A geographic coordinate system defines a framework for identifying locations on a 3D globe. Each geographic coordinate system (GCS) has a spheroid which sets size and shape. Each geographic coordinate system is also tied to the earth in a particular way. Because of this, the same location on the ground will have different coordinate values in different geographic coordinate systems. Displaying data in a projected coordinate system can exaggerate the differences which can be from a few centimeters to hundreds of meters. If you are using datasets that are based on different geographic coordinate systems, you will need to set a geographic, or datum, transformation.
A geographic transformation is always defined in a particular direction, like from NAD 1927 to WGS 1984. Transformation names will reflect this: NAD_1927_To_WGS_1984_1. The name may also include a trailing number, as the above example has _1. This number represents the order in which the transformations were defined. A larger number does not necessarily mean a more accurate transformation. Even though a geographic transformation has a built-in directionality, all transformation methods are inversible. That is, a transformation can be used in either direction. ArcGIS will apply a transformation appropriately based on the input and output geographic coordinate systems.
If a pair of geographic coordinate systems does not have any transformations, it is sometimes possible to build a chain of transformations by using a third geographic coordinate system. Most often, WGS 1984 is the common link. The Create Custom Geographic Transformation tool can also be used to define a new transformation if you have the necessary information: method and parameter values.
Why are there so many transformations?
Between any two geographic coordinate systems, there may be zero, one, or many transformations. Some geographic coordinate systems do not have any publicly known transformations because that information is considered to have strategic importance to a government or company. For many GCS, multiple transformations exist. They may differ by areas of use or by accuracies. Accuracies usually reflect the transformation method. File-based methods such as NTv2 and NADCON tend to be better than equation-based methods such as geocentric translation and coordinate frame. For more information on methods, see Geographic transformation methods.
Regardless of what method is used, each transformation is designed for a particular area, and arguments can be made for the application of each transformation. One important consideration is consistency, using the same transformation each time, to transform between two geographic coordinate systems. Because there are so many transformations, ArcGIS tools do not generally set a particular transformation for a pair of geographic coordinate systems. For lists of the available transformations, methods, and areas of use, see this geographic_transformations.pdf file.
Converting between NAD 1983 and WGS 1984
Originally, NAD 1983 and WGS 1984 were considered coincident. To minimize coordinate changes, NAD 1983 is tied to the North American and Pacific (for Hawaii, and so on) plates. WGS 1984 is tied to the International Terrestrial Reference System (ITRF), which is independent of the tectonic plates. Over time, the two coordinate systems have become increasingly different.
- NAD_1983_To_WGS_1984_1: Published accuracy from EPSG is 2 meters. This transformation applies to the entire North American continent. This transformation uses the geocentric translation method, with the transformation's parameters (dx, dy, and dz) all equal to zeroes. This transformation treats the NAD 1983 and WGS 1984 datums as though they are equivalent.
- NAD_1983_To_WGS_1984_2: Calculated by the U. S. Defence Mapping Agency (DMA), now known as the National Geospatial Intelligence Agency (NGA), for the Aleutian islands. Accuracy is listed by EPSG at +/-8 m.
- NAD_1983_To_WGS_1984_3: Calculated by the NGA for Hawaii. Accuracy is listed by EPSG at +/-4 m.
- NAD_1983_To_WGS_1984_4: Formerly applied within the 48 contiguous states, but is superseded by _5. This transformation method should no longer be used.
- NAD_1983_To_WGS_1984_5: Transformation parameters calculated by the U.S. National Geodetic Survey (NGS) using CORS stations, and ties WGS 1984 to ITRF96. Accuracy according to EPSG is +/- 1 meter.
- NAD_1983_To_WGS_1984_6, _7, and _8: Canadian NTv2 transformations, for the Quebec, Saskatchewan, and Alberta provinces, respectively.