Marion Jaud
email: jaud-marion.jaud@univ-brest.fr

Pauline Letortu

Claire Théry

Philippe Grandjean

Stéphane Costa

Olivier Maquaire

Robert Davidson

Nicolas Le Dantec

UAV survey of a coastal cliff face -Selection of the best imaging angle

Keywords: UAV, SfM photogrammetry, tilted camera, cliff face erosion, coastal monitoring, Normandy

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Coastal cliffs erosion is a significant hazard for the safety of people, buildings, utilities and infrastructure settled close to the coastline, especially given the a priori sudden and episodic nature of the erosion process in time and space. Risk management relies on regular diagnosis of the cliff face and assessment of the erosion rate. For very dynamic environments, like coastal chalk cliffs, frequent monitoring with high accuracy and high spatial resolution (no more than a few centimeters) is needed to detect rock falls and debris falls, quantify the eroded volumes and reveal the patterns of cliff failure, with the objective to better understand the processes triggering cliff failures (e.g.: [START_REF] Lim | Quantifying the Controls and Influence of Tide and Wave Impacts on Coastal Rock Cliff Erosion[END_REF]2]).

In situ direct measurements in these environments with sub-vertical relief are challenging [START_REF] Mancini | An Integrated Procedure to Assess the Stability of Coastal Rocky Cliffs: From UAV Close-Range Photogrammetry to Geomechanical Finite Element Modeling[END_REF]. Field surveys can be risky for the operators and data over sufficiently large portions of the coastline are needed to ensure spatial representativity. Remote sensing methods exist, either using photogrammetric techniques or laser scanner technologies, with different platforms operating at different ranges from the imaged target. Far-range remote sensing could be a solution in the future, but for now, satellite and aerial data do not enable to observe subtle changes because their resolution is not sufficient and because they generally capture only the cliff top [START_REF] Young | Comparison of Airborne and Terrestrial Lidar Estimates of Seacliff Erosion in Southern California[END_REF]. Thus, considering their high spatial and temporal resolution, their low cost and their operational flexibility, near-range remote sensing methods (land-based or using UAVs) are increasingly used for the cliff face monitoring [START_REF] Young | Comparison of Airborne and Terrestrial Lidar Estimates of Seacliff Erosion in Southern California[END_REF][START_REF] James | Straightforward reconstruction of 3D surfaces and topography with a camera: Accuracy and geoscience application[END_REF][START_REF] Agüera-Vega | Reconstruction of extreme topography from UAV structure from motion photogrammetry[END_REF][START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] Westoby | Cost-effective erosion monitoring of coastal cliffs[END_REF].

Among these near-range remote sensing methods, high-resolution measurements of the cliff face topography have been mainly performed with Terrestrial Laser Scanners (TLS) [START_REF] Young | Comparison of Airborne and Terrestrial Lidar Estimates of Seacliff Erosion in Southern California[END_REF][START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] Lim | Combined digital photogrammetry and time-of-flight laser scanning for monitoring cliff evolution[END_REF][START_REF] Rosser | Terrestrial laser scanning for monitoring the process of hard rock coastal cliff erosion[END_REF][START_REF] Rosser | Coastline retreat via progressive failure of rocky coastal cliffs[END_REF][12]. TLS surveys yield accurate and dense 3D point clouds, nevertheless a TLS is an expensive equipment, allowing to cover only limited areas in the range of few hundreds of meters of coastline in a day of survey. Furthermore, because they are cumbersome to set-up in the field, they required easy access and are therefore only suitable to certain sites. As they are operated from the foreshore at the cliff foot, a sufficient distance from the cliff is needed to optimize the field of view. Depending on the study area, some parts of the cliff face may be invisible regardless of the choice of TLS station on the beach. As reported in [START_REF] Michoud | Landslide detection and monitoring capability of boat-based mobile laser scanning along Dieppe coastal cliffs, Normandy[END_REF], boat-based Mobile Laser Scanning (MLS) enables to quickly scan a long coastline (several kilometers of coastline scanned in one hour) with median point spacing up to 10 cm, providing that meteorological and marine conditions are favorable and that it is possible to sail close to the shore. The use of TLS or MLS is therefore very dependent on coastal morphology, logistics and weather conditions.

Other near-range remote sensing methods offer interesting possibilities. Aerial LiDAR operated from Unmanned Aerial Vehicle (UAV) could become a potential alternative method in the future. At present time, the choice of on-boarded positioning sensors is very restricted because of limited payload constraints. As a consequence, direct georeferencing of UAV-borne LiDAR data is still poorly accurate (e.g. around 2.5 m according to [START_REF] Roca | Lidar-equipped uav for building information modelling[END_REF]). Terrestrial photogrammetry can be an effective survey method for cliff face reconstruction, providing data at centimeter resolution, being easy to implement and low cost [START_REF] James | Straightforward reconstruction of 3D surfaces and topography with a camera: Accuracy and geoscience application[END_REF][START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] Firpo | Use of Digital Terrestrial Photogrammetry in rocky slope stability analysis by Distinct Elements Numerical Methods[END_REF]. Nevertheless, easy and safe access to the area is necessary and some parts of the cliff may be invisible from a terrestrial point of view.

Here, we examine the capabilities of photogrammetric surveys of cliffs from UAVs. Unlike LiDAR, SfM photogrammetry does not require direct georeferencing. Also, unlike TLS or terrestrial photogrammetry, photogrammetric UAVs enable to quickly collect stereo-photographs over a large extent (about 600 m of coastline covered in 8 min), with reduced effects of occlusion and without needing to access the foot of the cliff because the take-off and landing can be performed at the cliff top [START_REF] Mancini | An Integrated Procedure to Assess the Stability of Coastal Rocky Cliffs: From UAV Close-Range Photogrammetry to Geomechanical Finite Element Modeling[END_REF][START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] Dewez | Cliff Collapse Hazard from repeated multicopter UAV acquisitions: return on experience[END_REF][START_REF] Cawood | LiDAR, UAV or compassclinometer? Accuracy, coverage and the effects on structural models[END_REF]. Furthermore, an advantage of photogrammetric UAV surveys is the possibility to change the viewing angle by tilting the camera in order to optimise the coverage of the cliff face and avoid occlusions. Some studies combine nadir and oblique (60° off-nadir) imagery collected over several UAV flights [START_REF] Mancini | An Integrated Procedure to Assess the Stability of Coastal Rocky Cliffs: From UAV Close-Range Photogrammetry to Geomechanical Finite Element Modeling[END_REF][START_REF] Rossi | Combining nadir and oblique UAV imagery to reconstruct quarry topography: methodology and feasibility analysis[END_REF]. In [START_REF] Dewez | Cliff Collapse Hazard from repeated multicopter UAV acquisitions: return on experience[END_REF], photographs from three flight paths with various aiming direction (horizontal, 45° oblique and vertical) are combined, mainly in order to limit distortions. In [START_REF] Agüera-Vega | Reconstruction of extreme topography from UAV structure from motion photogrammetry[END_REF], images are taken with horizontal axis orientation and with the axis tilted 45° downward. For forestry applications, UAV surveys are usually performed with a tilt angle of 45° [START_REF] Fritz | UAV-based photogrammetric point clouds -Tree stem mapping in open stands in comparison to Terrestrial Laser scanner point clouds[END_REF]. The viewing angle for oblique imagery is also a key issue for photogrammetric surveys in urban context [START_REF] Grenzdörffer | Photogrammetric image acquisition and image analysis of oblique imagery[END_REF][START_REF] Aicardi | UAV photogrammetry with obliques images: first analysis on data acquisition and processing[END_REF]. The aim of the present study is to assess the impact of the imaging angle on 3D reconstruction of the cliff face and to identify the most relevant angle range. In this context, several flights have been performed with a different imaging angle for each flight. The angles have been chosen between nadir and 40° off-nadir because it is the range of angles that can be achieved by agile satellites for high resolution imagery (lower than 1 m), such as the Pleiades satellites that are likely to play be exploited for in coastal monitoring applications. Based on the present study, some guidelines are also provided to parametrize UAV surveys.

