[Proj] Transformations with height data to bessel bring unrealistic results

[Melita Kennedy]

Hello Mark, 

The z values are being treated as ellipsoidal heights. Nowhere have you given any 
information to PROJ.4 that they are any particular vertical coordinate reference 
system. The transformation methods supported by the +wgs84 parameter work strictly 
with ellipsoidal heights, not geoidal or other gravity-related heights.

If you know you have gravity-related heights, you can either not pass them and ignore 
the output ellipsoidal heights or pass them, but replace them with the input gravity-
related heights. One reason to go ahead and pass in the gravity-related heights is 
that they may approximate the ellipsoidal heights in the area better than using zeroes.

Melita

-----Original Message-----
>
>Date: Thu, 21 Sep 2017 13:00:22 +0200
>From: Mark Johnson <mj10777 at googlemail.com>
>Subject: [Proj] Transformations with height data to bessel bring
>	unrealistic	results
>To: proj at lists.maptools.org, a.furieri at lqt.it
>
>When transforming positions with DHHN92 (EPSG:5783) height data, to Bessel
>based projections are returned.
>For my area (Berlin, Germany) the lowest height is just over 24 meters.
>Transformations using 34.79 all return  -6.13930772151798 when using
>ST_Transform, which performs a pj_transform in the background.
>Using -6.13930772151798 to transform back will return the original value.
>
>Between WSG84 and epsg:25833 there are no problems.
>
>I would be interested in learning the reason why this is so.
>
>Here some cs2cs samples with the results:
>
>ETRS89 / UTM zone 33N [epsg:25833]
># +proj=utm +zone=33 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
>
># DHDN / Soldner Berlin
># +proj=cass +lat_0=52.41864827777778 +lon_0=13.62720366666667 +x_0=40000
>+y_0=10000 +ellps=bessel +towgs84=598.1,73.7,418.2,0.202,0.045,-2.455,6.7
>+units=m +no_defs
>echo "389918.0707613 5819698.6197819 34.7900000"  | cs2cs +init=epsg:25833
>+to +init=epsg:3068
>23183.38 21047.17 -6.14
>echo 23183.38 21047.17 -6.139 | cs2cs +init=epsg:3068 +to +init=epsg:25833
>389918.07 5819698.62 34.79
>
># DHDN
># +proj=longlat +ellps=bessel
>+towgs84=598.1,73.7,418.2,0.202,0.045,-2.455,6.7 +no_defs
>echo "389918.0707613 5819698.6197819 34.7900000"  | cs2cs +init=epsg:25833
>+to +init=epsg:4314
>13d22'45.996"E 52d31'3.638"N -6.139
>echo 13.37770460000026 52.51627039998215 -6.139 | cs2cs +init=epsg:4314 +to
>+init=epsg:25833
>389796.59 5819544.81 34.80
>
># DHDN / 3-degree Gauss-Kruger zone 4
># +proj=tmerc +lat_0=0 +lon_0=12 +k=1 +x_0=4500000 +y_0=0 +ellps=bessel
>+towgs84=598.1,73.7,418.2,0.202,0.045,-2.455,6.7 +units=m +no_defs
>echo "389918.0707613 5819698.6197819 34.7900000"  | cs2cs +init=epsg:25833
>+to +init=epsg:31468
>4593626.95 5821241.65 -6.14
>echo "4593626.95 5821241.65 -6.14"  | cs2cs +init=epsg:31468 +to
>+init=epsg:25833
>389918.07 5819698.62 34.79
>
>Mark Johnson, Berlin Germany
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>End of Proj Digest, Vol 156, Issue 4
>************************************