[Proj] Stereo 1970 (EPSG 31700)

Thu Oct 7 09:46:58 EST 2010

Hello Noel,

I think you are right in everything you say - except the final conclusion
that 3-parameter transformations are to be preferred if the software
does not support Molodensky-Badekas.

Some specific comments:

> (Perhaps you can advise me if this indictment of geodetic software applies to Proj4.)

Yes, as far as I know, Proj4 (or cs2cs) does not support 10 parameters (M-B parameters)
in the +towgs84 parameter.

> It may be true (not positive as I haven't tested this) that the coordinate
> results of a given M-B transformation can be reproduced by some 7-parameter
> transformation as you suggest.

It was Melita Kennedy who taught me how to translate an M-B transformation
into an equivalent 7-parameter transformation. (Strictly speaking, I haven't
been able to test if I understood everything, since I don't have access to
independent software that supports M-B. But I am pretty confident.)

> ... observe the first 3 parameters of the 7-parameter transformations ...
> Shocking, isn't it?  They're scattered meaninglessly all over the place, ...

Well, let's say it is unfortunate and disappointing, if it is
important to be able to interpret and understand the parameters.

On the other hand, most of my customers just need some kind of black-box
mechanism that can transform long/lat from one datum to another, as
accurately as possible.  (Or as accurately as necessary, perhaps.)
So they don't care if the first 3 parameters are widely different
between 7-parameter transformations for neighbouring regions.

> Until all of (y)our software supports M-B, use a 3-parameter translation instead!

No, that's bad advice. There are plenty of examples for regions that
you say are too small (like medium-sized European countries), where
the best available 3-parameter transformation can give errors greater
than 15 meters, while there are published 7-parameter transformations
that give errors of just a few meters.

Example: transforming the British OSGB 1936 to WGS84:

Best published 3-parameter transformation: EPSG:1195, "OSGB 1936 to WGS 84 (1)".
EPSG Accuracy entry: 21 metre.
EPSG Scope says: "Accuracy 10m, 10m and 15m in X, Y and Z axes."

Best published 7-parameter transformation: EPSG:1314, "OSGB 1936 to WGS 84 (6)".
EPSG Accuracy entry: 2 metre.
EPSG Scope says: "Accuracy better than 4m and generally better than 2m."
(British sources say the worst error is 5 meters.)

There are many applications where a 5-meter error can be acceptable,
while 21 meters or more wouldn't be. (Fleet management, ambulance dispatch...)

So, if my software supports 3-parameter and 7-parameter datum shifts,
but not Molodensky-Badekas (10-parameter) or grid shift files (or if
you don't need the accuracy of a grid shift file), then what?
Surely it is better to get 2 - 4 meter accuracy instead of 21 meters,
even if I cannot interpret or understand the seven parameters at all
(just as long as they give good results).

Best regards,

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 Noel Zinn (cc)
Sent: den 7 oktober 2010 12:17
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] Stereo 1970 (EPSG 31700)

Hi Mikael,

It is true that there is no numerical problem using a 7-parameter transformation derived from observations in a small area, which means, I will add, derived poorly.

It is an unfortunate reality that more geodetic software supports 7-parameter transformations than supports Molodensky-Badekas (M-B) transformations, sometimes called 10-parameter transformations due to the additional 3 coordinates of the topographic rotation center, but these are givens of the adjustment and not additional parameters to be solved for.
(Perhaps you can advise me if this indictment of geodetic software applies to Proj4.)  Anyway, in the example you provide (EPSG Tfm Codes 4827 and
4829) the Slovakian authorities had this deficiency in mind in supplying a 7-parameter transformation to replace a M-B transformation.

It may be true (not positive as I haven't tested this) that the coordinate results of a given M-B transformation can be reproduced by some 7-parameter transformation as you suggest.

The problem with 7-parameter transformations derived in small area is more fundamental, however.  The 7 parameters of a 7-parameter (Helmert, Bursa-Wolfe, or similarity) transformation have well-known and well-documented physical interpretations.  The 3 translations represent the relative displacement of the geocenters of the two ellipsoids involved (in the ECEF X, Y and Z directions); the 3 rotations represent rotations about the X, Y and Z axes; and the scale represents an inflation (or deflation) of an ellipsoid (i.e. the linear unit).  These 7 parameters are not like the parameters of a multiple regression equation (MRE) of the kind that used to be published by the Defense Mapping Agency (DMA, predecessor to NIMA and
NGA) for transforming datums with more "accuracy" than a 3-parameter translation.  Those parameters can be pencil whipped into submission because they "mean" nothing.  The 7 parameters of a Helmert (et al) transformation mean something and that meaning is badly corrupted by the ill conditioning of an adjustment over a small area.