Study area

The area selected for this methodological study is a well-documented site, part of the DYNALIT observatory (French observatory of littoral zone dynamics), located along the English Channel, near the Cap d'Ailly in Varengeville-sur-Mer (NW of France, Normandy, Seine-Maritime) (Figure 1a). This portion of the coastline belongs to the northeastern part of the Parisian sedimentary Basin, where the Pays de Caux plateau abruptly ends in cliffs. This part of Seine-Maritime coastline is named the Alabaster Coast because coastal cliffs are white, made of chalk with flints of Upper Cretaceous [START_REF] Pomerol | Lithostratigraphy and biostratigraphy of the Lewes and Seaford chalks: A link across the Anglo-Paris Basin at the Turonian-Senonian boundary[END_REF][START_REF] Mortimore | Chalk physical properties and cliff instability[END_REF] (Figure 1b). At the top of the chalk strata lies a bed of clay and sandy sediment about 2-10 m thick, of Tertiary age (Paleogene) [START_REF] Bignot | Etude sédimentologique et micropaléontologique de l'Eocène du Cap d'Ailly (près de Dieppe-Seine-Maritime)[END_REF], which gives a brown color to the cliff (Figure 1b).

In this area, the studied cliff is about 40 m high, with a sub-vertical slope (from 75° to 90°) (Figure 1c), and is cut by a dry valley, called Petit Ailly. At this location, the average tidal range is 8 m (macrotidal environment), uncovering at low tide a foreshore characterized by a wide shore platform slightly inclined toward the sea and a gravel barrier near the cliff foot contact. Thanks to the large tidal range, the wide platform and the dry valley offering an easy access to the foreshore, the entire cliff face can be observed from the foreshore (Figure 1b). According to the surveys of the cliff top evolution on vertical aerial photographs (1966-2008, [25]) and of the cliff face evolution by terrestrial laser scanning (2010-2017, [START_REF] Letortu | years monitoring of coastal chalk cliff erosion in Normandy (France) by terrestrial laser scanning: main results[END_REF]), the erosion value is of 0.36 m/year. Both layers (chalk and Tertiary strata) are prone to erosion, which explains the high annual retreat rate in this area, in comparison with average regional retreat rate (0.15 m/year from Cap d'Antifer to Le Tréport, 1966-2008 [25]). The modalities of erosion include rock falls (large-scale movements affecting all or part of the cliff face) and debris falls (very small blocks or flakes (up to a decimeter scale) falling from across the cliff face) [START_REF] Varnes | Slope movement types and processes[END_REF]. Falls (from few m 3 to hundreds of thousands m 3 ) are ubiquitous across the cliff face.

Material and methods

The drone survey was realized using a DS6 electric hexacopter platform provided by DroneSys (Figure 2), thereafter named DRELIO. This multi-rotor UAV has a diameter of 0.8 m, weighs less than 4 kg and can handle a payload of 1.6 kg with about 20 min of flight autonomy. DRELIO is equipped with a collapsible frame so it can be folded back for easy transportation and with a parachute rescue system to ensure a soft landing in case of technical problems. The flight control is run by DJI® iOSD® software and the onboard flight control system is composed of a GPS and an autopilot.

A Nikon D700 digital reflex camera with a fixed focal length of 35 mm, taking one 12 Mpix photo (stored in JPEG fine format) every second in intervalometer mode, is mounted on a one-axis gimbal allowing forward-pointing of the camera. For data acquisition on the cliff face, various camera tilting angles (noted α) are tested in the forward direction. As a flight performed in "automatic mode" would not allow to keep the camera oriented toward the cliff face. When the camera is tilted, the flight is therefore performed in "assisted mode", i.e. without programing the drone flight plan. In such configuration, the UAV trajectory is less smooth than in "automatic mode", the position of the drone being adjusted continuously during the flight by an operator monitoring the real-time stream of a low-resolution video camera data that shows the area being imaged. For this study, four flights were performed during low tide on June 21 st , 2016, with various acquisition geometries:

-Flight 1: typical flight plan performed in "automatic mode" with nadir pointing camera; -Flight 2: forward-pointing camera tilted at α = 20° off-nadir; -Flight 3: forward-pointing camera tilted at α = 30° off-nadir; -Flight 4: forward-pointing camera tilted at α = 40° off-nadir.

With a changing angle from one flight to another, the distance from the UAV to the cliff face has to be adapted to keep the cliff face in the imaging field-of-view. The impact of viewing angle is clearly visible on raw images. Figure 3 shows an example of the same portion of the cliff face as captured by a raw image from each flight. Considering the payload limit, DRELIO cannot be equipped with precise navigation and positioning equipment. Thus, Ground Control Points (GCPs) are required for data processing. The GCPs consist of red discs 30 cm in diameter distributed on the beach, near the cliff top or the cliff foot (Figure 1d). For this study, 25 circular targets are distributed and positioned using a differential post-processed GPS (Topcon HiPer II GNSS receiver). The mean accuracy of the differential GPS (DGPS) survey is 3 cm horizontally and 4 cm vertically.

As 2.5-Dimensions Digital Elevation Models are not suited for depicting cliff faces, 3D dense point clouds are used in this study. The 3D point clouds are derived from photographs using a SfM-MVS workflow implemented in Agisoft® PhotoScan Professional (version 1.2) [START_REF] Jaud | Assessing the Accuracy of High Resolution Digital Surface Models Computed by PhotoScan® and MicMac® in Sub-Optimal Survey Conditions[END_REF]. The following steps are involved in 3D dense point cloud reconstruction: i) a camera alignment by bundle adjustment, with detection and matching of tiepoints to compute the camera parameters; and ii) the computation of the position of each tiepoint based on stereophotogrammetric equations. The GCPs are used i) for the self-calibration procedure (i.e. estimating internal parameters of the camera) and ii) for solving the bundle adjustment (i.e. estimating external orientation of the camera), so as to register the 3D reconstruction into a reference coordinates system (here, RGF93 Lambert 93-IGN69, the official reference system in France). The subset of GCPs taken into account for processing varies from one set of photographs (here, one flight) to another (from 11 to 22 GCPs), all GCPs being not visible on every dataset and the GCPs being selected in order to minimize the error estimate computed by PhotoScan®.

