**4. Discussion and Conclusions**

This study has tested the possibility of using SfM photogrammetry augmented with an RTK quadcopter for monitoring coastal topographic complexity at the beach-scale. The survey method had to respond to both resolution and time constraints, with final DEM resolutions of 0.1 m for a realistic representation of the topo-morphological features from submeter dimensions and a survey completed in two hours around low tide to cover the intertidal zone. The method implemented had to achieve effective measurements in a challenging environment characterized, for instance, by large topographic variations, differences in bed cover, such as rough surfaces alternating with textureless and reflective surfaces, such as sand, and the presence of water as thin patches or deeper puddles and channels, which can all represent important difficulties for photogrammetry.

To evaluate the effective measurement resolutions and precisions achieved by the survey method, and, hence, to be able to identify suitable protocols for collecting and processing the data that surpassed the above constraints, purpose-built SfM workflows were applied to aerial images collected at two coastal field sites (La Palue and the breach at Sillon de Talbert) and tested against different ground truths. Of interest for this application, because of their impact on the data collection time and DEM quality, we specifically assessed the effect of image resolution and using GCPs in addition to camera information during BBA. As much as possible, the error evaluations were diversified to enhance the spatial

coverage and the level of error detection afforded and, hence, to increase the chance of obtaining reliable error statistics.

Ideally, complete DEM comparisons should be undertaken to fully characterize the error magnitude and spatial distribution as it is now well-known that photogrammetric measurements can be affected by complex 3D deformations (e.g., the dome effect), which may remain undetected when using sparse ground controls [67,68]. In the absence of suitable ground truth at this scale, we analyzed the DoDs for different processing scenarios. This strategy proved effective for assessing the DEM reliability due to variations in the GCP number and distribution, showing that, in addition to aerial controls, at least five GCPs were necessary at Sillon de Talbert to achieve optimum quality that minimized measurement bias and random errors. Under this configuration, the global vertical precision (RMSE) improved two-fold in comparison to a processing workflow using all the targets as GCPs (*n* = 21) but no aerial controls. The benefit resulting from using RTK image positioning resided principally in an improved 3D geometry of the model, particularly at zones with limited to no ground controls. Using aerial controls only (akin to direct georeferencing), our results showed that the photogrammetric results were affected by vertical bias, explaining most of the error. The presence of vertical bias in models obtained using DG has been reported before and was explained by inaccurate IOP calibration (e.g., Refs. [49,52,56,69,70]). Likewise, our results showed that the addition of a single GCP was enough to reduce the vertical bias to the GSD level together with RMSE ~2 GSD, but the addition of other GCPs during BBA further improved the photogrammetric quality until a plateau was attained from 5 GCPs, with the RMSE mostly below 1 GSD.

Using ChkPts measured with RTK-GNSS enabled the assessment of both the horizontal and vertical error in RTK-assisted photogrammetry, showing a similar tendency to the DoD analysis, whereby 5 GCPs were necessary to achieve optimum accuracy and precision. Under this configuration, the global 3D precision (RMSE) remained below 0.05 m (3.6 GSD). We observed larger horizontal error over vertical error (ratios as large as 1:4), which is contrary to most previous research, where, generally, horizontal error is the lower bound (e.g., Refs. [46,56]). A reason may be the use of suboptimal photogrammetric targets for the present study. The targets we used had no marks at the center point where RTK-GNSS measurement is carried out, meaning that the target geolocation in the images can be prone to large horizontal uncertainties. The targets have been upgraded recently to include a chequerboard-like pattern, which has been recommended for pinpoint accuracy in RTK-GNSS measures and image positioning [71]. Nevertheless, we showed that error evaluation using ground targets can produce optimistic estimates, particularly when the error is evaluated at GCPs (used for photogrammetric processing). A difference in the error estimates between GCPs and ChkPts was also identified in Sanz-Ablanedo et al. [46], where it was suggested using a magnification coefficient to artificially inflate the error measures in the absence of independent ground controls (i.e., ChkPts). Although it may prove useful for guessing the precision within results (SDE), we showed, however, that using GCPs failed at detecting bias in the measurements, thus reinforcing that, ideally, numerous and well-distributed independent ChkPts should be used to characterize the DEM error.

