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ITRF-NAD83 TRANSFORMATION & DEFINITION OF NAD83(CSRS)
Mike Craymer
Geodetic Survey Division, Natural Resources Canada
Tel 613-947-1829, Fax 613-992-6628
April 16, 1998
Revised 1998-04-22
Revised 1998-05-20
Revised 2001-06-11: For notation consistency with Craymer et al., 1999.
Revised 2001-08-18: Added ITRF96-97 based on agreed GSD/NGS values;
differences with adopted IGS values in IGS Mail #2342 are negligable.
Revised 2001-12-12: Revisted entire paper; added ITRF97-00 transformation
as defined by the IERS.
Revised 2004-11-01: Replaced NAD83(CSRS98) with NAD83(CSRS) since CSRS98
is now in wide use and was used only to distinguish from a preliminary
CSRS96 version that saw little use; replaced NAD83/CSRS with NAD83(CSRS)
for consistency.
Revised 2012-01-26: Added ITRF2000-ITRf2005 and ITRF2005-ITRF2008
transformations defined by the IERS.
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The Geodetic Survey Division (GSD) of Natural Resources Canada and the U.S.
National Geodetic Survey (NGS) have recently agreed on a new common scheme
for transforming coordinates between the International Terrestrial
Reference Frame (ITRF) and NAD83. This effectively unifies the definition
of the NAD83 reference frame throughout both countries. This realization of
NAD83 is denoted as NAD83(CSRS) in Canada and NAD83(NSRS) in the U.S.
The new transformation is based upon the transformation between NAD83 and
ITRF96 at epoch 1997.0. The transformation of ITRF96 geocentric Cartesian
coordinates (Xi,Yi,Zi) at epoch t to NAD83(CSRS) coordinates (Xn,Yn,Zn) is
defined by
Xn = TX + (1+DS)*Xi - RZ(t)*Yi + RY(t)*Zi
Yn = TY + RZ(t)*Xi + (1+DS)*Yi - RX(t)*Zi
Zn = TZ - RY(t)*Xi + RX(t)*Yi + (1+DS)*Zi
where
TX = 0.9910 m
TY = -1.9072 m
TZ = -0.5129 m
DS = 0.00 ppb
RX(t) = -25.79 mas + dRX*(1997.0-t)
RY(t) = -9.65 mas + dRY*(1997.0-t)
RZ(t) = -11.66 mas + dRZ*(1997.0-t)
and
dRX = 0.0532 mas/y
dRY = -0.7423 mas/y
dRZ = -0.0316 mas/y
The later parameters are rates of change of rotation from the observation
epoch to the refernce epoch (1997.0) of the ITRF96-NAD83 transformation.
They represent the horizontal motion of the NAD83 reference frame due to
the tectonic motion of the North American plate. The rotation rates are
derived from the NUVEL1A plate motion model recommended by the IERS
Conventions (2000) [McCarthy, 2001].
To transform between NAD83 and other realizations of ITRF, it is first
necessary to apply an "incremental" transform to ITRF96. The parameters for
these incremental ITRF transformations are obtained from the values adopted
by the IERS [McCarthy, 2001]; see also the ITRF web site at
. The exception is for the
transformation between ITRF96 and ITRF97 where a systematic translation
exists at IGS stations. In this case, both GSD and NGS have adopted the
official IGS transformation defined in IGS Mail #2342 (converted to epoch
1997.0). There are small differences between the IGS values and those we
have adopted due to round off errors which are insignificant for practical
purposes.
