GPS AND THE GEOID IN AUSTRALIA |
The Australian Height Datum (AHD) was implemented on mainland Australia
in 1971, and in Tasmania in 1979 (ROELSE
et al, 1971; MITCHELL, 1990).
This was the first attempt to define a continent-wide levelling datum. Prior
to this, Australia had a multitude of levelling datums, each of which was
adopted by a government utility to suit its own purpose in a region. These
datums were usually based on a local tide gauge (HOLLOWAY,
1988).
The levelling data used in the AHD was largely of third order standard,
observed during the previous decade and a half. In addition, some earlier
first and second order levelling was included, as was a significant amount
of one-way levelling in Queensland and the Northern Territory. Hence the
standard of levelling throughout the network was not uniform. A total of
almost 100,000 km of levelling in 261 loops was adjusted (ROELSE
et al, 1971). The estimated internal precision of the AHD is about 8mm
per 
, where k is the length of the level run in kilometres.
That is, a height difference between points 100km apart should have a precision
of the order of a decimetre.
In the 1971 adjustment, AHD was tied to Mean Sea Level (MSL) at 30 tide gauges distributed fairly uniformly around the Australian mainland coast. The MSL at each of these tide gauges was derived from several years of readings. These 30 MSL estimates acted as a constraint in the levelling adjustment by being assigned a "fixed" height of 0.000 metres. In Tasmania, the AHD is connected to MSL at two tide gauges, Burnie and Hobart. The AHD (Tasmania) is independent of AHD (Mainland), with no connection ever being made between them.
Is the AHD an orthometric height system? The answer is NO, for several reasons, the most important of which are:
The second point is of particular concern for GPS heighting, as eqn (11.3-1) is no longer strictly valid as far as the AHD is concerned (refer to the early discussion regarding the insensitivity of the geometric method of geoid modelling to weaknesses in the height datum definition). Hence an understanding of the nature and magnitude of errors in the AHD is important if GPS is to used for heighting.
Astro-Geodetically Determined Geoids
The first such determination was carried out in 1967, using 600 astro-geodetic deflections of the vertical. In 1971 a new geoid was prepared, relative to the AGD, but based on almost double the number of astro-geodetic data (Figure 1 below). In classical geodetic practice the preparation of an astro-geodetic geoid was a necessary part of the process of datum definition known as the "development method", by which the assigned ellipsoidal coordinates of the datum origin station (in Australia's case, the Johnston Trig datum station) were altered in such a way as to ensure an astro-geodetic geoid that minimised the absolute values of the geoid undulations across the datum. The value of N at the Johnston station for a geoid that satisfied this "best-fit" condition should have been -6m. However, due to the legislated value of h at Johnston Origin of 571.2m on the one hand, and the levelled height H of 566.3m on the other, the implied geoid height is in fact +4.9m. Hence the geoid in Figure 5 has a datum shift of +10.9m relative to a "best-fit" geoid. Such a geoid map can be used for converting AHD heights to ellipsoid heights on the AGD, and hence transforming to the Cartesian formulation.
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Figure 1. Astro-geodetic geoid of Australia (mapped relative to the AGD).
Geoids from Geopotential Models
High degree spherical harmonic models such as OSU91 and EGM96 provide a very convenient representation of the geoid (Figure 2 shows an earlier OSU89A model).
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Figure 2. Geoid of Australia from OSU89A (relative to the WGS84 ellipsoid).
Table 1 shows the difference between two OSU geoid models: OSU89A and
OSU91A for a small Sydney network. Note that although there is an approximately
0.25m difference, there is also a small grade and hence the relative geoid
heights between points in the network will be slightly different (though
only at the few centimetre level), depending upon which geoid model is used.
| Name | Latitude | Longitude | NOSU89A | NOSU91A |  |
|---|---|---|---|---|---|
| B402 | S33°54'56.567" | E151°13'52.399" | 22.454 | 22.710 | .256 |
| BOTY | S33°58'23.355" | E151°14'10.566" | 22.217 | 22.432 | .215 |
| CETS | S33°55'05.557" | E151°13'57.743" | 22.443 | 22.696 | .253 |
| CPDH | S33°55'06.198" | E151°14'03.196" | 22.440 | 22.692 | .252 |
| G106 | S33°55'13.377" | E151°13'56.767" | 22.435 | 22.687 | .252 |
| GLEB | S33°52'15.439" | E151°11'05.280" | 22.679 | 22.988 | .309 |
| KYMA | S33°56'45.707" | E151°09'39.054" | 22.448 | 22.725 | .277 |
| LAKE | S33°56'18.011" | E151°12'40.436" | 22.398 | 22.654 | .256 |
| MBTS | S33°56'28.596" | E151°15'53.198" | 22.297 | 22.511 | .214 |
| MMCH | S33°51'33.954" | E151°13'18.439" | 22.679 | 22.972 | .293 |
| PETE | S33°54'36.572" | E151°10'31.635" | 22.551 | 22.846 | .295 |
| Q744 | S33°54'02.521" | E151°15'03.756" | 22.485 | 22.735 | .250 |
| Q855 | S33°54'01.506" | E151°14'56.739" | 22.489 | 22.740 | .251 |
| ROSE | S33°54'49.779" | E151°12'18.046" | 22.498 | 22.774 | .276 |
| UNSW | S33°55'08.060" | E151°13'52.148" | 22.442 | 22.697 | .255 |
| UU33 | S33°55'02.962" | E151°13'40.084" | 22.452 | 22.710 | .258 |
| WBTS | S33°51'10.704" | E151°17'09.094" | 22.618 | 22.876 | .258 |
| :
NOSU91A - NOSU89A |
Although the evaluated series (eqn (11.3-2)) gives N relative to a geocentric ellipsoid, the procedure described by eqn (11.3-8) can be used to transform the geoid height so that it may refer to a local (non-geocentric) ellipsoid such as that implicit for the AGD, as in the case of Figure 1.