A Terrestrial Laser Scanner (TLS) survey was acquired simultaneously to serve as reference for assessing the quality of the cliff face reconstruction according to the viewing angle. UAV to TLS point cloud comparisons are performed using CloudCompare® open source software. Many other studies [START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] Westoby | Structurefrom-Motion' photogrammetry: A low-cost, effective tool for geoscience applications[END_REF][START_REF] Eltner | Multi-temporal UAV data for automatic measurement of rill and interrill erosion on loess soil[END_REF][START_REF] Smith | Structure from motion photogrammetry in physical geography[END_REF] have used a TLS dataset as the reference for quantitative comparisons, acknowledging that it may also have bias. The TLS survey was carried out using a Riegl © VZ-400 TLS, with a vertical and horizontal angular resolution of 0.04°. The high-resolution point cloud is georeferenced indirectly, using 16 reflective targets. The absolute position of these targets is measured by a total station (Trimble® M3) while their relative position in the point cloud is obtained by semi-automatic detection in the TLS point cloud and re-scanning at very fine spatial resolution. The transformation providing the best fit between absolute and relative positions of the targets is computed by a least square algorithm. The residual error of this georeferencing process is of 1.25 cm for both TLS stations.

Results

The cliff face reconstructions provided by SfM-photogrammetry from UAV photographs are compared for the different flights. Figure 4 shows the coloured dense point clouds obtained with each viewing angle. As flights with tilting camera have been performed without automatic flight plan, the spatial extent of the reconstructed surface varies from one flight to another. The cliff height is changing in alongshore direction (from a few meters near the dry valley of Petit Ailly to 50 m height) and certain portions of the upper cliff section have not been captured in the photographs of the tilted-imaging flights due to a sub-optimal UAV trajectory (e.g. on Flight 3 or on the left part of Flight 4 as shown by Figure 4). For a consistent comparison, the UAV datasets are cropped according to the spatial coverage of the TLS dataset, as depicted by the red box on Figure 4. From this point forward, this study is exclusively focused on this comparison zone. Table 1 compiles some characteristics of the SfM reconstructions for each flight. There are two main reasons for the holes (gaps with no data) within the reconstructed surfaces: i) missing portions of the cliff not captured during the surveys for Flight 3 and Flight 4 due to a sub-optimal UAV trajectory (see Figure 4) or ii) occlusions of some parts of the cliff face due to the low incidence angle of the photographs. This latter effect is particularly noticeable for Flight 1 and to a lesser extent for Flight 2 (see Figure 4). The tiepoint distributions are shown in Figure 5. The number and density of tiepoints vary significantly from one flight to another. As expected, the number of tiepoints is low (0.7 tiepoint/m²) for Flight 1. The dense point cloud resulting from Flight 1 (2 584 935 points) counts about half as much points than the dense point clouds of Flights 2, 3 and 4. When compared to TLS point cloud, the cliff face reconstruction for Flight 1 presents a RMS error of 11.7 cm. Now comparing the 3 tilted-imaging flights, surprisingly the tiepoint density for Flight 2 is more than twice the tiepoint density obtained for Flights 3 and 4. Nevertheless, for Flights 3 and 4, the tiepoint distribution is rather homogeneous (Figure 5) and the lower number of tiepoints compared to Flight 2 does not affect the cliff face reconstruction. Indeed, the number of points in both resulting dense point clouds is quite similar for these three flights and the precision obtained relatively to TLS point cloud are of the same order of magnitude, with an RMS error of 5.5 cm for Flight 2, 5.9 cm for Flight 3 and 4.9 cm for Flight 4. 4) and quantitative comparison to the TLS point cloud. Apart from having the lowest point density and missing data within the reconstructed surface, the 3D reconstructions from Flight 1 are also affected by artifacts caused by the low incidence angle of the photographs. As shown in Figure 6, these artifacts consist in variations in point density following a pattern of stripes parallel to each other with an approximate "wavelength" (distance from one stripe to the next) varying between 52 and 59 cm. Overall, despite the disparities in tiepoint density, the accuracy of the reconstruction is very similar for Flights 2, 3 and 4. Still, the tilting angle does have an impact in certain specific configurations, such as overhanging surface (i.e. with negative slope) (Figure 7). As expected, for Flight 1, where the mean point cloud density is only 72.6 points/m² (Table 2), the cliff surface cannot be reconstructed because of large holes. Some small occlusions are still visible (Figure 7b) on the reconstruction obtained for Flight 2 (20° off-nadir), where the point cloud density is about 801 points/m². Surprisingly, the occlusions visible on the reconstruction obtained for Flight 3 are very few and very small (Figure 7c) ; yet, with 728 points/m², the point cloud density is lower than for Flight 2. Perhaps the spatial distribution of the points is more homogeneous for Flight 3, even if they are less numerous. With a tilting angle of 40°, Flight 4 has the best 3D reconstruction (Figure 7d) and the best mean point cloud density (867 points/m² -Table 2) over the selected overhanging portion of the cliff face.

Table 1 : Characteristics of the SfM reconstructions (on the comparison zone depicted in Figure

Discussion

-Impact of the cliff slope on the reconstruction

Up to that point, this article has mostly dealt with "viewing angle" (i.e. the angle between the camera line of sight and the nadir), whereas the key parameter is rather the "angle of incidence" (i.e. the angle between the ray incident on the cliff face and the normal to the cliff face). The angle of incidence mainly depends on the viewing angle and the cliff slope. But the viewing angle is a parameter that can be set before the flight and which remains steady during the survey, whereas the cliff slope is a priori unknown and varies spatially. The impact of the cliff slope is therefore studied empirically, as an environmental constraint.

Between 20° and 40° off-nadir, the tilting angle of the camera seems to have a limited impact on the quality of the cliff face reconstruction, except on overhanging areas (Tables 1 and2). However, the patchy distribution of tiepoints, especially pronounced for Flight 2 (Figure 5), suggests that tiepoint distribution is not only impacted by the imaging angle but also by the cliff slope. To test the effect of cliff slope on the quality of the 3D reconstruction according to the viewing angle, cliff slope has been computed and classified according to four ranges: i) 80° -90°, ii) 70° -80°, iii) 60° -70° and iv) lower than 60° (Figure 8). Comparing Figures 5 and8, some visual correlations can be identified between cliff slope and tiepoint distribution. For instance, zones with tiepoints for Flight 1 correspond to the lowest slopes. Figure 9 summarizes the densities of tiepoints and point clouds obtained for the different configurations of viewing angles (Flights 1 to 4) and for each class of cliff slope. As expected, Flight 1 is all the more effective as cliff slopes are low. Tiepoint density is ranges from 0.1 points/m² for cliff slope between 80° and 90° to 0.9 points/m² for cliff slope lower than 60°. For all cliff slope classes, point cloud density is lower for Flight 1 than for other imaging angles. Flight 2 also yields the best results in tiepoint detection for cliff slope lower than 80°. The pronounced maximum in the density of tie points does not occur below 60° as in Flight 1 but between 60° and 80°, with up to 3.5 points/m² for cliff slope between 70° and 80° and 3.4 points/m² for cliff slope between 60° and 70°. For Flights 3 and 4, tiepoint density does not vary much for the different classes of cliff slope (respectively from 1.1 to 1.3 points/m² for Flight 3 and from 0.8 to 1.0 points/m² for Flight 4). Surprisingly, tiepoint detection is globally less effective for Flights 3 and 4 than for Flight 2. Nevertheless, except for nadir imaging, the density of the point clouds remains roughly of the same order of magnitude for the different cliff slopes and for the different tilting angles (Flights 2, 3 and 4). Cliff slope has only a limited effect on the quality of the 3D reconstruction for off-nadir viewing angles.

