[Proj] proj4 definition for transverse mercator projection from RegCM3 model for North America

[Hailey Eckstrand]

Hello all,
I am trying to create the proj4 string for a netcdf file with the following
coordinate information:

variables:
        char Transverse_Mercator ;
                Transverse_Mercator:grid_mapping_name =
"transverse_mercator" ;
                Transverse_Mercator:longitude_of_central_meridian = -97. ;
                Transverse_Mercator:latitude_of_projection_origin = 47.5 ;
                Transverse_Mercator:scale_factor_at_central_meridian = 1. ;
                Transverse_Mercator:false_easting = 3925000. ;
                Transverse_Mercator:false_northing = 3175000. ;
        double lat(yc, xc) ;
                lat:units = "degrees_north" ;
                lat:long_name = "latitude" ;
                lat:standard_name = "latitude" ;
                lat:axis = "Y" ;
        double lon(yc, xc) ;
                lon:units = "degrees_east" ;
                lon:long_name = "longitude" ;
                lon:standard_name = "longitude" ;
                lon:axis = "X" ;
        double xc(xc) ;
                xc:long_name = "x-coordinate in Cartesian system" ;
                xc:standard_name = "projection_x_coordinate" ;
                xc:units = "m" ;
                xc:axis = "X" ;
        double yc(yc) ;
                yc:long_name = "y-coordinate in Cartesian system" ;
                yc:standard_name = "projection_y_coordinate" ;
                yc:units = "m" ;
                yc:axis = "Y" ;


The file gives the coordinates in their native projected coordinates as well
as the lat & lon coordinates.

>From this information, I created the following proj4 string:
+proj=tmerc +lat_0=47.5 +y_0=3175000.0 +x_0=3925000.0 +lon_0=-97.0 +k_0=1.0
+units=m +ellps=sphere

(The sphere ellipsoid is a guess as they didn't provide the geographic
coordinate system.)
So when I test out this proj4 string, these are the results I get:

proj -f "%f" +proj=tmerc +lat_0=47.5 +y_0=3175000.0 +x_0=3925000.0
+lon_0=-97.0 +k_0=1.0 +units=m +ellps=sphere
in> -126.0869 19.61229
in> -125.6792 19.77242
in> -125.2703 19.93048

out> 773317.154904   359897.643377
out> 824089.485710   370794.986195
out> 874706.342446   381466.440468

the projection coordinates should be:
600000   600000
650000   600000
700000   600000

and then the opposite transformation:

invproj -f "%f" +proj=tmerc +lat_0=47.5 +y_0=3175000.0 +x_0=3925000.0
+lon_0=263 +k_0=1.0 +ellps=sphere
in>  600000 600000
in>  650000 600000
in>  700000 600000

out>  -127.929260     -21.210147
out>  -127.514502     -21.293413
out>  -127.097731     -21.375966

and the coordinates should be:
-126.0869 19.61229
-125.6792 19.77242
-125.2703 19.93048

The longitude are at least in the ballpark, but the latitudes are completely
off.

If it helps, this data has been downloaded from NARCCAP, and it is the
RegCM3 model.
Any help would really be appreciated.
Thanks in advance,
Hailey
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