Larger-scale experiments were conducted at La Palue field site to validate the workflow. Three operators were necessary to carry out the field operations, which included GNSS measurements of ~20 photogrammetric targets distributed over the whole beach (~2500 × 400 m2), using the bike-mounted GNSS to acquire ground truth data near the water line, performing all the flights, for finally removing the targets, all within a two-hour window around low tide. Five "permanent targets" were prepared before the September survey, consisting of red-painted crosses. They were created over flat and stable areas of the study site, all man-made and localized above the highest high tides so as not to introduce error in photogrammetry, which could otherwise arise due to imprecise identification in images or terrain changes. This means, however, that the spatial distribution of these permanent targets was limited to the landward side of the site.

Between 177 and 1381 RTK-GNSS survey points were used to assess the photogrammetric reconstruction for different processing scenarios (e.g., varying image resolution) both before and after model densification. In comparison to Sillon de Talbert, the best-case vertical precision achieved at La Palue was slightly worse, which may be related to an increased flying height and the different error evaluation methods used. Larger DEM error was measured at peripheral zones where the effective overlap index (i.e., apparition in images) is reduced, which is consistent with previous observations (e.g., Refs. [44,46,72]). Although of a small magnitude, the effect was increasing measurement noise and potentially centimeter-scale deformations of the photogrammetric model. Enlarging the survey area, especially on the seaward side (e.g., by adding an additional alongshore flight track), could strengthen the photogrammetric block and reduce the error at these distant locations. Regardless of the model densification, the DEM errors showed a similar pattern (Figure 5), reinforcing the fact that the DEM shape is essentially the result of image alignment and photogrammetric optimization taking place before dense point matching. The image resolution used for initial tie point detection and 3D reconstruction played a large role in mitigating or inflating the error, with a ratio of 1:3 depending on the setting. The best results were obtained using "High" alignment accuracy, followed by "Medium" and "Highest", with the same order also observed in terms of the number of tie points retained. This suggests that the alignment accuracy setting is not fully representative of the tie point quality (e.g., density and precision). With our findings, we also suggest using RTK image positions (pair pre-selection) for speeding up image alignment, with two orders of magnitude improvement together with enhanced tie point quantity and quality. The final evaluation using four repeat surveys demonstrated a very good reproducibility of the complete workflow for DEM collection, shown by a large number of surface cells over hypothetical stable zones (~5870 m2) characterized by a range between repeat elevations below 3.5 cm and a standard deviation of 1.1 cm on average.

Using the measurement workflow enabled characterizing the submeter beach topographic roughness, creating realistic maps of bedform arrangement at the beach scale, whose interpretation is eased further through the provision of very-high-resolution orthophotos (0.1 m). This small-scale topographic complexity (e.g., patches of ripples and megaripples) was found to be widespread and represented a large volume of sediment not represented in the DEMs with metric resolutions and, hence, not accounted for in typical beach surveys. Through pursuing surveys, follow-up studies will be looking at bedform classification and interpreting the spatial patterns observed and their temporal evolution in relation to driving hydrodynamic processes. For dynamic environments such as beaches, this study further exemplified that photogrammetry has the potential to help characterizing morphological changes across a wide range of spatial and temporal scales.

**Author Contributions:** Conceptualization, S.B.; methodology, S.B. and J.A.; software, S.B. and P.S.; validation, S.B., P.S. and J.A.; formal analysis, S.B.; investigation, S.B.; data curation, S.B.; writing—original draft preparation, S.B.; writing—review and editing, S.B., P.S. and J.A.; visualization, S.B.; funding acquisition, S.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received funding from LTSER-France "Zone Atelier Brest-Iroise".

**Data Availability Statement:** DEMs and orthophotos collected at La Palue can be accessed at https: //doi.org/10.35110/092918bf-dfb1-4d8e-805b-6bd420158160 (accessed on 6 March 2022).

**Acknowledgments:** The authors wish to thank LTSER-France "Zone Atelier Brest-Iroise" for financing data acquisition at La Palue field site, as well as Stevenn Lamarche and Valentin Gil for help with RTK-GNSS measurements. Sillon de Talbert is a monitoring site of the French coastal observatory SNO-DYNALIT (https://www.dynalit.fr/, accessed on 6 March 2022). Four reviewers provided comments on the initial manuscript, whose help is gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript or in the decision to publish the results.
