# Feature: Do You Really Have WGS 84 Coordinates?

Professional Surveyor Magazine -

October 2000William Strange

The turning off of Selective Availability (S/A) makes the use of correct NAD 83/WGS 84 transformations even more important. Point positioning, now headed toward the one to two meter level, gives true WGS 84 (G873) coordinates. Correct transformations will be essential when combining these coordinates with NAD 83 coordinates.

For surveyors in the United States the answer to the above question is usually: "No, I have NAD 83 coordinates," regardless of how the GPS software may have labeled them. The following is an explanation for this common surveyor's dilemma. A detailed discussion of datums (i.e. reference frames) will not be provided. The reader is referred to the set of articles by Snay and Soler that have recently appeared in Professional Surveyor (December, 1999 and February through April, 2000) for any additional information needed to understand this discussion.

**What Has Happened?**

Most surveyors use some type of differential GPS (DGPS) positioning to compute station coordinates. DGPS reduction software requires, as input, coordinates of both GPS satellites and one or more ground reference stations. The most commonly used satellite coordinates are those broadcast by the GPS satellites and referenced to a WGS 84 datum realization. But ground reference stations having high accuracy WGS 84 coordinates are not available to civil users of DGPS. Thus, in North America, ground reference station coordinates are most commonly entered into GPS reduction software as NAD 83 coordinates. The software then performs a datum transformation aimed at converting the NAD 83 coordinates to WGS 84 coordinates to achieve compatibility with the satellite coordinates. (A datum transformation involves seven transformation parameters, three translations, three rotations, and a scale change.) The GPS reduction software uses the transformed ground station coordinates with the satellite WGS 84 coordinates to compute the coordinates of a user's station, and labels the computed coordinates as WGS 84 coordinates.

The problem is that most GPS data reduction software assumes that the realized WGS 84 and NAD 83 coordinate systems in North America are identical therefore, the seven transformation parameters used to go between the two are all zero. This assumption is not correct. The transformation parameters between the two datums are not all zero. Moreover, the parameters have changed over time as WGS 84, and NAD 83, have been re-realized. Because the incorrect zero parameter assumption is used, station coordinates in North America are actually being computed with WGS 84 satellite coordinates and NAD 83 coordinates for the ground reference stations. Under these conditions, the computed user station coordinates are referenced to the datum of the ground reference station coordinates, i.e., NAD 83. Thus, most GPS reduction software provides coordinates for users' stations that are labeled WGS 84 coordinates, but are in fact, NAD 83 coordinates.

**Why the Incorrect Transformation Parameters?**

To understand how the incorrect zero transformation parameter assumption came about, one needs to understand the difference between a datum as defined and a datum as realized. A modern datum such as WGS 84 or NAD 83 consists of a coordinate system (a set of three-dimensional Cartesian axes and a scale) and a reference ellipsoid. To provide users access to a datum, geodetic organizations define a datum and then realize that datum. A datum is defined by specifying in words the location and orientation relative to the Earth of the datum axes, the scale to be used, and size and shape of the reference ellipsoid. Realizing a datum consists of computing and making available to users, coordinates of two types of reference points, time varying satellite locations (orbits), and monumented ground reference stations.

To realize a datum, equations are developed and used to compute reference point coordinates from observations. Geodetic organizations try to develop equations that will provide reference point coordinates relative to the datum as defined. But these equations are never perfect and there can be common systematic error in the computed coordinates of reference points relative to the datum as defined. This systematic error is best viewed as meaning that the datum, as realized by reference point coordinates, differs from the datum as defined. With current datums, the defined and realized datums differ only by the order of a centimeter and the distinction is not usually important. But at the time WGS 84 and NGS 83 were first realized, this difference was about two meters. The datum as realized is the relevant datum for users. It is the only datum to which they have access.

When WGS 84 and NAD 83 were first developed in the mid- 1980s, the two datums were defined to be identical. But they were realized using different equations and observational data and were not necessarily identical as realized. However, because of the size of the random errors in the computed reference point coordinates, one could only say at the time that, the two datums, as realized, did not disagree beyond the limits of the available coordinate accuracy, about +2 meters. Given this uncertainty, it was decided to assume that the two datums as realized were identical to these datums as defined and therefore, all transformation parameters between the two realized datums were zero. This zero parameter assumption was published in WGS 84 and NAD 83 documentation. Based on this documentation, the zero parameter assumption was placed in GPS data reduction software at the beginning of the GPS era. It remains in most reduction software today, despite the fact that it is clearly incorrect for more recent realizations of WGS 84 and NAD 83.

