## 5 Discussion
### Predicting DEM Quality from Image Texture
Taking the mode of the histogram in Figure 10B would provide a value of 1000 (our previously quoted 10\({}^{3}\)), but the 5 th-95 th percentiles of breakpoint values fall between \(\sim\)800-3000 (i.e., within \(\sim\)1 order of magnitude) and moving the breakpoint in this range does not have an appreciable effect on resulting map quality (noting that PAN variance can generally cover a range of 5+ orders of magnitude in our study area but has no theoretical limit). In this discussion, the breakpoint analysis and quality maps only offer a relative view of DEM quality, complementary to the intersection error map produced by the ASP  
Figure 10: (**A**) Piecewise fitting, using two linear segments, carried out on 50% of blocked values shown in Figure 7D, bootstrapped 100 times (with replacement). The vertical red lines represent the breakpoints found in each fitting iteration. Results are shown for the BM-ck25 DEM and 5 \(\times\) 5 pixel variance window calculations. Note a linear y-scale is used here (as opposed to the logarithmic scale in Figure 8) to highlight the steep limb and plateau in the piecewise fitted relationship; (**B**) histogram of breakpoints taken from all variance window sizes (3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, and 9 \(\times\) 9 pixels) and iterations of piecewise fitting (n = 400 breakpoints), with median (1300 PAN variance) and 5 th/95 th percentiles identified. following stereo correlation. We only present results for the BM-ck25 3 m DEM, since it is closest to the default parameter ASP output, but we note that a similar breakpoint analysis on the other SPOT6 DEMs produced similar values near 10\({}^{3}\) PAN variance. This method ignores other causes of poor DEM quality, such as geometric issues with the terrain compared to satellite view angles, and reduces quality entirely to the input image texture. It is highly unlikely that image texture alone impacts DEM quality, and many other factors also influence the results (e.g., striping pattern of the intersection error in Figure 4 caused by sensor and satellite motion). In an attempt to elucidate these other issues and present a method for DEM quality assessment in study areas that may not have a large, flat, multi-textured surface such as our salary, we also tried to form a DEM variance versus PAN variance relationship off of the salary. We found that even when using very small (3 \(\times\) 3 pixel, or 9 \(\times\) 9 m) windows for the DEM variance calculation via plane fitting, the influence of true topographic signal (hillslopes in our study area are rarely perfectly planar at the 9 \(\times\) 9 m scale), overprints the DEM variance versus PAN variance relationship (Figure 56), making a breakpoint analysis infeasible on non-flat terrain. Despite these caveats, the breakpoint and quality maps presented here may serve as starting points for future research seeking to disentangle quality issues on optical DEMs produced via stereo correlation. It is clear that image texture has a very large influence on the quality of DEMs produced via stereo correlation, as qualitatively observed by many authors (e.g., [22; 27; 35; 40]). We suggest that at local (3 \(\times\) 3 - 9 \(\times\) 9 pixels) image variance values \(\lessapprox\)10\({}^{3}\), stereo correlation has rapidly degrading results. Above this approximate threshold, remaining DEM quality issues are independent of image texture (e.g., may be caused by sensor biases or geometric issues). Figure 11: Relative DEM quality maps based on the PAN variance breakpoint found in Figure 10B: (**A**) map-projected SPOT6 PAN B-scene from an area bordering the salary. (**B**) 5 \(\times\) 5 pixel window PAN variance for the same region, with the color bar centered on the breakpoint value (1300 PAN variance).