Datums

Latitude and longitude is a standard way of specifying a location on the earth. However, not all latitudes and longitudes are equal. These coordinates change depending on the geodetic datum in use.

The problem is that the earch is not a perfect sphere. It is not even a perfect spheroid. It's a little bit lumpy. Historically, datums have been designed for use within a specific area, and are accurate over that area only. An appropriate datum can be used as a reference frame both to describe locations and to describe distance and direction between two points.   

NZGD49, NZGD2000, and WGS84

The New Zealand Geodetic Datum 1949 (NZGD49) is an example of a datum designed for use within a limited area -- the New Zealand landmass. This datum is the basis of most of the topographic maps in circulation today. However, GPS technology has made the creation of globally-compatible datums possible. Indeed, all GPS units use the World Geodetic System 1984 (WGS84), although they may translate to another datum for display (note that data exported from the GPS unit may be delivered in the original datum). New Zealand has a new datum called the New Zealand Geodetic Datum 2000 (NZGD2000). Latitudes and longitudes in this datum are around 200m different from corresponding latitudes and longitudes in the NZGD49 datum. For tramping purposes, the NZGD2000 and WGS84 may be considered identical -- any differences are far smaller than GPS unit inaccuracies. The relationship between the two datums is described in this LINZ geodetic fact sheet. 

As future topographic maps will be designed for the NZGD2000 datum, it is important to understand which datum your map is using. The NZMS260 series uses the NZGD49 datum.

Projections

A projection is a technique for translating the curved shape of the earth onto a flat map. A good projection minimises distortion and provides accurate distance and angle measurements. Projections are only successful over a small part of the globe, as larger areas require ever greater distortions.

NZMG

The New Zealand Map Grid (NZMG) is a projection based on the NZGD49 datum. This map grid is used for all current New Zealand topographic maps.

Coordinate systems

Latitudes and longitudes

Latitudes and longitudes are a standard means of representing points. While a latitude, longitude pair may plot any point on the globe, the accuracy of the point is dependent on the datum in use. Coordinates are often written as degrees, minutes, and seconds of arc as follows: 43°35′53.3″ S, 170°08′33.0″ E or as decimal degrees: -43.5981468, 170.1425128. One second of arc (1″) equates to 30m, or 0.00028 in decimal degrees.

Eastings and northings

Coordinate systems may also be devised for a particular map projection. Easting, northing coordinate pairs may be used on the New Zealand Map Grid, and on New Zealand topographic maps. These are measures of the distance in metres both east and north of a standard reference point. Aoraki / Mount Cook is referenced as: 2279337, 5730602.

Grid references

A grid reference is a simplified reading designed for convenience over accuracy. The first part of the reference is the map sheet code. The remainder combines the easting and northing components. Since the reference is read off the paper of the map itself, it is only supplied with an accuracy of 100m.  Aoraki / Mount Cook's grid reference is: H36 793306. "H36" is the name of the map, 793 is the easting portion, and 306 is the northing portion. Note that these values are the central digits of the eastings and northings described above.

To read a grid reference, find the nearest vertical blue line to the left of the point and read off the two-digit number at the edge of the map. Estimate tenths from the line to the point. This is the third digit. Next, find the nearest horizontal blue line below the point and read off the two-digit number at the edge of the map. These are the forth and fifth digits. Estimate tenths from the line to the point. This is the sixth digit. Write the sheet number first (for example H36) followed by the 6-digit reference. An example of this technique is provided on each topographic map. 

Coordinates on this website

Coordinates are entered into this website and displayed in a variety of formats. When a coordinate is entered, the source value and coordinate system are stored. But the value is also converted into an NZGD2000 value and stored. This value is used for all calculations within the site. While coordinate conversions introduce a certain inaccuracy, generally this inaccuracy is less than that inherent in GPS systems. However, it is important to understand that a coordinate is limited in accuracy by its source. If a value has been read off the paper of a topographic map, then its accuracy will be limited to 100m at the very best -- even if a much more precise value is displayed. 

For reference, source coordinates are displayed in boldface throughout this site. Other coordinates are displayed as regular face. 

Behind the scenes

If you are interested in the techniques and mathematics of geodetic conversions in use on this site, take a look at the following resources:

• Conversion between Latitude and Longitude and New Zealand Map Grid
  The technique employs an iterative formula and complex numbers.
  
• Where in the World Are We?
  This useful document provides background on datums, inforrmation on converting geographic coordinates (latitude and longitude) to and from Cartesian coordinates (x, y, z), and information on datum transformations. The mathematics here includes trigonometry and matrix arithmetic. For reference, this website uses the seven-parameter transformation.