Datum Transformations

The Australians have adopted the techniques developed by Geomatics Canada for its National Transformation (Version 2) to define a precise means of converting from the Australian Geodetic Datum of 1966 to the newer Geocentric Datum of Australia 1994. The data files involve overlap, and those areas deserve special attention.

Datum shift data files for this transformation are being developed on a state-by-state basis. Therefore, there is more than one data file for this transformation. The coordinate conversion system considers AGD66 to be a single entity even through there are several different data files that overlap. Users are encouraged to sort data files to ensure that the desired data file is used in the regions of overlap.

Several of the states in Australia have been using the Australian Geodetic Datum of 1984 for some time now. This transformation technique implements the conversion of AGD84 to GDA 1994. Operationally, this technique is identical to the AGD66 to GDA94; however, different data files are used. See AGD66 to GDA94 via Grid Fileabove for more details.

The Average Terrestrial System of 1977 has been used in the Maritime provinces of Canada since 1977. This transformation uses data files in the Canadian National Transformation (version 2) format to determine the shift required to properly transform ATS77-based geographic coordinates to CSRS-based coordinates. Note that:

• each of the different provinces involved have produced a data file covering the geography of their respective provinces, and
• the individual data files are not in the public domain and must be obtained by users directly from the provincial governments involved.

This transformation is actually an approximation of the Seven Parameter Transformation

The approximation is arrived at by making three assumptions:

1. the sine of a small angle is equal to the angle (in radians) itself;
2. the multiplication of two sine terms is zero; and
3. the cosine of a small angle is one.

This approximation is valid only for small angles.

In all other aspects, this transformation is the same as the Seven Parameter transformation. In processing new data projects, use the Seven Parameter transformation in lieu of the Bursa/Wolf. The Bursa/Wolf approximation is provided for purpose of providing the means to reproduce numbers/calculations that were originally accomplished using the approximation.

Switzerland has adopted the Canadian technique to define the shift from CH1903 to CH1903+.

CSRS (Canadian Spatial Reference System) is the Canadian equivalent to the U.S.'s HARN; that is, a very accurate rework of NAD83 using GPS technology. This transformation allows direct conversion of NAD27 data to CSRS, without making a stop at NAD83. This conversion technique is implemented by a series of datum shift grid files of the Canadian National Transformation format. Unlike other implementations by Canadians, however, there are multiple overlapping files involved.

You can choose a fallback transformation to specify how data points outside the coverage of existing data files are to be handled. Again, the data files are being generated on a province-by-province basis. The individual files may, or may not, be in the public domain. You may need to acquire the appropriate data files yourself in order to use the transformation.

CSRS (Canadian Spatial Reference System) is the Canadian equivalent to the U.S.'s HARN; that is, a very accurate rework of NAD83 using GPS technology. Like the US HARN, the shifts are in the range of 1 to 2 feet (40 centimeters).

This conversion technique is implemented by a series of datum shift grid files of the Canadian National Transformation format. Unlike other implementations by Canadians, however, there are multiple overlapping files involved.

You can choose a fallback transformation to specify how data points outside the coverage of existing data files are to be handled.

Again, the data files are being generated on a province-by-province basis. The individual files may, or may not, be in the public domain. You may need to acquire the appropriate data files yourself in order to use the transformation.

German authorities have published a grid shift data file for transforming DHDN to ETRS89, applicable to German geography. Although this file covers all of Germany, it is appropriate only for specific uses.

Note that the official name may use the designation ETRF89 instead of ETRS89.  

Spain has also adopted the Canadian technique to define the shift from the European Datum of 1950 (ED50) to European Terrestrial Reference Frame, 1989 (ETRF89).

At the current time, the differences between ETRF89 and WGS84 are small. Further, a generally accepted means of converting between ETRF89 and WGS84 is unknown to the authors of the coordinate conversion system. This technique does nothing.

