The files contained in the directory, coord_96, provide 3-dimensional positions and velocities for both the antenna reference point (ARP) and the L1 phase center associated with each CORS. In addition, these files provide positions and velocities for selected geodetic monuments located near some of the CORS. Note that the ARP corresponds to the bottom of the pre-amp for most CORS antennas.
These positions and velocities are expressed in each of two different reference frames to meet the needs of the varied groups that use CORS data. One of these reference frames was instituted by the International Earth Rotation Service (IERS); it is called the IERS Terrestrial Reference Frame (ITRF). The other reference frame is the North American Datum of 1983 (NAD 83). For each of these two reference frames, the files present positions in both geocentric cartesian coordinates (X,Y,Z) and in geodetic coordinates (latitude, longitude, ellipsoid height) for the GRS80 ellipsoid. Also for each reference frame, the files present velocities in geocentric cartesian coordinates (Vx,Vy,Vz) and in local horizon coordinates (northward velocity, eastward velocity, upward velocity) where the vertical dimension is locally oriented normal to the GRS80 ellipsoid. NAD 83 positions given in these files are identical to those contained in the National Geodetic Survey's (NGS) Integrated Data Base.
The IERS publishes revised ITRF positions and velocities every year or so for a worldwide network of geodetic stations. Each IERS solution for these positions and velocities uses observations obtained from various geodetic techniques including GPS, very long baseline interferometry (VLBI), and satellite laser ranging (SLR). Each new solution not only incorporates an additional year of data, but also the then most current understanding of Earth's dynamics.
For the CORS network, NGS currently uses ITRF positions and velocities that are consistent with the IERS's solution known as ITRF96 with an epoch date of 1997.0 (that is, 1 January 1997). The epoch date denotes the date for which estimated positions correspond. An appropriate velocity must be applied to estimate positions for another date. A site's velocity characterizes various forms of crustal motion including the motion associated with plate tectonics, subsurface fluid withdrawal, and crustal loading/unloading. Relative to the ITRF, even points located on the rigid part of the North American tectonic plate move continuously at rates ranging from 9 to 21 mm/yr in the coterminous 48 states. For several of the older CORS, NGS has also computed ITRF positions and velocities that are consistent with the IERS solution known as ITRF94 (epoch 1996.0) and/or ITRF positions and velocities consistent with the IERS solution known as ITRF93 (epoch 1995.0).
Many users of CORS data prefer to position themselves relative to the NAD 83 reference frame that is used widely throughout North America for surveying and mapping activities. Also, the U.S. Coast Guard and the Federal Aviation Administration use NAD 83 positions to provide marine and air navigation information. The NAD 83 reference frame is defined so that the North American tectonic plate does not move as a whole relative to it. Thus, users can generally treat NAD 83 positions as unchanging over time except where regional or local crustal motion occurs, e.g., California and southern Alaska, or at locations on a different tectonic plate, e.g., Hawaii.
The International GPS Service for Geodynamics officially began using ITRF96 coordinates for generating precise GPS orbits on 1 March 1998. NGS adopted the ITRF96 positions and velocities for nine CORS that had participated in the IERS solution. The following paragraphs summarize how NGS determined ITRF96-consistent positions and velocities for the remaining CORS.
For each day since 1 March 1998, NGS has computed provisional ITRF96-consistent positions for that day by using the GPS data of just that day for all operational CORS plus for several permanent GPS sites associated with the IERS solution. In addition, for the time period before 1 March 1998, NGS computed provisional ITRF96-consistent positions for every 16-th day. The computations for a given day involved a network adjustment by applying the PAGE4/GPSCOM software (Mader et al., 1995) to 24-hour data sets having a 30-second sampling rate. Thus, for each CORS and for several additional permanent GPS sites, these computations generated a time series of ITRF96-consistent positions where each position corresponds to a different epoch date.
Using these time series, NGS estimated 3-dimensional ITRF96-consistent velocities for those CORS that had been online for at least 16 months as of March 1998. In particular, each estimated velocity component equals the slope of the line that best fits the time series for the corresponding positional component in a least squares sense. For each CORS that had been online for less than 16 months, NGS adopted a 3-dimensional velocity that had been predicted with the HTDP software (Snay, 1998). NGS then used the estimated or the predicted ITRF96- consistent velocity for a site, together with the site's time series of ITRF96-consistent positions, to estimate an ITRF96-consistent position for the site at epoch 1997.0 (that is, the position corresponding to 1 January 1997 on the best fitting line whose slope is consistent with the adopted velocity). Note that NGS will adopt an ITRF96-consistent position (epoch 1997.0) for a CORS only after the site's data have been involved in at least 10 daily solutions. Also, note that NGS subsequently set the vertical component of each estimated ITRF96 velocity to zero except at the sites that participated in the IERS solution. This action reflects the fact that CORS data spans too short a time period to provide statistically meaningful vertical velocities.
