=Paper=
{{Paper
|id=Vol-1323/paper3
|storemode=property
|title=AUSGeoid09 Performance in Mountainous Terrain: A Case Study in the Blue Mountains
|pdfUrl=https://ceur-ws.org/Vol-1323/paper3.pdf
|volume=Vol-1323
}}
==AUSGeoid09 Performance in Mountainous Terrain: A Case Study in the Blue Mountains==
https://ceur-ws.org/Vol-1323/paper3.pdf
AUSGeoid09 Performance in Mountainous Terrain:
A Case Study in the Blue Mountains
Joseph Allerton Volker Janssen A.H.W. (Bill) Kearsley
University of New South Wales Land and Property Information University of New South Wales
Sydney NSW 2052, Australia Bathurst NSW 2795, Australia Sydney NSW 2052, Australia
joe.allerton@hotmail.com Volker.Janssen@lpi.nsw.gov.au w.kearsley@unsw.edu.au
Abstract
AUSGeoid09 is the latest model used to convert Global
Navigation Satellite System (GNSS) derived ellipsoidal heights
to heights in the Australian Height Datum (AHD). While
previous studies have evaluated the performance of the
AUSGeoid09 model across Australia, such studies have not
focused on mountainous regions in particular. This paper
evaluates AUSGeoid09 in the Blue Mountains region of New
South Wales from a practical user’s point of view. Along a 90
km stretch of road incorporating flat to mountainous terrain,
comparisons were undertaken between AUSGeoid09-derived
heights and published AHD heights, using repeated Network
Real Time Kinematic (NRTK) GNSS observations. The
performance of AUSGeoid09 was also evaluated relative to its
predecessor, AUSGeoid98, and the latest gravimetric model
AGQG2009. It was found that AUSGeoid09 performs well
across the study area and provides a significant improvement
over AUSGeoid98. AUSGeoid09 generally allows AHD height
determination at the ±0.03 m level (1 sigma) in flat terrain and at
the ±0.06 m level (1 sigma) in mountainous terrain. However,
across the entire study area, AUSGeoid09-derived AHD heights
are consistently lower than the published AHD heights.
Comparison of the results obtained with AUSGeoid09 against
those using AGQG2009 in flat terrain illustrates the benefit that
the introduction of the geometric component of AUSGeoid09
has had on the determination of AHD heights with satellite
technology. However, for elevations above 500 m it appears that
the geometric component degrades the fit to AHD in the study
area, indicating that there is room for improvement in regards to
future versions of the AUSGeoid model.
Keywords: AUSGeoid09, geoid model, height datum, AHD,
NRTK, GNSS.
Copyright © by the paper’s authors. Copying permitted only for private and academic purposes.
In: B. Veenendaal and A. Kealy (Eds.): Research@Locate15, Brisbane, Australia, 10-12 March 2015, published at http://ceur-ws.org
Research@Locate '15 58
1 Introduction
Most countries have adopted Mean Sea Level (MSL) as zero height surface for their national vertical datum (e.g.
Featherstone & Kuhn, 2006; Janssen, 2009). Height above MSL is crucial information for a wide range of
applications, e.g. flood modelling, emergency management and engineering construction. In Australia, MSL was
approximated as the basis of the Australian Height Datum (AHD) by setting to zero the average MSL values of 32
tide gauges around the country for a period of about two years that began in 1966 (Roelse et al., 1971). The national
height datum is complemented by the Geocentric Datum of Australia 1994 (GDA94) for horizontal positions
(ICSM, 2009).
More than 40 years after its inception, it is well known that shortcomings in the AHD realisation (AHD71 for
mainland Australia and AHD83 for Tasmania) resulted in MSL not being coincident with the geoid at the tide
gauges involved. These shortcomings included not considering dynamic ocean effects (e.g. winds, currents,
atmospheric pressure, temperature and salinity), a lack of long-term tide gauge data, and the omission of observed
gravity. This means that the reference surface for AHD is not a truly level (geopotential) surface, although it was
intended to be so when created and is generally used as if it was level. In fact, AHD has variations from the level
surface of 1.5 m across Australia and is therefore considered a third-order datum (Morgan, 1992; Featherstone &
Filmer, 2012). However, for operational convenience and to avoid confusion, the non-level AHD continues to be
used as a practical height datum that provides a sufficient approximation of the geoid for many applications.
