EPSG Dataset :: v12.003

Time-specific Coordinate Frame rotation (geocen)

Coordinate Operation Method Details [VALID]

Name:

Time-specific Coordinate Frame rotation (geocen)

Code:

1066

Operation is Reversible:

Yes

Formula:

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The time-specific ooordinate transformation is an alternative approach to the time-dependent coordinate transformation. In this method the transformation parameter values are declared for a specified transformation reference epoch (an additional parameter for the transformation) and coordinates are adjusted to this epoch before the transformation is applied. This requires that the velocities for points whose coordinates are to be transformed are available. The time-specific transformation may then be applied as part of a concatenated coordinate operation in conjunction with one or two point motion operations (see EPSG Guidance Note 7-3 section 3) in two or three steps:

i) change the source CRS Cartesian coordinates from their dataset coordinate epoch to the transformation reference epoch at which the time-specific transformation is valid;

ii) apply the Time-specific Coordinate Frame rotation transformation;

iii) change the target CRS Cartesian coordinates from the transformation reference epoch at which the time-specific transformation is valid to any other desired coordinate epoch.

The transformation reference epoch of the Time-specific Coordinate Frame rotation transformation is used as the target epoch (t2) in step (i) and as the source epoch (t1) in step (iii). It is not used in step (ii).

Example:

Initial coordinates are referenced to the ITRF2008 CRS (EPSG code 5332) at coordinate epoch 2005.00. (Note: this happens to be the frame reference epoch for ITRF2008 but in other circumstancs the coordinate set could be referenced to a coordinate epoch different from the CRS's frame reference epoch).

Coordinates are required to be referenced to the PZ-90.11 CRS (EPSG code 7679) at coordinate epoch 2013.90.

Input point geocentric Cartesian coordinates and linear velocities:
XS = 2845 456.0813 m VX = –0.0212 m/yr
YS = 2160 954.2453 m VY = +0.0124 m/yr
ZS = 5265 993.2296 m VZ = +0.0072 m/yr
t = 2005.00 (years)
These are referenced to ITRF2008 at coordinate epoch 2005.00

Step 1: convert the coordinates in the source CRS from the dataset coordinate epoch (2005.00) to the epoch of validity of the time-specific transformation (2010.00) using the Point Motion (geocentric Cartesian) method described in EPSG Guidance Note 7-2.

XS(t=2010.00) = 2845456.0813 + (–0.0212) * (2010.0 - 2005.0) * 2845455.9753 m
YS(t=2010.00) = 2160954.2453 + (+0.0124) * (2010.0 - 2005.0) * 2160954.3073 m
ZS(t=2010.00) = 5265993.2296 + (+0.0072) * (2010.0 - 2005.0) * 5265993.2656 m

Step 2: transform the coordinates in the source CRS at coordinate epoch 2010.00 to the target CRS at coordinate epoch 2010.00 using the Coordinate Frame Rotation (geocentric domain) method described in EPSG Guidance Note 7-2. The time-specific transformation from PZ-90.11 to ITRF2008 (EPSG Dataset transformation code 7960) parameter values are:
tX = –0.003 m
tY = –0.001 m
tZ = 0.000 m
rX = 0.019 msec
rY = –0.042 msec
rZ = 0.002 msec
dS = 0.000 ppm
from which M = 1.0
t = 2010.00 years
This uses the Coordinate Frame rotation convention.

Because the transformation is required in the reverse direction to that defined, the relevant parameters need to have their signs reversed. Transformation parameter values (from ITRF2008 to PZ-90.11) then are:
tX = 0.003 m
tY = 0.001 m
tZ = 0.000 m
rX = –0.019 msec = –9.21145994108117E-11 radians
rY = 0.042 msec = 2.03621746066005E-10 radians
rZ = –0.002 msec = –9.69627362219071E-12 radians
M = 1.0
t = 2010.00 (years)

Then:
XT(t=2010.00) = 2845455.9772m
YT(t=2010.00) = 2160954.3078m
ZT(t=2010.00) = 5265993.2652m

Step 3: convert the coordinates in the target CRS from epoch 2010.00 to the required coordinate epoch 2013.90 using the Point Motion (geocentric Cartesian) method:

XT(t=2013.90) = 2845455.9772 + [–0.0212 * (2013.90 - 2010.00)] = 2845455.8945m
YT(t=2013.90) = 2160954.3078 + [+0.0124 * (2013.90 - 2010.00)] = 2160954.3562m
ZT(t=2013.90) = 5265993.2652 + [+0.0072 * (2013.90 - 2010.00)] = 5265993.2945m

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
X-axis translation	8605	Yes	The difference between the X values of a point in the target and source coordinate reference systems.
Y-axis translation	8606	Yes	The difference between the Y values of a point in the target and source coordinate reference systems.
Z-axis translation	8607	Yes	The difference between the Z values of a point in the target and source coordinate reference systems.
X-axis rotation	8608	Yes	The angular difference between the Y and Z axes directions of target and source coordinate reference systems. This is a rotation about the X axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Y-axis rotation	8609	Yes	The angular difference between the X and Z axes directions of target and source coordinate reference systems. This is a rotation about theY axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Z-axis rotation	8610	Yes	The angular difference between the X and Y axes directions of target and source coordinate reference systems. This is a rotation about the Z axis as viewed from the origin looking along that axis. The particular method defines which direction is positive, and what is being rotated (point or axis).
Scale difference	8611	Yes	Scale factor for source CRS axes minus one, where the scale factor is a multiplication factor to be applied to coordinates in the source CRS to obtain the correct scale in the target CRS. dS = (M – 1). If a distance of 100 km in the source CRS translates into a distance of 100.001 km in the target CRS, the scale difference is 1 ppm (the ratio being 1.000001). When the scale difference dS is expressed in parts per million (ppm), M = (1 + dS10-6). When the scale difference dS is expressed in parts per billion (ppb), M = (1 + dS10-9).
Transformation reference epoch	1049	No	The epoch at which a time-specific transformation is valid.

Meta Data

Remarks:

Note the analogy with the Time-specific Position Vector method (code 1065) but beware of the differences!

Information Source:

EPSG guidance note #7-2, http://www.epsg.org

Data Source:

EPSG

Revision Date:

February 21, 2019

Change ID:

[2016.061] [2018.001] [2019.006]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.