## 5 Discussion
### Predicting DEM Quality from Image Texture  
We are able to build a quantitative relationship between optical DEM quality and image texture on the flat, multi-textured salar surface unique to our study area (Figures 6-8). As expected, areas with lower image texture (i.e., \(\lessapprox\)10\({}^{3}\) PAN variance) had lower-quality DEM results (i.e., a rough surface, whereas the true salar is smooth and flat). In the following, we present further analysis of this relationship in order to generate maps of DEM quality (i.e., per-pixel DEM uncertainty maps) from input images alone. One way to analyze the banana plots in Figure 8 would be fitting functional relationships to the lines (e.g., exponential, powerlaw, etc.) to generate a predictive model of DEM quality. However, model selection and parameter tuning is a complex process, and the model will likely differ between correlation algorithms (differently shaped relationships). Furthermore, the observed relationship may be specific to our data (SPOT6 1.5 m PAN images) and study area. Given these caveats, we instead choose a simple approach to this analysis by fitting a piecewise function made up of two linear segments. This was chosen based on the graphical view of the relationships, where we observe a steeply dipping curve followed by a plateauing behavior in Figure 8 (noting the log-scaled y-axis). We seek an approximate breakpoint (location where two linear segments meet) in the PAN variance, below which DEM quality is increasingly worse and above which quality from image texture alone is high (i.e., correlation between images has high accuracy). The piecewise fitting breakpoint analysis is demonstrated in Figure 10 for the BM-ck25 3 m DEM. For this, we take the blocked values shown in Figure 7D and iterate over them in a bootstrapping approach that provides us with a distribution of breakpoints. This is performed for each of the pixel window variance calculations (3 \(\times\) 3, 5 \(\times\) 5, 7 \(\times\) 7, and 9 \(\times\) 9), resulting in an even larger distribution of potential PAN variance breakpoints to choose from (Figure 10B). From this distribution, we selected the median value (rounded to the nearest hundred), which was 1300 PAN variance. Using this PAN variance value as our breakpoint, we are able to generate DEM quality maps from the input image alone, both on the salar (Figure 11A-C) and off-salar in the mountainous parts of our study area (Figure 11D-F). Given the shape of the relationship between DEM variance and PAN variance on the salar, we may expect that all PAN variance values above 1300 would lead to high-quality DEM results because this is where the DEM quality begins to plateau (Figure 10A), and further improvements in local standard deviation are \(\ll\)0.03 m. On the other hand, as we move farther below 1300 PAN variance, DEM quality rapidly degrades in the steep limb of the relationship shown in Figure 10A. Thus, in Figure 11, the solid blue color indicates values above our PAN variance breakpoint(higher expected DEM quality), and the shades of red indicate values below (lower expected DEM quality). These quality differences are clear on the salar in a hillshade view (Figure 11C), where there is a much rougher surface and more holes observable in the low PAN variance areas (red colors in Figure 11B). On the other hand, in the mountainous terrain the difference is more subtle to observe, but, from the quality map in Figure 11E, it appears that the more highly textured ridges and valley areas may be expected to have higher quality DEM results (solid blue color), whereas many hillslopes have lower texture and thus worse DEM results.