This transformation is the Seven Parameter Transformation without the Rotation parameters. You could achieve the same results by using the Seven Parameter Transformation, setting the three rotation parameters to zero, and setting the remaining four parameters as appropriate.

The differences between GDA94 and WGS84 are small. Further, a generally accepted means of converting between GDA94 and WGS84 is unknown to the authors of the coordinate conversion system.

This transformation will produce the same results as the Seven Parameter Transformation with all three rotation parameters and the scale parameter set to zero.

As with the Seven Parameter Transformation, this transformation proceeds in three phases. First, the geographic coordinates are converted to three-dimensional Cartesian, geocentric coordinates using the ellipsoid of the original datum. Second, the three translation parameters, Delta X, Delta Y, and Delta Z, are used to translate the geocentric coordinates. Third, the resulting geocentric coordinates are converted back to geographic form using the target ellipsoid.

As in all other cases for the translation parameters, the geocentric parameters must be given in units of meters.

This transformation method supports a priority ordered list of grid files in arbitrary formats. It is specific to geodetic transformation definitions, and may not be used for datums. Each grid file entry includes the grid format, direction of the grid, and the path to the grid. The first grid that provides coverage of the input point will be used for conversion.

Grid Formats:

Grid direction must be ‘Fwd’ (Forward) or ‘Inv’ (Inverse/Reverse).

Transformation Definition Example Snippet:

[…]

METHOD GRID_INTERP \

GRID_FILE “NADCON,Fwd,.\GridData\Nadcon\arhpgn.l?s” \

GRID_FILE “NADCON,Fwd,.\GridData\Nadcon\alhpgn.l?s”

HARN (High-Accuracy Reference Network) has also been known as HPGN (High-Precision GPS Network): both terms refer to NAD83/91, which is a rework of NAD83 with the aid of GPS technology (since GPS was not functional in 1983). This technique selection implies the use of the algorithms and data files of the U. S. National Geodetic Survey's NADCON program to effect the shift between NAD83 and HARN.

As with the NADCON technique this transformation relies on the existence of data files that define the shift at various geographic points in a grid format. As is the case with the NAD27/NAD83 NADCON data files, these data files come in pairs and are in the public domain.

All of the data files used in this transformation adhere to a specific naming convention (as published by the National Geodetic Survey): they must have the proper .LAS and .LOS extensions, and the names and locations must be properly recorded in the Geodetic Data Catalog file. These files all overlap their neighbors by a substantial amount.

Since different results for the same point can be obtained depending upon which specific data files are used, users should pay significant attention to the order and choice of files. For example, if the geography one is working is primarily in Ohio, then the Ohio HPGN file should be listed first in the catalog file. This will cause that data file to take precedence over all others in the case of overlap.

Users can choose a fallback transformation to specify a fallback definition to be used when coordinate data not covered by the data files is processed.

This method is used to transform data from the older Tokyo Datum to the Japanese Geodetic Datum of 2000 (JGD2K). Associated data files define the transformation, and must be purchased from the Geographic Institute of Japan.

The data files, as supplied by the Geographic Institute of Japan, are in the form of text files, with no guarantee of records of fixed length, and which are not in any specific order. Since the most popular of these files covers all of Japan, the size of this particular file is quite large (approximately 12 MB). FME will, therefore, convert the text file into a binary form upon its first use.

The local DHDN to ETRS89 grid shift is used to transform coordinates in a more precise scale than the “DHDN to ETRS89” grid shift and does not necessarily cover all of Germany.

This transformation must be configured to point to the user-provided Grid Shift Binary (gsb) files required to execute the particular NTv2 transform required. To make the change, click Tools > FME Options > Coordinate Systems.

The USE method for this datum is DHDN_LOCAL. The corresponding transformation name is DHDN/local_FME_to_ETRS89/01.

Austrian authorities have published a grid shift data file for transforming MGI to ETRS89, applicable to Austrian geography. This covers all of Austria.

