Corners of SGPE bounding rectangles

To facilitate overlaying datasets, standard rectangular boxes for the region covered by the Southern Great Plains Experiment (SGPE), 1997, have been defined for each of the map projections which are likely to be used, as well as for geographic coordinate angles (longitude and latitude). The map projections supported are The maximum and minimum longitude and latitude were defined first. These boundaries were chosen to include all sites at which measurements were made or planned in Kansas and Oklahoma, and extend from 100.0 to 95.0 degrees west longitude, and 38.5 to 33.0 degrees north latitude.

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   618000
The 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.

Relations between spheroids and datums

North American mapping agencies are in the process of moving from the 1927 datum (NAD27), which uses the Clarke 1866 spheroid, to the 1983 datum (NAD83), which uses the GRS80 spheroid (identical to within a few mm to the WGS84 spheroid) derived from satellite geodessy. To further complicate matters, the 3-arcsecond digital elevation data compiled by the Defense Mapping Agency and distributed by the USGS uses an earlier satellite-derived spheroid, WRS72. The three spheroids differ not only in their major and minor semiaxes, but also in the location of the center of the spheroid relative to the center of mass of the Earth and in the direction of the x axis.

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 Parameters

Universal Transverse Mercator (UTM)

This is the projection used for higher resolution data sets, such as 30-meter DEMs and Landsat TM imagery. To avoid discontinuities, the entire SGPE region is projected in UTM Zone 14, although nornally areas east of 96 degrees west longitude would be projected in UTM zone 15.

	Projection units:	meters
	Spheroid:		GRS80/WGS84
	Central longitude:	-99 deg (W)
	False easting:		500,000 meters
	False northing:		0
NOTE 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.

Lambert Azimuthal Equal Area

This projection is suitable for maps covering the 48 conterminous U.S. states and is centered in South Dakota. It has been used by the EROS Data Center (EDC) for a series of land surface charactristics data sets.

	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

Albers Equal Area

This projection is also widely used for maps covering the conterminous 48 states, and is centered in southeast Kansas.

	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

Last change: 10 Dec 1997, R. A. White / raw@essc.psu.edu