<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML dir=ltr xmlns:o = "urn:schemas-microsoft-com:office:office"><HEAD><TITLE>Re: [Proj] Transformations in small areas - was Stereo 1970 (EPSG31700)</TITLE>
<META content=text/html;charset=iso-8859-1 http-equiv=Content-Type>
<META name=GENERATOR content="MSHTML 8.00.7600.16625"></HEAD>
<BODY style="PADDING-LEFT: 10px; PADDING-RIGHT: 10px; PADDING-TOP: 15px"
id=MailContainerBody leftMargin=0 topMargin=0 CanvasTabStop="true"
name="Compose message area">
<DIV><FONT face=Calibri>Thanks for the practical perspective,
Cliff.</FONT></DIV>
<DIV><FONT face=Calibri></FONT> </DIV>
<DIV><FONT face=Calibri>Processing Doppler data tied to Portuguese survey
monuments along the Angola coast in the 1980s led me to conclude that
Camacupa and the broadcast Doppler reference frame of the time were aligned
differently with respect to north. But that's a terrestrial or topographic
(mis)alignment, i.e. on the surface. Why model that with rotations about
the geocentric axes (as in Bursa-Wolfe)? Molodensky-Badekas, on the
other hand, translates the rotation center to the terrestrial surface where
it makes sense physically (enough reason) and it eliminates (almost all)
the correlations between the rotations and the geocentric translations (another
excellent reason). </FONT></DIV>
<DIV><FONT face=Calibri></FONT> </DIV>
<DIV><FONT face=Calibri>You are correct that there is a sweet spot for a
7-parameter transformation. The area has to be big enough in the DOP sense
described earlier (sufficiently reduced correlations), but not so large that the
distortions in a large local datum don't overwhelm the modeling power of a
paltry few (7) parameters, in which case grid interpolation is the right
answer. So, I agree with your conclusion ... it depends. That's not
the conventional wisdom, however!</FONT></DIV>
<DIV><FONT face=Calibri></FONT> </DIV>
<DIV><FONT face=Calibri>Regards,</FONT></DIV>
<DIV><FONT face=Calibri>Noel</FONT></DIV>
<DIV><FONT face=Calibri></FONT> </DIV>
<DIV><FONT face=Calibri>Noel Zinn, Principal, Hydrometronics
LLC<BR>+1-832-539-1472 (office), +1-281-221-0051 (cell)<BR><A
href="mailto:noel.zinn@hydrometronics.com">noel.zinn@hydrometronics.com</A>
(email)<BR><A
href="http://www.hydrometronics.com">http://www.hydrometronics.com</A>
(website)<BR></FONT></DIV>
<DIV style="FONT: 10pt Tahoma">
<DIV><BR></DIV>
<DIV style="BACKGROUND: #f5f5f5">
<DIV style="font-color: black"><B>From:</B> <A title=cjmce@lsu.edu
href="mailto:cjmce@lsu.edu">Clifford J Mugnier</A> </DIV>
<DIV><B>Sent:</B> Friday, October 08, 2010 11:44 AM</DIV>
<DIV><B>To:</B> <A title=proj@lists.maptools.org
href="mailto:proj@lists.maptools.org">PROJ.4 and general Projections
Discussions</A> </DIV>
<DIV><B>Subject:</B> Re: [Proj] Transformations in small areas - was Stereo
1970(EPSG31700)</DIV></DIV></DIV>
<DIV><BR></DIV>
<DIV dir=ltr id=idOWAReplyText22563>
<DIV dir=ltr><FONT color=#000000 size=2
face="Times New Roman"></FONT> </DIV>
<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">In my
<EM>PE&RS</EM> column on the Grids and Datums of Namibia, I quoted Professor
Charles Merry, now retired from the University of Cape Town:</FONT></DIV>
<DIV dir=ltr><FONT size=2></FONT> </DIV>
<DIV dir=ltr>
<P style="LINE-HEIGHT: 200%; MARGIN: 0in 0in 0pt" class=MsoBodyTextIndent><SPAN
style="LINE-HEIGHT: 200%; FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT
size=2>… “Turning now to Namibia, the results for this datum are summarized …
Although the rotations are not as large as those in Zimbabwe and are barely
significant, they do serve to model distortions in the geodetic network and
hence provide an improved fit between this network and the CTS.<SPAN
