The Geoid and Ellipsoid, and the AHD

Knowing how high we are above sea level doesn’t just happen. There is a whole research area dedicated to it – dedicated to making it more precise, refining the theories and onboarding new technologies, such as satellites, as they become available.

Recent research within the CRCSI’s Positioning Program is not only making height data more reliable but it’s ensuring that people using this data know how suited it is for their particular task. The Australian Height Datum, or AHD for those in the know, tells us how high above mean sea level we are at different points across country – an important piece of information for many industries. How are you meant to build infrastructure without it? Think water (or sewage) flow. But why do we need to refine it? A map is a map and a height is a height, right? Wrong! You might not know this, but our continent moves north-westerly by 7cm each year. And, depending on the density of the land (so what’s buried beneath) the downwards gravitational pull changes. All of this needs to be taken into account to get the AHD spot on.

The model we use now to determine AHD is AUSGeoid09. It takes GPS height measurements purely mathematically. Satellites measure our height above the ground relative to a simplified mathematical representation of the Earth known as the ellipsoid – this ellipsoid sometimes sits inside the Earth’s surface and sometimes above, depending on where you, it is just a model of the Earth. Ellipsoid and AHD heights differ by between -30 and +70 metres across Australia. So, to have your height in AHD you must convert the ellipsoid height to AHD height. And this is why we have specialists working on the modelling work.

Researchers at Curtin University and Geoscience Australia continue to refine the Australian coordinate system, so that the mathematics that convert the ellipsoid heights (measured by a GPS) to AHD is as precise as possible. This ensures our maps, surveying techniques and positioning technologies are at the cutting edge — essential for a range of applications from precision agriculture (that’s driverless tractors) to LiDAR mapping of our coastline (important for elevation and climate change models).

The work being done with the CRCSI will provide the next version of AUSGeoid with a rigorous uncertainty value offset between the ellipsoid and the AHD, which will vary as function of location. The uncertainty estimates will allow global navigation satellite system users to determine how precise and accurate their heights are at every location – not presently possible, anywhere in the world. So rather than just having to add the same uncertainty to their measurements, no matter where they take them, surveyors, engineers and the like will be able to have a location based uncertainty factor added to their height measurements.

Currently, a blanket value of 30-50mm is given as the uncertainty for AUSGeoid09. Our new geoid model and its spatially-dependent accuracy statement will give users and producers of height information much more confidence in the quality of their results. The CRCSI’s Positioning Program and Australia’s National Positioning Infrastructure plan have the objective to provide real-time, centimetre-level positioning services anywhere, anytime, with the highest possible accuracy and integrity. This project plays a big role in that and will have impacts far and wide. Moreover, Australia will be the first country in the world to provide a combined nation-wide model with uncertainty estimates for each and every location.

Our project team has published papers relating to this project, get your fix of the science: Fourier-based error propagation for the planar gravimetric terrain correction and The first Australian gravimetric quasigeoid model with location-specific uncertainty estimates.

Image courtesy of Geoscience Australia