-Factors impacting tiepoints detection

Considering the noticeable differences between Flights 2, 3 and 4, this comparison suggests that cliff slope and camera viewing angles are not the only parameters having an effect on the cliff face reconstruction process. Point cloud reconstruction is mainly affected by the effectiveness of tiepoint detection. Three main factors have been identified as likely to have an influence on tiepoint detection: i)

Firstly, the overlapping of the photographs on the cliff face impacts tiepoint detection. Image overlap (Figure 10) depends on the spatial coverage of the photographs and therefore of the imaging angle in relation to the cliff slope. For instance, for Flight 1 (Figure 10a), the viewing angle is nearly parallel to the cliff face, so the footprint of the photographs on the cliff face is very limited. But overlapping also depends on the flight characteristics, like the speed of the UAV and the distance to the cliff, which affect the ground coverage of images. To quantify the degree of overlapping of the photographs for a survey, an "effective overlap" parameter (i.e. the mean number of matched photographs capturing each tiepoint in the sparse point cloud) is computed for the comparison zone and for the whole survey (Table 3). The effective overlap on the cliff face increases with the off-nadir angle, from 3.19 for Flight 1 to 11.54 for Flight 4. ii)

Another factor likely to affect the tiepoint detection is the resolution of the photographs on the cliff face. The spatial resolution is mainly influenced by the distance between the UAV and the cliff face and by the angle of incidence. The smaller features or texture variations are no longer captured when the drone flies further away from the cliff face and the image resolution decreases, so they cannot be detected as tiepoints anymore. As the flights are not performed in "automatic mode" and because of variations in cliff heights, the UAV-cliff face distance varies during a flight. A mean distance between the UAV and the cliff face summit is computed (Table 3). The UAV-cliff face distance ranges from 46 m to 76 m for tilted-imaging flights and is 72 m for Flight 1. iii)

Finally, variations in cliff face illumination due to cloud cover variability can also have a significant impact on tiepoint detection. Due to the north-facing orientation of the cliff face, it is when the cloud cover decreases that the cliff face appears darker because it is then in its own shadow. Low light levels tend to make tiepoints detection more difficult on the photographs. As an example, on the cliff portion depicted in Figure 3, the luminosity on the cliff face is of 53.7% for Flight 1, 48.8% for Flight 2, 49.8% for Flight 3 and only 40.0% for Flight 4 (Table 3). It can be assumed that the tiepoints detection for Flight 4 would have been more effective with higher luminosity on the cliff face. We propose that tiepoint detection is less effective for Flight 3 than for Flight 2 because of the larger mean distance of the UAV to the cliff face summit and the lower image overlap on the eastern portion (Figure 10c), and that tiepoint detection is less effective for Flight 4 than for Flight 2 because of the larger mean distance of the UAV to the cliff face summit and the lower luminosity on the cliff face, the latter being detrimental to tiepoint detection.

In addition, other parameters, inherent to the study area, can influence the process of cliff face reconstruction, and particularly tiepoint detection. Indeed, the image matching is based on local invariant feature detection [START_REF] Lou | A Cost-Effective Automatic 3D Reconstruction Pipeline for Plants Using Multi-view Images[END_REF], such as SIFT descriptor [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], Harris [START_REF] Stephens | A combined corner and edge detector[END_REF] or SURF descriptors [START_REF] Bay | Speeded-up robust features (surf)[END_REF]. Nevertheless, the algorithm actually used in PhotoScan® is not publicly known [START_REF] Verhoeven | Mind your grey tone -Examining the influence of decolourization methods on interest point extraction and matching for architectural image-based modelling[END_REF]. These descriptors are scale and rotation invariant and partially intensity and contrast change invariant [START_REF] Lou | A Cost-Effective Automatic 3D Reconstruction Pipeline for Plants Using Multi-view Images[END_REF]. As a consequence, the surface roughness (likely to create shadows), the colors of the rock face and the resulting color contrast, the presence of vegetation (depending itself on the cliff slope and on the substratum), etc. can also impact on tiepoint detection. Furthermore, depending on the viewing angle, the SfM reconstruction process can be more or less impacted by geometrical distortions [START_REF] Letortu | Examining high-resolution survey methods for monitoring cliff erosion at an operational scale[END_REF][START_REF] James | Mitigating systematic error in topographic models derived from UAV and ground-based image networks: MITIGATING SYSTEMATIC ERROR IN TOPOGRAPHIC MODELS[END_REF]. Considering the number and diversity of involved parameters, it is difficult to further assess their individual impact on the SfM process of cliff face reconstruction.

Guidelines for flight parameterization

With the development of UAVs with retractable landing system and 3-axis gimbal, it will soon be possible to perform flights with an across-track pointing camera using the automatic mode of the autopilot. With such UAVs, flights can to be planned so as to find a good trade-off between viewing angle, limitation of occlusion effects, spatial resolution on the cliff face and flight safety (flying too close to the cliff face exposes to local wind effects as well as loss of GPS signal).

In this perspective, we propose some guidelines and abacuses to assist in UAV flight parameterization for alongshore cliff face monitoring. The following calculations are done for various camera configurations: 35 mm or 24 mm focal length, a CCD sensor of 35.9 mm x 24 mm and 6 Mpix, 12 Mpix, 20 Mpix or 32 Mpix images. As we consider alongshore surveys, we choose to capture the whole cliff height in a single photograph centered at mid-cliff height. The UAV will follow a cliff-parallel trajectory (Figure 11a), where the distance D of the UAV to the cliff face and the UAV flight height H, which are the convenient variables for programing waypoints in the UAV autopilot, will be selected to optimize the viewing angle and more generally the point cloud reconstruction process. These variables D and H are linked via the tilting angle α of the camera, following the equation ( 1):

𝐷 = 𝐻 × tan 𝛼 - 𝐻 𝐶𝑙𝑖𝑓𝑓 2 tan ( 𝜋 2 -𝛼) (1)
with: D: Horizontal distance between the UAV and the cliff face α: camera pointing angle H cliff : height of the cliff Given the choice a single flyover, the angle α and the cliff height H cliff define an axis oblique to the cliff that we call R-axis (Figure 11a). The range along the R-axis (i.e., the position of the drone), and thus the selected D -H pair, is mainly chosen according to the expected image resolution. As previously mentioned, the distance to the cliff face can also be impacted by safety constraints, and the flight height can be limited by flight regulations for example. The abacus in Figure 11b presents possible D-H pairs for various configurations of camera viewing angle and cliff height.