style="mso-spacerun: yes"> </SPAN>Again it must be emphasized that these
rotations have no physical interpretation.<SPAN style="mso-spacerun: yes">
</SPAN>As in all the countries investigated, except for South Africa, the scale
factor plays no major role.<SPAN style="mso-spacerun: yes">
</SPAN>Although the seven-parameter set does improve the fit, it is by no means
as remarkable an improvement as that experienced in Zimbabwe and it is debatable
whether the extra effort is worth it.<SPAN style="mso-spacerun: yes">
</SPAN>Consequently, we recommend that <I>(the-Ed.)</I> three-parameter
transformation shown: ΔX = +616.6 m ±1.3 m,
ΔY = +103.0 m<SPAN style="mso-spacerun: yes"> </SPAN>±1.3
m, ΔZ = –256.6 m ±1.3 m.<SPAN style="mso-spacerun: yes">
</SPAN>… As in Zimbabwe, the Namibian networks suffer from significant
distortions but in this case a seven-parameter transformation provides little
improvement over a three-parameter transformation.”</FONT> </SPAN></P>
<P style="LINE-HEIGHT: 200%; MARGIN: 0in 0in 0pt" class=MsoBodyTextIndent><SPAN
style="LINE-HEIGHT: 200%; FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT
size=2>-------------------------------------------</P>
<DIV dir=ltr><FONT color=#000000 size=2 face="Times New Roman">I have used
7-parameter transformations from time-to-time in the past several decades of my
practice, but when I have done so, I took particular notice of the distance of
the country/region of interest from the origin point of the classical
datum. When close, I use the Bursa-Wolfe 7-parameter model (such as the
distance of Trinidad & Tobago from La Canoa, Venezuela), and when a great
distance from the datum origin (such as the distance of the City of Guayaquil,
Ecuador from La Canoa, Venezuela), I have used the Molodensky model.
The differentiation allows scaling of the translation parameters. There is
zero difference in the accuracy of the resultant transformation, it just "looks"
better when perusing the relative magnitudes of the translation parameters for
other countries in the region. Who cares about the "look?" The local
government's Federal Agency with jurisdiction for official
approval.</FONT></DIV>
<DIV dir=ltr> </DIV>
<DIV dir=ltr>One can see that there are diminishing returns in blindly
increasing the area in order to justify a 7-parameter transformation.
Areas can increase so large that there are too many local distortions in varying
meridianol chains to allow a single transformation of any type other than a
"surface fit" such as implemented with a NadCon or NTv2 approach. The
generalization one can make for this is ... it depends ... :-)</DIV>
<DIV dir=ltr> </DIV>
<P style="LINE-HEIGHT: 200%; MARGIN: 0in 0in 0pt"
class=MsoBodyTextIndent></SPAN> </P></DIV></DIV></FONT>
<DIV dir=ltr id=idSignature61188>
<DIV><FONT color=#000000 size=2 face="Times New Roman"><SPAN
style="FONT-SIZE: 10pt">
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; mso-ansi-language: DE" lang=DE>Clifford J. Mugnier,
C.P., C.M.S.<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Chief of Geodesy,<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN
style="FONT-VARIANT: small-caps; FONT-SIZE: 10pt">Center for
GeoInformatics<o:p></o:p></SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Department of Civil Engineering <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Patrick F. Taylor Hall 3223A<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><B><SPAN
style="FONT-SIZE: 10pt">LOUISIANA STATE UNIVERSITY <o:p></o:p></SPAN></B></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Baton Rouge, LA<SPAN style="mso-spacerun: yes">
</SPAN>70803<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN
