Datums, Projections and Heights

Geodesy is the science relating to the determination of the size and shape of the Earth. To enable this to occur, positions (often in the form of coordinates and heights) need to be able to be expressed in terms of consistent and well defined reference systems. These systems are often referred to as datums and projections.

This page provides information about:

• Geodetic Datums
• Vertical Datums
• Projections

Other pages that may be of interest are:

• Orders of coordinates and heights
• Coordinate and Height Transformations

Answers to frequently asked questions about geodesy are also available.

Geodetic Datums

A geodetic datum defines a way of expressing positions on the globe and of calculating the direction and distance between two positions. Normally expressed in degrees, minutes and seconds of latitude and longitude, a geodetic datum combines a mathematical approximation of the shape of the earth (simplified to an ellipsoid) with a "realisation" that defines how the ellipsoid is positioned relative to the real world. The realisation is usually achieved by specifying the coordinates of a number of control marks within the datum's area of interest. In New Zealand these marks are traditionally monumented by black and white trig beacons seen on the tops of hills.

The official New Zealand geodetic datums are:

• New Zealand Geodetic Datum 2000 (NZGD2000)
• Ross Sea Region Geodetic Datum 2000 (RSRGD2000)

Other geodetic datums used in New Zealand include:

• World Geodetic System 1984 (WGS84)

Historical New Zealand geodetic datums include:

• New Zealand Geodetic Datum 1949 (NZGD1949)
• Chatham Islands Geodetic Datum 1971 (CIGD1971)
• Chatham Islands Geodetic Datum 1979 (CIGD1979)

Reference ellipsoids used in New Zealand:

• Geodetic Reference System 1980 (GRS80)
• International 1924
• World Geodetic System 1984 (WGS84)

Vertical Datums

A vertical datum is any level surface (e.g., mean sea level) taken as a surface of reference from which to reckon elevations. Although a level surface is not a plane, the vertical datum is frequently referred to as the datum plane, datum level, reference level, reference plane, vertical control datum or vertical geodetic datum.

In New Zealand there are three main vertical datums that are used. Each datum uses different types of heights. The types of heights can be broadly divided into those which relate to the Earth's gravity field (e.g., those which approximate the mean sea level surface) and those that do not (e.g., ellipsoidal heights obtained from GPS receivers).

Vertical datums used in New Zealand include:

• Mean sea level datums (normal-orthometric heights)
• New Zealand Geodetic Datum 2000 (ellipsoidal heights)

The official New Zealand geoid model is:

• New Zealand Geoid 2005 (NZGeoid05)

Other geoid models that are also used in New Zealand include:

• Earth Gravity Model 1996 (EGM96)

When surveyors determine cadastral boundaries, they are often defined in relation to the level of mean high water springs (MHWS). The Surveyor-General has issued some guidance for the determination of MHWS in the form of advisory note; however the professional judgement of the licensed surveyor is also of critical importance. Long-term tidal levels at standard ports around New Zealand have been produced that may assist surveyors and engineers in sea level determination.

Projections

Coordinates in terms of a geodetic datum relate to a curved surface (typically an ellipsoid). This means that it is not possible to represent them on a flat surface (e.g., a map) without introducing some sort of distortion. This dilemma can be demonstrated using an orange; it is not possible to lay the entire peel flat without breaking it in some way. To manage these distortions consistently a projection is used.

A projection is a consistent way of representing a curved surface (e.g., the Earth) as a flat surface (e.g., a map). There are many different types of projection that can be used; the most common being related to different geometric shapes (e.g., cylinders, cones, planes, etc.).

Projected coordinates have units of metres and are expressed in relation to a false origin. Typically computations using projection coordinates are easier to undertake than their curved geodetic equivalents. Because projections are related to specific geodetic datums, the conversion of coordinates between systems can be complicated.

The official New Zealand projections (in terms of NZGD2000) are:

• New Zealand Transverse Mercator 2000 (NZTM2000)
• NZGD2000 Meridional Circuits
• New Zealand Offshore Islands Transverse Mercator
• New Zealand Continental Shelf Lambert Conformal (NZCS2000)

Historical New Zealand projections include:

• New Zealand Map Grid (NZMG)
• Chatham Islands Transverse Mercator 1979 (CITM1979)
• North and South Island Yard Grid (NIYG, SIYG)

Coordinate Transformations

When using coordinates or heights from different sources it is important to ensure that they are in terms of the same datum and/or projection. If coordinates or heights are mixed then this can introduce errors (potentially of hundreds of metres) in the positions resulting from them.

A description of the different coordinate conversions and height conversions is available on this site. It is also possible to convert coordinates online and also download a software application for offline use (Microsoft Windows only).

Related Documents:

• Where in the world are we? - a general overview of datums and projections (2007) (PDF 1.1MB)
• LINZ Standards
• LINZ Specifications for geodetic contractors