**3. Results**

In the following, we present the results obtained at the two field sites, starting with the breach at Sillon de Talbert. With a reduced survey area compared to La Palue and dense ground controls, the breach at Sillon de Talbert represented an ideal testing ground for experimenting on the minimum number of GCPs for effective photogrammetric optimization using an RTK quadcopter. We then apply these findings to La Palue field site, and we validate the approach using larger-scale experiments and data validation methods. The implications of our findings and recommendations that arise from our results are discussed in Section 4.

#### *3.1. 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

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.** 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-1GCP1, (**e**) S-RTK-1GCP2, (**f**) S-RTK-3GCP1, (**g**) S-RTK-3GCP2, (**h**) S-RTK-5GCP and (**i**) S-RTK-9GCP. 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 using1mresolution DEMs.

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 (~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

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.

**Table 4.** Vertical error evaluation for the different scenarios presented in Figure 3 using ground targets (GCPs and ChkPts) measured with RTK-GNSS. The values between brackets correspond to GCP-based error.


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. Similar to previous observations, adding GCPs in addition to camera information progressively improved the model quality mainly by reducing the horizontal bias to negligible levels (<0.01 m) from 5 GCPs, while the measurement precision remained relatively unaffected. Overall, the photogrammetric errors amounted to global precisions (RMSE3D) of approximately 0.05 m under optimum configurations.

**Table 5.** Planimetric error (X easting and Y northing) evaluation for the different scenarios presented in Figure 3 using ground targets (GCPs and ChkPts) measured with RTK-GNSS. The values between brackets correspond to GCP-based error.


#### *3.2. La Palue Field Site*

Figure 4 presents the results of the topographic measurements using RTK-GNSS mounted on a bike. The raw data counted 2036 survey points separated on average by approximately 2.5 m (sigma = 0.75 m), showing that the data acquisition was carried out at an average speed of 9 km/h (2.5 m/s). Not shown in the figures, comparing the survey points with immediate neighbors (maximum distance of 0.2 m) enabled the point confidence to be evaluated at 39 locations, indicating a mean and maximum point confidence of 0.007 m and 0.015 m, respectively. As one may expect, the pitch-related errors due to the uneven terrain affecting the measurements were larger at the turning points (e.g., beach ends) since the bicycle was then moving up or down the beach (i.e., cross-shore), and where the local topography was suddenly changing (Figure 4b,c). The maximum forward slope recorded was just below 4◦, traducing to maximum horizontal (dx) and vertical (dz) pitch-related errors of 0.04 m and 0.01 m, respectively. Filtering the data based on pitch-related errors (dx) resulted in the rejection of 158 points. The final number of survey points retained for comparison with photogrammetry thus amounted to 1878 (Figure 4c).

**Figure 4.** Verification of survey points obtained using a bike-mounted RTK-GNSS at La Palue, with (**a**) the chronology of point acquisition; (**b**) pitch-related horizontal error (dx), where marker size is proportional to error magnitude (×1000 magnification factor) and (**c**) the elevation of survey points retained serving as ground truths for photogrammetric evaluation.