**What Are the Correct Transformation Parameters?**

Both WGS 84 and NAD 83 have been re-realized several times during the GPS era, causing transformation parameters to change. Table 1, (on page 38) compiled using several sources, gives estimates of transformation parameters between three realizations of WGS 84 (covering the GPS era) and NAD 83 (CORS 96), the most recent NAD 83 realization. The transformation parameters between the two current realizations, WGS 84 (G873) and NAD 83 (CORS 96), are known at the few centimeter level and are clearly not all zero. Indeed, the transformation parameters have never been zero during the GPS era, as shown by the table.

A few comments on Table 1 are in order. First, the transformation parameters given in the table for WGS 84 (G873) refer to a specific time epoch, 1997.0. To perform accurate transformations that take into account tectonic plate motion, the best approach is to treat WGS 84 (G873) as identical to ITRF 96 and use the ITRF 96 to NAD 83 (CORS 96) transformation given by Snay and Soler. Given the lack of true high accuracy, WGS 84 ground station coordinates, the likelihood of a surveyor actually needing to perform such a transformation is small. A second point is that, as discussed by Snay and Soler, the coordinate systems associated with the four most recent realizations of NAD 83 differ from one another only by small scale differences at the .005 ppm level. Thus, except for this small difference in the scale parameter, the transformation parameters given in Table 1 would hold for transforming from a given WGS 84 realization to the coordinate systems of any of the four most recent NAD 83 realizations. A word of caution: the coordinates of individual points can and have changed beyond what would be indicated by the small scale change when going from one NAD 83 realization to another. These changes result from improving the accuracy of point coordinates relative to the coordinate system being used, not to changes in the coordinate system.

**Why Does the Ground Reference Station Datum Dominate?**

DGPS positioning is performed in two ways—by using code observations (meter accuracy results) and by using carrier phase observations (centimeter accuracy results). With code positioning, the observations from one or more reference stations of known position are used to compute a set of "correctors." These "correctors" correct the user's observations before user station coordinates are computed. One of the things "corrected for" is any difference between the datum used for the ground reference station coordinates and that used for satellite coordinates. The correctors make the satellite coordinates compatible with the datum of the ground reference station coordinates. In almost all cases in North America this ground reference station datum is NAD 83.

With carrier phase positioning, the observations from a ground reference station and the user's station are combined and used to compute the coordinate difference between the reference station and the user's station. This difference is added to the coordinates of the reference station to obtain the coordinates of the users station. Here also, if the ground reference station coordinates are referred to NAD 83, the user station coordinates are also referred to NAD 83. However, when using WGS 84 satellite coordinates and NAD 83 ground reference station coordinates in the computations, an error is introduced into the computed NAD 83 coordinates of the user station. This error takes the form of a rotation of the differential coordinate vector. But, because WGS 84 and NAD 83 do not differ from one another by more than about two meters, the rotation is small and, because most carrier phase positioning by surveyors involves relatively short (<100km) station separations, the introduced error is at the subcentimeter level and can usually be ignored.

**Does Your Software Use the Zero Parameter Assumption? **

With respect to carrier phase DGPS positioning, there is a simple test a user can perform to see if GPS software is using the zero transformation assumption. Take a set of carrier phase observations from two stations, make a run in which the reference station coordinates are entered into the reduction software as NAD 83 coordinates, and ask for WGS 84 output coordinates. Perform another run inputting the same reference station coordinates, but this time labeling them WGS 84 coordinates. Again, ask for WGS 84 coordinates to be output. If the two sets of output coordinates are identical, your software is using the zero transformation assumption. If not, the provider of the software needs to specify what transformation parameters were used.

With code positioning where the user software computes correctors, a similar test to that described above can be performed by first declaring the base station coordinates to be NAD 83 coordinates and then declaring them to be WGS 84 coordinates. If real time broadcast correctors are used, the test cannot be performed, and the provider of the correctors must specify the datum to which the correctors refer. We note that the stations operated by the U. S. Coast Guard provide correctors that relate coordinates to NAD 83 as currently realized.

**What Are the Consequences of Mislabeled Coordinates?**

But, with the turning off of Selective Availability (SA) the situation is different. With SA off, point positioning gives true WGS 84 (G873) coordinates accurate to a few meters. Now the transformation given in Table 1 needs to be used to transform these WGS 84 (G873) coordinates if they are to be used in conjunction with NAD 83 coordinates, both those correctly labeled as NAD 83 coordinates and those mislabled as WGS 84 coordinates. GPS users must, therefore, become aware of the current incorrect WGS 84 coordinate labeling and the correct WGS 84 (G873) to NAD 83 transformation to avoid future problems.

**William Strange** *retired in 1998 from the position of Chief Geodesist of the National Geodetic Survey.*

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