Musings on DEMs

 Two DEMs created by mean aggregation from 1 m DTM. Aspect corrected to be in true north, but the SSO is not.  The divergence here is about 4.5 degrees. Fabric direction parallels ridges and valleys, and should be orthogonal to the aspect direction.

TRI purports to be a roughness (or ruggedness) measure, but is in fact a slope measure. TRI averages the difference in elevation for the central point and its eight neighbors, and has meters as the unit.  If it divided by the distance between the two points, it would have a directional derivative.  Taking the average would lead to an "average adjacent neighbor" slope algorithm.  I cannot find a reference for this algorithm, but there is a steepest downhill neighbor (O'Callahan and Mark, 1987) and average adjacent neighbor (Sharpnack & Akin, 1969). Because it lacks only the division by the horizontal distance, TRI correlates strongly with all the various slope algorithms and does not provide an independent measure of the landscape.  Figure 1 shows the correlation between slope and the TRI computed by 4 GIS programs (MICRODEM, WhiteBox, GDAL, and SAGA).  This uses a DTM with 1" spacing at latitude 36 with noticeably rectangular pixels. Figure 1.  Slope co...

  Uses a 1 m UTM grid from latitude 36 south. Evans slope algorithm, using 8 neighbors to computer the dzdx and dzdy partial derivatives.  Diagonal spacings are not used in the algorithm.  Unless otherwise noted, using the standard 3x3 window. Four data series. UTM.  The original data set, and mean aggregation resampling. Geographic.  Mean aggregation resampling.  Average effective DEM spacing is the average of the spacing in the x and y directions. Filtered DEM, using a mean filter.  The average effective DEM is one half of the filter size times the original DEM grid spacing (1 m). Changing window size of the computation region.  The slope computations use a window size, taking the 8 neighbors at increasing distances.  The average DEM spacing is average distance to points used in the x and y directions, which are the same because only the UTM DEM is used.  This would be the same as using a thinned/decimated DEM. All four series follow t...

Used the following geomorphometry programs GDAL: GDAL 3.8.5, released 2024/04/02 GRASS: version 8.2 MICRODEM: version 2024.8.18  SAGA: version 9.3.0 WhiteBox: version 12/7/2022 DEMs used Started with 10x10 km, 1 m DTM from USGS in Glacier National Park MICRODEM used mean aggregation to create 30 m and 1 arc second versions Created slope maps. The tables show the number of pixels in each of the slope grids Full grid shows the size of the grid, including missing data. Valid elevations shows the number of elevation in the aggregated DTMs.  For the UTM version, the data extends to the edge of the grid.  For the geographic, there are triangular regions on each side due to the rotation between UTM and geographic grids. Valid slopes shows the number of slopes calculated by each program SAGA and Whitebook compute a slope for every pixel with an elevation, requiring special code along the edges. GDAL and GRASS compute a slope for some of the edge pixels. MICRODEM does not com...