# New Zealand Geodetic Datum 2000 ellipsoidal heights

New Zealand Geodetic Datum 2000 (NZGD2000) coordinates include an ellipsoidal height measured using GNSS (global navigation satellite system) observations. Ellipsoidal heights often need to be converted to a vertical datum.

New Zealand Geodetic Datum 2000 (NZGD2000) is a geodetic datum that uses coordinates expressed as latitude (Φ), longitude (λ), and ellipsoidal height (H). Ellipsoidal heights are measured based on a mathematical surface called the reference ellipsoid. NZGD2000 uses the Geodetic Reference System 1980 (GRS80) ellipsoid.

Reference ellipsoids

The reference ellipsoid is an approximation of the Earth's shape that is convenient for computing coordinates in systems where speed is important, such as GNSS (global navigation satellite system). These ellipsoidal heights are valuable for monitoring change, such as measuring how much a site moves over time.

Ellipsoidal heights, combined with latitude and longitude can exactly represent the position of a point. However they do not conform with common expectations of a height system, such as water always flowing from a greater to a lesser height. For example, at the bottom of the South Island the ellipsoid is at sea level while at the top of the North Island the ellipsoid is 35 metres below sea level. This is because they do not account for the complexities of the Earth’s gravity field.

Converting ellipsoidal heights to a gravimetric vertical datum is simple if the vertical datum has an accompanying geoid model. Some GNSS software can make this conversion and provide an output in the required vertical datum.

NZGD2000 ellipsoidal heights can be converted to the gravity-based New Zealand Vertical Datum (NZVD2016) to achieve normal-orthometric heights by applying a correction from the geoid model NZGeoid2016 (New Zealand Quasi-Geoid 2016).

More information about height conversion can be found here: Converting between NZVD2016, NZGD2000 and local vertical datums