Consequently, in practice, AHD heights are often accepted as being equivalent to orthometric heights.
Over the last two decades, Global Navigation Satellite System (GNSS) technology has become the primary
positioning tool due to its accuracy, speed and accessibility. In particular, Network Real Time Kinematic (NRTK)
GNSS is being utilised for a wide range of surveying, mapping, agriculture, mining and construction applications,
providing users with instant and highly accurate position information over distances of several tens of kilometres.
The advantage of NRTK is its ability to provide corrections (accounting for atmospheric and satellite orbit errors)
that are based on a Continuously Operating Reference Station (CORS) network rather than a single reference station
(e.g. Wang et al., 2010; Janssen & Haasdyk, 2011; Penna et al., 2012).
GNSS-based heights refer to a reference ellipsoid, i.e. a purely mathematical representation of the earth, and
therefore have no physical meaning. In most practice, however, heights are required that correctly reflect the flow
of water (or at least sufficiently approximate it), e.g. for flood modelling or drainage and pipeline design. Hence, a
reliable geoid model is required to derive AHD heights from measured ellipsoidal heights (e.g. Kearsley, 1988).
These geoid models provide N values (N), also known as geoid undulations or geoid-ellipsoid separations, that can
be used to convert GNSS-derived ellipsoidal heights (h) to AHD heights (H) and vice versa (provided N and h refer
to the same ellipsoid):
H=h–N (1)
For many years, the use of geoid models (or quasigeoid models – see Vaniček et al. (2012) for a discussion of
the difference) has helped GNSS users to compute AHD heights from ellipsoidal heights. In the Australian context,
AUSGeoid09 is the latest model that best fits AHD (Brown et al., 2011; Featherstone et al., 2011).
While the performance of AUSGeoid09, along with the improvements it provides over its predecessor
AUSGeoid98, have been investigated previously (e.g. Janssen & Watson, 2010; Brown et al., 2011), these studies
have not focused on mountainous regions. Considering that gravity can change dramatically within a few kilometres
on the earth’s surface in Australia (Darbeheshti & Featherstone, 2009), especially in mountainous terrain, and that
observed gravity data are generally sparse in these areas (usually observed along the roads to allow easy access), it
is necessary to investigate mountainous regions in particular.
This paper evaluates AUSGeoid09 performance in the Blue Mountains in New South Wales (NSW), from a
practical user’s point of view, using NRTK GNSS-derived ellipsoidal heights and published AHD heights.
AUSGeoid09 is compared to its gravimetric component (AGQG2009) and its predecessor (AUSGeoid98) in the
study area.
2 AUSGeoid09
AUSGeoid09 was released in March 2011 by Geoscience Australia, replacing the previous model AUSGeoid98
(Featherstone & Guo, 2001). Both models refer to the GRS80 ellipsoid, which was adopted as the reference
ellipsoid for GDA94, and cover the same geographical area between 108ºE and 160ºE longitude and between 8ºS
and 46ºS latitude. However, AUSGeoid09 is provided as a 1’ by 1’ grid (approximately 1.8 by 1.8 km), making it
four times denser than its predecessor (Featherstone et al., 2011).
Previous versions of AUSGeoid were predominantly gravimetric-only quasigeoids, and it was assumed that
these were sufficiently close approximations of AHD – an assumption we now know to be incorrect. In contrast,
AUSGeoid09 is a combined gravimetric quasigeoid plus a geometric model, providing a direct connection to AHD
and thereby allowing a more reliable determination of AHD heights from GNSS observations (Brown et al., 2011).
The empirically derived geometric component accounts for the offset between the gravimetric quasigeoid
(AGQG2009 – see Featherstone et al., 2011) and AHD, which is predominantly caused by AHD not taking into
account sea surface topography including the differential heating of the oceans. Since the warmer or less dense
Research@Locate '15 59
water off northern Australia is about 1 metre higher than the cooler or denser water off southern Australia, AHD is
about 0.5 m above the quasigeoid in northern Australia and roughly 0.5 m below the quasigeoid in southern
Australia (Janssen & Watson, 2010; Brown et al., 2011). The introduction of the geometric component takes care of
most of this 1-metre trend across Australia (0.6-metre trend across NSW), thereby providing a better overall fit to
AHD.
