This past spring, I became a professor again when I was asked to teach "Satellite Geodesy" for the Department of Surveying Engineering at New Mexico State University.

To prepare myself for the two hours of lecture and the three-hour lab I conducted every week, I had to learn about the department's two different state-of-the-art GPS receiver systems. Both were new to me, so I started by studying the documentation on both receivers and software. Everything went smoothly until I came to the section titled "Coordinate Systems," where the user was asked to select a horizontal datum. Both manuals instructed users to "Choose WGS 84." Around the world, the civilian community does not survey on the WGS 84 datum. Stating that WGS 84 and NAD 83 are the same is incorrect. This article is devoted to comparing WGS 84 and NAD 83, and ultimately explaining why we don't survey on the WGS 84 datum.

Horizontal Datums

There are three basic requirements to define a horizontal datum:
1. Select an ellipsoid,
2. Select an origin, and
3. Determine an orientation.
The easiest way to understand the concept of a horizontal datum is through the example of the North American Datum of 1927 (NAD 27), which was used well into the 1980s. The ellipsoid selected for NAD 27 was the Clarke 1866. The origin was the geodetic coordinates of the triangulation station at Meade's Ranch in Kansas, which had been established by an earlier adjustment. The orientation was the geodetic azimuth from Station Meade's Ranch to Station Waldo, a water tower in the town of Waldo, Kan.

NAD 27 served the nation well; horizontal angles and horizontal distances were projected onto the ellipsoid, and each control point had a calculated latitude and longitude. NAD 27 fit the geoid well in North America and parts of Central America. Geoid heights, though not calculated, were small enough that when observations were reduced from the earth's surface to the ellipsoid, the height used was the height above sea level.

The launching of near-earth satellites, starting with Sputnik I, eventually made NAD 27 unusable. All near-earth satellites orbit around the center of mass of the earth, so an ellipsoid for satellite positioning also had to have its origin at the center of mass. The ellipsoid had to be such that it best fit the entire earth, not just a small portion like the North American continent. The center of the Clarke 1866 ellipsoid was approximately 300 meters away from the center of mass, and the semimajor axis, a, was too large.

As a result, earth-centered datums for satellite positioning needed to be developed, and two U.S. government agencies, the Department of Defense (DoD) and NOAA's National Geodetic Survey (NGS), each developed earth-centered datums.

World Geodetic Systems

The DoD was was the leader in the field of developing earth-centered datums for satellite positioning. From 1960 to 1984, the DoD developed four different datums, all named "World Geodetic System" (WGS). These were WGS 60, WGS 66, WGS 72 and WGS 84. To quote the DoD, "The World Geodetic System provides the basic reference frame and geometric figure for the earth, models the earth gravimetrically, and provides the means for relating positions on various local geodetic systems to an earth-centered, earth-fixed (ECEF) coordinate system." The Navstar Global Positioning System (GPS) is in the WGS 84 reference system. The ellipsoid for WGS 84 is also named WGS 84.

North American Datum of 1983

The NGS developed the North American Datum of 1983 (NAD 83) to provide the civilian community with an earth-centered, earth-fixed system. The fundamental task of NAD 83 was a simultaneous least squares adjustment involving 1,785,722 observations and 266,436 stations in the United States, Canada, Mexico and Central America. Greenland, Hawaii and the Caribbean Islands were connected to the datum through Doppler satellite and Very Long Baseline Interferometry (VLBI) observations.

The computations were performed with respect to the ellipsoid of the Geodetic Reference System of 1980 (GRS 80), recommended by the International Association of Geodesy (IAG). The ellipsoid is positioned in such a way as to be earth-centered (geocentric), and the orientation is that of the Bureau International de l'Heuer (BIH) terrestrial system of 1984 (BTS-84).

Table 1. Defining (Fundamental) Parameters

Relationship of NAD 83 to WGS 84

Both NAD 83 and WGS 84 were to be geocentric and oriented as the BIH terrestrial system. In principle, the three-dimensional coordinates of a single point should be the same in both systems; in practice, small differences are sometimes found.

Why is the WGS 84 ellipsoid different? The original intent was that both NAD 83 and WGS 84 use GRS 80 as a reference ellipsoid. However, the DoD made some changes. The defining parameters of the two datums are given above in Table 1.

