Musings on DEMs

 To test this, we started with a 1 m DTM and did mean aggregation to get a 1" geographic DTM and a 30 m UTM grid. We created slopes using 16 algorithm/GIS program combinations. The matrices show the Pearson correlation coefficient comparing each pair of slope grids.  The matrix is symmetrical about the white-colored principal diagonal. The dark green shows pairs that produce identical results, and correspond with the four algorithms (Evans, Horn, Zevenbergen and Thorne, and quadradic/Florinsky).  Differences in the r values reflect different results from each algorithm's computation of the directional derivatives. Within each of the four algorithms, at least two programs produce identical results.  The other programs differ, because they do not correctly compute different spacings in the NS and EW directions, and if they allow the user to input a scaling factor allow only a single degree to meter conversion.  In addition to the difference arising from the comput...

 My comparison of slope computations has 21 combinations of algorithm and GIS program, requiring some thought on how to organize the results.  These four graphs show some preliminary results, without identifying any of the guilty parties. These results are for a one arc second DEM, for which some of the programs are not well equipped to handle. Rows and columns each have a slope grid produced by a different algorithm/program.  T he white principal diagonal is where a grid would be compared with itself.    We do not know the "correct" slopes, so we can only discuss differences. The results suggest that using a 5x5 window requires a lot more thought since the results are so different compared to the traditional 3x3 window. Pearson correlation coefficient between the slope grids computed by two methods.  Those in the top, dark green box in the legend, produce identical results.  This matrix is symmetrical. There can be a high correlation coefficient if th...

 I have been comparing slope algorithms, and the results from different software.  I have been looking at 4 algorithms, and a half dozen GIS programs.  Most use a 3x3 window, but one has an option for a 5x5 window.  It turns out I had implemented a 5x5 window in MICRODEM, but never really looked at the results. This uses a one arc second DEM with about 20,000 elevation postings, which accounts for the jagged histograms below.  This looks only at the three algorithms currently implemented in MICRODEM (the other program has similar results, perhaps not as extreme). The slopes computed with the 5x5 window are significantly smaller than those with a 3x3 window, and for this scale of DEM should probably not be used.  Perhaps your preferences might be different with a 1 m lidar-derived DEM.

    We start with a DTM on the New Zealand horizontal and vertical datums.  The peak is at 162.0 m. GDAL warp to WGS84 horizontal, EGM2008 vertical.  The "features" every 50 m horizontally and vertically come from GDAL.  The peak is now at 162.3.  Because there have been shifts both horizontally and vertically, the shapes of the contour lines have changed. Resampling by mean aggregation to 30 m in red (square pixels), and 1 arc second in green (rectangular pixels, 24.8x30.8 m), with 2 m contours.  The centroids of the pixels shown with square symbol labelled with the elevation.  Peak in the 30 m DEM is at 159.7 m, with that of the 1" DEM also at 159.7 m but displaced to the NE.  The peak can only be at a pixel centroid; the distance between nearest centroids varies throughout the DEM.  Resampling drives elevations toward the mean, dropping peaks and ridges and raising valleys. Contours from the 1 m DEM overlaid in blue, which should much...

   Guth, P. (2024). How long is one arc second?. Zenodo.  https://doi.org/10.5281/zenodo.13963457  ] One arc second DEMs are still the best available digital topography for much of the world, and are appropriate for many analyses even when higher resolution DEMs are available.   SRTM was the first of these DEMs, but should now be replaced with the Copernicus DEM (Bielski and others, 2024; Guth and others, 2024). Many operations with DEMs, such as computation of slope, aspect, or hillshades, requires the data spacing, and an arc second DEM has different spacings in the x and y directions.   At point software required reinterpolating to a UTM or similar projection, but it is an easy operation to correctly compute the two spacings (Guth and Geoffroy, 2021). There are several ways to compute the two spacings: ·          Require the user to specify a single value, which might be the average of the two spacings. · ...