Ask Norm - April 1999

Question 1: Errors in the Molodensky "freebie"?
Question 2: Can anyone define the "Denominator of Flattening Ratio"?

Q1.  I suspect that there are some errors in the Molodensky "freebie".  If I enter the following parameters: (reference point of the geodetic network of the Netherlands)

Can you explain the difference? 

Casual Cartographer Readers Respond

-Andre in The Netherlands.
A. It was a discussion with a client that originally sparked the idea of
the 'Roll Your Own' Molodensky.  It seemed pretty simple since the "primary" effect of the Molodensky is to essentially translate the XYZ geocentric coordinates of the two datums involved.

After developing the program, and doing tests similar to the one you have done, I found that my originaly assumption was not true.  There is a lot more to the Molodensky than the geocentric origin translation. In trying to resolve this issue, I could not find anything about, for example, who Molodensky was or exactly how one would go about computing real Molodensky parameters.

What I did find is that what I had computed was essentially the parameters for what is correctly referred to as the Three Parameter Transformation.  Additional testing found that the numbers provided by this technique produced reasonably good results in small regions, and that the results were indeed substantially better than nothing.  Thus, rather than scrap the whole idea, we placed a disclaimer in the README.TXT file, the Help file, and on our Web page indicating that what the program really computed was the Three Parameter Transformation parameters; and that these were approximations to the actual Molodensky parameters.  However, the approximation seemed to work reasonably well in the absence of anything else.

Since then, I have received information from a highly regarded source which instructed me that the Molodensky is produced by calculations similar to those done by our "freebie" but there are several differences.  Principal among the several differences is that the translation portion of the calculation is done at the "primary" point of the datum.  Since this implies that one knows what the primary point of the datum is, the true Molodensky technique is inappropriate for our purpose.

That is, the primary purpose of the "Roll Your Own" Molodensky program was simply to develop a datum transformation for a particular data set for a particular region where all one knew was the "old" lat/long for a point or two, and a new (probably GPS'ed) lat/long for the same point. In this situation, knowning the "primary" point is out of the question.

So, I think it was a bad decision on our part to use the term Molodensky in the title of our little freebie.  Technically, it probably should have been called "Roll Your Own Three Parameter Transformation".  But then again, I'm not sure that many people would have had the faintst clue as to what that would be.

Thank you for reading our newsletter.  As I am a 'Casual Cartographer' I don't pretend to know all the answers.  My only claim is that I've been a Casual Cartographer longer than a lot of other folks.  So, I greatly appreciate your input; your keeping me honest.  Especially about such things as Molodensky which not often used with regard to US geography.

Norm Olsen

Casual Cartographer Readers Respond:

> Hello Norm,
>
> I saw your reply to the "roll your own Molodensky". (see below)
>
> Andre found quite large differences; however I believe this is mainly
> caused by the WGS84 coordinate which he uses. To my opinion the WGS84
> coordinate of the point of origin should be
>
> 52 09 18.6199
> 05 23 13.9324
>
> I used the TRAFO program of the Dutch University of Technology to calculate
> this.
>
> Furthermore, the values which are given by Andre are simply the 3
> translations taken from a seven parameter transformation. (so valid only if
> using together with three non-zero rotations and a scale factor .)
>
> The Molodensky parameters for Holland are:
>
> -593.16
> -26.15
> -478.54
>
> (WGS to Bessel)
>
> I found differences in the calculated parameters of the order of 10 meters
> with the freebee which I put on the fact that you presume the height to be
> 0 in both systems. This introduces a 3D error of 40 meters for the Dutch
> system, for instance.
>
> If ever you produce a revised version which allow an ellipsoid height to be
> input, I would be very interested! Yes, check it out. We updated it August 1999.
>
> best regards,
>
> Paul Koren
> Sokkia BV
> Almere
> The Netherlands

Q2. Can anyone define the "Denominator of Flattening Ratio"? [posted on the gistrans-l mailing list]

Susan Muleme (susan@avenza.com) Cartographic and Software Support Technician Avenza Software Inc.Visit: www.avenza.com 905.639.3330 x26 or 905.639.2329

*****Developers of MAPublisher & pdfPLUS*****
               Changing the way maps are made!

A. Hello Susan . . .

I'm new to the [gistrans-l] list. Mentor Software distributes coordinate conversion software and provides same for some of the biggies in the business.

It appears that this is what many folks call the flattening.  Actually, the flattening, f, is a small number, i.e. in the range of 0.003.  What most folks call the flattening is actually one over f, i.e. the reciprocal of the flattening.  Thus, the number you are working with is
actually the reciprocal of the flattening.  It appears that "Denominator of the Flattening Ratio" is new and interesting term for "Reciprocal of the Flattening".

294.98 is the flattening (actually the reciprocal of the flattening) for the Clarke 1866 ellipsoid.  I do not have any experience with MAPublisher, so I can't comment on it or why it insists on choosing Merit over Clarke 1866.

The vectors are in Lambert (we are still waiting to find out azimuthal, conformal, conic etc.).

If you've been given two standard parallels, you are dealing with a coniche parallels are specified makes no difference to the mathemagics.  Thus, while m projection.  If the term Lambert has also been given, you are dealing with the Lambert Conformal Conic, two standard parallel variation.  Note, that the order in which tany folks refer to a Northern Parallel and a Southern Parallel, others will refer to Standard Parallel 1 and Standard Parallel 2.  The projection code simply computes a rather strange equivalent to the average of the two (called the cone constant) and it matters not in which order the two are given. These are the specs for the vector image. The std. parallels are both to the south of the central parallel.

The Origin Latitude of the Lambert Conformal Conic, two standard parallel variation is a completely separate issue.  It specifies the latitude which is to produce a zero Y coordinate (before the application of the false northing). Since most geographic coordinates are defined such that all coordinates in the useful range are positive, the Origin Latitude is usually specified to be a bit south of the southern extent
of the map.  This choice is rather arbitrary as it has no affect on the degree or distribution of projection distortion in the map.

The fact that the Origin Latitude is north of the two standard parallels is probably related to the fact that in raster images, Y increases as you go down, or to the south.  Thus, perhaps, the origin latitude to the north of the standard parallels is to compensate for this.

Hope this helps.

Norm

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