[Proj] How to convert a sphere to ellipsoid with correct datum?

Jan Hartmann j.l.h.hartmann at uva.nl
Wed Sep 1 05:54:44 EST 2010

  In my opinion this is a bug. When trying to convert  a lonlat value 
from one ellipse to another, cs2cs ignores the change of ellipsoid. Some 
time ago a decision was made to only perform a datum transform when both 
input and output projections had a full datum description, i.e. both 
ellipsoid and towgs84 parameters.  This is the right way of doing datum 
transform, but unfortunately it also seems to prevent a conversion from 
latlong to latlong on different ellipses where no datum shift has to be 
applied (+nadgrids=@null doesn't work in this case).

Funny thing is that for projected coordinates a transform between 
different ellipses *does* work. It took me a long time to figure this 
out when trying to convert 19th century latlon values, as computed on a 
slightly smaller ellipsoid, to contemporary latlon values on the Bessel 
ellips, where no datum shift had taken place, i.e. where the direction 
and alignment of the axes of the ellipsoid were the same and only their 
extents were different. The solution turned out to be to convert the 
original latlongs to an intermediate projection on the original 
ellipsoid, convert those projected coordinates to a modern projection 
based on the modern ellipsoid, and convert those modern coordinates back 
to latlon values on the target ellipsoid.

I don't like this procedure, as the original 19th century triangulation 
was computed with spheroidical coordinates that were only afterwards 
converted to a planar projection. There were small errors on those 
original tables (around 50 meters) that were extremely hard to pinpoint, 
so every intermediate computational step should be avoided. Especially 
so when the point of reference for the ellipsoid computation is a place 
as outlandish as Amsterdam. I think I solved the problem now, but IMHO 
it shouldn't have existed in the first place. The same location on the 
world globe has *different* latlong values when computed on the basis of 
different ellipsoids, and that is not shown by cs2cs.


On 09/01/10 11:23, Heiko Klein wrote:
> Hi,
> I'm working with meteorological model-data. The models usually use a
> spherical earth. Since the resolution of the models is now ~1km, I have
> to think more about converting those data for people using GIS systems.
> I have only a very rough understanding of datum, geocentric and
> geodetic. Up to now I've only used the ellps-parameters of proj to
> describe the earth.
> If I understand it correctly, a spherical earth is completely described
> by the major axis, and geodetic and geocentric coordinates are the same?
> Using the following does not change the coordinates
> ./cs2cs +proj=latlong +ellps=sphere +a=6371000 +e=0 +to +proj=latlong
> +ellps=WGS84
> 10 60
> 10dE	60dN 0.000
> since it calculates completely in geocentric coordinates?
> Giving a WGS84 datum on both input and output gives geodetic coordinates?
> /cs2cs +proj=latlong +ellps=sphere +a=6371000 +e=0 +datum=WGS84 +to
> +proj=latlong +ellps=WGS84 +datum=WGS84
> 10 60
> 10dE	60d9'58.075"N 8921.648
> Why should the sphere-datum be WGS84? Using NAD27 gives me geocentric
> coordinates?
> ./cs2cs +proj=latlong +ellps=sphere +a=6371000 +e=0 +datum=NAD27 +to
> +proj=latlong +ellps=WGS84 +datum=WGS84
> 10 60
> 10dE	60dN 0.000
> Does there exist a correct 'datum' for a sphere? Isn't it all the same
> for a sphere? Why do I have to give it at all?
> If I have a measurement station with GPS coordinates, latitude and
> longitude, are they geocentric or geodetic?
> And the final and most important question: What is the best description
> of a spherical earth to convert from with cs2cs?
> Best regards,
> Heiko
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