style="mso-spacerun: yes"> </SPAN>(225) 578-8536 [Academic]
<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Voice and Facsimile:<SPAN
style="mso-spacerun: yes"> </SPAN>(225) 578-4578 [Research]
<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Cell: (225) 238-8975 [Academic &
Research]<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Honorary Life Member of the <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Louisiana Society of Professional Surveyors
<o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Fellow Emeritus of the ASPRS <o:p></o:p></SPAN></DIV>
<DIV style="MARGIN: 0in 0in 0pt" class=MsoNormal><SPAN
style="FONT-SIZE: 10pt">Member of the Americas Petroleum Survey
Group<o:p></o:p></SPAN></DIV><BR></SPAN></FONT></DIV></DIV>
<DIV dir=ltr><BR>
<HR tabIndex=-1>
<FONT size=2 face=Tahoma><B>From:</B> proj-bounces@lists.maptools.org on behalf
of Noel Zinn (cc)<BR><B>Sent:</B> Fri 08-Oct-10 07:27<BR><B>To:</B> PROJ.4 and
general Projections Discussions<BR><B>Subject:</B> Re: [Proj] Transformations in
small areas - was Stereo 1970 (EPSG31700)<BR></FONT><BR></DIV>
<DIV>
<P><FONT size=2>Mikael,<BR><BR>> But I thought you extended the advice to
people like me, who usually have<BR>> to choose between different published
datum shifts.<BR><BR>Guilty, I confess, but there is a reason. There are
two ways to change a<BR>practice, from the top down (datum shift "derivers" in
this case) and from<BR>the bottom up (datum shift "choosers" or "consumers" in
this case). Fashion<BR>is known to work both ways. Haute Couture at
the top and "street smarts" at<BR>the bottom. Well, having observed
geodetic practice on this topic during<BR>the last decade I despair. Top
down change isn't happening. Authoritative<BR>agencies that should know
better (NATO among them) are cranking out bad<BR>7-parameter datum
transformations (e.g. for Cyprus, way too small by any<BR>standard). The
time has come for bottom-up change. Datum transformation<BR>consumers need
to be more discriminating. I was purposely being<BR>provocative.<BR><BR>As
I wrote previously, "small" can be defined quantitatively based on
the<BR>dilution of precision of the 7-parameter adjustment. Dilution of
precision<BR>(DOP) is a GPS concept, a unitless number that is a function of the
number<BR>of GPS satellites available and their distribution in space relative
to the<BR>observer (it's related to the trace of the variance-covariance
matrix<BR>mathematically). DOP is the multiplier of random observation
error into<BR>random coordinate error. It needs to be as small as
possible. Well,<BR>7-parameter derivation adjustments have a DOP,
too. I call it P7DOP. The<BR>number of survey points used
corresponds to the number of satellites and the<BR>distribution in space
corresponds to the area over which the survey points<BR>are spread. Reduce
either (number of survey points or the area) and DOP<BR>increases. Not
good. An acceptable DOP is a judgment call, but at least<BR>it's a
quantitative judgment. Australia with 80 survey points gives a DOP<BR>of
2.2. This means that if the average coordinate random error of
the<BR>survey points used is 1 meter (could be better or worse), then the
average<BR>parameter error is 2.2 meters. I judge that to be
acceptable. Germany with<BR>80 survey points gives a DOP of 10.2
(unacceptable to me). With just 20<BR>survey points the Germany DOP is 21
(even worse). That's how it works.<BR>Most surveyors and navigators want
their GPS DOPs to be under 3.<BR><BR>Your dissection of the OSGB 7-parameter
shift is a little difficult for me<BR>to follow, but creative. You begin
by noting that a 3-parameter and a<BR>7-parameter transformation ought to agree
at some point. It's interesting<BR>to note that at a single point it's
