[Proj] TM06 for Portugal

[Mikael Rittri]

Roger Oberholtzer wrote:

> How would you convert WGS84 lat/long into TM06 
> northing/easting? I know that WGS84 is so close 
> to ETR89 here that one 'could' use the WGS84 values
> in the transform from ETRS89 to TM06. But how 
> would I do it the 'proper' way with proj? 

For this purpose, there are seven-parameter 
transformations that are time-dependent (since 
the ETRS89 follows the contintental drift of 
Eurasia, while WGS84 does not).  

The British Ordnance Survey cites the following 
datum shift from ITRS2005 to ETRS89: 

tX =  0.056 m
tY =  0.048 m
tZ = -0.037 m
rX =  0.000054 sec * deltatime
rY =  0.000518 sec * deltatime
rZ = -0.000781 sec * deltatime
s  =  0 ppm

where deltatime is the difference, in years, between 
the time when the ITRS2005 coordinates were observed,
and the fixed epoch of ETRS89, which is 1989.0. 
http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesyst
emsinfo/guidecontents/guide6.html

For example, today its June 8, 2010, which is the 
159th day of the year, so expressed in decimal years
it is today 2010 + 159/365 = 2010.44.  So deltatime
would be 2010.44 - 1989.0 = 21.44.  

I believe ITRS2005 can be regarded as equivalent to 
WGS84 with centimeter accuracy (although I am a bit
out of my depth here).  If so, the datum shift can 
be interpreted as going from from WGS84 to ETRS89, 
and in Proj.4 we want to express it in the opposite
direction.  So we reverse all signs.  (The Ordnance 
Survey uses the same rotation sign convention as
Proj.4, so that is one worry less.)

So, as an accurate datum shift for ETRS89, we get 

  +towgs84=-0.056,-0.048,0.037, < -0.000054 * 21.44 >, < -0.000518 *
21.44 >, < 0.000781 * 21.44 >, 0

or 

  +towgs84=-0.056,-0.048,0.037,-0.00115776,-0.01110592,0.01674464,0

At least today.  

There may be more recent versions of this kind of 
transformation.  I believe they are known as 
"14 parameter transformations" in general.  
Also, there may be regional versions that are 
more accurate for Portugal.

Disclaimer: I am not a geodesist, and I haven't
tested this datum shift on any real data. 

Mikael Rittri
Carmenta AB
Sweden
www.carmenta.com

-----Original Message-----
From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Roger Oberholtzer
Sent: Monday, June 07, 2010 1:38 PM
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] TM06 for Portugal

(full text at
http://lists.maptools.org/pipermail/proj/2010-June/005233.html )