Geographic transformation methods Moving your data between coordinate systems sometimes includes transforming between the geographic coordinate systems. Because the geographic coordinate systems contain datums that are based on spheroids, a geographic transformation also changes the underlying spheroid. There are several methods, which have different levels of accuracy and ranges, for transforming between datums. The accuracy of a particular transformation can range from centimeters to meters depending on the method and the quality and number of control points available to define the transformation parameters. A geographic transformation is always defined in a particular direction. When working with geographic transformations, if no mention is made of the direction, the command will handle the directionality automatically. For example, if converting data from WGS 1984 to NAD 1927, you can pick a transformation called NAD1927toWGS19843 and the software will apply it correctly.
Feb 12, 2014 It might be possible that the transformation *model* could be that accurate, but only if you have extremely accurate (and precise) control points that can be used to generate the transformation parameters. Even the best 7 parameter transformations I've seen are probably no better than the cm level and most are probably at the decimeter level.
A geographic transformation always converts geographic (longitude-latitude) coordinates. Some methods convert the geographic coordinates to geocentric (X,Y,Z) coordinates, transform the X,Y,Z coordinates, and convert the new values back to geographic coordinates. These include the Geocentric Translation, Molodensky, Coordinate Frame, and Molodensky-Badekas methods.
Other methods, such as NADCON and NTv2 use a grid of differences and convert the longitude-latitude values directly. Equation-based methods Equation-based transformation methods can be classified into the following four method types. Usually the transformation parameters are defined as going from a local datum to WGS 1984 or another geocentric datum. Three-parameter methods The simplest datum transformation method is a geocentric, or three-parameter, transformation. The geocentric transformation models the differences between two datums in the X,Y,Z coordinate system.
One datum is defined with its center at 0,0,0. The center of the other datum is defined at some distance (DX,DY,DZ) in meters away. The three parameters are linear shifts and are always in meters. Seven-parameter methods A more complex and accurate datum transformation is possible by adding four more parameters to a geocentric transformation. The seven parameters are three linear shifts (DX,DY,DZ), three angular rotations around each axis (rx,ry,rz), and a scale factor. The rotation values are given in decimal seconds, while the scale factor is in parts per million (ppm).
The rotation values are defined in two different ways. It's possible to define the rotation angles as positive either clockwise or counterclockwise as you look toward the origin of the X,Y,Z systems. The United States, Australia, New Zealand, and a few other countries define the equations such that the rotation values are positive counterclockwise. This method is called the Coordinate Frame Rotation transformation. Europe uses a different convention called the Position Vector transformation. Both methods are sometimes referred to as the Bursa-Wolf method.
In the Projection Engine, the Coordinate Frame and Bursa-Wolf methods are the same. Both Coordinate Frame and Position Vector methods are supported, and it is easy to convert transformation values from one method to the other simply by changing the signs of the three rotation values.
For example, the parameters to convert from the WGS 1972 datum to the WGS 1984 datum with the Coordinate Frame method are (in the order DX,DY,DZ,rx,ry,rz,s): (0.0, 0.0, 4.5, 0.0, 0.0, -0.554, 0.227) To use the same parameters with the Position Vector method, change the sign of the rotation so the new parameters are: (0.0, 0.0, 4.5, 0.0, 0.0, +0.554, 0.227) It's impossible to tell from the parameters alone which convention is being used. If you use the wrong method, your results can return inaccurate coordinates. The only way to determine how the parameters are defined is by checking a control point whose coordinates are known in the two systems.
The Molodensky-Badekas method is a variation of the seven-parameter methods. It has an additional three parameters that define the XYZ origin of rotation. Sometimes this point is known as the origin of the datum, or geographic coordinate system. Given the XYZ origin of rotation point, it is possible to calculate an equivalent Coordinate Frame transformation. The DX, DY, and DZ values will change but the rotation and scale values will remain the same. Molodensky method The Molodensky method converts directly between two geographic coordinate systems without actually converting to an X,Y,Z system.
The Molodensky method requires three shifts (DX,DY,DZ) and the differences between the semimajor axes (Da) and the flattenings (Df) of the two spheroids. The Projection Engine automatically calculates the spheroid differences according to the datums involved. Abridged Molodensky method The Abridged Molodensky method is a simplified version of the Molodensky method. Grid-based methods Grid-based transformation methods include the following: NADCON and HARN methods The United States uses a grid-based method to convert between geographic coordinate systems. Grid-based methods allow you to model the differences between the systems and are potentially the most accurate method. The area of interest is divided into cells.
