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Historical CORS Coordinates and Helmert Transformation Parameters from the ITRS to NAD83 Reference Frames

The NGS utility Horizontal Time-Dependent Positioning (HTDP) can be used to transform between NAD83 reference frames and various International Terrestrial Reference Frame (ITRF) and International GNSS Service (IGS) realizations of the International Terrestrial Reference System (ITRS). The transformations are performed using the following Helmert parameters along with crustal motion models.Because crustal motion models are part of the transformation process, using the Helmert parameters by themselves generally will not yield correct results if the input and output epochs are not the same. In other words, these parameters alone are not guaranteed to correctly transform to NAD83 at a selected epoch if the input ITRS coordinates are at a different epoch.

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From IGS08 to NAD83(2011/PA11/MA11) - Ended Support on Jan 27, 2017 (includes CORS coordinates and velocities)

Coordinates and Velocities of the Antenna Reference Point (ARP) of All Processed Stations

Computed Modeled
Cartesian Geodetic Cartesian Geodetic
IGS08 epoch 2005.0 - All processed stations Download Download Download Download
NAD83(2011)
Stations in CONUS, Alaska, Puerto Rico, U.S. Virgin Islands		 Download Download Download Download
NAD83(PA11)
Stations in U.S. islands on the Pacific plate		 Download Download Download Download
NAD83(MA11)
Stations in U.S. islands on the Mariana plate		 Download Download Download Download

Helmert Parameters Used in Transforming Coordinates from IGS08 to NAD83

Parameters
t0 = 1997.0 		Definition Unit From IGS08 To
NAD83(2011) NAD83(PA11) NAD83(MA11)
Tx(t0) x-translation meters 0.99343 0.9080 0.9080
Ty(t0) y-translation meters -1.90331 -2.0161 -2.0161
Tz(t0) z-translation meters -0.52655 -0.5653 -0.5653
εx(t0) x-rotation mas 25.91467 27.741 28.971
εy(t0) y-rotation mas 9.42645 13.469 10.420
εz(t0) z-rotation mas 11.59935 2.712 8.928
s(t0) scale ppb 1.71504 1.10 1.10
T'x(t0) x-translation rate meters/year 0.00079 0.0001 0.0001
T'y(t0) y-translation rate meters/year -0.00060 0.0001 0.0001
T'z(t0) z-translation rate meters/year -0.00134 -0.0018 -0.0018
ε'x(t0) x-rotation rate mas/year 0.06667 -0.384 -0.020
ε'y(t0) y-rotation rate mas/year -0.75744 1.007 0.105
ε'z(t0) z-rotation rate mas/year -0.05133 -2.186 -0.347
s'(t0) scale rate ppb/year -0.10201 0.08 0.08

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

From ITRF2000 to NAD83(CORS96/PACP00/MARP00) - Ended Support on Sep 06, 2011 (includes CORS coordinates and velocities)

Coordinates and Velocities of the Antenna Reference Point (ARP) of All Processed Stations

Cartesian Geodetic
ITRF2000 - All processed stations Download Download
NAD83(CORS96) - Stations in CONUS, Alaska, Puerto Rico, U.S. Virgin Islands
NAD83(PACP00) - Stations in U.S. islands on the Pacific plate
NAD83(MARP00) - Stations in U.S. islands on the Mariana plate 		Download Download

Helmert Parameters Used in Transforming Coordinates from ITRF2000 to NAD83

Parameters
t0 = 1997.0 		Definition Unit From ITRF2000 To
NAD83(CORS96) NAD83(PACP00) NAD83(MARP00)
Tx(t0) x-translation meters 0.99563 0.9102 0.9102
Ty(t0) y-translation meters -1.90131 -2.0141 -2.0141
Tz(t0) z-translation meters -0.52145 -0.5602 -0.5602
εx(t0) x-rotation mas 25.91467 27.741 28.971
εy(t0) y-rotation mas 9.42645 13.469 10.420
εz(t0) z-rotation mas 11.59935 2.712 8.928
s(t0) scale ppb 0.61504 0 0
T'x(t0) x-translation rate meters/year 0.00069 0 0
T'y(t0) y-translation rate meters/year -0.00070 0 0
T'z(t0) z-translation rate meters/year 0.00046 0 0
ε'x(t0) x-rotation rate mas/year 0.06667 -0.384 -0.020
ε'y(t0) y-rotation rate mas/year -0.75744 1.007 0.105
ε'z(t0) z-rotation rate mas/year -0.05133 -2.186 -0.347
s'(t0) scale rate ppb/year -0.18201 0 0

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

From ITRF97 to NAD83(CORS96) - Ended Support in 2002

Helmert Parameters Used in Transforming Coordinates from ITRF97 to NAD83(CORS96)

Note: these parameters are a composition of the ITRF97 to ITRF96 transformation as adopted by IGS and the ITRF96 to NAD83(CORS96) transformation. This composite transformation was jointly adopted by the United States and Canada per NGS policy.