AUSGeoid09 has been shown to convert ellipsoidal heights to AHD heights with an accuracy of ±0.03 m (1
sigma) across most of Australia, with the exception of some pocket areas where the misfit can be larger than ±0.1 m
due to errors caused by factors such as the ageing levelling network, geoid height variability or data deficiency
(Brown et al., 2011). Using a more practical approach, Janssen & Watson (2010) found that AUSGeoid09 generally
allows GNSS-based height determination in NSW at the ±0.05 m level (1 sigma). In contrast, its predecessor
AUSGeoid98 only provides an absolute accuracy of ±0.4 m (Featherstone & Guo, 2001; Featherstone et al., 2001).
A recent study by Sussanna et al. (2014) investigated the performance of AUSGeoid09 in two mountainous
regions of NSW, based on two sizable GNSS network adjustment datasets. In the Mid Hunter (elevations ranging
between 20 m and 1,400 m), AUSGeoid09 was able to deliver AHD heights at the ±0.04 m level (1 sigma) and
provided a substantial improvement over its predecessor, clearly demonstrating the benefits of its geometric
component on GNSS-derived AHD height determination. In the Snowy Mountains (elevations ranging from 200 m
to 2,200 m), AHD height determination was achieved at the ±0.07 m level (1 sigma) and moderate improvement
over AUSGeoid98 was evident. However, a slope was detected for AUSGeoid09 residuals, and it appears that the
geometric component may have overcompensated for sea surface topography in this area.
3 Testing methodology
Owing to the increased use of GNSS CORS networks, the absolute accuracy of N values is now more important
than ever for AHD height determination using satellite positioning techniques (Janssen & Watson, 2010). In this
paper, the performance of the AUSGeoid09 model in mountainous terrain is evaluated in the Blue Mountains, based
on the comparison of repeated NRTK GNSS observations and published AHD heights.
A number of spirit-levelled benchmarks with known AHD heights of sufficient quality (Class LB Order L2 or
better) on public record in the Survey Control Information Management System (SCIMS) were used as test points.
SCIMS is the state’s database containing about 250,000 survey marks across NSW, including coordinates, heights
and other information (Kinlyside, 2013). For a discussion of the terms class and order, the reader is referred to
ICSM (2007) and Dickson (2012). It should be noted that the published AHD heights of the benchmarks used as
test points are not guaranteed to be error-free. Consequently, they can only be treated as benchmarks defining AHD
in the study area (and comparisons are thus made to the national height datum), not as representing true orthometric
heights.
In order to replicate a practical scenario, these test points were occupied multiple times using the NRTK GNSS
technique to obtain ellipsoidal heights. NRTK observations were based on CORSnet-NSW (e.g. Janssen et al.,
2013), an expanding state-wide network of more than 160 GNSS CORS providing fundamental positioning
infrastructure for New South Wales (Figure 1). As recommended by Janssen & Haasdyk (2011), the windowing
technique was applied to increase reliability of the resulting positions and each test point was re-observed several
times (using a tripod for stability) to ensure redundancy and allow for changes in satellite geometry between
occupations.
3.1 Windowing technique
The windowing (or averaging) technique is often applied to improve the positioning result for real-time
applications if the GNSS rover is allowed to remain stationary for a short period of time. Windowing is achieved by
determining the average of several epochs observed at a point, thus increasing the reliability of the resulting
position. It is important to note that windowing reduces the effect of extreme, short-lived outlier observations, but
can still produce results that are significantly offset from the mean. Janssen & Haasdyk (2011) suggest observing
for 1-2 minutes to obtain an averaged position in order to reduce the effects of individual coordinate solution
outliers. If high-quality vertical coordinates are required or the user is distant from the nearest CORS, it is advised
to use a 2-minute observation window. It was also shown that double occupations, i.e. re-observing each point after
waiting about 10-30 minutes or more, increases the reliability of the resulting position.
