Transformation fro ED50 TM 0 to ED50 UTM31N

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10-08-2013 11:50 PM
RichardMyers
New Contributor
Hi,

I have recently been tasked with understanding how different pieces of software have managed to give variations on the x value when converted between the above CRS. The ED50 TM 0 CRS was customized by an oil and gas operator specifically for the North sea.

The only difference between the two projections are the central Meridian. I was wondering what sort of error I should expect transforming between the two and how ArcGIS performs the transformation?

Thanks,

Richard
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8 Replies
JimCousins
MVP Regular Contributor
I would not expect any transformation errors if the only difference is the central meridian. Differences crop up when the spheroid is changed. You are basically just shifting location, a 1 point transformation. If you wish to be doubly certain, Melita Kennedy at ESRI is the coordinate expert.
Best Regards,
Jim
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RichardMyers
New Contributor
Hi Jim,

Thanks very much for your response. That is what I thought however the difference I got in the x with one piece of software still puzzles me.

I will contact Melita just to be certain as it a transformation we need to be accurately done. Do you know how I would contact her?

Thanks,

Richard
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JimCousins
MVP Regular Contributor
I do not have a direct contact for her, but she does monitor the forums. You could also run a standard support ticket, and seek a definitive answer through that.
Best Regards,
Jim
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MelitaKennedy
Esri Notable Contributor
How big are the differences? As Jim says, I wouldn't expect any problems when converting between close central meridians. To confirm, the TM 0 is using CM=0 while 31N has a CM=3. If you're seeing issues around farther from +3, it may be possible due to the limitations in the TM inverse. What ArcGIS version are you using? At 10.1, we upgraded our TM inverse so that it would reliably 'round-trip' out to about 85 degrees from the central meridian. Before that, you could see creep at around 8-9 degrees from the central meridian at mid-latitudes, and close at higher latitudes (like the North Sea).

Melita
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RichardMyers
New Contributor
Hi Melitta,

Yes that is correct about the central Meridians and no to the distance from the central Meridian (only a couple of degrees). The issue is in fact not with ESRI software but another package that gives an error of approximately 1.9m in the x compared with ESRI and other software packages.

I was keen to understand how an error may occur with such a simple transformation. My guess is they have their parameters incorrectly set-up for TM0 in some way. I have raised this issue with the other company and they flat out deny any issue.  

Could I have the equation that ESRI uses to do the conversion?

Thanks,

Richard
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MelitaKennedy
Esri Notable Contributor
Hi Richard,

If you haven't yet, you should narrow down whether the difference is occuring in the 'inverse' or 'forward' equations (or both). That is, are the software packages showing different values when unprojecting from TM 0 to lat/lon? Generally, everyone's forward algorithms (lat/lon to TM) match well, it's the inverses that have issues.

The TM parameters are simple. I've seen differences when a repeating decimal like 33.3333333333 is cropped too far. And the spheroid/ellipsoid, International 1924, has simple values too. There are some spheroids where there's disagreement on what the parameters should be, so that's another to check, but it's pretty unlikely in this case.

I cannot post our TM algorithm, particularly for the inverse. We use an adjusted version of the US military's version. This is not the same as John Snyder's version from Map Projections: A Working Manual, but very close.

Another possibility is that the other software package has hard-coded transformation values with each coordinate reference system definition. Even though input/output are both ED50, perhaps they're using different transformations.

Can you post a test point?

I would suggest trying other software like PROJ4 or GEOTRANS. GEOTRANS is still online here.

Melita
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RichardMyers
New Contributor
Hi Melita,

I will have a look at the forward/inverse conversions. A test point is shown below (TM0);


x - 549299.1200
y - 6794068.3100


Thanks,

Richard
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MelitaKennedy
Esri Notable Contributor
Hi Richard,

In the Esri projection engine:

longitude = 0.9194693205
latitude = 61.2762659541

UTM 31N

x = 388458.9484
y = 6795497.6362

A developer I worked with suggested running the same point on a round-trip: TM0 to lat/lon to TM0.

Melita
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