Appendices

Datum Transformation Methods

7 PARAMETER (POINT VECTOR ROTATION)

The Seven Parameter PVR (also known as the Bursa-Wolfe) method incorporates three translations, three rotations, and a scale correction factor.

The rotations are defined as positive clockwise, as may be imagined to be seen by an observer in the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place. The MAPublisher and Geographic Imager implementation of the

Seven Parameter PVR method uses the "Helmert" style of transformation. This family of transformations is usually performed in three steps. First, a geodetic input point is transformed to 3D geocentric coordinates according to the horizontal datum. Then a core transformation is performed, and finally, the geocentric coordinates are transformed back to geodetic coordinates. The control parameters for a Helmert transformation specify the details of the core transformation. In general, the core transformation consists of a rotation around the x-axis, a rotation around the y-axis, a rotation around the z-axis, a scaling that is the same for all dimensions, and a vector shift (any combination of x, y, and z), performed in that order.

The parameters to define a Seven Parameter PVR transformation are: 

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
X Rotation	rX
Y Rotation	rY
Z Rotation	rZ
Scale	k

Note:  To properly define a seven-parameter translation, you MUST know which rotation sense is used for your transformation parameters.

7 PARAMETER (COORDINATE FRAME ROTATION)

The Seven Parameter CFR method incorporates three translations, three rotations, and a scale correction factor. The rotations are defined as positive counter-clockwise, as may be imagined to be seen by an observer in the origin of the coordinate frame, looking in the positive

direction of the axis about which the rotation is taking place. The MAPublisher and Geographic Imager implementation of the Seven Parameter CFR method uses the "Helmert" style of transformation. This family of transformations is usually performed in three steps. First, a geodetic input point is transformed to 3D geocentric coordinates according to the horizontal datum. Then a core transformation is performed, and finally, the geocentric coordinates are transformed back to geodetic coordinates. The control parameters for a Helmert transformation specify the details of the core transformation. In general, the core transformation consists of a rotation around the x-axis, a rotation around the y axis, a rotation around the z-axis, a scaling that is the same for all dimensions, and a vector shift (any combination of x, y, and z), performed in that order.

The parameters to define a Seven Parameter CFR transformation are:

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
X Rotation	rX
Y Rotation	rY
Z Rotation	rZ
Scale	k

 

Note:  To properly define a seven-parameter translation, you MUST know which rotation sense is used for your transformation parameters.

CANADIAN NATIONAL TRANSFORMATION VERSION 2 (NTV2)

MAPublisher and Geographic Imager support the definition of a geodetic datum based on the Canadian National Transformation Version 2.0 directly. The Canadian National Transformation originally defined an accurate transformation from NAD27 to NAD83 for Canada, but the method has been adopted by Australia, New Zealand, Spain, and several other locations around the world. The shift values for a geographic area are stored in a single grid file, representing latitude and longitude shifts (named with the extension .gsb).

MAPublisher or Geographic Imager uses grid files in a format published and provided by the Canadian Government. While the definition of this method is supported, it does require additional files to implement new datum transformations using this method. Contact information is as follows:

Address:  Natural Resources Canada Geodetic Survey Division Geomatics Canada Room 440 615 Booth Street Ottawa, Ontario K1A 0E9

Phone:         (613) 995-4410 FAX:             (613) 995-3215 Email:          information@geod.NRCan.gc.ca Web:            www.geod.NRCan.gc.ca

Note:  When browsing through the data source some objects may be flagged with a red exclamation point symbol. These objects are incomplete definitions. MAPublisher and Geographic Imager include a number of datum transformation definitions that require supplementary data files to function properly. These objects are not able to be used until the supplementary files are added. Some are proprietary and must be purchased from a specific government agency.

CUSTOM MRE

This is a customizable variation of the DMA Multiple Regression Equations transformation methods. It allows users to set up input files containing the coefficients for the latitude, longitude, and height equations used in the transformation, as well as a scale factor and offsets for latitude and longitude.

Parameters needed to define a Custom MRE transformation are:

Parameter	Often Noted as
Latitude Coefficient File	lat_coefficient_file
Longitude Coefficient File	lon_coefficient_file
Height Coefficient File	hgt_coefficient_file
Scale Factor	scale_factor
Latitude Offset	lat_offset
Longitude Offset	lon_offset

 

ED50 TO ED87 NORTH SEA

The ED50 to ED87 North Sea Transformation consists of a 4th order reversible polynomial that is used to convert coordinates between the ED50 and ED87 datums. This formula was published in a 1991 note created by the Norwegian Mapping Authority (Statens Kartverk) entitled Om Transformasjon mellom Geodetiske Datum i Norge. The ED50ToED87NorthSea transformation method is hard-coded and does not require any parameters. 

FOUR PARAMETER METHOD

Based on the Helmert family of transformations, a Four parameter transformation is similar to a Seven parameter transformation, except it does not include rotations.