Most CORS already had official NAD 83 positions and velocities before NGS computed ITRF96-consistent positions and velocities for these sites. The pre-existing NAD 83 positions had been obtained by transforming previously derived ITRF94-consistent positions (Appendix A). A site's pre-existing NAD 83 velocity had been predicted with the HTDP software when the site first came online. ITRF94-consistent velocities that corresponded to these predicted NAD 83 velocities were then obtained by an appropriate transformation (Appendix B). In most cases, the new ITRF96-consistent position and velocity of a site will not transform exactly into the site's pre-existing NAD 83 position and velocity. This discrepancy occurs, not only because new ITRF96 positions and velocities have been derived from significantly more days of data than the ITRF94 positions and velocites, but also because NGS (in cooperation with the Geodetic Survey of Canada) has adopted a transformation from ITRF96 to NAD 83 which differs slightly from the transformation that had been used to convert from ITRF94 to NAD 83 (Appendices A and B). In an effort to best serve the majority of users, NGS intends to avoid changing NAD 83 positions and velocities to the extent practicable. Thus, when NGS adopts a new ITRF96-consistent position (epoch 1997.0) and velocity for a CORS, the agency applies the new transformation to determine a provisional NAD 83 position (epoch 1997.0) and velocity. This provisional velocity is adopted in place of the pre-existing NAD 83 velocity if and only if the horizontal components or the vertical components of these two velocities differ by more than 5 mm/yr in magnitude. The provisional position is adopted in place of the pre-existing position if and only if their corresponding positions at epoch 1997.0 differ from one another by more than 2 cm horizontally or 4 cm vertically. In the case that no pre-existing NAD 83 coordinates exist for a site, then NGS simply adopts the site's transformed ITRF96 position and velocity.
The transition from ITRF94 to ITRF96 resulted in updating NAD 83 positions for approximately 10 percent of the sites in the current CORS network. In May 1996, the transition from ITRF93 to ITRF94 had resulted in updating NAD 83 positions for all sites in the CORS network (Appendix C). The directories, coord_96, coord_94, and coord_93--besides containing positions and velocities for ITRF96, ITRF94, and ITRF93, respectively--also contain the respective NAD 83 positions and velocities corresponding to these three ITRF realizations. Hence, current NAD 83 positions and velocities are contained in coord_96. Previously adopted NAD 83 positions and velocities may be found in coord_94 and/or coord_93.
The National Spatial Reference System contains several hundred thousand stations whose NAD 83 positions were determined before the CORS network was established. The accuracy of a differential NAD 83 position between one of these previously existing stations and a CORS depends mostly on the geodetic observations that were used to position the previously existing station. For stations in the High Accuracy Reference Network (HARN), the accuracy of a differential horizontal position between an A- or B-order station and a CORS will almost always be better than 7 cm and usually better than 5 cm (Milbert, 1998). In states where the first-order stations have been adjusted to agree with the HARN, the accuracy of a differential horizontal position between a first-order station and a CORS will almost always be better than 30 cm and usually better than 20 cm. In states where the first-order stations have yet to be adjusted to the HARN, the accuracy of a differential horizontal position between a first-order station and a CORS may be only 1 meter, although such accuracies usually will be better than 0.5 meters. These accuracies reflect discrepancies in the positions of the previously existing stations relative to the NAD 83 reference frame. It should be emphasized that positional differences among previously existing stations in a local area will be much more accurate than their common discrepancy relative to the NAD 83 reference frame. In particular, the accuracy of a positional difference between two existing A-order stations is generally better than one part in 10,000,000 of their interstation distance; between two existing B-order stations, one part in 1,000,000; and between two existing first-order stations, one part in 100,000.
With respect to the vertical coordinate, a HARN station could have an NAD 83 ellipsoid height which is in error by as much as 25 cm, although an error of 10 cm or less is more common. More recent HARN stations have more accurate ellipsoid heights than earlier HARN stations.
