# Distortion grid transformations (NZGD1949 to NZGD2000)

The transformation grid method can be used to change horizontal coordinates between New Zealand Geodetic Datum 1949 (NZGD1949) and New Zealand Geodetic Datum 2000 (NZGD2000).

The transformation grid method uses a grid of values to ‘map’ the change of coordinates between datums. This method needs to be used when distortion within the datum itself (such as tectonic motion or localised deformation) needs to be considered in the coordinate change. Coordinates can remain in the geographic format (latitude, longitude, height) throughout the entire process, in contrast to the 3- or 7-parameter similarity transformation methods which need Cartesian coordinates (X,Y,Z).

A transformation grid has been created to convert coordinates from New Zealand Geodetic Datum 1949 (NZGD1949) to New Zealand Geodetic Datum 2000 (NZGD2000). The transformation has been calculated on a grid of approximately 20-kilometre spacing, over the main land areas of New Zealand.

The estimated accuracy of this transformation varies due to the complexity of the deformation that has occurred, and accuracy degrades over time as the land continues to deform. In the year 2000 the average error across New Zealand was ±0.2 metres, but by 2020 the errors were up to ±5 metres due to earthquakes.

## Using the NZGD1949 to NZGD2000 distortion grid

To convert coordinates from NZGD1949 to NZGD2000:

• use the distortion grid to interpolate a correction at the NZGD1949 coordinate
• add this correction to the NZGD1949 coordinate to determine the NZGD2000 values.

To reverse the transformation and convert a coordinate from NZGD2000 to NZGD1949:

• use the NZGD2000 coordinate to compute an estimate of the NZGD1949 to NZGD2000 transformation value, using the distortion grid to interpolate a correction
• subtract the interpolated correction from the NZGD2000 coordinates, to provide an initial estimate of the NZGD1949 coordinate
• use the initial estimate of the NZGD1949 coordinate to interpolate a more accurate correction between NZGD1949 to NZGD2000
• subtract this correction second transformation value from the original NZGD2000 coordinate to determine a final NZGD1949 coordinate.

The NZGD1949 to NZGD2000 distortion grid file and interpolation software used by Toitū Te Whenua can be downloaded. Alternatively, our online conversions page also uses this transformation.

Example coordinates are transformed using the distortion grid.

Datum Transformation Examples

#### Note

The NZGD1949 to NZGD2000 Distortion Grid is provided in the NTv2 ASCII format. NTv2 is a format developed by the Geodetic Survey of Canada specifically for the purpose of distributing grid transformation data.

NTv2 on Government of Canada website

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