The following table summarizes the incremental ITRF transformation
parameters:
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From To t0 TX(cm) TY(cm) TZ(cm) RX(mas) RY(mas) RZ(mas) DS(ppb)
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ITRF88 ITRF96 1988.0 -1.8 0.0 9.2 -0.1 0.0 0.0 -7.4
ITRF89 ITRF96 1988.0 -2.3 -3.6 6.8 0.0 0.0 0.0 -4.3
ITRF90 ITRF96 1988.0 -1.8 -1.2 3.0 0.0 0.0 0.0 -0.9
ITRF91 ITRF96 1988.0 -2.0 -1.6 1.4 0.0 0.0 0.0 -0.6
ITRF92 ITRF96 1988.0 -0.8 -0.2 0.8 0.0 0.0 0.0 0.8
ITRF93 ITRF96 1988.0 -0.6 0.5 1.5 0.39 -0.80 0.96 -0.4
+ rates of change 0.29 -0.04 -0.08 0.11 0.19 -0.05 0.0
ITRF94 ITRF96 1988.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
ITRF96 ITRF97 1997.0 0.207 0.021 -0.995 0.12467 -0.22355 -0.06065 0.93496
+ rates of change -0.069 0.010 -0.186 0.01347 -0.01514 0.00027 0.19201
ITRF97 ITRF00 1997.0 -0.67 -0.61 1.85 0.00 0.00 0.00 -1.55
+ rates of change 0.00 0.06 0.14 0.00 0.00 -0.02 -0.01
ITRF00 ITRF05 2000.0 -0.01 0.08 0.58 0.000 0.000 0.000 -0.40
+ rates of chnage 0.02 -0.01 0.18 0.000 0.000 0.000 -0.08
ITRF05 ITRF08 2005.0 0.05 0.09 0.47 0.000 0.000 0.000 -0.94
+ rates of chnage -0.03 0.00 0.00 0.000 0.000 0.000 0.00
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For a given transformation parameter P, its value at epoch t is obtained
from:
P(t) = P(t0) + dP*(t-t0)
where t0 is the reference epoch in the above table and dP is the rate of
change of the parameter, and P(t0) is the parameter at the reference epoch,
given in the above table. To transform between ITRF00 and ITRF96, it is
necessary to take the sum of the transformation parameters for ITRF96-
ITRF97 and ITRF97-ITRF00, both at epoch t. These transformation parameters
can then be added with those between ITRF96 and NAD83(CSRS) to give the full
transformation from ITRFxx to NAD83(CSRS).
The above transformations have been implemented in a portable Fortran
program called TRNOBS. It transforms GHOST and GeoLab coordinate and
coordinate difference records between various ITRFs and NAD83(CSRS). TRNOBS
is available via anonymous FTP from:
NOTES
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1) All of the above rotations are defined as clockwise rotations in a
right-handed coordinate system following the convention used in IERS
reports. Customary mathematical and geodetic convention is to use
anti-clockwise rotations in right-handed systems.
2) The same transformation parameters have also been adopted by the U.S.
National Geodetic Survey, except for ITRF reference frames prior to ITRF96.
For more information about NGS's transformations, see their web page at
.
3) For more information about the ITRF, see Boucher and Altamimi [1996] and
Altamimi et al. [2001], or visit the ITRF web site at
.
REFERENCES
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Altamimi et al. (2001). "The Terrestrial Reference Frame and the Dynamic
Earth", EOS, Transactions, Vol. 82, No. 25, June 19, 2001.
Craymer, M., R. Ferland and R. Snay (1999). "Realization and Unification of
NAD83 in Canada and the U.S. via the ITRF", Proceedings of the
International Symposium of the International Association of Geodesy,
Section II, ÒTowards an Integrated Geodetic Observing System (IGGOS)Ó,
Munich, October 5-9, 1998. Revised 11 March 1999.
Craymer, M.R. (2006). "The Evolution of NAD83 in Canada". Geomatica, Vol. 60,
No. 2, pp. 151-164, 2006. And "The Evolution of NAD83 in Canada: Addendum".
Geomatica, Vol. 60, No. 4, 2006.
Boucher, Claude and Zuheir Altamimi (1996). "International Terrestrial
Reference Frame", GPS World, September 1996.
McCarthy, Dennis D. (2000). "IERS Conventions (2000)". Draft IERS Technical
Note, Intentional Earth Rotation Service, Paris, August 2000.