## 4 Results
### Image Texture as a Proxy for DEM Quality
#### 4.3.3 Flat-Area DEM Variance versus Image Texture  
The impression of PAN variance (i.e., image texture) compared to DEM quality as viewed in hillshaded images (Figure 4) and the lower PAN variance in output DEM holes (Figure 5A) lead us to a quantitative analysis of PAN variance versus DEM quality measured on the flat-lying salar. We emphasize that this unique, perfectly flat surface in our study area  
Figure 5: (**A**) Comparison of PAN variance in DEM pixels with elevation values versus no-data holes (shown here for the BM-ck25 3 m DEM); (**B**) holes in output DEM for each of the 3 m DEMs generated from the AC image pair (cf. Table 1); (**C**) holes in output DEM for the BM-ck25 at 3, 6, 12, and 24 m resolution, which is 2, 4, 8, and 16\(\times\) the input PAN image resolution, respectively. allows us to extract DEM quality as measured by DEM variance in local, plane-detrended windows matching the windows for PAN variance calculation. In Figure 6A, we selected a 2000 \(\times\) 3000 pixel clip of the PAN B image from the central salar. Each pixel is 3 m resolution, where the orthorectified PAN B-scene was resampled from the original 1.5 m to match the output SPOT6 DEM resolution, and the number of pixels analyzed excluding holes in the DEM is \(\sim\)6\(\times\)10\({}^{6}\), or an area of \(\sim\)54 km\({}^{2}\). The PAN variance, calculated here in a 5 \(\times\) 5 window, spans \(\sim\)5 orders of magnitude due to variations in salt patches and wind-blown dust on the salar, providing a large range for comparison (Figure 6B). The DEM variance, also in a 5 \(\times\) 5 pixel window, spans \(\sim\)5 orders of magnitude (Figure 6C) showing the large variability in DEM quality on the flat salar. Figure 6: **(A)** 2000 \(\times\) 3000 pixel (6000 \(\times\) 9000 m) clip of the SPOT6 PAN B-scene from the central salar (cf. Figure 2A). Grayscale variations (image texture) caused by salt and wind-blown dust; **(B)** variance calculated in a 5 \(\times\) 5 pixel window from the original PAN scene; **(C)** DEM variance for the SPOT6 BM-ck25 3 m DEM, also calculated in a 5 \(\times\) 5 pixel window using plane-fitting and the variance of point-to-plane distances. Note the reversed color scales in **(B)** (low to high, red to blue) compared to **(C)** (low to high, blue to red), in order to highlight the fact that lower PAN variance values (red colors in **(B)**) correspond to higher DEM variance values (red colors in **(C)**), and vice versa; **(D)** the variables shown in map view in **(B,C)** plotted graphically using a 2D histogram to highlight density of the \(\sim\)6 \(\times\) 10\({}^{6}\) underlying pixels (not plotted), as well as median bins calculated from all pixels. The map-view comparison in Figure 6B,C is plotted graphically in Figure 6D. DEM variance is in units of m\({}^{2}\), but this can be viewed as a standard deviation uncertainty measurement (i.e., the variability of height in the window) by taking the square root. For instance, 10\({}^{0}\), 10\({}^{-1}\), 10\({}^{-2}\), 10\({}^{-3}\), and 10\({}^{-4}\) m\({}^{2}\) DEM variance are equivalent to standard deviation DEM uncertainties of 1, 0.3, 0.1, 0.03, and 0.01 m, respectively. Rather than plotting every DEM variance (y-axis) and PAN variance (x-axis) pixel value, we instead use a 2D histogram to represent the point density. A clear, banana-like shape emerges from the densest part of this 2D histogram (brightest colors), and plotting a binned median taken from all pixels (not plotted) further confirms this overall pattern in the DEM variance vs. PAN variance relationship. At PAN variances of \(\sim\)10\({}^{-10}\), there is a continual decrease in DEM variance, but this begins to plateau around 10\({}^{3}\) PAN variance, where we do not see continual improvement in DEM quality (further decreasing DEM variance). The scattered nature of the relationship between DEM variance and PAN variance is apparent in Figure 6D by the wide spread of the 2D histogram.