[Proj] stere/sterea and Polish "System 65" (epsg:2174)

[Maciek Sieczka]

Hi

According to the epsg definition file in PROJ, Polish stereographic grid 
"System 65 zone IV" is assigned number 2174. The +proj there is "stere", 
same as for the three remaining zones (2170-2173). Lately, after Frank 
Warmerdam has ported the "sterea" projection to his PROJ4, I have noticed 
that this "sterea" projection is a much better match for "System 65" than 
the old "stere" - according to some benchmarking I did based on an official 
reference provided by Polich geodetic service. Please see the following (the 
+towgs84 I'm using is slightly more detailed than the one defined in epsg 
file but it's the proper one, based on Kadaj R., 2001, 
http://www.geonet.net.pl/gfx/pliki/uklady_new.doc):

1.
Results obtained in a reference, official coord conversion utility TRANSPOL 
provided by Polish geodetic governal agency. Converting from Polish "System 
92" (Transverse Mercator/GRS80, epsg:2180) to "System 65 zone IV" 
(Stereographic/Krassowsky, epsg:2174):

input x,y in "System 92" (epsg:2180):
266000 326000
266000 328000
268000 328000
268000 326000
output x,y,z in "System 65" (epsg:2174):
5525494.71524 3633213.57243   -10.687
5527493.58245 3633150.79002   -10.928
5527556.37718 3635149.66409   -11.105
5525557.49078 3635212.45193   -10.863

2.
same coords converted by cs2cs with "stere":
[pingwin at localhost]$ echo "266000 326000
266000 328000
268000 328000
268000 326000" | cs2cs -Es +init=epsg:2180 +to epsg=:2174 +proj=stere 
+towgs84=33.4297,-146.5746,-76.2865,-0.35867,-0.05283,0.84354,-0.8407728 
+units=m
266000 326000   5525496.11      3633217.19 -40.48
266000 328000   5527494.87      3633154.34 -40.47
268000 328000   5527557.73      3635153.11 -40.42
268000 326000   5525558.95      3635215.97 -40.43

3.
and cs2cs with "sterea":
[pingwin at localhost] echo "266000 326000
266000 328000
268000 328000
268000 326000" | cs2cs -Es +init=epsg:2180 +to +init=epsg:2174 
+init=epsg:2174 proj=sterea 
+towgs84=33.4297,-146.5746,-76.2865,-0.35867,-0.05283,0.84354,-0.8407728 
+units=m
266000 326000   5525494.72      3633213.57 -40.48
266000 328000   5527493.58      3633150.79 -40.47
268000 328000   5527556.38      3635149.66 -40.42
268000 326000   5525557.49      3635212.45 -40.43


As you see the x,y results obtained with "sterea" are identical to the 
reference (yippie!) and with "stere" they differ about 1-4 meters.

Issues arise:
1. Wouldn't it be good to replace the "stere" epsg 2171-2174 with "sterea" 
in the epsg and esri PROJ4 definitions?
2. It would also make sense to change their descriptions into what it should 
be - "System 1965" ("Uklad 1965" in Polish). "Pulkovo 42" is wrong and 
missleading as in Poland we have another, different grid called "System 
1942".
3. Does anybody guess why the z coords in both stereographic cases are so 
much different from the reference?

Maciek

P.S.
As some of you might remember there was a thread on a related topic few 
months ago started by me on this list. Now when I know a little more it is a 
good occasion to sort things out. If more benchmarking is required please 
let me know.