Parameters needed to define a four-parameter transformation are: 

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
Scale	k

 

GEOCENTRIC TRANSLATION

A three-parameter translation between two geocentric coordinate systems. This is a non-simplified Molodensky transformation. There are three steps that are performed by this transformation. First, the input point is represented as a Cartesian point in three dimensions on the input datum. The coordinates of this point are then translated using the dx, dy, and dz parameters. Finally, the translated point is converted to a geodetic point on the output datum.

HARN

MAPublisher and Geographic Imager support the definition of a geodetic datum based on an NGS High Accuracy Reference Network (HARN). The National Geodetic Survey is establishing HARNs within the U.S. on a state-by-state basis.

You can think of a HARN as a geodetic datum, most easily viewed as an enhanced NAD83 datum. HARNs are also known as NAD83/91 and High Precision Grid Networks (HPGN). The NGS HARN method is actually very similar to the NGS NADCON method. As with the NADCON method, the shift values for a geographic area are stored in a set of grid files, one representing latitude shifts (named with the extension .las) and one representing longitude shifts (named with the extension .los). The major difference is that the HARN data files contain shifts from NAD83 to a HARN instead of NAD27 to NAD83. MAPublisher and Geographic Imager use grid files in a format published and provided by the National Geodetic Survey. Questions about the availability of other HARN grid files (and the HARN systems in general) should be addressed to: 

Address:  NGS Information Services, NOAA, N/NGS12 National Geodetic Survey SSMC-3, #9202 1315 East-West Highway Silver Spring, MD 20910-3282

Phone:   (301) 713-3242 Web:      www.ngs.noaa.gov

The current HARNs are already pre-defined within MAPublisher and Geographic Imager. As new HARNs are completed and made available, they will be added to avenza.xml.

Note:  The definition of datum transformations using this method includes parameters specifying the required grid files. If the system cannot find the specified file the shift will be marked unusable in the Datasource, and may not be selected for use.

LONGITUDE ROTATION

The Longitude Rotation datum shift method is a transformation on a two-dimensional or three-dimensional geographic coordinate system that changes the longitude values by a rotation value and leaves the latitude and elevation values unchanged.

The one parameter to define a longitude rotation is the angle of rotation.

MADRID TO ED50 POLYNOMIAL

The Madrid to ED50 Polynomial transformation method allows the transformation of coordinates between the Madrid 1870 and the ED50 datums.

For a detailed reference on the Madrid to ED50 Polynomial transformation, refer to 2.3.1.3 "Polynomial transformation for Spain" in the EPSG Surveying and Positioning Guidance Note Number 7, part 2: http://www.epsg.org/guides/G7-2.html

Note:  This datum transformation has been computed for a specific area of use and specific datums. The base Geodetic Datasource contains the standard datum transformations using this method. Creating new transformations using this method or using the transformation for data outside of the pre-determined envelopes may cause unreliable results.

MOLODENSKY

The Molodensky transformation method shifts coordinate values between local and geocentric datums using three linear shift parameters. It provides a general solution with limited accuracy. The Molodensky method provides a transformation that is accurate to within 5-10 metres.

 For a detailed discussion of the Molodensky algorithms and parameters for a variety of local geodetic datums, please refer to Defense Mapping Agency, Technical Report TR 8350.2, 1991 Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems. The Molodensky method can be defined for local geodetic datums worldwide.

MOLODENSKY-BADEKAS

The Molodensky-Badekas 10 parameter transformation method allows for very high accuracy transformation of coordinates between datums over large areas. For a detailed reference on Molodensky-Badekas coordinate transformations, refer to the EPSG Surveying and Positioning Guidance Note Number 7, part 2: www.epsg.org/guides/G7-2.html.

Parameters needed to define a Molodensky-Badekas transformation are:

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
Scale	k
X Rotation	rX
Y Rotation	rY
Z Rotation	rZ
X Ordinal	Xp
Y Ordinal	Yp
Z Ordinal	Zp

 

MRE (MULTIPLE REGRESSION EQUATIONS)

The DMA Multiple Regression Equations transformation method shifts coordinate values between geodetic datums. It can be defined for local geodetic datums worldwide. The DMA Multiple Regression Equations methods uses Doppler-derived parameters and provides a general solution with limited accuracy. It provides a transformation that is accurate to within 3-10 metres.

For a detailed discussion of the DMA Multiple Regression Equations algorithms and parameters for a variety of local geodetic datums, please refer to Defense Mapping Agency Technical Report TR 8350.2, 1991Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems.

The main advantage of the DMA Multiple Regression Equations methods lies in the modeling of distortions for datums that cover continental-sized land areas. This achieves a better fit in geodetic applications than the Molodensky method.