In a preliminary test, the benefit of using the windowing technique in this study was assessed by occupying
several test points multiple times and collecting NRTK-based positions for short (10 epochs) and longer (3 minutes)
observation windows. The standard deviations of the ellipsoidal height observations on each test point were then
investigated to determine which observation window length should be used in the following analysis.
Research@Locate '15 60
Figure 1: CORSnet-NSW network map as of February 2015 (LPI, 2015).
3.2 Evaluation of AUSGeoid09 in flat and mountainous terrain
Using equation 1, observed NRTK GNSS-derived ellipsoidal heights (h) were converted to AHD heights (H)
using three quasigeoid models (i.e. AUSGeoid09, AUSGeoid98 and AGQG2009) and compared to the published
AHD height (HAHD) at each test point. The test points were chosen to ensure that an even number of these were
located in flat terrain and mountainous terrain in order to allow evaluation of AUSGeoid09 performance in both
terrain conditions.
Descriptive statistics were used to quantify the performance of AUSGeoid09 in determining AHD heights from
GNSS observations in the study area. Since it is necessary to consider residuals of different signs, the Root Mean
Square (RMS) was also utilised. Furthermore, a comparison between AUSGeoid09 and its predecessor
AUSGeoid98 as well as AUSGeoid09’s gravimetric component (AGQG2009) was performed to quantify the
improvement gained in mountainous areas and investigate the effect of introducing the geometric component.
4 Study area
The performance of AUSGeoid09 in mountainous terrain was evaluated in the Blue Mountains located west of
Sydney, NSW. The study area incorporates 23 test points along Windsor Road and Bells Line of Road between
Castle Hill in the east and Lithgow in the west (Figure 2). It exhibits initially flat terrain (blue test points) changing
into substantially undulating terrain with large differences in elevation (red test points), thus representing typical
mountainous terrain conditions encountered in Australia (Figure 3).
The eastern half of the study area follows Windsor Road, connecting the Sydney suburb of Castle Hill in the east
with the townships of Windsor and Richmond towards the west. This line is approximately 40 km long and exhibits
relatively flat terrain, gently changing between about 10 m and 125 m in elevation. The western half of the study
area is located along Bells Line of Road, a winding mountain road connecting the townships of Richmond and
Lithgow. This line is approximately 50 km long and exhibits undulating terrain with elevations ranging from about
185 m to 1,100 m. AUSGeoid09 N values range from 23 m to 26 m in the study area, steadily increasing from east
to west.
Research@Locate '15 61
Figure 2: Location of the test points (SCIMS benchmarks) in the study area.
1200
23 22
1000 21 20
19
Elevation (m)
800
18
600 17
16
400
15 13
200 21
14 8 5 4 3
12 1110 9 7 6
0
0 10 20 30 40 50 60 70 80 90
Chainage (km)
Figure 3: Cross section of the test points, indicating the range in elevation (AHD height).
5 Data collection and analysis
5.1 Field work issues
Naturally, it is desired to obtain the largest possible sample of high-quality test points and utilise high-precision
positioning techniques in order to provide a solid base for analysis. In practice, however, compromises have to be
made due to constraints in regards to time and resources. While a lot of first-order levelled benchmarks (LAL1) are
available close to Sydney, most of these have an ‘unknown’ classification for the horizontal class and order (UU).
This means that the published horizontal coordinates are generally only accurate to several tens of metres, in some
cases up to 200 m. Furthermore, the locality sketches for most of these benchmarks were drawn in the early 1960s
(when the benchmarks were placed) and did not have many useful references to locate the marks 50 years later.
While SCIMS indicates whether a mark has been ‘destroyed’ or ‘not found’ or even ‘found intact’, the marks that
have not been classified as such are not guaranteed to still exist. Most of the benchmarks were placed on the side of
the road and not located near identifiable features such as road intersections, houses or other physical structures.
References mainly consisted of fencing, power poles and mile posts. Understandably, these features have been
replaced, removed or have deteriorated over time.
As a result, many of these marks could not be recovered and second-order levelled marks (LBL2) had to be used
instead. Along Bells Line of Road, only 8 marks were found out of the initially selected 25 benchmarks, and the
dataset was therefore expanded with three LBL2 marks towards the east (Kurrajong) to obtain a larger sample for
analysis. While the majority of marks used along Bells Line of Road are classified LAL1, all 12 marks used along
Windsor Road are classified LBL2.
