For each of the map projections, the minimum and maximum values of the x (easting) and y (northing) coordinates on the boundaries of the longitude/latitude box were determined, and expanded outwards to the nearest multiple of 1000 meters (UTM) or 10,000 meters (Albers) or the nearest odd multiple of 500 meters (Lambert).
The corners and dimensions of the boxes are as follows:
Dimensions Min X Max X Max Y Min Y E-W N-S Long/Lat(deg) -100.0 -95.0 38.5 33.0 5.0 5.5 (arcsec) -360000 -342000 138600 118800 18000 19800 Lambert Azimuth -500 487500 -708500 -1332500 488000 624000 Albers -380000 100000 1740000 1100000 480000 640000 UTM 14 406000 874000 4269000 3651000 468000 618000The corners specified above should be used with GIS software packages such as Arc/Info. For gridded data used with image processing packages such as LAS or ERDAS, the coordinates of the upper left corner of the image specified by the LAS .ddr file or in the ERDAS header record refer to the center of the upper left pixel; i.e., they are offset by one-half pixel from the corner of the bounding rectangle (the necessary adjustments are made automatically by Arc routines such as IMAGEGRID and GRIDIMAGE). To overlay data at different resolutions, therefore, the LAS/ERDAS upper left corner easting or longitude should be increased by one-half the grid cell size, and the northing or latitude decreased by one-half the grid cell size.
The USGS has published tables of differences between NAD27 and NAD83 at points on a regular grid, from which the difference for any given (longitude, latitude) coordinate can be computed by interpolation. This has been incorporated into the PROJ.4 nad2nad program by Gerry Evenden at the USGS (available by anonymous ftp from kai.er.usgs.gov). The Data Users Guide for the USGS DEMs includes equations (Appendix H) relating coordinates in the GRS80 (WGS84) spheroid to WGS72. Based on my understanding of this information (Warning -- I may have misunderstood it), I compiled a table of offsets from NAD27 to NAD83 and WGS72 at the four corners of the SGPE region. Each value below represents the change in longitude or latitude of the specified SGPE corner point when going from NAD27 to NAD83 or GRS80; the equivalent distance in meters is also given.
Corner: NW NE SE SW GRS80 longitude -1.46" -0.88" -0.77" -1.36" (-35 m) (-21 m) (-20 m) (-35 m) latitude +0.06" +0.05" +0.45" +0.38" (+2 m) (+2 m) (+14 m) (+12 m) WGS72 longitude -2.01" -1.43" -1.33" -1.91" (-49 m) (-35 m) (-34 m) (-50 m) latitude -0.06" -0.06" +0.32" +0.26" (-2 m) (-2 m) (+10 m) (+8 m)Note that, because the radii and eccentricities of the spheroids are different, the differences between eastings and northings for a given map projection will include not only the offsets given above, but also the difference in arc lengths associated with the angular displacement between a given point and the coordinate origin for the projection. For example, at mid latitudes, the UTM northing computed from the origin (at the Equator) using the spheroid radii for NAD83 is on the order of 200 meters greater than for NAD27.
Projection units: meters Spheroid: GRS80/WGS84 Central longitude: -99 deg (W) False easting: 500,000 meters False northing: 0NOTE that this projection uses the GRS80 spheroid (corresponding to the NAD83 datum). As discussed above, a point having a given longitude and latitude in the NAD27 datum, which uses the Clarke 1866 spheroid (also used for the Albers Equal Area projection, will not be at exactly the same location as a point having the same longitude and latitude relative to NAD83. For the SGPE region, the total offset ranges from 21 to 37 meters.
Projection units: meters Spheroid: sphere of radius 6,370,997 meters Central longitude: -100 deg (W) Central latitude: 45 deg N False easting: 0 False northing: 0
Projection units: meters Spheroid: Clarke 1866 1st standard parallel: 29 deg 30 min N 2nd standard parallel: 45 deg 30 min N Central meridian: -96 deg (W) Latitude of origin: 23 deg N False easting: 0 False northing: 0