Note:  The DMA Multiple Regression Equations methods is an application of the theory of least squares. The coefficients for the mathematical regression equations are determined by fitting a polynomial to predicted shifts in a local area. If the DMA Multiple Regression Equations methods is applied outside of the local area for which the coefficients of the equations are determined, the results may be unpredictable.

NADCON

The NGS NADCON method transforms coordinate values between the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). The NGS NADCON method provides a transformation that is accurate to within 0.15-0.5 metres. (Please refer to NOAA Technical Memorandum NOS NGS-50 NADCON - The Application of Minimum Curvature-Derived Surfaces in the Transformation of Positional Data from the North American Datum of 1927 to the North American Datum of 1983).

The NGS NADCON method applies a simple interpolation algorithm using a gridded set of standard datum shifts as parameters. The shift values for a geographic area are stored in a set of grid files, one representing latitude shifts (named with the extension .las) and one representing longitude shifts (named with the extension .los). MAPublisher and Geographic Imager use grid files in a format published and provided by the National Geodetic Survey. Questions about the availability of other NADCON grid files (and the NGS NADCON method in general) should be addressed to:

 

Address:  National Geodetic Survey 11400 Rockville Pike Rockville, MD 02852

Phone:          (301) 713-3242 Web:             www.ngs.noaa.gov

 Note:  The definition of datum transformations using this method includes parameters specifying the required grid files. If the system cannot find the specified file the shift will be marked unusable in the Datasource, and may not be selected for use. 

NTF TO RGF93

Converts coordinates from NTF (Nouvelle Triangulation de la France) to RGF93 (Réseau Géodesique Français) using a grid file defined by IGN (Institut Géographique National, the French National Geographical Institute). The default grid file assumes a Greenwich prime meridian. 

ORDNANCE SURVEY GRID (OSTN 02)

To cope with the distortions in the OSGB36 TRF, different transformations are needed in different parts of the country. For this reason, the national standard datum transformation between OSGB36 and ETRS89 is not a simple Helmert datum transformation. Instead, Ordnance Survey has developed a rubber-sheet type transformation that works with a transformation grid expressed in easting and northing coordinates. The grids of northing and easting shifts between ETRS89 and OSGB36 cover Britain at a resolution of one kilometre. From these grids, a northing and easting shift for each point to be transformed is obtained by a bi-linear interpolation.

The National Grid Transformation copes not only with the change of datum between the two coordinate systems but also with the TRF distortions in the OSGB36 triangulation network, which make a simple datum transformation of the Helmert type limited to applications at 5m and larger accuracy levels. This transformation removes the need to estimate local Helmert transformations between ETRS89 and OSGB36 for particular locations.

Because the National Grid Transformation works with easting and northing coordinates, other ETRS89 coordinate types (3-D Cartesian or latitude and longitude) must first be converted to eastings and northings. This is done using the same map projection as is used for the National Grid (see section 7 below), except that the GRS80 ellipsoid rather than the Airy ellipsoid is used. After the transformation, the resulting National Grid eastings and northings can be converted back to latitude and longitude (this time using the Airy ellipsoid) if required.

Note:  The definition of datum transformations using this method includes parameters specifying the required grid files. If the system cannot find the specified file the shift will be marked unusable in the Datasource, and may not be selected for use.

POLYNOMIAL

The Polynomial datum shift methods use a collection of parameters that define a high order mathematical function for transforming between two horizontal datums. These equations are usually created by local and regional geodetic authorities. They generally provide high accuracy transformations but are limited to specific areas of use. In many cases, the accuracy of these transformations is around one metre.

For a detailed description of generalized polynomial datum transformations, please refer to the OGP guidance notes. These are freely available from www.epsg.org.

Note:  Polynomial datum shifts are generally computed for specific areas of use. Since the derivations of the formula are based on a limited number of reference points, using the transformation for data outside of the pre-determined envelopes may cause unreliable results.

SIX PARAMETER METHOD

Based on the Helmert family of transformations, the six parameter transformation is very similar to a seven parameter transformation, except it does not contain a scale parameter.

The Six parameters needed, are: 

Parameter	Often Noted as
X Translation	dX
Y Translation	dY
Z Translation	dZ
X Rotation	rX
Y Rotation	rY
Z Rotation	rZ

 

TOKYO TO JGD2000

Converts coordinate from the Tokyo datum to the JGD 2000 (Japan Geodetic Datum of 2000) using a grid file defined by GSI (Japanese Geographical Survey Institute).

UTM Zones Map

US State Plane Zones Map

Note:  For each zone, the projection's parameters vary — e.g. the Florida East zone and Georgia West zone coordinate systems create a different geometry, although both are based on Transverse Mercator. For example, see the specific definitions in Coordinate Systems > Projected > North America > United States > US State Plane NAD83 > NAD83 (US Feet) in the MAPublisher and Geographic Imager libraries.