This transformation type consists of a static 7 parameter Helmert, with defined X,Y,Z translations/rotations and scale at the reference epoch (t0). The additional 7 velocity parameters define the rate of change at the reference epoch (t0). In addition to the standard 14 parameters, the reference epoch is also written into the definition of the transformation as a "15th" parameter.
In order to access these transformations, a matching date needs to be entered in the Date fields on both the source and target side of the transformation. The difference between the reference epoch and the user entered date is calculated and multiplied by the rate of change for that specific parameter. This new calculated value is then added to the original static parameter.
For example, consider the scenario of transforming between the ITRF2014 to ITRF96 datums using EPSG:9083. Below is an example of how the amount of X translation will be calculated assuming a user entered date of January 1st, 2025. This same technique is applied to all of the static parameters, and then they are used for the transformation after accounting for the velocities.
X translation (X)= 6.4 mm
Rate of change of X-axis translation (△x trans)= 0.79 mm/yr
Time Reference (t0)= Jan 1, 2000
Target Date (t1)= Jan 1, 2025
△t = t1-t0
△t = 25
X translation2= X + (△x trans * △t )
X translation2 = 6.4mm + (0.79 mm/yr * 25yr)
X translation2 = 26.15 mm
Both Coordinate Frame Rotation and Position Vector Rotation definitions of the 14 Parameter Time-Dependent transform are available. To properly define the parameters, you must know which rotation sense is used for your transformation parameters.
Coordinate Frame Rotation
Rotation is positive counter-clockwise, as may be imagined to be seen by an observer at the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place.
Position Vector Rotation
The rotations are defined as positive clockwise, as may be imagined to be seen by an observer at the origin of the coordinate frame, looking in the positive direction of the axis about which the rotation is taking place.
See also Time Dependent Transformations