Conclusion

In this study, we assessed the effectiveness of various imaging angles to perform UAV longshore surveys of a cliff face. Our results show that surveys with nadir pointing camera are nearly irrelevant, particularly for sub-vertical cliffs. In addition, the comparisons show that 20°, 30° and 40° off-nadir imaging angles provide satisfying results in terms of accuracy and texture restitution, higher tilting angles being more relevant for sub-vertical or overhanging parts of the cliff.

This study also highlights that imaging angle and cliff slope are not the only parameters impacting the SfM-photogrammetric process of cliff face reconstruction. The effectiveness of tiepoint detection also appears to be a key parameter. The tests presented in this article indicate that tiepoint detection is influenced by the photographs overlap, the distance between the UAV and the cliff face (and thus, the spatial resolution of the photographs) and the illumination of the cliff face. It is difficult to identify a priori which parameters have most impact on cliff face reconstruction and the extent to which they can affect diachronic comparisons of dense point clouds for the purpose of monitoring coastal erosion. Future work could be focused on the identification of other proxies than precision to estimate the reliability of dense point clouds obtained by SfM-photogrammetry.

Figure 1 :

 1 Figure 1: Location of the site (a), cliff face panorama (b), 2016/06/21 cliff face profiles (c), positions of GCPs for TLS and drone surveys (d)

Figure 2 :

 2 Figure 2 : DRELIO 10 hexacopter platform with tilted camera for photogrammetric surveys of the cliff face.

Figure 3 :

 3 Figure 3 : Comparison of the same portion of the cliff face situated on the eastern part of the studied area depicted on the raw photographs collected with the different acquisition geometries (see the positions of the points A and B marking out the selected cliff portion on Figure 1b): Flight 1 with nadir pointing camera (a), Flight 2 with forward-pointing camera tilted at α = 20° off-nadir (b), Flight 3 with α = 30° off-nadir (c) and Flight 4 with α = 40° (d).

Figure 4 :

 4 Figure 4 : Comparison of the whole dense point clouds reconstructed by SfM photogrammetry for the different flights. The red box depicts the spatial coverage of the TLS dataset used for the following comparisons. The dashed line indicates the position of the cliff top.

Figure 5 :

 5 Figure 5: Tiepoint distribution over the comparison zone for the different flights.

Figure 6 :

 6 Figure 6: Comparison of the texture restitution zooming on a portion of the cliff face (yellow rectangle of the top figure) a) for Flight 1 with nadir pointing camera versus b) for Flight 4 with forward-pointing camera tilted at α = 40° off-nadir.

Figure 7 :

 7 Figure 7: Comparison of the dense point clouds on an overhanging portion of the cliff face (blue rectangle on the top figure) for the different flight configurations. Table 2: Quantitative comparison of the reconstruction of the overhanging surface depicted in Figure 7. Point cloud density (pts/m²) Flight 1 (nadir) 72.6 Flight 2 (20°) 801.1 Flight 3 (30°) 728.0 Flight 4 (40°) 867.1

Figure 8 :

 8 Figure 8: Classification of the cliff slope.

Figure 9 :

 9 Figure 9: Influence of the cliff slope on the quality of reconstruction for the various viewing angles.

Figure 10 :

 10 Figure 10: Configuration of the image overlap on the cliff face in the comparison zone.Table 3: Comparison of other acquisition parameters likely to affect the tiepoint detection. Luminosity has been measured on the cliff portion shown in Figure 3 (between sections A and B). Effective overlap is computed on the cliff face over the comparison zone and for the whole survey using raw images (with top of the cliff and beach). Mean distance is computed forthe comparison zone between the UAV position and the cliff face summit.Effective overlap Mean distance of the UAV to the cliff face summit

  Figure 11cshows the mean spatial resolution obtained for various configurations of the viewing angles and cameras as a function of D (UAV-cliff distance), following the equation (2):𝑟 𝑐𝑙𝑖𝑓𝑓 = 𝐷 × 𝑠 𝑝𝑖𝑥 𝑓 × 𝑠𝑖𝑛 2 (𝛼)(2) with: r cliff : image resolution on the cliff face D: Horizontal distance between the UAV and the cliff face s pix : physical size of the pixel on the CCD sensor f: focal length α: camera pointing angle It has to be noticed that Equation 2 and Figure11only provide the mean image resolution, whereas in practice the spatial resolution decreases from the cliff foot to cliff top. Knowing the required image resolution, the focal length and the image quality, Figure11chelps to find the appropriate camera angle and distance from the cliff face and Figure11benables to find the corresponding UAV flight height.

Figure 9 :

 9 Figure 9: Schematic configuration diagram of UAV alongshore survey of cliff face (a) and abacuses to find the best trade-off between distance to the cliff face and flight height (b) and between distance to the cliff face and image resolution (c) for various configurations of camera viewing angles (α = 20°, 30° and 40°), focal length and image quality (6 Mpix, 12 Mpix, 20 mpix, 32 Mpix).

Acknowledgement

The authors acknowledge financial support provided by the TOSCA project EROFALITT from the CNES (the French space agency). This work is also part of the "Service National d'Observation" DYNALIT, via the research infrastructure ILICO.


Pauline Letortu
email: pauline.letortu@univ-brest.fr

Stéphane Costa

Olivier Maquaire

Christophe Delacourt

Emmanuel Augereau

Robert Davidson

Serge S Suanez

Jean Nabucet

Stéphane Costa

Retreat rates, modalities and agents responsible for erosion along the coastal chalk cliffs of Upper Normandy: the contribution of terrestrial laser scanning

Keywords: Coastal chalk cliff, Retreat rates, Retreat modalities, Agents for erosion, Terrestrial laser scanning, Upper Normandy

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Introduction

To understand the regressive dynamics of coastal cliffs, the knowledge of retreat rates at fine scale and the study of agents leading to erosion are major challenges [START_REF] Trenhaile | The geomorphology of rock coasts[END_REF][START_REF] Sunamura | Geomorphology of Rocky Coasts[END_REF][START_REF] Griggs | Coastal cliff and platform[END_REF][START_REF] Stephenson | Rock Coasts[END_REF]. Erosion is traditionally quantified by studying the rates of retreat of a spatial object tracked over time, often the cliff top [START_REF] Bird | Coastal Geomorphology. An introduction[END_REF]. However, these average retreat rates are incomplete information because they do not reflect the sudden nature of the hazard. This results in rock falls that threaten populations located at the cliff top and at the cliff foot. Thus, retreat occurs in "jerks", generated by the interaction of both internal factors (e.g., rock strength and structure) and external factors (e.g., rainfall, temperature variations, and wave action). The contribution of the latter to triggering rock falls is difficult to determine (Letortu et al., in press). "Rock fall" is used in this paper to describe movements of coherent rock [START_REF] Varnes | Slope movement types and processes[END_REF]. From Varnes' typology, two types of movement can be distinguished according to the fallen volume: 1) debris falls describe the small-scale release of tiny blocks or flakes (up to decimeter) from across the cliff face; and 2) rock falls describe large-scale movements from all or part of the cliff face. The former are common on rocky slopes but are often omitted in quantification due to their fine scale or unsuitable point of view. Far from negligible, their participation is estimated at about 10% of the total retreat [START_REF] May | The nature and rates of changes on chalk coastlines[END_REF][START_REF] Hénaff | Le recul des falaises crayeuses du Pays de Caux: détermination des processus d'érosion et quantification des rythmes d'évolution[END_REF] and may be an early sign of instability. Monitoring these jerks requires a high spatial and temporal resolution and a horizontal point of view that enables all changes to be monitored [START_REF] Young | Comparison of short-term seacliff retreat measurement methods in Del Mar, California[END_REF].

