[Proj] Vertical and geocentric coordinate support in OGR/PROJ4

[Greg Troxel]

Mikael Rittri <Mikael.Rittri at carmenta.com> writes:

> We have some customers who need to convert between 
> height-above-geoid and height-above-WGS84-ellipsoid, 
> but they don't need much accuracy: a couple of 
> meters error is okay. My advice has been to use 
> some representation of EGM2008, as the most detailed 
> global geoid model.

That sounds reasonable.

> I would like to learn more about the maximal (or typical)
> deviation between EGM2008 and other geoid models. For 
> Europe, my impression is that most of the national height 
> systems differ less than 0.5 m from the common European 
> height system EVRF2007 (see "Map Projections for Europe", 
> page 101, http://www.ec-gis.org/document.cfm?id=425&db=document ).
> A curious exception is a difference of 2.3 m for 
> Belgium, which uses (or has used) a height system 
> based on mean low tide of some kind, instead of 
> mean sea level. I think Ireland has some similar 
> height system. 

NGS has some podcasts/lectures available about height, and they are well
worth listening to:

  http://www.ngs.noaa.gov/corbin/class_description/NSRS_Modernization_0411.shtml

(and see related items).

One thing that wasn't clear to me at first is that 'geoid model' can
mean several things.  The most straightforward is about the distance of
a particular equipotential above the ellipsoid.  But one can also make a
model that gives the difference between orthometic heights in some datum
and ellipsoid heights.  Such a model implicitly includes distortions in
the vertical datum.  But if what you really want is to obtain orthometic
heights from GPS, that's what you want.

This page lists some of the US geoid models.  Note that if you compare
the values at a point, GEOID09 and EGM2008 will differ not only because
of only GEOID09 matching NAVD88, but because NAD83 ellipsoid heights are
different from WGS84 ellipsoid heights.   That might be the case in
Europe if there is a modern regional datum distinct from ITRF/WGS84.
Near me (42N 71W), GEOID09 is -27.3m and EGM2008 is -28.1m.  But, this
doesn't mean that the models differ by 0.8m -- because the NAVD88 zero
surface is not necessarily the WGS84 geoid.

http://www.ngs.noaa.gov/GEOID/

> But I am not sure about the difference between EVRF2007 
> and EGM2008. I have looked at a few sample points where 
> there was a difference of up to about 0.4 m. I haven't 
> found any conversion method between EVRF2007 and EGM2008, 
> or any estimate of the differences. Does anyone know?

From a quick scan of EVRF2007, it appears that it is conceptually
similar to NAVD88, in that it's based on leveling and has a single fixed
point.  (But it's apparently dynamic height rather than orthometric.)
So a geoid model that relates the EVRF2007 0 height surface to the WGS84
ellipsoid would not necessarily have the same values as EGM2008.

http://www.bkg.bund.de/nn_164706/geodIS/EVRS/EN/EVRF2007/evrf2007__node.html__nnn=true

> For the rest of the world, I am even less sure of 
> things. I have heard that the true mean sea level 
> can differ by a couple of meters from the geoid, 
> since mean sea level is not an equipotential surface 
> (due to variations in water temperature, salinity, 
> and whatever). But since national heights can be 

and persistent/average winds.

> measured from low tide - or maybe from something else - 
> I guess one can expect even larger deviations.  

I think the key question is what people who say they want "height above
geoid" really want.  I would think people that don't have a significant
understanding of geodesy probably want "orthometric height in the same
datum as my other data", which is a reasonable thing to want.

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