Slopes for Arc Second DEMs when Software Allows only One Data Spacing

 Arc second DEMs like the Copernicus DEM have rectangular pixels, with 1 second spacing which translates to different spacings in meters in the x and y directions.  Most software now uses a slope algorithm which correctly deals with the rectangular pixels, but some GIS programs still assume square pixels and requires the user to select a single spacing.

MICRODEM can call two of those programs, and uses the average of the x and y spacings.  To test this selection, the x or the y spacing could also be used.  The two programs which use only one data spacing  produce identical results, so only one of the two was used.

MICRODEM produces the same results for the slope algorithms as other programs that use different x and y spacings for the arc second DEMs.

Slope histograms.  For this DEM, the 1x1" spacing is about 24.77x30.83 m.  When the average spacing is used, GDAL agrees with MICRODEM.  If the smaller x spacing is used, the slopes are steeper because the horizontal distance is in the denominator in the slope forumula.  If the larger y spacing is used, the slopes are gentler.

Scattergrams.  The different spacings for GDAL have the same correlation coefficient compared to MICRODEM, but the slopes shift in value depending on the spacing selected (note where the 75x75 point occurs relative to the data points.

If you use software that cannot correctly handle slope for arc second grids, your choices in order of priority should be:
  1. Use other software (GRASS, MICRODEM, WhiteBox, Arc GIS geodesic)
  2. Lobby the software to revise their code.
  3. Use your software, with the average spacing.



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