Let me illustrate this point with my own EPSG tfm code examples.  Codes 15714, 15716, 15718, 15720, 15722, 15724, 15716 and 15728 offer 7-parameter transformations from Bogota 1975 to Magna-Sirgas for regions I through VIII in Colombia and codes 15730 through 15737 offer M-B parameters for the same regions respectively.  Code 1125 offers a 3-parameter translation between Bogota 1975 and WGS84, which EPSG regard to be the same as Magna-Sirgas at the 1-meter level.  So, the 3 parameters of tfm 1125 provide a 1-meter assessment of the geocentric displacement between the International 1924 ellipsoid of Bogota 1975 and GRS80 of Magna-Sirgas.  Now, observe that these same 3 translations (307, 304, -318) are pretty much the same as the first 3 parameters of all the M-B transformations for the eight regions (tfm codes 15730 through 15737).  Finally, observe the first 3 parameters of the 7-parameter transformations for the eight regions (tfm codes 15714, 15716, 15718, 15720, 15722, 15724, 15716 and 15728).  Shocking, isn't it?  They're scattered meaninglessly all over the place, a consequence of the ill conditioning of deriving a 7-parameter transformation in an area an eighth the size of Colombia.

The derivation of a 7-parameter Helmert (et al) transformation over a small area is pencil whipping, not geodesy.  Until all of (y)our software supports M-B, use a 3-parameter translation instead!

Regards,
Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

--------------------------------------------------
From: "Mikael Rittri" <Mikael.Rittri at carmenta.com>
Sent: Thursday, October 07, 2010 2:13 AM
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
Subject: Re: [Proj] Stereo 1970 (EPSG 31700)

