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Coordinates and Lat/Long in different Projections

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#1
Mark Boucher

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I haven't had to deal with projection until recently.

We sent a spreadsheet with decimal Lat/Long data. The receiver used this and sent back a spreadsheet with their data. Their Lat/Long values were much different. I supected a projections issues and began to dig in and learn more. I converted both to points in ArcMap and there were big differences (hundreds of feet in some cases). I started by trying to project my lat/long points to another geographic system to come close to theirs. (I'm haven't gotten an email response from them yet).

Using the "Calculate Geometry..." option from the right click menu in the attribute table, I can calculat the X or Y using the data frame or the data set coordinate system. Nice!

When I change the data frame projection, and recalculate the X Y I don't always get different results. For example, WGS72 and WGS84 give me exactly the same Lat/Long. Some projections drop the decimal places in the decimal degrees, some drop the decimals in the results in feet.

Any info sources or websites out there to understand the limits on these projections and why the decimal places are sometimes dropped?

Thanks in advance.

Edited by Mark Boucher, 26 August 2010 - 07:45 PM.

Mark
"We may not be big, but we're slow."

#2
Nick H

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... there were big differences (hundreds of feet in some cases).


I think that towards the west coast the difference between WGS84 and NAD27 is in this order of magnitude. Perhaps this might be the problem?

Regards, N.
Caversham, Reading, England.

#3
ProMapper

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I haven't had to deal with projection until recently.

We sent a spreadsheet with decimal Lat/Long data. The receiver used this and sent back a spreadsheet with their data. Their Lat/Long values were much different. I supected a projections issues and began to dig in and learn more. I converted both to points in ArcMap and there were big differences (hundreds of feet in some cases). I started by trying to project my lat/long points to another geographic system to come close to theirs. (I'm haven't gotten an email response from them yet).

Using the "Calculate Geometry..." option from the right click menu in the attribute table, I can calculat the X or Y using the data frame or the data set coordinate system. Nice!

When I change the data frame projection, and recalculate the X Y I don't always get different results. For example, WGS72 and WGS84 give me exactly the same Lat/Long. Some projections drop the decimal places in the decimal degrees, some drop the decimals in the results in feet.

Any info sources or websites out there to understand the limits on these projections and why the decimal places are sometimes dropped?

Thanks in advance.

Hi Mark

Well, any map is made on minimum two mathematical approximations, and they are the SPHERICAL MODEL or Datum and PROJECTION. Now WGS84, WGS72, NAD 87, NAD 83 are all spherical models. Now a map is a representation of somewhat spherical earth on plain paper or just two dimensions, so a projection like UTM, LCC, Polyconic, Plate Caree is needed to flatten it out to certain approximations.

So if the spherical model remains the same then theoretically speaking, a change in projection say from UTM to LCC or reverse, will not change the speherical co-ordinates (lat/long) of that detail. If any change happens then it is due to the approximations adopted in calculations and generally it will be miniscule unless someone has tweaked with the precision settings of the software.

Now the other scenario, if the spherical model is changed, that is WGS84 to NAD83 or some other local model of that country, then the lat long values will change to the extent of shift between the two spherical models. The shifts are given in seven parameters or three parameters for a pair of spherical models, say WGS84 to NAD83 or WGS84 to NAD27 and so on. The seven parameters are generally used in Bursa Wolfe datum transformation and the three parameters can also get you close but not very accurate with Molodensky transformation. Many software can do the transformation on the fly without you getting into feeding the parameters but you must know the datum the original data is in and which datum you want it to be transformed into. If you go wrong here, you can get very wrong results.

So now you need to know which spherical model your client is using and then you can do the datum transform on the supplied co-ords and change it to your system, say from NAD27 to WGS84.

I hope I have been able to give a satisfactory and lucid enough answer.

Anu
http://www.mapsandlocations.com

#4
Holograph

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If the lat/lon coordinates are in the U.S. the main culprit may be what Nick and Anu have mentioned - it may be a difference between NAD27 and NAD83 datum, which are the two standards that have been used in the U.S. For instance, if some of the coordinates were obtained from USGS quads, many of those quads, especially the digital ones, are still in the NAD27 datum. Other more recent digital datasets would normally be in the NAD83 datum or perhaps WGS84 if the coordinates were obtained from GPS.

You don't mention any specific points, so it is hard to say what the other possibilities might be. For instance, if someone took your lat/lon coordinates and projected them into X-Y (a.k.a easting and northing) map coordinates for whatever purposes, then projected them back to lat/lon before returning the results to you, and in the process used a different projection system or datum, then the coordinates would not return to the same values.

In a very simplified nutshell, the datum tells you what the latitude and longitude of a given point is and what direction is considered true north. Different datums can differ for historical or technical reasons. For instance, the latitude and longitude of the tallest radio mast on Telegraph Hill in Tuolomne County, California is:

N 38° 01' 52.358", W 120° 21' 05.812" in the NAD83 datum.
N 38° 01' 52.631", W 120° 21' 02.121" in the NAD27 datum.
N 38° 01' 52.337, W 120° 21' 05.769" in the WGS84 datum (i.e GPS).

Obviously the mast hasn't moved, the only thing that is different is the conventions that were used to decide what the coordinates are. If you calculate the difference between the NAD83 (which are the current official coordinates of the U.S.) and other systems you find that the NAD27 coordinates appear to be "off" by 90.4 meters (297 feet)., and the WGS84 coordinates are "off" by 1.2 meters (4 feet).

As long as all the coordinates are stated in the same datum, you wouldn't see any large discrepancies, it is only when one set of coordinates are in one datum, and another set of coordinates are in another datum that you find discrepancies.

If you want a short, informal history of datums in the U.S. you can see this article on datums.

#5
Mark Boucher

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Thanks Nick, Anu, and Holograph for your insights. I'll work with this and see what I can figure out.
Mark
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