Parameters
t0 = 1997.0 		Definition Unit From ITRF97 To NAD83(CORS96)
Tx(t0) x-translation meters 0.98893
Ty(t0) y-translation meters -1.90741
Tz(t0) z-translation meters -0.50295
εx(t0) x-rotation mas 25.91467
εy(t0) y-rotation mas 9.42645
εz(t0) z-rotation mas 11.59935
s(t0) scale ppb -0.93496
T'x(t0) x-translation rate meters/year 0.00069
T'y(t0) y-translation rate meters/year -0.00010
T'z(t0) z-translation rate meters/year 0.00186
ε'x(t0) x-rotation rate mas/year 0.06667
ε'y(t0) y-rotation rate mas/year -0.75744
ε'z(t0) z-rotation rate mas/year -0.03133
s'(t0) scale rate ppb/year -0.19201

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

From ITRF96 to NAD83(CORS96) - Ended Support in 2000

Helmert Parameters Used in Transforming Coordinates from ITRF96 to NAD83(CORS96)

Note: these parameters were jointly adopted by the United States and Canada to define the relationship between ITRF96 and NAD 83(CORS96) per NGS policy.

Parameters
t0 = 1997.0 		Definition Unit From ITRF96 To NAD83(CORS96)
Tx(t0) x-translation meters 0.9910
Ty(t0) y-translation meters -1.9072
Tz(t0) z-translation meters -0.5129
εx(t0) x-rotation mas 25.79
εy(t0) y-rotation mas 9.65
εz(t0) z-rotation mas 11.66
s(t0) scale ppb 0
T'x(t0) x-translation rate meters/year 0
T'y(t0) y-translation rate meters/year 0
T'z(t0) z-translation rate meters/year 0
ε'x(t0) x-rotation rate mas/year 0.0532
ε'y(t0) y-rotation rate mas/year -0.7423
ε'z(t0) z-rotation rate mas/year -0.0316
s'(t0) scale rate ppb/year 0

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

From ITRF94 to NAD83(CORS94) - Ended Support in 1998

Helmert Parameters Used in Transforming Coordinates from ITRF94 to NAD83(CORS94)

Note: these parameters are not consistent with HTDP because they predate the relationships encoded in HTDP between ITRF96 and NAD 83(CORS96) and between ITRF96 and ITRF97. Those relationships were jointly adopted by the United States and Canada per NGS policy.

Parameters
t0 = 1996.0 		Definition Unit From ITRF94 To NAD83(CORS94)
Tx(t0) x-translation meters 0.9738
Ty(t0) y-translation meters -1.9453
Tz(t0) z-translation meters -0.5486
εx(t0) x-rotation mas 27.55
εy(t0) y-rotation mas 10.05
εz(t0) z-rotation mas 11.36
s(t0) scale ppb 0
T'x(t0) x-translation rate meters/year 0
T'y(t0) y-translation rate meters/year 0
T'z(t0) z-translation rate meters/year 0
ε'x(t0) x-rotation rate mas/year 0.09
ε'y(t0) y-rotation rate mas/year -0.77
ε'z(t0) z-rotation rate mas/year 0.02
s'(t0) scale rate ppb/year 0

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

From ITRF93 to NAD83(CORS93) - Ended Support in 1996

Helmert Parameters Used in Transforming Coordinates from ITRF93 to NAD83(CORS93)

Note: these parameters are not consistent with HTDP because they predate the relationships encoded in HTDP between ITRF96 and NAD 83(CORS96) and between ITRF96 and ITRF97. Those relationships were jointly adopted by the United States and Canada per NGS policy.

Parameters
t0 = 1995.0 		Definition Unit From ITRF93 To NAD83(CORS93)
Tx(t0) x-translation meters 0.9769
Ty(t0) y-translation meters -1.9392
Tz(t0) z-translation meters -0.5461
εx(t0) x-rotation mas 26.40
εy(t0) y-rotation mas 10.10
εz(t0) z-rotation mas 10.30
s(t0) scale ppb 0
T'x(t0) x-translation rate meters/year 0
T'y(t0) y-translation rate meters/year 0
T'z(t0) z-translation rate meters/year 0
ε'x(t0) x-rotation rate mas/year 0
ε'y(t0) y-rotation rate mas/year 0
ε'z(t0) z-rotation rate mas/year 0
s'(t0) scale rate ppb/year 0

where:

  • mas = milliarcseconds
  • ppb = parts per billion
  • Counterclockwise rotation of axes are positive

Equations Used in Transforming Coordinates from IRTF to NAD83

The equations given below transform ITRF (as well as IGS) positional coordinates (xITRF, yITRF, zITRF) with an epoch date at time t to NAD83 positional coordinates (xNAD83,yNAD83, zNAD83) at the same epoch date. Positional coordinates for a different epoch date (and for a particular reference frame) can only be obtained by knowing the velocity (time rate of change) of the point in the same reference frame. HTDP includes models that estimate these velocities, allowing transformation of coordinates at different epochs and between several commonly used reference frames.

xNAD83 = Tx(t) + [1 + s(t)] · xITRF + εz(t) · yITRF - εy(t) · zITRF
yNAD83 = Ty(t) - εz(t) · xITRF + [1 + s(t)] · yITRF + εx(t) · zITRF
zNAD83 = Tz(t) + εy(t) · xITRF - εx(t) · yITRF + [1 + s(t)] · zITRF
where:
  • mr = 4.84813681×10-9: conversion factor from milliarcseconds (mas) to radians; and
  • Tx(t) = Tx(t0) + T'x · (t-t0)
  • Ty(t) = Ty(t0) + T'y · (t-t0)
  • Tz(t) = Tz(t0) + T'z · (t-t0)
  • s(t) = s(t0) + s' · (t-t0)
  • εx(t) = [ εx(t0) + ε'x · (t-t0) ] · mr
  • εy(t) = [ εy(t0) + ε'y · (t-t0) ] · mr
  • εz(t) = [ εz(t0) + ε'z · (t-t0) ] · mr

NOAA CORS Network (NCN)