[Qgis-user] GDA94 and WGS84 transformations

[Even Rouault]

Hi,
> 
> I'm having trouble understanding how QGIS handles the conversion from the
> Australian datum to WGS84 in the UTM grid.
> 
> GDA94 (EPSG:4283) /  MGA94 Zone 5X (EPSG:2835x)
> WGS84 (EPSG:4326) /  UTM South     (EPSG:3265x)
> 
> As far as I know the only difference between those two is the ellipsoid
> flattening parameters:
> GDA94: 298.257222101
> WGS84: 298.257223563
> 
> When converting from WGS84 <--> GDA94 in degrees, I get exact same
> coordinates
> 
> GDA94 115.82318346600005 -31.948283257999947
> WGS84 115.82318346600005 -31.948283257999947
> 
> This is expected, since the CRSs transformation assumes the two ellipsoids
> are identical:
> 
> EPSG:1150 GDA94 to WGS 84 (1)
> Approximation at the +/- 3m level using inappropriate assumption that GDA94
> is equivalent to WGS 84. Accuracy changed from 1m to 3m due to tectonic
> plate motion over more than 15 years.
> +proj=noop

This is a much stronger assumption than the 2 ellipsoids are identical. This is an assumption 
that the 2 *datums* are considered identical because you don't care about positional 
accuracy below 3 meters.
This approximation is only used during the step where geodetic datum changes are used, not 
for forward or reverse map projections

> 
> However when going from degrees to UTM or MGA, I get different values:
> 
> GDA94 115.82318346600005 -31.948283257999947
> To
> MGA50 388777.573657*112836372* 6464692.233*647795394063*
> UTM50 388777.573657*624074258* 6464692.233
> *548169955611*
> WGS84 115.82318346600005 -31.948283257999947
> To
> MGA50 388777.573657112836372 6464692.233647795394063
> UTM50 388777.573657624074258 6464692.233548169955611
> 
> MGA50 388777.573657112836372 6464692.233647795394063
> To
> UTM50 388777.573657624074258 6464692.233548169955611
> 
> I don't know why UTM and MGA coordinates differ, since the transformation
> used still assumes WGS and GDA have the same ellipsoid:
> 
> INVERSE(EPSG):16150, INVERSE(EPSG):1150
> Inverse of UTM zone 50S + Inverse of GDA94 to WGS 84 (1)
> +proj=pipeline +step +inv +proj=utm +zone=50 +south +ellps=WGS84 +step
> +proj=unitconvert +xy_in=rad +xy_out=deg

If you go from GDA94 to MGA50, GRS80 will be used as the ellipsoid for map projection 
purposes:

$ projinfo -s GDA94 -t "GDA94 / MGA zone 50" -o PROJ
[...]

EPSG:17350, Map Grid of Australia zone 50, 0 m, Australia - 114°E to 120°E

PROJ string:
+proj=pipeline +step +proj=axisswap +order=2,1 +step +proj=unitconvert +xy_in=deg 
+xy_out=rad +step +proj=utm +zone=50 +south +ellps=GRS80


If you go from GDA94 to UTM50S, WGS84 will be used as the ellipsoid for map projection 
purposes:

$ projinfo -s GDA94 -t EPSG:32750 -o PROJ --spatial-test intersects
[...]

unknown id, GDA94 to WGS 84 (1) + UTM zone 50S, 3 m, Australia - GDA

PROJ string:
+proj=pipeline +step +proj=axisswap +order=2,1 +step +proj=unitconvert +xy_in=deg 
+xy_out=rad +step +proj=utm +zone=50 +south +ellps=WGS84


Which accounts for those submillemtric differences in projected coordinates.

But remember that if you went from GDA94 to WGS84 or a projected CRS based on WGS84, 
you have an inaccuracy of 1 - 2 meters... So if you care about submillemetric accuracy, you 
must remain in the same datum (WGS84, UTM50 / WGS84) or (GDA94, MGA50 / GDA94)

Even

-- 
Spatialys - Geospatial professional services
http://www.spatialys.com
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