The reference ellipsoid is an arbitrary reference surface that is a raw approximation of the Earth’s shape, which is basically a sphere “flattened” at its poles. The length of one of the axes at the Equator is chosen so that the ellipsoid coincides at this latitude with the mean sea level. It is the first-order definition of the non-spherical shape of the Earth as an ellipsoid of revolution. To first order, it accounts for over 90% of the geoid.

The reference ellipsoid is basically a convenience so that users don’t have to work with larger numbers, and to get more precision in calculations. Sea surface height measurements from the centre of the Earth are on the order of 6000 km. By removing a reference surface, the heights relative to the ellipsoid are on the order of 100 metres. Thus, one can gain several digits of accuracy in numerical calculations.

In fact, any reference surface could be used. A sphere would work, but sea surface height differences from this surface could be as large as 20 km, thus one would lose precision than by using an ellipsoid.

*fig 1. Schematic of the Reference ellipsoid with respect to the geoid*.

In altimetry, the Topex/Poseidon and the WGS84 ellipsoids are typically used:

For Topex/Poseidon, Jason-1, Jason-2 (T/P ellipsoid)::

– radius: 6378136.3

– inverse Earth flattening coefficient:298.257

For ERS-1, ERS-2, Envisat (WGS84):

– radius: 6378137 m

– inverse Earth flattening coefficient: 298.257223563