Local Coordinates

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09-21-2011 08:56 AM
ScottHolbird
New Contributor
I am trying to create a custom transformation to convert UTM Z13 coordinates to a local grid. I have created  a .gdf file with the correct transformation parameters and have it stored in the correct location. When I use the 'Project' tool I am not given access to the 'Geographic Transformation' method drop down box. I am assuming this is where the .gdf is accessed to perform the tranformation. Any ideas on this?

Scott
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7 Replies
NobbirAhmed
Esri Regular Contributor
Could you elaborate little more?

Your OS, ArcGIS version, coordinate system of the local grid, and if possible the transformation parameters.
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ScottHolbird
New Contributor
Operating system is Windows 7 Pro and the ArcGIS version is 10.0
I am trying to create a coordinate transformation from UTM Z13 to a Local Grid.
I have established the local grid system with the following:
Projection: Transverse Mercator
False Easting: 500,000
False Northing: 0
Central Meridian: -105
Scale Factor: 0.9996000
Lat. of origin: 0
Linear unit: meters
GCS: WGS 1984
Datum: WGS 1984
Spheroid: WGS 1984

I am using coordinates in UTM Z13 with the following:
Projection: Transverse Mercator
False Easting: 500,000
False Northing: 0
Central Meridian: -105
Scale Factor: 0.9996000
Lat. of origin: 0
Linear unit: meters
GCS: NAD 83
Datum: NAD 83
Spheroid: GRS 80

I have calculated the parameters from known points in both coordinate systems to be:
East translation: -495745.892m
North translation: -5717240.125m
Z translation: None
X, Y rotation: 0 (none) both systems have the identical north orientation
Scale factor: 1.000477 Local grid is slightly larger than the UTM

I have managed to get the .gtf file to work in 'project' but it appears the new translated points are only about half way to where they should be (about half of the East and West translation). I have done this by using the 'position vector' method. I also do not know what value to enter in the 'scale differance (ppm)'.

Any help you can offer Nobbir would be appreciated.

Scott
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MelitaKennedy
Esri Notable Contributor
Hi Scott,

Geographic transformations are designed to convert between two geographic coordinate systems only, not between two projected coordinate systems. The X/Y/Z axis translations are offsets in the 3D geocentric frame (X and Y are in the equator's plane, Z is polar axis), which is why the results aren't correct.

Instead, I think you should try to make a custom projected coordinate system for your local grid data. Based on what you've posted, it looks very possible. You can't use the standard UTM definition with it, because the local grid is definitely not in UTM.

The easiest way to do it is to remove any existing coordinate system from the local grid data--"clear" it using the data's property page in ArcCatalog.

Add it and the reference data to ArcMap.

Set the data frame's coordinate system to your calculated parameters. You may need to adjust the parameter values, but ArcMap will convert the reference data to the new system automatically and you'll be able to immediately check the fit. Use the UTM zone definition as the basis, but change these parameters:

false easting: 4254.108m
false northing: -5717240.125m
Scale factor: 1.0000768092 (0.9996 * 1.000477)
other parameters stay the same

You probably also need to multiply the false easting/northing values by 1.000477, but try this first and see what it looks like.

Hope this helps,
Melita
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ScottHolbird
New Contributor
Melita,
Your solution did help somewhat but also posed a few more questions. Following the steps outlined I did get the points to almost align. Without adjusting the False Easting/Norhting the UTM points are all West of there intended point by a consistant 238.500m. Adjusting the Easting only, points are out 236.471. by adjusting both the East/North the UTM points are out 2700m almost due North.

My second question is that I would like to convert all of our UTM datasets into the Local Grid with a custom projection, the help menus are a little vague on how this is done, any suggestions.

Thank You so much
Scott H
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MelitaKennedy
Esri Notable Contributor
Hi Scott,

If you're seeing direct east-west or north-south offsets between the (undefined) local grid data and UTM-based data, you should be able to adjust the false easting and/or northing parameter values to get rid of the offsets. That is, adjust the data frame's custom projected coordinate system. That values I recommended were based on your calculations, I've found that often these values need modified to get the best fit.

