[Proj] Proj4 and Epoch

Chris Crook ccrook at linz.govt.nz
Tue Mar 8 15:04:41 EST 2016

I think the following doesn't work ...

> So, I suspect you have to transform to the standard epoch in some frame,
> and then to another frame, and then to the epoch you want.

The reason is that it is the conversion between frames that is time dependent.

There are three different things happening here.

One is about different realisations of a reference frame (eg NAD83(2011) is a realisation of a datum based on the 2011 National Adjustment), or WGS84 is actually a series of reference frames such as WGS84(G730), WGS84(G1762).  Each of these is realised at a date (epoch) but is used to represent coordinates at multiple epochs.  These are just different reference frames.

The second is about time dependent transformations between reference frames, which depend on the epoch of the coordinate, ie the epoch at which the conversion applies.  So for example the conversion between most geodetic datums (such as the ITRF datums such as ITRF2005, ITRF2008) involves a 14 parameter transformation  consisting of the 7 parameters of a Bursa Wolf transformation and 7 rates of change of parameters (eg scale difference at reference epoch and rate of change of scale difference per year).  This is not handled in the conventional GIS coordinate system defintions and conversion software AFAIK.  With the increasing use of global coordinate systems such as ITRF2008 (because of satellite based positioning) this is something that we will need to address.

The third is about time dependent transformations to account for ground deformation.  This is not so much about converting between reference frames, but about accounting for that fact that objects that we consider as fixed to the ground, and intuitively expect to have a constant coordinate, are actually moving in a global sense due to plate tectonics and other forms of ground deformation.  So if we want to use coordinates in the conventional GIS sense to identify or calculate relationships between objects then we need to have the coordinates at a common epoch - it doesn't make sense to compare the position of one object in 2000 with the position of another object in 2016.

The HTDP software represents the deformation of the North American continent and can be used to convert positions between  different epochs (or perhaps more accurately to transform the position of a "ground fixed" object from its coordinate at one epoch to its coordinate to another.

Similarly in New Zealand we have a deformation model that transforms between epochs, though the implementation is slightly different in that it is part of the definition of the NZGD2000 datum.  So to convert a coordinate from NZGD2000 to, for example WGS84(G1762), requires applying a time dependent transformation based on the deformation model to convert to the underlying datum (ITRF96) and then a 14 parameter Bursa Wolf transformation to convert to WGS84(G1762).  This approach is designed to ensure that coordinates of "ground fixed" marks remain substantially constant,  despite tectonic deformation moving the points in a global sense.

The North American and NZ approaches are slightly different (in that in NZ the deformation model is explicitly part of the definition of the datum), but the effect is very similar.

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