NGS ADOPTS TRANSFORMATION
The National Geodetic Survey, in concurrence with Canada's Geodetic Survey Division, has adopted the following equations for transforming ITRF97 positional coordinates (XI, YI, ZI) at a specified epoch date (denoted t) to their corresponding NAD 83 values (XN, YN, ZN) at this same epoch date :
XN = TX(t) + [1 + S(t)]*XI + RZ(t)*YI - RY(t)*ZI
YN = TY(t) - RZ(t)*XI + [1 + S(t)]*YI + RX(t)*ZI
ZN = TZ(t) + RY(t)*XI - RX(t)*YI + [1 + S(t)]*ZI
t is expressed in years, for example, 1999.3096 = 0 hours on 23 April 1999;
TX(t) = [0.9889 + 0.0007*(t - 1997.0)] meters;
TY(t) = [-1.9074 - 0.0001*(t - 1997.0)] meters;
TZ(t) = [-0.5030 + 0.0019*(t - 1997.0)] meters;
RX(t) = [25.915 + 0.067*(t - 1997.0)]*m radians;
RY(t) = [9.426 - 0.757*(t - 1997.0)]*m radians;
RZ(t) = [11.599 - 0.031*(t - 1997.0)]*m radians;
S(t) = [-0.93 - 0.19*(t - 1997.0)]*(10-9) (unitless); and
m = 4.84813681*(10-9) (the conversion factor from milli-arc seconds to radians)
These equations correspond to the composition of two separate transformations: first, a transformation from ITRF97 to ITRF96 as adopted by the International GPS Service [IGS, 1999]; and second, a transformation from ITRF96 to NAD 83 as previously adopted by the National Geodetic Survey and Canada's Geodetic Survey Division [Snay, 1999; Craymer et al., 2000].
The IGS-adopted transformation from ITRF97 to ITRF96 reflects the fact that ITRF97 coordinates for about 50 global GPS tracking sites systematically differ from their corresponding ITRF96 coordinates by about 15 mm in position (for an epoch date of August 1999) and 2 mm/yr in velocity. This discrepancy in coordinates exists even though the International Earth Rotation Service had defined the ITRF97 coordinates for these and several hundred additional sites so that their "average" discrepancy from corresponding ITRF96 coordinates is minimized in a weighted least squares sense. The total collection of sites had been positioned by various techniques including GPS, very long baseline interferometry (VLBI), satellite laser ranging (SLR), and Doppler orbitography and radiopositioning integrated by satellite (DORIS).
Although ITRF97 and ITRF96 coordinates agree on average for the complete set of sites, GPS use is widespread and high accuracy GPS applications depend fundamentally on the coordinates of the 50 GPS tracking sites. Hence, NGS is adopting the new transformation to make NAD 83 coordinates for the 50 GPS tracking sites, as derived by transforming their ITRF97 coordinates, consistent with previous NAD 83 coordinates for these 50 sites, as derived by transforming their ITRF96 coordinates.
The adopted transformation from ITRF97 to NAD 83 has been incorporated into Version 2.4 of the HTDP (Horizontal Time-Dependent Positioning) software [Snay, 1999] which is available for download and/or online use.
Craymer, M., R. Ferland, and R. Snay (2000) Realization and unification of NAD83 in Canada and the U.S. via the ITRF. In R. Rummel, H. Drewes, W. Bosch, H. Hornik (eds), Towards an Integrated Global Geodetic Observing System (IGGOS), IAG Section II Symposium, Munich, October 5-9, 1998. International Association of Geodesy Symposia, Vol. 120, Springer, Berlin.
IGS (1999) International GPS Service electronic mail, message number 2432, 20 August 1999.
Snay, Richard A. (1999) Using the HTDP software to transform spatial coordinates across time and between reference frames, Surveying and Land Information Systems, Vol. 59, No. 1, pp. 15-25. [ pdf version ]