possible to derive many 3-parameter<BR>shifts, not just (dX, dY, dZ). (rX,
rY, dS), (rY, rZ, dS) and (dY, rX, rY)<BR>are among the many
possibilities. The derivation of a 7-parameter<BR>transformation at a
single point is a singularity; can't be done (but I know<BR>that you didn't mean
to imply that).<BR><BR>You then go on to detail the consequences of the 20.489
ppm dS (change in<BR>scale). This is an enormous dS by 7-parameter
standards and an omen of a<BR>questionable transformation. Multiplied by
the earth radius in Great<BR>Britain, this dS results in a height change of 130
meters. Shouldn't that<BR>have been handled by the
translations? Or is this really a scale change<BR>between OSGB and
WGS? Not likely. This dS is twice the ppm difference<BR>between the
smallest foot (Clarke's) and largest foot (British 1936) in the<BR>EPSG Unit of
Measure table. So, it's physical reality is questionable, as<BR>is further
reasoning derived from this dS frankly. We can (and should)<BR>derive
parameters with valid physical interpretations using the<BR>Molodensky-Badekas
model.<BR><BR>The UK is a tough place to think about the interplay among the 7
parameters.<BR>There are six places in the world where it's easy: the two poles
and the<BR>four intersections of the X and Y axes with the Equator. Take
one of them,<BR>0N/0E in the Gulf of Guinea, the intersection of Greenwich and
the Equator.<BR>At that point dX is indistinguishable from dS (i.e. 100%
correlated), dY is<BR>indistinguishable from rZ, dZ is indistinguishable
from rY, and rX does<BR>nothing. How large an area does it take to
reduce those correlations<BR>enough? Until you get to that size, deriving
(and using in my opinion) a<BR>7-parameter transformation is poor geodetic
practice.<BR><BR>Regards,<BR>Noel<BR><BR>Noel Zinn, Principal, Hydrometronics
LLC<BR>+1-832-539-1472 (office), +1-281-221-0051
(cell)<BR>noel.zinn@hydrometronics.com (email)<BR><A
href="http://www.hydrometronics.com/">http://www.hydrometronics.com</A>
(website)<BR><BR>--------------------------------------------------<BR>From:
"Mikael Rittri" <Mikael.Rittri@carmenta.com><BR>Sent: Friday, October 08,
2010 4:36 AM<BR>To: "PROJ.4 and general Projections Discussions"
<proj@lists.maptools.org><BR>Subject: Re: [Proj] Transformations in small
areas - was Stereo 1970 (EPSG<BR>31700)<BR><BR>> Hello
Noel,<BR>><BR>>> I appreciate the exchange.<BR>><BR>> So do I.
What you say is quite interesting.<BR>><BR>>> ... my advice to use
3-parameter translations in a small area ...<BR>><BR>> Okay, I can accept
this as an advice to people who derive new<BR>> datum shifts, like yourself.
As long as you can estimate the<BR>> error, and the error is acceptable, why
not? But I thought you<BR>> extended the advice to people like me, who
usually have to choose<BR>> between different published datum shifts. I
agree that a 7-parameter<BR>> datum shift is not necessarily better than a
3-parameter one, and<BR>> the accuracies quoted by EPSG are often hard or
impossible to compare.<BR>> But I don't see that I should avoid using a
published datum shift,<BR>> just because it uses 7 parameters in a "small"
area.<BR>><BR>>> 7-parameter derivations in small frontiers are ill
conditioned (my<BR>>> thesis)<BR>>> ...<BR>>> because
7-parameter transformations are no more "accurate" in a small<BR>>> area
than a 3-parameter translation derived from the same data set.<BR>><BR>> I
am sure you are right, for a given value of "small".<BR>>
What surprised me is when you said that Romania and even Germany<BR>> are
small in this sense. Romania is about 700 km in diameter,<BR>> Germany
is 800 km, while Australia (which you said is large enough)<BR>> is 3800 km.
