## 3 Results
### The Breach at Sillon de Talbert  
Figure 3 presents the results of photogrammetric quality evaluation for the different scenarios tested during model optimization. The reference DEM used for assessing the other DEMs was produced using scenario S-RTK-GCP. This decision was based on the consideration that using all the external information available during photogrammetric \begin{table}
\begin{tabular}{c c} \hline \hline
**Error Metric** & **Formula** \\ \hline Mean Error (ME) & ME =\(\frac{1}{N}\sum\limits_{i=1}^{N}(y_{i}-x_{i})\) & (1) \\ Standard Deviation of Error (SDE) & SDE =\(\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}(y_{i}-\overline{x_{i}})^{2}}\) & (2) \\ Root-Mean Square Error (RMSE) & RMSE =\(\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}(y_{i}-x_{i})^{2}}\) & (3) \\  & RMSE =\(\sqrt{\text{ME}^{2}\text{+SDE}^{2}}\) & (4) \\
3D Error (\(\text{ }_{\text{3D}}\)) & \(\text{3D}=\sqrt{\chi^{2}+\chi^{2}+\,Z^{2}}\) & (5) \\ Mean Unsigned Error (MUE) & MUE =\(\frac{1}{N}\sum\limits_{i=1}^{N}|y_{i}-x_{i}|\) & (6) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Error metrics used for evaluation of measurement quality. optimization would produce the most reliable DEM. Besides, comparing the DEMs obtained using the other scenarios with this reference DEM enabled assessing the effect of using camera information or not, as well as the effect of GCP number and distribution. Figure 3 shows that the less reliable DEMs in terms of vertical precision (SDE) are those obtained using scenarios S-GCP and S-RTK, with respective precisions of 0.027 m and 0.029 m (\(\sim\)2 GSD). Not using camera information during photogrammetric optimization (Figure 3b), the DEM quality degraded noticeably where there was no GCP (e.g., peripheral parts of the DEM). Using only camera information (i.e., no GCPs) resulted in slightly poorer precision, but, most importantly, the S-RTK model was affected by a mean error of 0.37 m. This vertical bias was confirmed using ChkPts, showing ME = 0.36 m (Table 4). Progressively adding GCPs in addition to camera information during model optimization improved the DEM accuracy and precision (Figure 3d-i). A plateau was attained from five GCPs, whereby the bias was approximately zero and precision reached its minimum  
Figure 3: Assessment of model optimization at Sillon de Talbert showing (**a**) the reference DEM obtained with scenario S-RTK-GCP overlapped with depth contours every 0.2 m, as well as DoDs between the reference DEM and DEMs obtained using scenario (**b**) S-GCP, (**c**) S-RTK, (**d**) S-RTK-1 GCP\({}_{1}\), (**e**) S-RTK-1 GCP\({}_{2}\), (**f**) S-RTK-3 GCP\({}_{1}\), (**g**) S-RTK-3 GCP\({}_{2}\), (**h**) S-RTK-5 GCP and (i) S-RTK-9 GCP. Color coding for DoDs and error at photogrammetric targets is same for all. Photogrammetric targets used as GCPs and ChkPts are shown as triangles and circles, respectively. DEM comparisons were performed using 1 m resolution DEMs. at approximately 0.01 m (i.e., <1 GSD, Figure 3h,i). When one or three GCPs were used together with camera information, the GCP position had a noticeable effect on the DEM quality (Figure 3d-g), especially on residual bias, with variable results. As shown in Table 4, using GCPs for error evaluation prevented detecting the vertical registration error in the DEMs and produced optimistic precision estimates. The SDE values estimated using GCPs were consistently lower by an order of magnitude than those estimated at ChkPts or those derived from model comparisons with the reference DEM (Figure 3). On the contrary, the MEs estimated using ChkPts and DEM comparisons were very consistent with each other. The SDE calculated using ChkPts remained slightly lower, suggesting better vertical precision. The photogrammetric horizontal error estimated using GCPs and ChkPts is presented in Table 5 for the same DEMs. The results show larger horizontal error compared to vertical error for all the scenarios tested, with a ratio between horizontal and vertical error generally around 3:1.