Due to unstable and subvertical cliff faces, quantification is difficult and sometimes dangerous. For these reasons, remote sensing technologies are mainly used. Aerial images can be used but the data accuracy is, at best, pluridecimeter and the point of view is inappropriate (vertical or oblique). Recent advances in remote sensing technology, in particular the improvement in the spatial resolution, may provide effective measurement tools. They may also offer the opportunity of conducting surveys at higher temporal frequency. Satellite data are interesting but their spatial resolution still appears insufficient for monitoring debris falls. Photogrammetry is not used because its reliability is affected by the height of the cliffs [START_REF] Lim | Combined digital photogrammetry and time-of-flight laser scanning for monitoring cliff evolution[END_REF] but new developments are promising. Terrestrial Laser Scanning (TLS) is particularly convenient because the temporal and spatial resolution, as well as the point of view, can be defined by the user.

The TLS technique, described as "one of the most promising surveying techniques for rockslope characterization and monitoring" [START_REF] Abellán | Detection of millimetric deformation using a terrestrial laser scanner: experiment and application to a rock fall event[END_REF], has been widely used in the study of mass transfers to: 1) identify structural and geomorphological characteristics of landslides [START_REF] Oppikofer | Characterization and monitoring of the Åknes rockslide using terrestrial laser scanning[END_REF][START_REF] Sturzenegger | Quantifying discontinuity orientation and persistence on high mountain rock slopes and large landslides using terrestrial remote sensing techniques[END_REF][START_REF] Rothmund | Landslide surface monitoring based on UAV-and ground-based images and terrestrial laser scanning: accuracy analysis and morphological interpretation[END_REF], landslide mapping [START_REF] Rowlands | Landslide laser scanning: a new look at an old problem[END_REF] and displacement tracking [START_REF] Delacourt | Remote-sensing techniques for analysing landslide kinematics: a review[END_REF][START_REF] Oppikofer | Collapse at the eastern Eiger flank in the Swiss Alps[END_REF][START_REF] Oppikofer | Investigation and monitoring of rock slope instabilities in Norway by terrestrial laser scanning[END_REF][START_REF] Teza | Characterization of landslide ground surface kinematics from terrestrial laser scanning and strain field computation[END_REF][START_REF] Travelletti | Monitoring landslide displacements during a controlled rain experiment using a long-range terrestrial laser scanning (TLS)[END_REF][START_REF] Travelletti | Performance of Image Correlation Techniques for Landslide Displacement Monitoring[END_REF][START_REF] Abellán | Detection of millimetric deformation using a terrestrial laser scanner: experiment and application to a rock fall event[END_REF][START_REF] Abellán | Detection and spatial prediction of rock falls by means of terrestrial laser scanner monitoring[END_REF];

2) analyze rock falls including those affecting cliffs [START_REF] Lim | Combined digital photogrammetry and time-of-flight laser scanning for monitoring cliff evolution[END_REF][START_REF] Lim | Erosional processes in the hard rock coastal cliffs at Staithes, North Yorkshire[END_REF][START_REF] Rosser | Terrestrial laser scanning for monitoring the process of hard rock coastal cliff erosion[END_REF][START_REF] Rosser | Coastline retreat via progressive failure of rocky coastal cliffs[END_REF][START_REF] Quinn | Identifying the behavioural characteristics of clay cliffs using intensive monitoring and geotechnical numerical modeling[END_REF][START_REF] Dewez | Probabilistic coastal cliff collapse hazard from repeated terrestrial laser surveys: case study from Mesnil Val (Normandy, northern France)[END_REF][START_REF] Abellán | Terrestrial laser scanning of rock slope instabilities[END_REF][START_REF] Kuhn | Coastal cliff monitoring and analysis of mass wasting processes with the application of terrestrial laser scanning: A case study of Rügen, Germany[END_REF];

3) analyze warning movements of falls [START_REF] Rosser | Patterns of precursory rockfall prior to slope failure[END_REF][START_REF] Abellán | Detection of millimetric deformation using a terrestrial laser scanner: experiment and application to a rock fall event[END_REF][START_REF] Abellán | Detection and spatial prediction of rock falls by means of terrestrial laser scanner monitoring[END_REF][START_REF] Royán | Spatio-temporal analysis of rock fall pre-failure deformation using Terrestrial LiDAR[END_REF].

In our study, TLS is used for repeated surveys in order to observe the evolution of the cliff face at two sites with a similar lithological context but subject to different marine forcing (abandoned and active cliffs). The aim is to quantify erosion at fine scale, to visualize the modalities of retreat and to contribute to the debate about the agents responsible for erosion of the Upper Normandy chalk cliffs. This paper first explains the study area and details the material and the TLS survey methodology. Then, the results of the cliff face monitoring are described and discussed.

Study area

Regional setting

Upper Normandy is located in the northwestern part of France, on both sides of the 50th northern parallel, along the English Channel (epicontinental sea, 86 m deep on average).

The environment is macrotidal with a tidal range of 8 m. Swell is limited but the wind sea can reach a significant wave height of 4 m in Dieppe (annual return period). Upper Normandy has a marine west coast climate. From Météo-France data , average winter temperatures are positive but an average of 26 daily freeze/thaw cycles is recorded per year (minimal temperature can reach -15°C). Rainfall is distributed over the year (≈800 mm) although fall and winter are the wettest seasons (51 mm in August and 94 mm in November).

Daily rainfall can exceed 77 mm in October. The Upper Normandy cliffs, 60-70 m high on average, extend 120 km from Le Havre (SW) to Le Tréport (NE) (Seine-Maritime) (Fig. 1). At their foot, there is a marine erosion platform (from 150 to 350 m wide), hidden, at the upper part of the beach, by a thin gravel beach. The cliffs are intersected by numerous drained or dry valleys perpendicular to the coast, protected at their outlet by often wide (from 30 to 100 m) gravel beaches due to the presence of groins or harbor jetties.

At the northwestern end of the sedimentary Paris Basin and in contact with the English Channel, the Upper Normandy cliffs between Cap d'Antifer and Le Tréport are made of chalk with flints, dated as Upper Cretaceous [START_REF] Pomerol | Lithostratigraphy and biostratigraphy of the Lewes and Seaford chalks: a link across the Anglo-Paris basin at the Turonian-Senonian boundary[END_REF][START_REF] Mortimore | Coastal chalk cliff instability[END_REF].

