## 4 Discussion
Slight deviations in the models at rock overlangs between epochs result in overestimated change estimates because these overhangs are nearly perpendicular to the plane in which the data are modeled. An additional comparison was made in Figures 11b and 16b with filling holes in the baseline models only. There is a modest increase observed in volume estimates when holes are filled in the baseline surface as well as the model surface. While variance in the volumes is observed from the analysis based on modeling resolution, this variance is relatively small when considering the results from a highway risk assessment perspective (e.g., the difference between 20 and 28 m\({}^{3}\) at Site A is insignificant when compared with the volume of 3900 m\({}^{3}\) determined for Site C). Hence, the fluctuations in volume estimates across the resolution ranges are not as substantial as the natural variability that exists based on the rock structure across large spatial extents. Nonetheless, hole filling by TPS works well for creating realistic surface and the models proved to be consistent with the topography. As evidenced in Figures 10, 15, and 20, there are relatively similar magnitude-frequency relationships for a given resolution whether holes were filled or not. However, hole filling clearly improved the ability to capture larger events that were sometimes split in the models without hole filling. The search window size should be set sufficiently large to ensure most holes are filled to avoid underestimating volumes (Figures 11b and 16b); although, it should be recognized that a large search window will significantly increase computation time. Interestingly, in Figure 14 the rockfall clustering results are similar with different levels of hole filling. Even when large holes were filled (e.g., ws = 50), the 2014 data matched the 2013 data well, as evidenced by the fact that many of those holes did not result in new artificial clusters being identified. This indicates that the TPS is reasonably estimating the surface, even when interpolating across these large holes. Indeed, the hole filling was important to better define the shapes and sizes of the existing clusters, particularly for grouping smaller clusters that were likely part of the same event. In analyzing Figure 22, the power law magnitude-frequency relationships fit the data trends well across multiple orders of magnitude. However, the power law relationship tends to provide a weaker fit for smaller rockfalls (e.g., \(<\)0.01 m\({}^{3}\) for sites A and B). Interestingly, for Site C, the predictive, power law magnitude-frequency relationship holds until considering volumes that are less than 0.0001 m\({}^{3}\) (beyond what is shown in Figure 22). This threshold volume is essentially at the practical limits of the modeling (0.05 m) and survey techniques (0.05 m significant change threshold based on the estimated geo-referencing accuracy). In contrast, Sites A and B exhibit fewer small rockfalls than predicted based on the power law relationship. This may be due in part to censoring as survey resolutions are approached, but it also suggests that the hole filling method is not generating substantial artificial rockfalls. The correlation coefficients in Figure 22 indicate that hole filling generally leads to improved magnitude frequency fits as well (except for site B where hole filling reduces the effectiveness of capturing small failures). Still, it is possible that there may be some artificial rockfalls \"detected\" in the clustering analysis. Because of their small size, these smaller rockfalls are difficult to reliably verify with field or photographic techniques. Overall, the clustering results for larger events compare well with a qualitative analysis of high-resolution photographs between epochs. Additionally, at Site A more rockfalls were detected on the west portion of the site than the east portion.