Another issue that arose (as expected) was the inability to observe directly over a benchmark due to limited
skyview or multipath issues. This problem was overcome by placing an arbitrary (eccentric) mark, i.e. nail in
bitumen or hard ground, a short distance away at a location with more favourable observing conditions. The AHD
height of the benchmark was then transferred to the arbitrary mark using a total station, measuring four sets of
reciprocal zenith angles and slope distances to determine the vertical distance between the two marks. A spirit level
and staff were not used because this could not be achieved by only one person in the field. This procedure was
required for four test points along Bells Line of Road (SS342, SS341, SS336 and SS319). Finding a larger number
Research@Locate '15 62
of the initially selected marks would have increased the sample size and may have reduced the percentage of
benchmarks observed using arbitrary marks. Fortunately, field work was not hampered by encounters with native
wildlife (Janssen, 2012).
5.2 Windowing technique and ellipsoidal height quality
A preliminary test was undertaken to assess the benefit of using the windowing technique in this study. A
number of test points were occupied several times (generally between 30 minutes and several days apart), collecting
NRTK-based positions based on 10 epochs of data as well as 3 minutes of data. Table 1 states the number of
occupations and the standard deviation (STD) of the ellipsoidal height observations on each test point. It can be
seen that the longer averaging window improves the mean standard deviation slightly and appears to remove two
relatively large values of 0.030 m and 0.041 m. Based on these findings, it was decided to occupy all remaining test
points for 3-minute observation windows.
Table 1: Assessment of the windowing technique based on the standard deviation of ellipsoidal height observations
(STD given in metres).
Test No. Occ. No. Occ. STD (h) STD (h)
Mark ID
Point (10 epoch) (3 min) (10 epoch) (3 min)
17 SS342 4 3 0.030 0.017
18 SS341 8 8 0.009 0.017
19 SS336 6 7 0.041 0.022
20 SS335 6 8 0.017 0.023
21 SS332 8 8 0.016 0.025
22 SS44364 4 4 0.010 0.013
23 SS319 6 6 0.013 0.007
Mean 0.020 0.018
The average quality of all observed GNSS ellipsoidal heights indicated by the GNSS rover was 0.014 m ± 0.003
m along Windsor Rd (flat terrain) and 0.025 m ± 0.009 m along Bells Line of Road (mountainous terrain).
However, research has shown that these quality indicators can be overly optimistic (e.g. Wang et al., 2010; Janssen
& Haasdyk, 2011). In order to get a better appreciation of the quality of the observed ellipsoidal heights, the vertical
precision of all 3-minute occupations on each test point was investigated. An average STD of 0.010 m was achieved
in flat terrain (ranging from 0.001 m to 0.027 m), while the average STD increased to 0.019 m (ranging from 0.002
m to 0.042 m) in mountainous terrain. These findings, along with a thorough investigation of the collected data,
provided confidence that the dataset was free of outliers.
5.3 Flat terrain: Windsor Road
Each test point was occupied at least three times with NRTK GNSS using CORSnet-NSW and 3-minute
observation windows. The average ellipsoidal height was determined, and AHD heights were calculated by
applying the N values from three different quasigeoid models, i.e. AUSGeoid09, AUSGeoid98 and AGQG2009.
The AGQG2009 model was kindly provided by Geoscience Australia as it is not readily available to the public in
order to avoid confusion between this gravimetric-only model and the published AUSGeoid09. The derived AHD
heights for each test point were then compared to the published SCIMS values, which were used as control in this
study, to evaluate the performance of AUSGeoid09 and compare the models.
Table 2 shows the differences between NRTK GNSS-derived AHD heights (using the three quasigeoid models)
and published AHD heights (AHDSCIMS) for the test points situated in flat terrain along Windsor Road. Descriptive
statistics show that AUSGeoid09 allows AHD height determination with an accuracy of about -0.026 ± 0.016 m (1
sigma) in this part of the study area. As all differences are negative, the Root Mean Square (RMS) provides a
similar value, i.e. 0.030 m. Using AUSGeoid09 rather than its predecessor AUSGeoid98 resulted in substantially
better agreement with published AHD heights, e.g. illustrated by the RMS dropping from 0.211 m to 0.030 m – an
improvement by a factor of 7.0.