GRS 80 was defined by the constants a, w, GM and J2. DoD used the normalized form of the coefficient of the second zonal harmonic, J2, as a fundamental constant, while GRS 80 used the unnormalized form. Also, the normalized value used by DoD was obtained by using the mathematical relationship

C2,0 = -J2/ (5)1/2

and rounding the results to eight significant figures. Quantities depending directly on the form factor, such as flattening, generally differ after the eighth significant digit, while linear quantities, such as the semimajor axis, generally differ after the tenth significant digit. Because of this, the following parameters are used by people in our business:

In relative positioning with GPS, the computer software packages give the "difference in coordinates" between two receivers, and these differences are in the WGS 84 coordinate system. For practical purposes, these coordinate differences will be identical to the NAD 83 coordinate differences. What we do, as surveyors, is add the coordinate differences to the coordinates of the published coordinates of the point occupied by one receiver, and the published coordinates are on the NAD 83 datum. You would be hard pressed to find a control point with published WGS 84 coordinates other than on a military base.

The Datums and Coordinate Systems in 2006

NAD 83, as defined in 1985-86, has not changed. The ellipsoid used is still GRS 80 and the origin has not changed. Modern geodetic practices and modern instrumentation show that this origin is approximately 2.1 meters away from the center of mass of the earth. The purpose of the datum is for civilian surveying and mapping and, as such, must be stable and not change.

In order to keep up with modern technology, the NGS has adopted the International Terrestrial Reference System (ITRS) for all Continuously Operating Reference Stations (CORS). According to the ITRS website, "The International Terrestrial Reference System (ITRS) is a world spatial reference system co-rotating with the Earth in its diurnal motion in space. The IERS [International Earth Rotation Service], in charge of providing global references to the astronomical, geodetic and geophysical communities, promotes the realization of the ITRS. Realizations of the ITRS are produced by the IERS ITRS Product Center under the name International Terrestrial Reference Frames (ITRF)." Each ITRF has a year associated with it; ITRF for the year 2000 is ITRF00. The important thing is the ITRF's use of the GRS 80 ellipsoid. To date, there have been four ITRF solutions: ITRF94, ITRF96, ITRF97 and ITRF00. With each solution, the center of the ellipsoid has been repositioned to the latest location of the earth's center of mass.

Every CORS station controlled by NGS gives ITRF coordinates in the 2000 reference frame, epoch 1997.0, denoted as "ITRF00 (Epoch 1997.0)." NAD 83 coordinates are also given, calculated using a 14-parameter transformation. This is shown as "NAD 83 (Epoch 1997.0)." As stated earlier, both ITRF and NAD 83 use the GRS 80 ellipsoid.

What About WGS 84?

The first version of WGS 84 was released in 1987; it was concurrent with the development of NAD 83. As mentioned above, rounding off problems with the defining parameters changed the flattening such that the ellipsoid could not be named GRS 80.

Since 1987, WGS 84 has been updated three times:
1. 1994 update WGS 84(G730): this version was updated to ITRF92.
2. 1996 update WGS 84(G873): this version was supposed to be updated to ITRF94, but instead was updated to ITRF97.
3. 2001 update WGS 84(G1150): this version was updated to ITRF00.
I contacted a colleague of mine to learn what datum is used by other countries throughout the world. The answer to my question was ITRF, using the GRS 80 ellipsoid. Like NGS, some countries use a transformation from ITRF to their own datum, and the ellipsoid for that datum is GRS 80. Basically, only the DoD uses WGS. In the civilian community, the only people who use WGS are the owners of code receivers, including the hobby receivers and those used for vehicle navigation, which caculate point position using pseudoranges.

If surveyors are not using WGS 84, then is the manufacturer's documentation and software providing wrong answers? No. The answers are correct because the software is using only the ellipsoid of WGS 84, which is close enough to GRS 80 that the computed solutions are correct. As I stated earlier, relative positioning takes the coordinate differences between two receivers and adds these differences to the known coordinates of one of the stations. The known station is on the NAD 83 datum and the coordinate differences are WGS 84 differences. The known station could be from a State HARN, the national CORS network, or calculated from either a HARN or CORS. Remember, HARNs and CORS are from different adjustments and should not be used together in your surveys. This, however, will not be a problem after 2007 when NGS will put all control points together in one national system; all control points will be designated NAD 83 (NSRS), denoting the National Spatial Reference System.

Acknowledgement: Much of the material for this article came from NOAA Professional Paper NOS 2, North American Datum of 1983, edited by Charles R. Schwarz, National Geodetic Survey, December 1989.