Musings on DEMs

Two versions of a DTM, created by aggregation from a 1 m UTM grid in Glacier National Park, Montana.  At this latitude, almost 49N, the arc second spacing is about 20.35x30.89 m.  Visually the two appear identical, so they do a good job capturing the terrain.  The histogram shows they are indeed very similar. The points in the grids are not at the same locations.  At places they coincide, and at worst they are offset by about 10 m in x and 15 m in y.  In this heavily glaciated area, there are slopes up to 800%. To map the differences, one of the grids must be reinterpolated.  The maps above show both possible reinterpolations.  The maximum differences are about 80 m; 2.5 m captures 90% of the points from the 5th to the 95th percentiles.  The biggest differences are on the ridge tops and valleys, where the ridge crest and the steam location can be offset by up to 15 m depending on how the two grids line up at the location. These two DTMs "shou...

  This graph is for Glacier National Park.  It has a lot more elevations, so with the same number of bins it has much smoother curves than the last example.   But what is more interesting, the MICRODEM example, using the different x and y spacing, is not the same as it was in the previous example compared to using GDAL and using a data spacing that is the average of the x and y spacings.  They match below about 30% slopes, and above about 80%, but in between there are some significant differences. Bottom line, software should adapt, and the coding is not that hard.  Most programs currently get it right.

 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 becaus...