[Proj] +towgs84 approximation error

Martin Desruisseaux martin.desruisseaux at geomatys.com
Fri Mar 24 07:53:55 EST 2017

Hello Jochem

Le 24/03/2017 à 11:29, Jochem a écrit :

> I think we should make a distinction between reference systems and
> reference frames here (I assume you are familiar with that). As each
> frame of a system will have different parameters. For a frame only one
> set of parameters is needed. If these are multiple sets, one could
> combine the information of all these stochastic transformations in to
> one best least-squares estimated set of parameters.
In the case of NAD27 to WGS84 transformations in the EPSG database, all
the 80 transformations are between the same geodetic datum (I think
"geodetic datum" was the old ISO 19111 terminology for "reference
frame", but they are renaming that in the new ISO 19111 revision). There
is +towgs84 parameters for the whole USA, then different +towgs84 for
various smaller geographic areas (e.g. East of Texas, West of Texas,
etc.). The transformations for local areas have smaller errors than the
transformations for the whole USA. I do not know how those parameters
were determined, but I could imagine starting from the same set of
stations and using e.g. only the stations in Texas for determining the
+towgs84 parameters in Texas, etc.

For map projection libraries, this imply that:

  * For coordinate conversions, we only need the source and target CRS.
  * For coordinate transformations, in addition of the source and target
    CRS we also need the area of interest if we want to choose the most
    accurate transformation among the various possibilities.

> However, this is the case for the national grid (RD) of the Netherlands. RD
> is defined as the transformation (in ISO19111 terminology this would be a
> conversion?) from ETRS89, including a 7 parameter transformation, but also
> an correction grid on projected coordinates is used:  
> ETRF2000(R05) <--7par--> pseudo_NL_Bessel <--proj--> pseudo_RD <--corr-->
> true_RD

This look like a datum shift to me, so it would still be a
transformation in ISO 19111 terminology. Even if the new CRS is
officially defined by Bursa-Wolf parameters and all software produce the
same numerical results, the relationship with objects in the real world
would still have stochastic errors: if we have a ETRF2000 coordinate
that describes the location of a physical object, and if we transform
that coordinate to RD, then the location described by the new coordinate
may be slightly aside the physical object (otherwise we would not have
to do least-square fitting). Or did I missed something?

Note: this is not an objection to your change proposal. This is rather
an emphasis that coordinate operations should be associated to metadata
that allow users to evaluate implications of what they are doing.


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