This transformation must be configured to point to the Grid Shift Binary file AT_GIS_GRID.gsb. To make the change, click Tools >FME Options > Coordinate Systems. You can also just place the AT_GIS_GRID.gsb file in the default location:

<FME Install Directory>/Reproject/GridData/Austria/AT_GIS_GRID.gsb.

This file, available freely at the website of the Austrian Federal Office for Metrology and Survey, http://www.bev.gv.at, is required to execute the particular NTv2 transform required.

The USE method for this datum is MGI. The corresponding transformation name is MGI/Grid_FME_to_ETRS89/01.

This transformation is the DMA (US Defense Mapping Agency [now known as NIMA]) implementation of the Molodensky transformation. (The formulas used were extracted from Defense Mapping Agency Technical Report 8350.2-B, 1 December 1987.) Effectively, it is a variation of the Geocentric Transformation that produces very similar results and can be calculated without iteration. Most importantly, the parameter use for this transformation is the same as the Three Parameter Transformation.

In addition to the Seven Parameter Transformation parameters, Molodensky-Badekas allows a rotation origin point to be specified. The additional parameters are:

Rotation Origin X: The X component of the point (in the source Cartesian coordinate reference system) about which the rotation will be performed.

Rotation Origin Y: The Y component of the point (in the source Cartesian coordinate reference system) about which the rotation will be performed.

Rotation Origin Z: The Z component of the point (in the source Cartesian coordinate reference system) about which the rotation will be performed.

This transformation is based on the series of Multiple Regression developments published by the US Defense Mapping Agency (NIMA) in Technical Report 8350.2-B, December 1987. Essentially, these are formulas developed from applying linear regression techniques to a varying number of points where the source and target ellipsoid coordinates are rather precisely known.

These regression formulas are based on normalized input coordinates. It is assumed that the normalized coordinates define the useful range of the datum transformation. In theory, therefore, a geographic coordinate that produces a normalized coordinate greater than 1.0 or less than -1.0 would normally be considered to be outside the useful range of the transformation. In this implementation of the regression technique, a geographic coordinate is considered to be outside the useful range of a transformation if the absolute value of either normalized coordinate exceeds 1.4.

In the event that a coordinate is given that is outside of the useful range of the multiple regression formula as described above, a fallback technique is used to calculate a datum shift. In this case, the fallback technique is the Molodensky, the Six Parameter Transformation, or the Seven Parameter Transformation depending upon how many parameters have been defined in the base definition. That is, when defining the datum definition, temporarily set the technique specification to Seven Parameter and set the desired fallback parameters. Then, the technique can be set back to the Multiple Regression selection and the parameters values will be preserved.

Currently, the parameters to such a transformation consist of a preprocessed transformation definition file. These files contain all of the coefficients of the multiple regression formula in a compact form. This form also facilitates the actual testing of each parameter file individually as the DMA-provided test case is included in the file. Currently, no provisions are made for users to implement their own multiple regression parameter files. This may change in the future.

This transformation represents the integration of the algorithms originally published by the National Geodetic Survey of the US and Geomatics Canada in the forms commonly known as the NADCON program and the National Transformation (Versions 1 and 2). That is, this transformation is the means by which one would convert from the North American Datum of 1927 (NAD27) to the North American Datum of 1983 (NAD83).

All of the techniques encapsulated in this transformation rely on access to data files that define the amount of the shift from NAD27 to NAD83 in a grid form. The coordinate conversion system uses algorithms identical to those used by the respective government-published programs to interrogate the data files and determine the shift for any given coordinate.

The shift data is stored in a single data file for the Canadian National Transformation (either version) and neither of these data files is in the public domain. The recommended NTv2 file is distributed with FME. In the case of the US NADCON data files, two files are required for each region covered. One file contains the latitude shift and the second contains the longitude shift. These files are in the public domain and are usually included in the distribution of this product. Should updates become available, you can use the data files in the exact form as they are published by the National Geodetic Survey.