Comparing the results obtained with AUSGeoid09 against those using AGQG2009 illustrates the benefit that the
introduction of the geometric component of AUSGeoid09 has had on the determination of AHD heights with
satellite positioning technology. In this case, the RMS improved by a factor of 2.5, dropping from 0.076 m to 0.030
m. For all test points, AUSGeoid09 provided heights that are about 30-50 mm closer to the published AHD values
than those obtained using AGQG2009. This improvement is consistent with the geometric component of
AUSGeoid09 generally amounting to about -0.05 m or less in this area (Brown et al., 2011), considering that a
negative geometric component results in a smaller N value and therefore a larger derived AHD height. While the
range of differences for all three models remains at a similar level of 0.06 m, it is obvious that AUSGeoid09
provides heights that are much closer aligned with the published values than the other two models. In other words,
Research@Locate '15 63
the evolution from AUSGeoid98 to AGQG2009 and AUSGeoid09 has significantly improved the fit between
GNSS-derived and published AHD heights.
Table 2: Agreement of NRTK GNSS-derived AHD heights (using different quasigeoid models) to SCIMS in flat
terrain (Windsor Road) – all values stated in metres.
Test Class/ No. Occ.
Mark ID AHDSCIMS ∆AHDAG09 ∆AHDAG98 ∆AHDAGQG09
Point Order (3 min)
1 SS61355 LBL2 3 126.160 -0.037 -0.203 -0.092
2 PM31480 LBL2 4 95.893 -0.026 -0.200 -0.081
3 SS44875 LBL2 3 79.272 -0.015 -0.190 -0.071
4 SS17350 LBL2 4 77.988 -0.020 -0.200 -0.075
5 PM29273 LBL2 4 59.921 -0.031 -0.218 -0.087
6 PM67548 LBL2 6 14.102 -0.028 -0.220 -0.081
7 PM41505 LBL2 6 14.045 -0.035 -0.230 -0.087
8 SS10399 LBL2 6 24.293 -0.004 -0.198 -0.052
9 PM45758 LBL2 6 17.167 -0.015 -0.204 -0.059
10 SS75618 LBL2 4 11.445 -0.037 -0.225 -0.073
11 PM74693 LBL2 3 11.552 -0.062 -0.251 -0.095
12 PM45486 LBL2 3 44.985 -0.002 -0.190 -0.031
Mean -0.026 -0.211 -0.074
STD 0.016 0.018 0.019
RMS 0.030 0.211 0.076
Min -0.062 -0.251 -0.095
Max -0.002 -0.190 -0.031
Range 0.060 0.061 0.064
5.4 Mountainous terrain: Bells Line of Road
The same procedure was applied to the remainder of test points, located in mountainous terrain along Bells Line
of Road. The resulting differences between NRTK GNSS-derived AHD heights (using the three quasigeoid models)
and published AHD heights (AHDSCIMS), along with descriptive statistics, are shown in Table 3.
It can be seen that AUSGeoid09 allows AHD height determination with an accuracy of about -0.060 ± 0.039 m
(1 sigma) in this part of the study area. As all differences are negative, the Root Mean Square (RMS) provides a
similar value, i.e. 0.071 m. Again, AUSGeoid09 provides substantially better agreement with published AHD
heights than its predecessor AUSGeoid98, e.g. illustrated by the RMS dropping from 0.174 m to 0.071 m – an
improvement by a factor of 2.5.
It should be noted that test points 18 & 23 (SS341 & SS319) show much larger discrepancies (at the 120 mm
level) to the published AHD heights than all other test points in the study area. This suggests that the published
heights of these marks may be incorrect (possibly due to mark movement) or deficiencies may be present in the
quasigeoid model used. At SS341, this substantial disagreement is evident across all three models investigated, and
neighbouring marks do not exhibit similar behaviour, supporting that subsidence may be the cause. At SS319, the
AGQG2009-derived AHD height agrees much better (at the 40 mm level) with the published AHD height,
suggesting that in this case the discrepancy may not be due to mark subsidence but rather be caused by deficiencies
in the geometric component of AUSGeoid09. In both cases, however, the limited data available precludes a
definitive answer.