Changing the accuracy setting during photogrammetric image alignment had major repercussions on the data processing time, as well as on the measurement density and quality (Table 6 and Figure 5). The image alignment time (1407 images) varied by two orders of magnitude, from 27 min ("Low"), through 43 min ("Medium") and 105 min ("High1" and "Highest"), to an outright maximum of 2721 min (~45 h, "High2") when "source" pair preselection was unused. The number of tie points after the alignment was the maximum using the "Highest" accuracy setting, followed by "High1" and "High2", with ~1:5 variations overall (from 550,000 to 2,500,000 points). However, after the automatic filtering of less reliable tie points, the number of tie points decreased from a maximum of ~435,000 points with "High1", through "Medium", "High2", "Highest" and, finally, "Low" accuracy settings with ~80,000 points (again, 1:5 variations overall). The comparison of the photogrammetric models obtained (DEMs at 1 m resolution) with the ground truths provided by RTK-GNSS shows a similar tendency, with DEM quality (Table 6) in decreasing order for "High1" (SDE = 0.042 m or 1.6 GSD), "High2", "Medium", "Highest" and, finally, "Low" (SDE = 0.125 m or 5 GSD) alignment accuracy with 1:3 variations overall. The photogrammetric deviations from the ground truth were essentially to be related to the measurement precision since no significant bias (i.e., ME ~0) was detected in the results. However, Figure 5 shows that the systematic errors, although of small magnitude, may still be present in the DEMs, taking the form of undulations. The color grading shows an error magnitude of ±0.04 m for the better-quality models ("High1", "High2", "Medium"), eventually exceeding 0.1 m at some locations when the "Highest" and "Low" accuracy settings were used. Using ground targets (GCPs and ChkPts) for error evaluation produced error statistics with no appreciable differences between the scenarios tested (differences were found to be non-significant at *p* = 0.05), and, for this reason, they are not presented.

**Table 6.** Effect of changing the image alignment accuracy setting during sparse DEM reconstruction at La Palue field site in terms of processing time, number of tie points (before and after filtering) and measurement error. Deviations between photogrammetric models (1 m resolution) and GNSS-RTK survey points, from which vertical error statistics are extracted, are presented in Figure 5.


In comparison to previous tests, changing the depth filtering setting during dense model reconstruction had lesser effects on the DEM quality. Using RTK-GNSS for ground truthing produced nearly identical error statistics for all the settings, shown by SDE = 0.033 m for no filtering and "Mild" and SDE = 0.032 m for the "Moderate" and "Aggressive" settings, respectively. For this reason, Table 7 presents errors evaluated as DEM comparisons using the case of no filtering as a reference. Deviations from this reference DEM were essentially found at steep sections of the study site (e.g., cliff faces), resulting in potentially large elevation deviations over small spatial extents (indicated by the neat difference between MUE and SDE). Elevation deviations increased (in magnitude and occurrence) with increasing depth filtering, until a plateau was reached ("Moderate" and "Aggressive" have identical error statistics).

**Figure 5.** Evaluation of image alignment accuracy setting during sparse DEM reconstruction showing vertical errors at 177 RTK-GNSS survey points for (**a**) low, (**b**) medium, (**c**,**d**) high and (**e**) highest alignment accuracy setting. For all scenarios tested, "source" reference pair preselection was used, except for panel (**d**). Photogrammetric targets used as GCPs and ChkPts are shown as triangles and circles, respectively. Error evaluation was performed using1mresolution DEMs.

**Table 7.** Evaluation of depth filtering during dense DEM reconstruction at La Palue field site. Except for the reference DEM using no depth filtering, for which errors are estimated in comparison to 1381 RTK-GNSS survey points, vertical error statistics are the result of intercomparing DEMs with the reference DEM. All DEMs evaluated were reconstructed using "High" image alignment accuracy (Figure 5c) and "High" reconstruction quality for sparse and dense DEM reconstructions, respectively (cf. explanations in the text). Evaluations were performed using 0.1 m resolution DEMs.


Figure 6 presents the DEM obtained at La Palue using the standard workflow designed for this study (Table 2) and produced on a 0.1 m grid. The measured beach topography shows marked 3D morphologies, particularly on the northern side of Kerdra point and at the seaward DEM boundary, with numerous channels incised in the sand and humps and hollows representing sand accumulations and depressions (Figure 6a). The smallerscale topography, which is apparent in the orthophoto and is suggested by uneven and rugged elevation contours, is somehow subdued by the general topography when viewed at this scale. The fine grid spacing was advantageous to allow comparisons at a large

number of RTK-GNSS survey points (1381 points). The photogrammetric errors (Figure 6b) show a similar spatial organization with the ones identified previously using 1 m DEMs reconstructed from sparse point clouds (Figure 5). DEM precision using the standard workflow was characterized by SDE = 0.032 m (i.e., 1.2 GSD, Figure 6c,d).