Since the coverage of the data files is limited, the coordinate conversion system uses a fallback technique to calculate datum shifts for coordinates that are not covered by the data files.

For practical GIS applications, there is no difference between NAD83 and WGS84. Both are very precise measurements of the same thing, and what differences there are between the two are largely due to how the statistical noise was handled. Also, there are no published techniques or generally accepted means of converting from NAD83 to WGS84. The end result of all this is that this transformation does nothing.

France has developed a technique to define the shift from the New Triangulation of France Datum (NTF) to Reference Geodesique pour la France (RGF93).  This technique makes use of a single grid file called gr3df97a.txt which must be placed in the FME's Reproject directory to work. For all intents and purposes, RGF93 is considered equivalent to WGS84.

At the current time, the differences between NZGD2K and WGS84 are small. Further, a generally accepted means of converting between NZGD2K and WGS84 is unknown to the authors of the coordinate conversion system. This technique does nothing.

New Zealand has also adopted the Canadian technique to define the shift from the New Zealand Geodetic Datum of 1949 (NZGD49) to New Zealand Geocentric Datum of 2000 (NZGD2K). This implementation is somewhat simpler in that only a single data file is used.

The ROME1940 to IGM95 grid shift is used to transform coordinates between these two datums used in Italy.

This transformation must be configured to point to the user-provided Grid Shift Binary file R40WGS_t.gsb required to execute the particular NTv2 transform required. To make the change, click Tools > FME Options > Coordinate Systems. You can also just place the R40WGS_t.gsb file in the default location: <FME Install Directory>/Reproject/GridData/Italy/R40WGS_t.gsb.

The USE method for this datum is ROME40. The corresponding transformation name is MonteMario_Grid_FME_to_IGM1995.

This transformation is a rigorous implementation of the standard three-dimensional transformation. The seven provided parameters must indicate the transformation to convert source datum coordinates to target datum coordinates. For many typical GIS applications, you can simply change the sign of each of the seven parameters to affect an inverse. However, this technique is not exact. For precise results, a rigorous inversion is necessary in order to determine the appropriate parameters.

Essentially, this transformation proceeds in three phases. First, the geographic coordinates are converted to three-dimensional Cartesian, geocentric coordinates using the ellipsoid of the original datum. Second, the three-dimensional transformation defined by the seven parameters is applied producing a modified set of geocentric Cartesian coordinates. Third, the resulting geocentric coordinates are converted back to geographic form using the target ellipsoid.

The seven parameters are:

Delta X: the amount the intermediary geocentric X coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

Delta Y: the amount the intermediary geocentric Y coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

Delta Z: the amount the intermediary geocentric Z coordinate is translated. This value must be given in meters and the direction of the translation is given by the sign of the value.

X Rotation: the amount of rotation about the X axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

Y Rotation: the amount of rotation about the Y axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

Z Rotation: the amount of rotation about the Z axis which is applied to the intermediary geocentric coordinates. This value is given in seconds of arc, and the direction of the rotation is indicated by the sign of the value.

Scale: a scale factor that is applied to the intermediary geocentric coordinates. The value is given as a value in parts per million and is the difference of the actual scale factor and unity. For example, a value for the scale parameter of -2.5 produces an actual scale factor of 0.9999985. That is, the actual scale factor used is arrived at by multiplying the parameter value by 1.0x10-06 and adding the result (algebraically) to 1.0.

This transformation is the Seven Parameter Transformation without the Scale parameter. You could achieve the same results by using the Seven Parameter Transformation, setting the scale parameter to zero, and setting the remaining six parameters as appropriate.

This transformation implements the formulas published by the U. S. Defense Mapping Agency in Technical Report 8350.2-B, December 1987 for transforming WGS72-based geographic coordinates to WGS84-based coordinates. The transformation is hard-coded and does not require any parameters.