Slope Computations--Grid and Window Size

 

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 the same general trend, with the average slope decreasing as the DEM spacing increases.

  • At the 30 m spacing, the large window size leads to a slightly larger average slope compared to the mean aggregation.  Mean aggregation drives the elevations toward the central value by removing both high and low values.  For small reductions in the size the DEM grid (small increases in the pixel size/data spacing), mean aggregation and decimation/thinning do not differ greatly in their effects, but we are seeing small difference here, with thinning yielding slightly larger average slopes.
  • The filtered DEMs decrease average slopes with small filter sizes, but match the other analyses at larger spacing.

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