If these two test points were removed from the analysis, the accuracy of AUSGeoid09-derived AHD heights
improves to -0.046 ± 0.025 m (1 sigma), while the RMS improves to 0.052 m and the range drops from 0.111 m to
0.070 m. In addition, AUSGeoid09 improves the fit to published AHD by a factor of 3.2 over its predecessor
AUSGeoid98, with the RMS dropping from 0.164 m to 0.052 m.
Comparison of the results obtained with AUSGeoid09 and AGQG2009 shows that, contrary to the findings in
flat terrain, the introduction of AUSGeoid09’s geometric component overall has not had a positive effect in this part
of the study area. While the range of differences from published AHD heights improved slightly, the RMS actually
increased by a factor of 1.4, from 0.050 m to 0.071 m. (If test points 18 & 23 were removed from the analysis, the
RMS increases by a factor of 1.3, from 0.039 m to 0.052 m.) Closer inspection reveals that for elevations below 500
m, the geometric component improved the fit to published AHD heights by about 15 mm. However, for elevations
above 500 m, the geometric component appears to degrade the fit by about 10-30 mm. For elevations above 1,000
m, this negative effect is even larger, exceeding 70 mm. While it is recognised that the sample size is small, this
may indicate possible problems with the geometric component at high elevations – not surprisingly, as it is well
known that suitable datasets for the generation of the geometric component are notoriously sparse in mountainous
regions. It is also understood that the gravimetric geoid is weaker in mountainous regions because (1) gravity data
Research@Locate '15 64
are limited, (2) existing gravity data are biased along the ridges (roads) and creeks for ease of access, and (3) the
terrain effect is less well modelled in regions of large elevation changes in topography.
Table 3: Agreement of NRTK GNSS-derived AHD heights (using different quasigeoid models) to SCIMS in
mountainous terrain (Bells Line of Road) – all values stated in metres.
Test Class/ No. Occ.
Mark ID AHDSCIMS ∆AHDAG09 ∆AHDAG98 ∆AHDAGQG09
Point Order (3 min)
13 PM45491 LBL2 3 201.224 -0.019 -0.184 -0.037
14 PM45501 LBL2 3 186.888 -0.027 -0.191 -0.045
15 PM1677 LAL1 4 251.366 -0.044 -0.197 -0.060
16 SS347 LAL1 3 454.364 -0.050 -0.184 -0.064
17 SS342 LAL1 3 542.686 -0.014 -0.133 -0.009
18 SS341 LAL1 8 626.173 -0.122 -0.230 -0.109
19 SS336 LAL1 7 801.360 -0.073 -0.165 -0.038
20 SS335 LAL1 8 932.277 -0.071 -0.147 -0.032
21 SS332 LAL1 8 918.139 -0.034 -0.111 0.017
22 SS44364 LBL2 4 1046.127 -0.084 -0.144 -0.010
23 SS319 LAL1 6 1092.527 -0.125 -0.189 -0.043
Mean -0.060 -0.170 -0.039
STD 0.039 0.034 0.033
RMS 0.071 0.174 0.050
Min -0.125 -0.230 -0.109
Max -0.014 -0.111 0.017
Range 0.111 0.119 0.126
Investigating the effect of the geometric component in more detail, it is interesting to note that the improvement
of fit to published AHD steadily decreases from east to west in the study area, from about 55 mm in the western
outskirts of Sydney to zero near Kurrajong. Heading further west through the Blue Mountains, the geometric
component increasingly degrades (almost linearly with distance) the GNSS-based determination of AHD heights in
the study area, culminating in up to 80 mm at the highest elevations near Lithgow (Figure 4). This can be explained
by the decreasing density of datasets available for the empirical determination of the geometric component away
from metropolitan areas. It is also interesting to note that across the entire study area, featuring both flat and
mountainous terrain, AUSGeoid09-derived AHD heights are always lower than the published AHD heights. This
indicates that there is room for improvement in regards to future versions of the AUSGeoid model, provided
additional datasets are collected in this region.