Once you have the best-fit coordinate system set in the data frame, make sure it has a easily-identifiable name and save it to Favorites. Here's awkward part. Because ArcGIS doesn't know what folders it can write to, it saves a .prj file of the Favorite in:

XP: C:\Documents and Settings\your_login\Application Data\ESRI\Desktop10.0\ArcMap\Coordinate Systems
Win7: C:\Users\your_login\AppData\roaming or local\ESRI\Desktop10.0\ArcMap\Coordinate Systems

Find the file and copy it to your ArcGIS home, Coordinate Systems, Projected Coordinate Systems folder. Now you can access this definition with Define Projection Tool or the Project Tool, for instance.

If you can't get a good fit using a custom projected coordinate system, you might have to use the spatial adjustment toolbar to 'force' the UTM data to local grid.

Melita
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markdenil
Regular Contributor II
Am I missing something here?
are some posts missing from the tread?

The only difference I can see between the two systems:
local grid system . . . . . . . . UTM Z13
------------ . . . . . . . . . . . --------
Transverse Mercator . . . . . .Transverse Mercator . . Projection
500,000 . . . . . . . . . . . . . . 500,000 . . . . . . . . . . .False Easting
0 . . . . . . . . . . . . . . . . . . . 0 . . . . . . . . . . . . . . .False Northing:
-105 . . . . . . . . . . . . . . . . -105 . . . . . . . . . . . . . .Central Meridian
0.9996000 . . . . . . . . . . . . . 0.9996000 . . . . . . . . . .Scale Factor
0 . . . . . . . . . . . . . . . . . . .0 . . . . . . . . . . . . . . . .Lat. of origin
meters . . . . . . . . . . . . . . .meters . . . . . . . . . . . . Linear unit
WGS 1984 . . . . . . . . . . . . .NAD 83 . . . . . . . . . . . . GCS
WGS 1984 . . . . . . . . . . . . .NAD 83 . . . . . . . . . . . .Datum
WGS 1984 . . . . . . . . . . . . .GRS 80 . . . . . . . . . . . Spheroid

.. is the datum (et.al.)

Both NAD83 and WGS84 versions of UTM  are supported in Arc...
and how is the local grid "..the local grid is definitely not in UTM"?? It looks like a UTM to me.


Scott's 'transformation' values are clearly just a misunderstanding about what the transformation does, but for the life of me I can't see where Melitia's suggeted parameters come from either.

Why a false easting of 4254.108m?        the original post gave 500,000
why a false northing of -5717240.125m? the posting gave 0
why a Scale factor of 1.0000768092?
  yes, 0.9996 * 1.000477 = 1.0000768092, but the target sf was given as 0.9996000

Mark Denil
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ScottHolbird
New Contributor
Hi Melita,
I did adjust the false easting by the amount the points were off from target points and had a very good fit. Saved .prj file for future use. Used new .prj file to assess 7 other points I had with coordinates in both systems. Once completed I calculated geometry of points and found only 3 points were out by 1 mm. Thanks for your help.

Hi Mark,
Perhaps some confusion on the data I posted. The first post was under the assumption of doing a 'Custom Coordinate Transformation' where I had assigned a projection and datum to the local grid. Where in fact this was inncorrect. The following is what I have.

Local Grid - No Projection or Datum
UTM Grid - False Easting 500,000
             - False Northing 0
             - CM -105
             - SF: 0.9996000
             - Lat of Origin: 0
             - Linear Unit: Meters
             - GCS: NAD 83
             - Datum: NAD 83
             - Spheroid: GRS 80

From the coordinate pairs I have (3) I calculated the tranformation parameters using a two-dimensional conformal transformation, and they are:
East Translation: -495745.892m
North Translation: -5717240.125m
Z Translation: None (no elevations for either points)
X and Y rotation: None (Both grids have same north orientation)
Scale Factor: 1.000477

What Melita requested I do was to apply the transformation parameters to a custom projection. First the false eastings and northings had to be adjusted so each grid had coincidental grid origin. Since the false easting of the UTM was 500,000 the East Translation needs to be adjusted, thus     500,000 - 495,745.892 = 4254.108. Melita also suggested I multiply the false east/north by the scale factor, in this case it is not necessary,I took care of this in my Conformal transformation parameter calculations.

I am not sure if this will help you any. It did solve my problem with this particular situation but I am faced with many other transformations that have a rotation. I had originally intended to do the transformation with Arc 'Create Custom Geographic Transformation'. The problem with this is that you need a GRS in the Local grid wich I do not have and I also need the transformation parameters for the rotation. Arc does not seem to offer any help on this.

I hope this clears up some issue.
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