On this highly karstified frame [START_REF] Rodet | Les karsts de la craie: étude comparative[END_REF], there are residual flint formations and Quaternary loess [START_REF] Lautridou | Le cycle périglaciaire pléistocène en Europe du Nord-Ouest et plus particulièrement en Normandie[END_REF]. The main tectonic deformations (NW-SE) have led to the outcrop of various Upper Cretaceous geological strata (Fig. 1). The different stages of chalk have slight variations in facies and fine sedimentary discontinuities, which generate some subtle resistance contrasts [START_REF] Juignet | Mid-Cretaceous sequence stratigraphy and sedimentary cyclicity in the western Paris Basin[END_REF][START_REF] Laignel | Les altérites à silex de l'ouest du Bassin de Paris: caractérisation lithologique, genèse et utilisation potentielle comme granulats[END_REF][START_REF] Lasseur | La Craie du Bassin de Paris (Cénomanien-Campanien, Crétacé supérieur)[END_REF].

From the oldest to the newest, Cenomanian chalk outcrops a few meters at the base of the cliffs of Cap d'Antifer and Etretat, and east of Fécamp. It is heterogeneous, sometimes rich in detrital components (clay and quartz), and may be glauconitic or nodular. Turonian chalk is the overlying strata. It is composed of clayish, grayish to whitish chalk, with frequent nodular [START_REF] Laignel | Les altérites à silex de l'ouest du Bassin de Paris: caractérisation lithologique, genèse et utilisation potentielle comme granulats[END_REF]. Over these chalk strata, a bed of clay and sand sediments about 10 to 30 m thick of Paleogene age [START_REF] Bignot | Étude sédimentologique et micropaléontologique de l'Éocène du Cap d'Ailly (près de Dieppe, Seine-Maritime)[END_REF] replaces the usual residual flint formation [START_REF] Laignel | Les altérites à silex de l'ouest du Bassin de Paris: caractérisation lithologique, genèse et utilisation potentielle comme granulats[END_REF]Costa et al., 2006a), especially in Sainte-Marguerite-sur-Mer, Varengeville-sur-Mer (these two towns are located along Cap d'Ailly) and Sotteville-sur-Mer (Fig. 1).

Fig. 1: Presentation of the study area

The regressive dynamics of the Upper Normandy cliffs are expressed by instantaneous rock falls affecting all or part of the cliff. At the foot of the slopes, a fine gravel beach develops but the deposits are only a few meters thick. The tracking and distribution of these beaches are affected by rock falls and man-made structures (harbor jetties and groins), which are obstacles to longshore drift. The absence of a beach or a reduced amount of beach sediments at the cliff foot may alter the effectiveness of marine actions, and therefore the intensity and modalities of erosion (Costa et al., 2006b).

The regressive dynamics followed by the cliff top between 1966 and 2008 (photogrammetry and orthophotography) reveal a retreat rate of 0.15 m y -1 with high spatial variability in Upper Normandy [START_REF] Costa | Quantification of the Normandy and Picardy chalk cliff retreat by photogrammetric analysis[END_REF][START_REF] Letortu | Le recul des falaises crayeuses haut-normandes et les inondations par la mer en Manche centrale et orientale: de la quantification de l'aléa à la caractérisation des risques induits[END_REF][START_REF] Letortu | Vitesses et rythmes de recul des falaises crayeuses de Haute-Normandie (France): méthodologie et variabilité du recul[END_REF]. However, these average retreat rates provide only fragmentary information because they do not describe the sudden nature of the departure of material. For example, on 19 December 2012 in Dieppe, a rock fall of approximately 100,000 m 3 resulted in a cliff top retreat of 40 m in a few seconds while the average annual retreat rate on this site is 0.21 m y -1 [START_REF] Letortu | Vitesses et rythmes de recul des falaises crayeuses de Haute-Normandie (France): méthodologie et variabilité du recul[END_REF][START_REF] Michoud | Landslide detection and monitoring capability of boatbased mobile laser scanning along Dieppe coastal cliffs, Normandy[END_REF].

Site selection

To decipher the relative contribution of marine and subaerial agents in the erosion rates, two neighboring sites with similar lithological contexts (cliff made up of Coniacian and Santonian chalk) but subject to different marine forcing were selected (Figs. 1 and2). One site is an

Material and methods

TLS surveys

Terrestrial laser scanner is a measuring instrument that uses pulse laser technology to determine the distance from the device to the point to be measured. This distance is based on a non-contact and reflectorless acquisition of a point cloud and is measured by the time between the transmission of an infrared laser pulse and the return of the reflected pulse. The instrument used in this study is a RIEGL LMS-Z390i emitting a wavelength of 1,550 nm, which records a single time-of-flight without any access to the complete signal form (full waveform). The theoretical range of this device is 400 m for an 80% reflective surface and 140 m for a 10% reflective surface [START_REF] Riegl | Documentation technique du TLS[END_REF]. This technique is subject to use restrictions of two types: geometric and radiometric.

Regarding the geometric limitations, [START_REF] Lichti | Error modelling, calibration and analysis of an AM-CW terrestrial laser scanner system[END_REF] demonstrated the influence of the incidence angle on the measurement accuracy. This method is also affected by radiometric limitations including environmental ones. The accuracy and resolution of the scan depend on the reflection of the scanned material and the atmospheric water content. During our surveys, meteorological conditions were often good: no rainfalls, clear visibility and low wind.

A discussion on the principles of TLS and its performance is provided by [START_REF] Teza | Terrestrial laser scanner to detect landslide displacement fields: a new approach[END_REF].

The main parameter that controls the spatial resolution is the distance between the measured point and the TLS device. The area near the TLS device has a high spatial resolution (millimeter). The distance to the scanned object is dependent on the length of the coast being monitored and its height (the vertical swath of TLS is only 80°).

During repeated surveys at these two sites, 19 point clouds were acquired over 28 months (between 10/07/2010 and 02/12/2013), every 4-5 months (Fig. 3). The TLS station is 33 m from the abandoned cliff of Dieppe 1 W and 37 m from Dieppe 2 N.

For Petit Ailly, the TLS station is positioned at 80 m. For repeated surveys of high accuracy, the process of data acquisition requires additional equipment (Fig. 2): targets, a total station (TPS400 Leica TC410C) and a DGPS (Trimble with a base station 5,700 and a mobile receiver 5,800). The total station, where the point of setup is previously known by DGPS measurements, can replace the point cloud acquired in a relative coordinate system in an absolute coordinate system (Lambert 93 and associated RGF93 and IGN69). Although the TLS instrumental precision is ± 0.003 m to 50 m, the main source of error in data processing comes from the georeferencing of the point cloud in an absolute coordinate system via the targets [START_REF] Jaud | Techniques d'observation et de mesure haute résolution des transferts sédimentaires dans la frange littorale[END_REF]. The use of a large number of targets (16 at Dieppe 1 W, 13 at Dieppe 2 N, 17 at Petit Ailly) and the maximizing of their distance from the TLS, as long as they all remain visible, reduce the alignment error of the point cloud.

