# Reference ellipsoids

An important feature of a geodetic datum is the reference surface. The reference surface approximates the shape of the Earth, so that geodetic coordinates can be located on a curved surface. The most common reference surface for geodetic datums is an ellipsoid.

The reference ellipsoid is a simplified model of Earth’s shape. The ellipsoid provides a standardised model for determining locations on the Earth's surface, making it convenient for fast and efficient calculations.

Due to the efficiency of a reference ellipsoid, it is a critical component of GNSS (global navigation satellite system) technology. However, because it is only a generalised shape, it does not take in to account the details of the Earth’s irregular shape and topologies, meaning that ellipsoidal height has few practical applications, and that a separate vertical datum is still required.

Vertical datums

An ellipsoid is a simple geometric shape that looks like a slightly flattened sphere. It is created by spinning an ellipse around an axis, and it is defined mathematically by two parameters: the axis and flattening. In New Zealand, we commonly use an oblate-ellipsoid. This means the ellipsoid is formed by spinning it along the minor axis while inversely flattening it. Although it is the closest fit to the Earth's shape, it can still differ from the Earth’s actual shape by up to 100 meters.

## Reference ellipsoids common in New Zealand

### Geodetic Reference System 1980 (GRS80)

GRS80 (Geodetic Reference System 1980) was established in 1980 using a combination of satellite data, terrestrial measurements and space geodesy techniques. It is the reference ellipsoid New Zealand Geodetic Datum 2000 (NZGD2000).

GRS80 is an oblate ellipsoid, meaning it is slightly flattened at the poles and bulging at the equator. It is designed to provide a consistent and accurate approximation of the Earth’s shape over large areas, and is the most frequently used reference ellipsoid for global positioning, mapping and geodetic surveying.

### World Geodetic System 1984 (WGS84)

WGS84 (World Geodetic System 1984) was developed to support the United States’ global positioning system, GPS. It is not the same as the similarly named WGS84 datum.

World Geodetic System 1984 (WGS84)

The WGS84 ellipsoid is similar to GRS80, with different inverse flattening values determining the amount they are flattened. This is related to the way they were derived and the result of different rounding methods.

## International 1924

The International 1924 reference ellipsoid (also known as the Hayford 1910 reference ellipsoid) was defined by geodesist John Fillmore Hayford in 1910 mostly using data from Europe and the USA. It was refined and adopted by the International Union of Geodesy and Geophysics (IUGG) in 1924. The International 1924 ellipsoid was widely used through the 20th century, including as the reference surface for New Zealand Geodetic Datum 1949 (NZGD1949). It has largely been replaced by more accurate global ellipsoids such as GRS80.

### Parameters of common geoids

This table shows the parameters of reference ellipsoids common in New Zealand
EllipsoidSemi-major axis ( a )Inverse flattening ( 1 / f )
GRS806 378 137 m298.257 222 101
WGS84 6 378 137 m298.257 223 563
International 19246 378 388 m297