# Geoid

A geoid is a three dimensional surface of equal gravitational potential which is perpendicular to the direction of the gravity vector at all points. Since the mass distribution of the Earth is not uniform and the direction of gravity changes accordingly, the resultant shape of the geoid is irregular. Although there are an infinite number of these equipotential surfaces for the Earth, the term 'geoid' is often used to describe the equipotential surface which best corresponds with mean sea level. Across Australia, mean sea level and its onshore realisation, the Australian Height Datum (AHD), correspond to within approximately ±0.5m of the geoid.

## Why the AHD and the geoid do not coincide

To establish the AHD, the mean sea level at 32 tide gauges from around the Australian coastline were assigned a value of 0.000m AHD. Given that the warmer/less dense water off the coast of northern Australia is approximately one metre higher than the cooler/denser water off the coast of southern Australia, the AHD is about 0.5m above the geoid in northern Australia and roughly 0.5m below the geoid in southern Australia.

## Working with the geoid, AHD, and ellipsoid

Heights obtained from Global Navigation Satellite System (GNSS) receivers are known as ellipsoidal heights and are referenced to a simplified mathematical representation of the Earth known as the ellipsoid. Ellipsoidal heights differ from geoid/AHD heights by between -30 and +70 metres across Australia. This is known as the geoid-ellipsoid separation, or N value. To convert ellipsoidal heights to geoid/AHD heights, a geoid model can be used. Older geoid models allowed Global Positioning System (GPS) users to convert ellipsoidal heights to derived AHD heights (accurate to ±0.5m) by subtracting the geoid¿ellipsoid value from the ellipsoidal height.

Figure 1. AUSGeoid09 allows
GPS users to convert between
GPS heights and AHD heights.
In southwest Australia, the AHD
is up to 33 metres below the
ellipsoid and in northeast
Australia the AHD is up to
72 metres above the ellipsoid.

AUSGeoid09 is Australia's newest geoid model for converting ellipsoidal heights to AHD heights and is accurate to 0.03m across most of Australia. Unlike previous versions of AUSGeoid ('93, '98) which provided geoid-ellipsoid separations, AUSGeoid09 provides the AHD to ellipsoid separations.

## The geoid in Antarctica

An accurate definition of the geoid is severely constrained in Antarctica by the lack of gravity information, especially across the inland of the continent.

Antarctic geoid map, edition 1 was produced by Bureau of Mineral Resources (now Geoscience Australia) for Scientific Committee on Antarctic Research (SCAR), in about 1980, from the GEM10C geo-potential model.

Antarctic geoid map, edition 2 was produced in 1990 by AUSLIG (now Geoscience Australia) and shows the geoid-ellipsoid separations, in terms of the Geodetic Reference System 1980 (GRS80) ellipsoid, with 5 metre contour intervals. This edition used the OSU89A geopotential coefficients produced by Professor Rapp of Ohio State University. The program used to compute the geoid separations was provided by Dr. Kearsley of the University of New South Wales.

The current situation with the geoid in Antarctica remains hampered by the continuing lack of ground gravity data. Although limited by the amount of data used in the Antarctic region, a grid of separation values (initially from the OSU91A geopotential model and subsequently from EGM96), was produced to allow interpolation of a separation. However, the United States National Imagery and Mapping Agency (NIMA) now provides an online EGM96 N value service, which supersedes the previously available Geoscience Australia interpolation.

Note: The NIMA algorithm applies additional corrections to the EGM96 N values: an offset of -0.53m to align it to the World Geodetic System 1984 (WGS84) ellipsoid and a terrain correction. This means that these files will differ from the 'pure' EGM96 N values previously provided in the files for interpolation. The difference is about half a metre in an absolute sense, but will generally have little effect in a relative sense (differences in N value). Care must be used if you are working with information derived from the two different sources.

The SCAR Geoscience Standing Scientific Group is looking at future possibilities to improve the geoid in Antarctica. These include:

• the new global geoid currently being evaluated by the International Geoid Service (IGeS)
• a specifically developed geoid for the Antarctic, using enhanced gravity data and sea level connections to GPS campaign points.