**Figure 6.** Quality assessment of the 0.1 m resolution photogrammetric DEM obtained using the standard workflow. (**a**) DEM overlapped with depth contours every 0.2 m; (**b**) vertical error at photogrammetric targets (GCPs and ChkPts) and 1381 RTK-GNSS survey points; (**c**) probability distribution function (PDF) of pitch-related error (dx) binned at 0.005 m and (**d**) PDF of photogrammetric vertical error in comparison to RTK-GNSS survey points binned at 0.01 m.

Four repeat photogrammetric surveys carried out between September 2020 and April 2021 are compared in Figure 7. Using the range and standard deviation of repeat bed elevations, representing the temporal variability in the elevation for each surface cell, shows that large portions of the back beach (i.e., dune and cliff tops), as well as rock deposits and outcrops, can be considered stable over the 7-month period during which the DEMs were obtained (here defined as cells with an elevation range between the four surveys below 0.035 m). Filtering the unstable surface cells left 587,105 invariant cells at a horizontal resolution of 0.1 m, and characterized by an overall (i.e., averaged over all the stable cells) range and standard deviation of repeat bed elevations of 0.025 m and 0.011 m, respectively. Averaging the repeat elevations over the stable cells of the DEM produced a multi-temporal ground truth backing the entire beach over all the sides except seaward, and with elevations spanning over 50 m (Figure 7d). The comparison of the 17 September 2020 survey with the ground truth (Figure 7e) suggests centimeter-scale deformations, which may echo deformations previously identified using RTK-GNSS survey

points (Figures 5 and 6). The quantitative comparison shows ME and SDE of ~10−<sup>3</sup> m and 0.01 m, respectively.

**Figure 7.** Assessment of photogrammetric workflow replicability at La Palue. (**a**) Cell variability using all repeat surveys (*n* = 4); (**b**) cell variability and (**c**) cell elevation range after thresholding to retain only supposedly stable cells (*n* = 587,105 cells); (**d**) resulting ground truth elevations over stable cells and (**e**) comparison of 17 September 2020 survey with the ground truth.

Figure 8 presents the first applications of very-high-resolution coastal monitoring at the La Palue field site, used here for beachface topographic complexity detection and mapping. Three zones are analyzed in more detail, corresponding to regions of return flows, creating narrow channels incising sand superimposed with complex small-scale topographies, such as (mega)ripples and hummocky patterns of different forms and dimensions. For detecting submeter bedforms, the 0.1 m resolution DEM was detrended from metric topography by subtracting the 1 m resolution DEM. Doing so left only the small-scale topographies not accounted for in the DEMs with resolutions of 1 m or above (Figure 8b).

The qualitative analysis of the orthophotos and DEMs suggests that the approach was suitable for characterizing sub-metric beach topography, creating realistic maps of the bedform arrangement at the beach scale (cf. Figure 8a,b). The submeter-scale topography is most evident at steep sections of the beach, such as seaward of the berm and where there is a sand-cobble transition, but is otherwise widely spread. It includes large patches of ripples and megaripples, channels of varied dimensions, and zones of water resurgence. Quantitatively, the net volume embodied in the sub-metric topography amounted to ~6000 m3, which is equivalent to a layer of sand of 0.011 m over the entire beach.

**Figure 8.** Application of RTK quadcopter and SfM photogrammetry for very-high-resolution measurement of topographic roughness and bedform mapping at the beach-scale at La Palue field site. (**a**) Orthophoto and the different zones investigated in panels (**c**–**h**); (**b**) 0.1 m resolution DEM detrended from metric topography (cf. explanation in the text); (**c**–**h**) 0.1 m resolution orthophotos and detrended DEMs cropped to the areas of interest. Detrended elevations below 0.02 m are not shown to help with figure comprehension. The colorbar is same for all DEMs.
