[Proj] GRS80 vs GRS80 +towgs84=0,0,0

[Martin Vermeer]

On Sat, Dec 03, 2005 at 08:53:46PM +0100, Maciek Sieczka wrote:
> Hi,
> 
> I've encountered one small thing using cs2cs I don't understand. There
> is a difference in results when converting between WGS84 and GRS80 based
> systems - when the towgs84=0,0,0 is given for GRS80 and when it is not:
> 
> cs2cs -f "%.6f" +proj=latlong +ellps=WGS84 +to +proj=tmerc +lat_0=0
> lon_0=19 +k=0.9993 +x_0=500000 +y_0=-5300000 +ellps=GRS80 +towgs84=0,0,0
> 
> 17d01'0.0E 51d07'0.0N
> 361227.112181   362969.278159 0.000063
> 
> But, if I don't specify the +towgs84=0,0,0 in the target coordinate
> system, I obtain a slightly different result:
> 
> cs2cs -f "%.6f" +proj=latlong +ellps=WGS84 +to +proj=tmerc +lat_0=0
> +lon_0=19 +k=0.9993 +x_0=500000 +y_0=-5300000 +ellps=GRS80
> 
> 17d01'0.0E 51d07'0.0N
> 361227.112178   362969.278057 0.000000
> 
> The difference is less than 1 mm, but anyway - why? I thought that no
> matter if I specify the towgs84=0,0,0 for GRS80 or not I would obtain
> the same results. 
> 
> Maciek

I would guess this relates to the notorious "GRS80 vs WGS84
flattening" bug.

The official flattening of the GRS80 reference ellipsoid is
1/298.257222101. That of WGS84 is 1/298.257223563. Difference presumably
due to limited numerical precision when constructing WGS84. Otherwise
they are the same. This propagates into UTM coordinates on the
mm level, when using the two different ellipsoids. 

Note that I have no idea what proj does internally: perhaps adding the
+towgs84 switch overrides the earlier +ellps=GRS80 for the target's
projection ellipsoid. This is easily tested: try +ellps=WGS84 on output,
without +towgs84. You should get the same result... actually you won't:
I get

361227.112180   362969.278180 0.000000

so this is not the whole story...

Actually GRS80 and WGS84 are entirely different beasts: the former is a
reference system (ellipsoid + normal gravity model and related
parameters) while the latter is a geodetic datum realized by points on
the Earth's surface.

There are several such realizations around: ITRF, ETRF, EUREF, ... at
various epochs. On the few-decimetre level they are identical, which is
good enough for GIS applications, but for geodesy they are not.

- Martin

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