The National Geodetic Survey (NGS) publishes grids to convert between NAD 1927 and other older geographic coordinate systems and NAD 1983. These transformations are grouped into the NADCON method. The main NADCON grid, CONUS, converts the contiguous 48 states. The other NADCON grids convert older geographic coordinate systems to NAD 1983 for:. Alaska. Hawaiian islands. Puerto Rico and Virgin Islands.
St. Lawrence, and St. Paul Islands in Alaska The accuracy is approximately 0.15 meters for the contiguous states, 0.50 for Alaska and its islands, 0.20 for Hawaii, and 0.05 for Puerto Rico and the Virgin Islands. Accuracies can vary depending on how good the geodetic data in the area was when the grids were computed (NADCON, 1999). The Hawaiian islands were never on NAD 1927.
They were mapped using several datums that are collectively known as the Old Hawaiian datums. New surveying and satellite measuring techniques have allowed NGS and the states to update the geodetic control point networks. As each state is finished, the NGS publishes a grid that converts between NAD 1983 and the more accurate control point coordinates. Originally, this effort was called the High Precision Geodetic Network (HPGN). It is now called the High Accuracy Reference Network (HARN).
Four territories and 46 states have published HARN grids as of January 2004. HARN transformations have an accuracy approximately 0.05 meters (NADCON, 2000).
The difference values in decimal seconds are stored in two files: one for longitude and the other for latitude. A bilinear interpolation is used to calculate the exact difference between the two geographic coordinate systems at a point. The grids are binary files, but a program, NADGRD, from the NGS, allows you to convert the grids to American Standard Code for Information Interchange (ASCII) format. Shown at the bottom of the page is the header and first row of the CSHPGN.LOA file.
This is the longitude grid for Southern California. The format of the first row of numbers is, in order, the number of columns, number of rows, number of z-values (always one), minimum longitude, cell size, minimum latitude, cell size, and not used. The next 37 values in this case are the longitude shifts from -122° to -113° at 32° N in 0.25°, or 15 minute, intervals in longitude. NADCON EXTRACTED REGION NADGRD 37 21 1 -122.00000.0.25.00000.007383.004806.002222.000347.002868.005296.007570.009609.011305.012517.013093.012901.011867.009986.007359.004301.001389.001164.003282.004814.005503.005361.004420.002580.000053.002869.006091.009842.014240.019217.025104.035027.050254.072636.087238.099279.110968.
PROJ.4 - General Parameters PROJ.4 - General Parameters This document attempts to describe a variety of the PROJ.4 parameters which can be applied to all, or many coordinate system definitions. This document does not attempt to describe the parameters particular to particular projection types. Some of these can be found in the GeoTIFF. The definitative documentation for most parameters is Gerald's original documentation available from the main PROJ.4 page. Virtually all coordinate systems allow for the presence of a false easting (+x0) and northing (+y0). Note that these values are always expressed in meters even if the coordinate system is some other units.
Some coordinate systems (such as UTM) have implicit false easting and northing values. A prime meridian may be declared indicating the offset between the prime meridian of the declared coordinate system and that of greenwich. A prime meridian is clared using the 'pm' parameter, and may be assigned a symbolic name, or the longitude of the alternative prime meridian relative to greenwich. Currently prime meridian declarations are only utilized by the pjtransform API call, not the pjinv and pjfwd calls.
Consequently the user utility cs2cs does honour prime meridians but the proj user utility ignores them. The following predeclared prime meridian names are supported.
These can be listed using the cs2cs argument -lm. Greenwich 0dE lisbon 9d07'54.862'W paris 2d20'14.025'E bogota 74d04'51.3'E madrid 3d41'16.48'W rome 12d27'8.4'E bern 7d26'22.5'E jakarta 106d48'27.79'E ferro 17d40'W brussels 4d22'4.71'E stockholm 18d3'29.8'E athens 23d42'58.815'E oslo 10d43'22.5'E Example of use.
The location long=0, lat=0 in the greenwich based lat/long coordinates is translated to lat/long coordinates with Madrid as the prime meridian. Cs2cs +proj=latlong +datum=WGS84 +to +proj=latlong +datum=WGS84 +pm=madrid 0 0 (input) 3d41'16.48'E 0dN 0.000 (output) Datum shifts can be approximated by 3 parameter spatial translations (in geocentric space), or 7 parameter shifts (translation + rotation + scaling).
The parameters to describe this can be described using the towgs84 parameter. In the three parameter case, the three arguments are the translations to the geocentric location in meters.