Let the geocentric cartesian coordinates (Xi, Yi, Zi) in meters denote the ITRF96 position for a geodetic site at epoch date E in years. The corresponding NAD 83 position (Xn, Yn, Zn) at this same epoch date may be computed by the equations:
Xn = Tx + (1 + S)*Xi + Rz*Yi - Ry*Zi
Yn = Ty - Rz*Xi + (1 + S)*Yi + Rx*Zi
Zn = Tz + Ry*Xi - Rx*Yi + (1 + S)*Zi
where
Tx = 0.9910 m Rx = (125033 + 258*(E - 1997.0))*(10**-12) radian
Ty = -1.9072 m Ry = ( 46785 - 3599*(E - 1997.0))*(10**-12) radian
Tz = -0.5129 m Rz = ( 56529 - 153*(E - 1997.0))*(10**-12) radian
S = 0.0 (unitless).
Note that the three rotations--Rx, Ry, and Rz--are time-dependent because the North American plate is moving with respect to ITRF96.
NGS recommends that the above equations also be used for transforming ITRF94 positions to NAD 83 positions because the IERS defined ITRF96 in such a way that its origin, scale, and orientation, and their time evolution would be identical to those of ITRF94 (Sillard et al., 1998). Nevertheless, before the above values were adopted in mid-1998, NGS had been using a transformation from ITRF94 to NAD 83 based on the following values:
Tx = 0.9738 m Rx = (13357 + 42*(E-1996.0))*(10**-11) radian
Ty = -1.9453 m Ry = (4872 - 372*(E-1996.0))*(10**-11) radian
Tz = -0.5486 m Rz = (5507 + 10*(E-1996.0))*(10**-11) radian
S = 0.0 (unitless).
Let the coordinates (Vxi, Vyi, Vzi) in m/yr denote the ITRF96 velocity for a geodetic site whose ITRF96 position is (Xi, Yi, Zi) in meters as expressed in geocentric cartesian coordinates. The corresponding NAD 83 velocity (Vxn, Vyn, Vzn) may be computed by the equations:
Vxn = Vxi + Wz*Yi - Wy*Zi
Vyn = Vyi - Wz*Xi + Wx*Zi
Vzn = Vzi + Wy*Xi - Wx*Yi
where
Wx = 258*(10**-12) radian/year
Wy = -3599*(10**-12) radian/year
Wz = -153*(10**-12) radian/year.
NGS recommends that the above equations also be used for transforming ITRF94 velocities to NAD 83 velocities. Nevertheless, before the above values were adopted in mid-1998, NGS had previously used a velocity transformation from ITRF94 to NAD 83 based on the following values:
where
Wx = 42*(10**-11) radian/year
Wy = -372*(10**-11) radian/year
Wz = 10*(10**-11) radian/year.
On May 10, 1996, an improved set of positions and velocities were placed in the CORS coordinate files. NGS was able to improve CORS coordinates as a result of three factors: (1) the correction of an error in the software used to model positional variation of antenna phase centers, (2) a change in the ITRF realization used (ITRF94 replaced ITRF93) and the epoch date used for positions (1996.0 replaced 1995.0), and (3) the use of many more days of data than was previously available.
For users who employ NAD 83 coordinates, the most significant changes correspond to changes in ellipsoid height for about half of the CORS antennas. Some ellipsoid heights changed by as much as 17 cm. These large changes are primarily due to the correction of a software error in modeling positional variation of antenna phase centers as a function of satellite location. NAD 83 horizontal positions generally changed less than 2 cm. Horizontal changes primarily correspond to the increase in accuracy realized by using many more days of data than was previously available.
Changes in ITRF coordinates also reflect the effects of replacing ITRF93 with ITRF94 and replacing the 1995.0 epoch date with 1996.0. The use of a new ITRF realization and a new epoch date caused only small changes in NAD 83 coordinates because different transformation parameters are used to convert ITRF94 positions to NAD 83 positions than those parameters used to convert ITRF93 positions to NAD 83 positions.
Mader GL, Schenewerk MS, Ray JR, Kass WG, Spofford PR, Dulaney
RL, and Pursell DG (1995) GPS orbit and Earth orientation
parameter production at NOAA for the International GPS
Service for Geodynamics in 1994. International GPS Service
for Geodynamics 1994 Annual Report, 197-212, edited by
Zumberge JF, Liu R, and Neilan RE, Jet propulsion
Laboratory, Pasadena, CA 91109.
Milbert KO (1998) An evaluation of the High Accuracy Reference
Network relative to the Continuously Operating Reference
Stations, http://www.ngs.noaa.gov/PUBS_LIB/HARN_CORS_COMP/.
Sillard P, Altamimi Z, Boucher C (1998) The ITRF96 realization
and its associated velocity field. Geophysical Reseach
Letters, 25:3223-3226.
Snay, RA (1998) Using the HTDP software for transforming spatial
coordinates across time and between reference frames.
Surveying and Land Information Systems, in press.