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. The area of interest is divided into cells. The National Geodetic Survey (NGS) publishes grids to convert between North American Datum (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 these areas:
- Alaska
- Hawaiian Islands
- Puerto Rico and Virgin Islands
- St. George, 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, 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 of 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 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 .25 32.00000 .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
National Transformation version 2
Like the United States, Canada uses a grid-based method to convert between NAD 1927 and NAD 1983. The National Transformation version 2 (NTv2) method is quite similar to NADCON. A set of binary files contains the differences between the two geographic coordinate systems. A bilinear interpolation is used to calculate the exact values for a point.
Unlike NADCON, which can only use one grid at a time, NTv2 is designed to check multiple grids for the most accurate shift information. A set of low-density base grids exists for Canada. Certain areas, such as cities, have high-density local subgrids that overlay portions of the base, or parent, grids. If a point is within one of the high-density grids, NTv2 will use the high-density grid; otherwise, the point "falls through" to the low-density grid.
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If a point falls in the lower-left part of the above picture between the stars, the shifts are calculated with the high-density subgrid. A point whose coordinates are anywhere else will have its shifts calculated with the low-density base grid. The software automatically calculates which base or subgrid to use.
The parent grids for Canada have spacings ranging from 5 to 20 minutes. The high-density grids usually have a cell size of 30 seconds, or 0.08333333°.
Unlike NADCON grids, NTv2 grids list the accuracy of each point. Accuracy values can range from a few centimeters to around a meter. The high-density grids usually have subcentimeter accuracy.
Australia and New Zealand adopted the NTv2 format to convert between geographic coordinate systems as well. Australia has released several state-based grids that convert between either Australian Geodetic Datum of 1966 (AGD 1966) or AGD 1984 and Geocentric Datum of Australia of 1994 (GDA 1994). The state grids have been merged into countrywide grids. New Zealand has released a countrywide grid to convert between New Zealand Geodetic Datum of 1949 (NZGD 1949) and NZGD 2000.
National Transformation version 1
Like NADCON, the National Transformation version 1 (NTv1) uses a single grid to model the differences between NAD 1927 and NAD 1983 in Canada. This version is also known as CNT in ArcInfo Workstation. The accuracy is within 0.01 meters of the actual difference for 74 percent of the points and within 0.5 meters for 93 percent of the cases.