic 
observations were made before 1966 to provide azimuth 
control (orientation) to the long-line traverses used to 
establish the old Australian Geodetic Datum 1966 
(Bomford 1967). 
Landgate extracted the GDA94 geodetic coordinates of 
these points, which allowed the computation of the 
vertical deviations with a fairly good geographical 
distribution across the State (Fig. 2). The formulas for 
computing vertical deviations from astronomical latitude 
(ct>) and longitude (A) and geodetic latitude ( 9 ) and 
longitude (X.) are given in, e.g., Featherstone & Riieger 
(2000) and Jekeli (1999) so will not be duplicated here. 
Since the astronomic observations are made at the Earth's 
surface, this yields Helmert deviations. 
The accuracy of these astrogeodetic deviation data 
is difficult to ascertain {cf. Featherstone, 2006), 
principally because of errors in timing measurements 
of the astronomic longitude observations collected over 
four decades ago. A crude estimate of the standard 
deviation in each of the north-south (^) and east-west 
(q) vertical deviation components is about one arc- 
second. Kearsley (1976) highlights problems of using 
astrogeodetic deflections because of 1-2 arc-second 
systematic errors, while achieving precisions of 0.6 arc- 
seconds. Unfortunately, little information remains 
about the original observations, but most were 
probably collected with Kern DKM3 theodolites 
available before 1966. 
Computed AUSGeoid98 vertical deviations 
AUSGeoid98 (Featherstone et al. 2001) vertical 
deviations are provided in the data files released by 
Geoscience Australia, as well as the primary dataset of 
quasigeoid heights. An accompanying public-domain 
Windows™ program, WINTER v5.08, bicubically 
interpolates these vertical deviations from the regular 
two arc-minute grid to the points of interest. WINTER 
and the AUSGeoid98 data files are freely available from 
Geoscience Australia (http://www.ga.gov.au/geodesy/ 
ausgeoid/). 
Figures 3 and 4 show the vertical deviations computed 
from AUSGeoid98. Since they are derived from regional 
gravity data, geological features are evident {cf. 
Featherstone, 1997), most noticeably the Darling Fault 
close to the Western Australian south west coast (-116° E 
in Figure 3), the eastern portion of the Albany-Fraser 
Orogen (from -33° S, -122° E to -29° S, -125° E in Figures 
3 and 4) and the western MacDonald Ranges (-25° S, 
-128° E in Figure 4). Other geological features are visible, 
but this is not the aim of this article; see Featherstone et 
al. ( 2000 ) instead. 
The AUSGeoid98-derived vertical deviations refer to 
the quasigeoid. Therefore, they are not strictly Pizetti 
deflections, as discussed earlier, but the difference is 
probably less than one arc-second. The difference 
between Helmert and Pizetti deviations is due to the 
curvature and torsion of the plumbline through the 
topography, which depends on the height of the 
observation point (Jekeli 1999). As discussed in 
Featherstone (2006), since the topography in Australia is 
generally benign, the curvature and torsion effect is likely 
to be less than one arc-second, which is less than the 
estimated precision of the astronomically observed 
deviations. 
Tlius, for the purposes of this evaluation, plumbline 
curvature and torsion and differences between 
quasigeoid-derived and geoid-derived Pizetti deviah’ons 
are neglected. This assumption will be validated later. 
Comparisons 
The observed astronomic-Helmert deviations were 
compared with the AUSGeoid98-derived deviations. The 
astronomic-Helmert deviations were computed from 
coordinates in Landgate's database according to the 
formulas in Featherstone & Riieger (2000). The GDA94 
geodetic coordinates of these points were used to 
bicubically interpolate the AUSGeoid98 vertical 
deviations using the WINTER v5.08 software. 
Table 1 shows descriptive statistics of the differences 
(astronomic minus gravimetric), both with (Table la) and 
without (Table lb) 15 outliers as detected by the three- 
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