+0.06
5 1
8
+0.03
12
Difference in Fit (m)
13
0
17
-0.03
20
-0.06
23
-0.09
0 10 20 30 40 50 60 70 80 90
Chainage (km)
Figure 4: Difference in fit to published AHD heights between AUSGeoid09 and AGQG2009 derived AHD heights
in the study area. Positive values indicate improvement of fit due to the geometric component.
Research@Locate '15 65
5.5 Cross sections
In order to provide a visual perspective of the results obtained in the study area, cross sections were generated
showing published AHD heights and NRTK GNSS-derived AHD heights based on the three quasigeoid models
investigated (Figure 5). The cross sections run from left to right in a west-to-east direction and have been scaled and
exaggerated (separately for each part of the study area) to allow a clearer visual comparison.
Across both terrain types, it is clearly evident that AUSGeoid09 provides a far better fit to published AHD
values than its predecessor AUSGeoid98. In flat terrain, AUSGeoid09-derived heights are consistently closer to
published AHD than AGQG2009-derived heights, showing the benefit of the geometric component. The shape of
all quasigeoid-derived cross sections is very similar to the shape of AHD in this part of the study area. In
mountainous terrain, the shape of all quasigeoid-derived cross sections is very similar but deviates from the shape
of published AHD in several cases. This behaviour is most obvious at test point 18 (SS341), a mark that has already
been identified as possibly being affected by subsidence. The cross sections also visualise that the geometric
component of AUSGeoid09 appears to increasingly degrade the fit to published AHD for the marks investigated
west of test point 17.
Figure 5: Cross sections showing published AHD heights and NRTK GNSS-derived AHD heights using different
quasigeoid models, separately scaled and exaggerated in each part of the study area.
6 Conclusion
This paper has evaluated the performance of AUSGeoid09 in the Blue Mountains region of New South Wales,
from a practical user’s point of view. Along a 90 km stretch of road incorporating flat to mountainous terrain,
comparisons were undertaken between AUSGeoid09-derived heights and published AHD heights, using repeated
NRTK GNSS observations on 23 test points. The performance of AUSGeoid09 was also evaluated relative to its
predecessor, AUSGeoid98, and the latest gravimetric quasigeoid model AGQG2009.
In a preliminary test, it was confirmed that the windowing technique can reduce the effect of extreme, short-lived
outlier observations and increase the reliability of NRTK GNSS-derived positions. Consequently, it was decided to
occupy the test points for 3-minute observation windows.
It was shown that AUSGeoid09 performs well across the study area and provides a significant improvement over
AUSGeoid98. AUSGeoid09 generally allows AHD height determination at the ±0.03 m level (1 sigma) in flat
terrain and at the ±0.06 m level (1 sigma) in mountainous terrain. This level of accuracy agrees well with findings
reported in previous studies and is very encouraging, particularly in light of GNSS technology and CORS networks
being increasingly used to provide vertical control. However, across the entire study area, AUSGeoid09-derived
AHD heights were found to be consistently lower than the published AHD heights.
Comparison of the results obtained with AUSGeoid09 against those using AGQG2009 in flat terrain illustrates
the benefit that the introduction of the geometric component of AUSGeoid09 has had on the determination of AHD
heights with satellite positioning technology. However, it was also found that the geometric component appears to
degrade the fit to AHD for elevations above 500 m in the study area. This indicates that there is room for
improvement in regards to future versions of the AUSGeoid model.
It is recognised that this study is based on a much smaller sample than initially planned. Consequently, it is not
suggested that the results presented can be generalised to apply to other mountainous regions. The availability of
higher-quality horizontal coordinates for first-order benchmarks in SCIMS would have been very beneficial in
regards to locating a larger number of test points in the available time frame. Levelled benchmarks are important for
the maintenance of the national height datum, and it should therefore be possible to locate these marks more easily.
It is recommended that this well-known issue be addressed by the custodians of SCIMS in the future, particularly in
Research@Locate '15 66
light of the planned introduction of a next-generation datum for Australia (Haasdyk et al., 2014) and the increasing
need to preserve existing survey mark infrastructure (de Belin, 2012; Ward, 2014).
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