# Given long, lat, x and y, how do I find the projection?

I am using an app called farsite that outputs shapefiles that show how forest fires will grow. I am getting output in coordinates as X and Y values rather than (lon,lat) and am looking for a conversion routine to (lon, lat). If I knew the name of the coordinate system it might help my search, but I do not even know that. I have gone to google maps and have looked at the expected (lon, lat) so I have a rough translation equation, but I am sure that someone else has a better one (mine is linear with a scale and offset, which I fear is too simplistic)

Here is a sample point (X, Y): 162206 386691 (Lon,Lat): -115.326662 47.582952

Can someone please steer me to a reference or conversion routine?

Thanks in Advance - Steve Tufty

• Maybe the question could be stated as: Given unprojected and projected values for a set of points, is there a way I can find the projection that is being used? – Kirk Kuykendall Feb 1 '11 at 22:29
• what projection is your input data in? I'll bet that it doesn't reproject the results. – Ian Turton Feb 1 '11 at 22:44
• Thanks for your feedback - The input data is in the same format, as a matter of fact, I mapped the 3 input shape files and the output files and they align just fine. The issue is that boss wants it on Bing maps, which wants (lon, lat) – user1843 Feb 1 '11 at 23:55

Looks like Thompson Falls, MT. The current state plane coordinate system (1983) for Montana projects (-115.326662 47.582952) to (162339, 386636), which is (133, -55) meters off: not awful, but not good, either. You could be using a custom datum or maybe your site coordinates are actually off by that much. It's unlikely any other standard coordinate system could produce coordinates in this range.

If this looks right, any software that unprojects state plane coordinates will do the job. There's an online Montana government applet for one-off conversions. Shapefiles are best processed with GIS software.

• Yes, whuber, it is Thompson Falls. I have some 7000 points that I need to run through this converter so I can map them on Bing maps. Thank you for your pointer to the Montana Site. Now at least I know what to search for. – user1843 Feb 1 '11 at 23:56
• some possible reasons for the 133, -55 offset would be the dif between nad27 and nad83 on the projected side (original data if I understand correctly), and WGS84, WGS83 on the geographic side. BTW the thing that keeps me straight is to remember lat,lon is an angular measurement from GMT and the equator. So no linear measurement (of any dimension) will be exactly correct without performing a transformation. – Brad Nesom Feb 3 '11 at 7:26
• @Brad That's a good guess. According to NADCON (ngs.noaa.gov/cgi-bin/nadcon.prl ), the datum shift at this location is (74, -7), only half of what is needed. I considered this anyway, but doubted someone would be using the MT 83 SP coordinates with the 1927 datum. I think it more likely that the determination of the (lat, lon) corresponding to the point was "eyeballed" with low precision. – whuber Feb 3 '11 at 14:18
• I would agree whuber – Brad Nesom Feb 3 '11 at 18:58

I think this is NAD83 State Plane Montana (meters). As far as I can tell without actually installing and using it, Farsite assumes input data is in the same coordinate system already and thus, any output data will be using the same coordinate system.

One way to figure out an unknown coordinate system is to take known values for the same area--like you have lat/lon--and project them into coordinate systems that you know are used in that area. In the US, that would be the various State Plane or UTM zones, occasionally a statewide system. If you get values that match your data, you've probably discovered the coordinate system.

• Should have answered more quickly! – mkennedy Feb 1 '11 at 23:22
• Thanks mkennedy. The trick with this (as I know now) is that there is an implicit assumption that the origins are (0,0) and that they line up if the (ax+b) linear transformations are to work. I do not think this is true when going to (lon,lat) from the NAD83 State Plane Montana. It is closewr to (a(x-c) + b) – user1843 Feb 2 '11 at 0:03
• @Steve To stave off possible confusion, I want to observe that (a) the projection from (lat, lon) to SPC is nonlinear; (b) the projection (in most coordinate systems) is typically followed by an affine transformation of the form you specify; and (c) surveyors often privately apply another affine transformation to create a "local" coordinate system. There is no "implicit assumption" about the origin; indeed, there is usually an explicit offset (called "false easting" and "false northing"), which is the case for the MT SPCS. Melita is correct (as always); she describes the method I used. – whuber Feb 2 '11 at 16:31

If I interpret Farsite Help correctly, it doesn't reproject your data. So you just need to check which coordinate system your input data is in.

• Thanks underdark, however I have some 20 input files (moisture index, fuel, topo, etc) which all are (seemingly) in this same original coordinate system. I can apparently convert sooner than later, but I still have to convert to (Lon, Lat). – user1843 Feb 2 '11 at 0:00

You might check to see if there's an on-line version of Blue Marble's Projection Recovery Tool.

The Projection Recovery Tool automates the process of determining the original projection information associated with mapping data when that information is lost and no longer associated with the data.