> Hello Noel,
>
>> The least-squares adjustment of 7 transformation parameters
>> (3 translations, 3 rotations and a scale) for an area as small as the
>> country of Romania is badly ill-conditioned.
>
> Now I am confused.
>
> What you say is that it is a difficult statistical problem to derive a
> 7-parameter transformation from observations in a small area. But if
> someone I can trust has already derived a 7-parameter transformation,
> then there is no numerical problems when using it, is there?
>
>> In these cases use a 3-parameter transformation instead.
>> Or a Molodensky-Badekas transformation ... as has become common in
>> some smaller countries (e.g. Luxembourg, Venezuela) ... if you can
>> find (or derive) one.
>
> Well, but if a Molodensky-Badekas transformation is okay, then there
> is always a 7-parameter transformation that gives the same result.
> For all I know, the Romanian authorities may have started out by
> deriving a Molodensky-Badekas transformation, and then decided to
> publish it as the equivalent 7-parameter transformation.  If that is
> what they did, there would be no reason to suspect that their
> transformation is less accurate than the 3-parameter transformations,
> is there?
>
> (An example: the datum shift EPSG:4829, "S-JTSK to ETRS89 (3)", is a
> Molodensky-Badekas transformation, and the datum shift EPSG:4827,
> "S-JTSK to ETRS89 (4)", is the same transformation expressed as a
> 7-parameter transformation.)
>
> Best regards,
>
> 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 Noel Zinn (cc)
> Sent: den 6 oktober 2010 16:47
> To: PROJ.4 and general Projections Discussions
> Subject: Re: [Proj] Stereo 1970 (EPSG 31700)
>
> Although the third of the three EPSG transformations cited herein has
> the
> (Romanian) National Agency for Cadastre and Land Registration as its
> source (and is, therefore, authoritative) and it has more parameters
> (7 versus 3 for the Shell and NIMA transformations), it should not be
> regarded as more accurate.  The least-squares adjustment of 7
> transformation parameters (3 translations, 3 rotations and a scale)
> for an area as small as the country of Romania is badly
> ill-conditioned.  The 7 parameters are highly correlated and,
> therefore, are driven by small survey errors, not physical reality.
> Simply stated, the translations pull in one direction and the
> rotations in another.  Australia is big enough, but not Romania.  Not
> even Germany.  In these cases use a 3-parameter transformation
> instead.  Or a Molodensky-Badekas transformation ... as has become
> common in some smaller countries (e.g. Luxembourg, Venezuela) ... if
> you can find (or derive) one.
>
> Noel Zinn, Principal, Hydrometronics LLC
> +1-832-539-1472 (office), +1-281-221-0051 (cell)
> noel.zinn at hydrometronics.com (email)
> http://www.hydrometronics.com (website)
>
> --------------------------------------------------
> From: "Mikael Rittri" <Mikael.Rittri at carmenta.com>
> Sent: Wednesday, October 06, 2010 2:38 AM
> To: "PROJ.4 and general Projections Discussions"
> <proj at lists.maptools.org>
> Subject: Re: [Proj] Stereo 1970 (EPSG 31700)
>
>> Hello, Thibaut.
>>
>> For the record, www.epsg-registry.org gives three datum shifts from
>> Pulkovo 1942(58) to WGS84 that are valid in Romania.
>>
>> Code Accuracy Source Proj.4 syntax
>> 15496 10 meters Shell SIEP +towgs84=44.107,-116.147,-54.648
>> 15497 7 meters NIMA TR8350.2 +towgs84=28,-121,-77
>> 15995 3 meters www.ancpi.ro (*)
>> +towgs84=2.329,-147.042,-92.08,-0.309,0.325,0.497,5.69
>> (*) National Agency for Cadastre and Land Registration
>>
>> The third one seems to be more accurate than the two you mentioned.
>> Of course, this may not matter if your main concern is to get ArcMap
>> and Qgis to agree.
>>
>> Actually, it is possible that the Shell datum shift is more accurate
>> than the NIMA one, since accuracies that EPSG quotes from different
>> sources are not comparable.  I think accuracies from NIMA are usually
>> one-sigma (about 67 percent confidence), but I don't know about Shell.
>> But my impression is that the ANCPI datum shift is the most accurate.
>>
>> By the way, I noticed that the code EPSG:31700 is deprecated, because
>> it used the the geodetic datum Dealul Piscului 1970, EPSG:6317.  This
>> was deprecated in September 2008 because
>>
>>   "Datum does not exist but is an alias for S-42 in Romania" (Change
>> ID 2008.011).
>>
>> And S-42 is (in this context) the same as Pulkovo 1942(58).
>> So, EPSG:31700 has been replaced by EPSG:3844, "Pulkovo 1942(58) /
>> Stereo70".
>>
>> Best regards,
>>
>> Mikael Rittri
>> Carmenta AB
>> Sweden
>> www.carmenta.com
>>
>> ________________________________
>>
>> From: proj-bounces at lists.maptools.org
>> [mailto:proj-bounces at lists.maptools.org] On Behalf Of Thibaut Gheysen
>> Sent: den 4 oktober 2010 17:24
>> To: PROJ.4 and general Projections Discussions
>> Subject: Re: [Proj] Stereo 1970 (EPSG 31700)
>>
>>
>> I checked in Arcmap, there are two "geographic coordinate system
>> transformations" for stereo 1970 to wgs84. I used the first with
>> those parameters : +towgs84=44.107,-116.147,-54.648,0,0,0,0. The
>> suggested
>> proj.4 definition correspond to the second "geographic coordinate
>> system transformations" in ArcMap.
>>
>> All is fine now.
>>
>> Thanks for your help,
>> Thibaut.
>>
>>
>> 2010/10/4 Thibaut Gheysen <gheysen.t at gmail.com>
>>
>>
>> Thanks Frank.
>> I use QGis 1.5 from osgeo4w (I don't know exactly which version of
>> Proj.4 is used).
>> I just try with your suggested definition. It's better but I always
>> have a deviation of about 5 meters.
>>
>> Thibaut.
>>
>>
>> 2010/10/4 Frank Warmerdam <warmerdam at pobox.com>
>>
>>
>> Thibaut Gheysen wrote:
>> > Hi,
>> >
>> > I have a problem in QGIS with the Stereo 1970 coordinate system
>> > (EPSG 31700).
>> > I have a shapefile in the WGS 84 coordinate system (from a GPS device).
>> > I projected this shapefile in Stereo 1970 using ArcMap.
>> > In ArcMap, the source and projected points are in the same place.
>> > In Qgis, I have a deviation of about 100 meters when displaying
>> > this 2 shapefiles and activating the "on the fly projection" (stereo.jpg).
>> > This deviation is the same that the one I obtain in ArcMap without
>> > "geographic coordinate system transformations".
>>
>>
>> Thibault,
>>
>> I'm not sure exactly what version of PROJ.4 you are using, but after
>> my "datum shift identification upgrade" the EPSG dictionary for proj
>> now has this as the suggested definition of 31700:
>>
>>
>> +proj=sterea +lat_0=46 +lon_0=25 +k=0.99975 +x_0=500000 +y_0=500000
>> +ellps=krass +towgs84=28,-121,-77,0,0,0,0 +units=m +no_defs
>>
>> Perhaps you could try with this?
>>
>> Best regards,
>> --
>> ---------------------------------------+-----------------------------
>> ---------------------------------------+-
>> ---------------------------------------+--------
>> I set the clouds in motion - turn up   | Frank Warmerdam,
>> warmerdam at pobox.com
>> light and sound - activate the windows | http://pobox.com/~warmerdam
>> <http://pobox.com/%7Ewarmerdam>
>> and watch the world go round - Rush    | Geospatial Programmer for Rent
>>
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