Gravimetric Geoids
The first gravimetrically-determined geoid was computed in 1969. Subsequent to that, several refinements to the computational procedures have occurred over the last two decades, but it is only in the last few years has there been a revival of interest in an Australia-wide gravimetric geoid. The task of computing a national geoid (to support GPS activities) was formally assumed in July, 1989, by Australia's national geodetic agency: the Geodetic Services Section of the Australian Surveying and Land Information Group (KEARSLEY & GOVIND, 1991). AUSLIG generated the AUSGEOID93, and most recently the AUSGEOID98 models. These computations were based on the combined gravimetric and geopotential method (based on eqn (11.3-4)). The latest geoid model, AUSGEOID98, is available in electronic form, either as point values or grids, for map sheets at several scales, or over the Internet.
Geometric Methods
By their nature these geoid models are local, computed by the GPS surveyor, and have relevance only in the area of the GPS survey. HOLLOWAY (1988) describes several tests using this method of GPS heighting. In addition, the algorithm for obtaining the plane surface fit to the geoid "spot" heights is also described. Figure 3 is an example of the geoid height map that can be derived using such an interpolation method, in this case for a GPS network in South Australia. There were 45 stations in this network that had both GPS and AHD heights. This is far more than would normally be available. Hence the contour map of the geoid shows considerable detail. (It must be emphasised however that the map is not an independent determination of the geoid separation in this area as it also contains errors in the AHD.)
Figure 3. Geoid map derived from interpolating spot values of GPS height minus levelled height for a network in South Australia. (HOLLOWAY, 1988)
A variety of geoid height information was available: OSU89, AUSGEOID93 and
AHD minus GPS-derived ellipsoidal height. Table 2 summarises the results
of the comparisons. Note that the datum for the GPS network is the Mather
pillar at the University of New South Wales. Any error in the height of
this fixed station will influence (in an absolute sense) all the derived
GPS heights.
| Name | NOSU89A | NGRAV | 1 |
hGPS | H | NGPS | 2 |
|---|---|---|---|---|---|---|---|
| B402 | 22.454 | 22.498 | .044 | 59.008 | 36.410 | 22.598 | -.100 |
| BOTY | 22.217 | 22.269 | .052 | 41.407 | 19.003 | 22.404 | -.135 |
| CETS | 22.443 | 22.482 | .039 | 109.199 | 86.605 | 22.594 | -.112 |
| CPDH | 22.440 | 22.486 | .046 | 90.837 | |||
| G106 | 22.435 | 22.470 | .035 | 81.777 | 59.075 | 22.702 | -.232 |
| GLEB | 22.679 | 22.646 | -.033 | 24.225 | 1.45* | 22.77* | -.12* |
| KYMA | 22.448 | 22.412 | -.036 | 24.336 | 1.812 | 22.524 | -.112 |
| LAKE | 22.398 | 22.406 | .008 | 59.685 | 37.15* | 22.53* | -.12* |
| MBTS | 22.297 | 22.300 | .003 | 47.437 | 24.962 | 22.475 | -.175 |
| MMCH | 22.679 | 22.705 | .026 | 33.206 | 10.375 | 22.831 | -.126 |
| PETE | 22.551 | 22.531 | -0.020 | 29.272 | 6.604 | 22.668 | -.137 |
| Q744 | 22.485 | 22.521 | .036 | 99.863 | 77.206 | 22.657 | -.156 |
| Q855 | 22.489 | 22.519 | .030 | 78.809 | 56.15* | 22.66* | -.14* |
| ROSE | 22.498 | 22.520 | .022 | 82.964 | |||
| UNSW | 22.442 | 22.480 | .038 | 88.192 | 65.579 | 22.613 | -.133 |
| UU33 | 22.452 | 22.505 | .053 | 50.332 | 27.623 | 22.709 | -.202 |
| WBTS | 22.618 | 22.652 | .034 | 108.506 | 85.748 | 22.758 | -.106 |
NGPS = hGPS - H NGRAV computed from OSU91A + observed gravity data (AUSGEOID93) * implies accuracy of orthometric height is weak |
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© Chris Rizos, SNAP-UNSW, 1999