So you are saying that the threshold for "smallness" is<BR>> somewhere
between 800 and 3800 km.<BR>> I would have expected the threshold
to be more like 100 km.<BR>><BR>> My example of the 3-parameter transform
for OSGB 1936 may, as you<BR>> say, not be the best possible 3-parameter
transform for this datum.<BR>><BR>>> Tfm Code 1039 provides us the
opportunity to test my assertion...<BR>><BR>> That would be quite
interesting, but a bit of work as you say.<BR>> But I think I can predict
roughly how good the best 3-parameter<BR>> transformation could
be.<BR>> The idea is that a 3-parameter and a 7-parameter
transform<BR>> for the same area ought to agree exactly on at least one
point.<BR>> Around this fixed point, the advantage of the 7-parameter
transform<BR>> is that it can supply a rotation and a scale change.
Well, three<BR>> rotations in 3D space, but they should correspond to a
single<BR>> rotation around an oblique axis through the fixed point.<BR>>
I think this single rotation would be about as large as the<BR>> three basic
rotations, but I could be wrong. Anyway, in the<BR>> OSGB example, I
think the main improvement of the 7-parameter<BR>> transform comes from the
scale change, not the rotations (since<BR>> they are fairly small), and the
scale change is -20.489 ppm.<BR>> If the best possible 3-parameter transform
for OSGB agrees with<BR>> the given 7-parameter transform in the middle of
Great Britain,<BR>> then the maximal radius is about 540 km, and 540 km *
20.489 ppm =<BR>> = 11 meters.<BR>> So, the best
possible 3-parameter transform for OSGB has to<BR>> deviate from the given
7-parameter transform by up to 11 meters,<BR>> (either at Land's End in the
southwest or the Orkney Islands in<BR>> the north). Since the
7-parameter transform is claimed to be at<BR>> most 5 meters wrong, this
means that the best 3-parameter transform<BR>> is worse. (In the best
possible case, the 5-meter error would<BR>> occur in both Land's End and
Orkney, in a direction that makes<BR>> the 3-parameter transform wrong by
only 6 meters. But that's<BR>> optimistic.)<BR>><BR>> From this kind of
argument, I think one could estimate the<BR>> threshold of "smallness" from
the rotations and scale change<BR>> of a 7-parameter transformation, together
with its accuracy.<BR>><BR>> A more general "smallness" threshold could
perhaps be computed<BR>> from the average rotations and scale changes among
many typical<BR>> 7-parameter transforms (and their
accuracies).<BR>><BR>> Best regards,<BR>> Mikael Rittri<BR>>
Carmenta AB<BR>> Sweden<BR>> www.carmenta.com<BR>><BR>>
-----Original Message-----<BR>> From: proj-bounces@lists.maptools.org<BR>>
[<A
href="mailto:proj-bounces@lists.maptools.org">mailto:proj-bounces@lists.maptools.org</A>]
On Behalf Of Noel Zinn (cc)<BR>> Sent: den 8 oktober 2010 05:27<BR>> To:
PROJ.4 and general Projections Discussions<BR>> Subject: [Proj]
Transformations in small areas - was Stereo 1970 (EPSG<BR>>
31700)<BR>><BR>> Thanks, Mikael. I appreciate the
exchange.<BR>><BR>> [Complete message at<BR>> <A
href="http://lists.maptools.org/pipermail/proj/2010-October/005429.html">http://lists.maptools.org/pipermail/proj/2010-October/005429.html</A>
]<BR>> _______________________________________________<BR>> Proj mailing
list<BR>> Proj@lists.maptools.org<BR>> <A
href="http://lists.maptools.org/mailman/listinfo/proj">http://lists.maptools.org/mailman/listinfo/proj</A><BR>><BR><BR>_______________________________________________<BR>Proj
mailing list<BR>Proj@lists.maptools.org<BR><A
href="http://lists.maptools.org/mailman/listinfo/proj">http://lists.maptools.org/mailman/listinfo/proj</A><BR></FONT></P></DIV>
<P>
<HR>
<P></P>_______________________________________________<BR>Proj mailing
list<BR>Proj@lists.maptools.org<BR>http://lists.maptools.org/mailman/listinfo/proj</BODY></HTML>