Elevation Data
General Comments - Data source and Usage

Elevation datasets were obtained from the U.S. Geological Survey. A variety of mapping datasets are available for public download at:


The datasets used for this work are called '1:250,000 - scale Digital Elevation Models' or DEM's.  Complete descriptions of the format and origin of these datasets can be found at the website above. The data is divided into files that cover one half of a quadrangle, so the grand canyon quad [36N-37N, 114W-112W] is found in a 'grand canyon west' file [36N-37N, 114W-113W] and a 'grand canyon east' file [36N-37N, 113W-112W]. Each file covers a one degree latitude by one degree longitude box. The elevation is given on a rectangular grid with 3 arcsec by 3 arcsec resolution. This amounts to a rectangle of 93 meters from north to south and an east to west width that ranges from about 80 meters at the southern most edge of the Arizona quads (31 N) to about 74 meters at the Arizona/Utah state line (37 N) to about 68 m at the top of the region of study (43 N). In this work the curvature of the Earth is modeled as spherical with a radius of 6370.0 km (tiny effects such as oblateness are ignored) so the length of a fixed amount of longitude angle shrinks as the cosine of the latitude, as one moves north.

The 3 arcsec resolution implies that each half quad file has a 1200 x 1200 array of numbers.  Actually the USGS DEM's contain the values on all four edges. In other words the files contain a 1201 x 1201 array of numbers and any two files for adjacent areas will have one column or one row of duplicate data. Computer routines were written and used to slightly modify the data format and merge quads and perform other tasks. In particular, the resolution can be reduced by averaging together adjacent cells. Most all of the topographic maps on this set of pages were made with 12 arcsec resolution. The 12 arcsec data is just obtained from the straight average of a 4 x 4 group of 3 arcsec cells. The 12 arcsec resolution is comparable to the resolution of the lightning strike data (discussed elsewhere) and also has the advantage of reducing the size of the topographic data.

The topographic maps on this set of pages are all done in the Mercator projection. That is, latitude and longitude are treated as a flat rectangular coordinate system, so north to south lines are always vertical and east to west lines are always horizontal. The aspect ratio for the maps in this study is chosen to correct for the center of the region plotted.  So a map of the Arizona region that runs from latitude 37 N to 31 N is chosen to have the correct width for the center (34 N, in this case).  Equal areas on the map correspond to increasingly larger areas on the ground as one goes from north to south on the map, although the correction over a portion of the globe this size, is small.

The DEM's were also used to tabulate the amount of area that occurs at each elevation. The full 3 arcsec by 3 arcsec grid was used for this purpose. The changing width of these rectangles with latitude was taken into account. The following is a fragment of the data for the douglas and marble canyon quads.

Elevation   Douglas      Marble Canyon
bin (m)      quad           quad

0000         0.0              0.0
0100         0.0              0.0
0200         0.0              0.0
0300         0.0              0.0
0400         0.0              0.0
0500         0.0              0.0
0600         0.0              0.0
0700         0.0              0.0
0800         3.5              0.0
0900        89.6             0.0
1000      358.6             0.0
1100      676.3             0.0
1200     2866.0            0.0
1300     5468.2            0.0
1400     4455.2        362.3
1500     2990.4      2293.8
1600     1443.7      3927.2
1700     1053.7      4936.0
1800       686.4      3345.7
4700           0.0            0.0
4800           0.0            0.0
4900           0.0            0.0
Total    21102.8    19896.0

The values are area in square km, so for instance there are 89.6 sq km of area in the 900 m to 1000 m range in the douglas quad. Note that the total area of a quad changes by about 6% from latitude 31 N to 36 N.

There are imperfections in the elevation data.  These two pages describe two distinct types of problems and their relevance to the study.

Edge Mis-match Problem
Plateau Ring Problem