Data processing

The main steps in the data processing are 1) georeferencing and point cloud assembly; 2) point cloud cleaning; 3) meshing and interpolation to produce a Digital Elevation Model (DEM); and 4) creation of a DEM of Difference (DoD) [START_REF] Jaud | Techniques d'observation et de mesure haute résolution des transferts sédimentaires dans la frange littorale[END_REF]

Error margin

To quantify the error between the DEM, fixed areas were selected, such as urban furniture in Dieppe or groin at Petit Ailly in each original point cloud (just after georeferencing, step 1 previously described). These fixed areas are equivalent to approximately 7,000 points. These data were processed with the same methodology previously mentioned in order to obtain a DEM about fixed areas at each site. The final DoD revealed the margin of error of measurement. The lowest margin of error was ± 0.01 m in Dieppe 2 N. At Petit Ailly, the accuracy was ± 0.03 m. In Dieppe 1 W, it was ± 0.04 m. These differences were mainly due to the quality of topometric data. The greatest difference was located in Dieppe 1 W because topometric measurements were temporarily disturbed by a docking cross-Channel ferry and renovation of the passenger terminal (building visible in Fig. 2).

Results

Retreat rates and spatial distribution of erosion

During the repeated surveys, in Petit Ailly, the total retreat of the cliff face was 0.57 m (± 0.03 m), corresponding to an annual retreat rate of 0.24 m y -1 . Dieppe 1 W receded by 0.08 m y -1 while Dieppe 2 N receded by 0.06 m y -1 (Fig. 4). Between both orientations of Dieppe, the retreat rate differences are within the margin of error. These first results highlight that the site of Petit Ailly had a more intense retreat than Dieppe (0.24 m y -1 against 0.06-0.08 m y -1 ), marked by sudden accelerations (up to 1.16 m y -1 for the DoD F, Fig. 4). Unsurprisingly, abandoned cliffs receded more slowly than active cliffs (3-4 times slower). This difference confirms the strong influence of marine actions on the regressive dynamics of the chalk cliffs.

For both sites, the retreat rates were higher for the period including all or part of winter than other seasons. For example, in Petit Ailly during winter 2011/2012, the retreat rate was 0.17 m y -1 while during spring and summer 2012, it was 0.06 m y -1 . TLS surveys provide a fine location of erosion -the cliff foot corresponds to the first third of the cliff height and the cliff top is the rest. The cliff top receded faster than the cliff foot, at both cliffs, the active (Petit Ailly) and the abandoned ones (Dieppe): 1) 0.25 m y -1 at the cliff top against 0.21 m y -1 at the cliff foot at Petit Ailly; and 2) 0.07-0.10 m y -1 at the cliff top against 0.02-0.03 m y -1 at the cliff foot in Dieppe (Fig. 4).

Proportion of rock falls and debris falls in the retreat

Understanding the evolution of cliff faces depends on the frequency of surveys and the erosive dynamics of cliffs. Their frequency (every 4-5 months) does not ensure that a starting area that appears homogeneous in the DoD is the result of a single rock fall.

Successive rock falls may be located at the same place. However, these different dynamics could be determined thanks to an inventory of falls collected weekly by the non-profit organization ESTRAN on the coastline studied (Letortu et al., 2014, in press). Due to the centimeter accuracy of the data and the high spatial resolution of the TLS, it is possible to separate debris falls (Fig. 5, photographs a and b) and rock falls (Fig. 5, photographs D and F). Thus, on the active cliff, debris falls represented 25% of the total retreat over the period studied (Fig. 9). Debris falls are responsible for a retreat of 0.06 m y -1 , against 0.18 m y -1 for rock falls over 28 months under a total retreat rate of 0.24 m y -1 . The rate related to debris falls is consistent with the retreat rate for the abandoned cliffs (0.06-0.08 m y -1 ) where only debris falls were observed (Fig. 9). Fig. 9: Retreat rates as a function of departure area and type of movement

One of the modalities of cliff retreat highlighted

The DoD B in Fig. 8 shows departures of rocky material at the active cliff foot (east face).

These departures occur by two rock falls, which have various depths. Rock fall A generates a maximal basal notch of 2.26 m (59 m 3 ) while rock fall B creates a maximal notch of 1.61 m (89 m 3 ). Later, in the DoD D (Fig. 8), debris fall b (0.61 m maximum deep, 2 m 3 ) and rock fall D (2.05 m maximum deep, 86 m 3 ) occur near these initial notches. Notches seem to propagate instability gradually at their periphery and often towards the top of the cliff. A few months later (DoD F), rock falls of the whole cliff face are observed at or next to these locations (rock falls F and G with a volume of 1,636 m 3 and 194 m 3 , respectively). This study highlights one of the retreat modalities: the creation of a basal notch that, by overhanging, will gradually destabilize the top of the cliff to generate a rock fall of massive volume from the whole cliff face.

Discussion

Due to its centimeter precision and high temporal frequency, monitoring by TLS has provided a new understanding of the retreat of chalk cliff faces at the study sites. Some of the results generate discussion, which is organized in four points: 1) the spatial distribution of the retreat over the short and long terms; 2) the proportion of debris falls in retreat; 3) the modality of cliff retreat; and 4) the determination of possible agents and processes responsible for erosion.

Over 28 months of repeated surveys, the cliff top retreated faster than the cliff foot for both active and abandoned cliffs. At the abandoned cliff, this result seems to be a normal evolution because, since the polder construction in the early 1980s, the slope has evolved exclusively under subaerial agents. These agents are particularly efficient at the cliff top.

Over a longer timescale, the retreat rates should not converge. The final result should be a terrestrial slope. In contrast, this situation may appear surprising at the active cliff of Petit Ailly. The foot of the active cliff should be more eroded due to a combination of marine and subaerial agents. This result can be explained by the lithology and the timescale of our study.

This active cliff has a specific morphostructural context: the chalk has overlying Tertiary strata. In these strata, there are water tables from where runoff may affect the chalk cliff top.

This process may create a temporarily high retreat of the chalk cliff top. Over a longer timescale, the retreat difference between the foot and the top of the cliff should change. Indeed, there is a "disconnect in the timescale of our monitoring and the cliff morphology" [START_REF] Rosser | Coastline retreat via progressive failure of rocky coastal cliffs[END_REF]. On the active cliff, these two rates should evolve to fit with the subvertical profile of the current cliff (Fig. 10). Otherwise, the form of the cliff should change. Our study also highlights that debris falls correspond to 25% of the total retreat of the active cliff. They are responsible for a retreat rate of 0.06 m y -1 , while rock falls are responsible for a retreat rate of 0.18 m y -1 during the 28 months. This share is much greater than those reported by [START_REF] May | The nature and rates of changes on chalk coastlines[END_REF] and Hénaff et al. (2002) (10% and 11%, respectively).

Nevertheless, as suggested by [START_REF] Costa | Dynamique littorale et risques naturels: L'impact des aménagements, des variations du niveau marin et des modifications climatiques entre la baie de Seine et la baie de Somme[END_REF], this proportion of debris falls is highly variable in time and may be quickly removed. [START_REF] Costa | Dynamique littorale et risques naturels: L'impact des aménagements, des variations du niveau marin et des modifications climatiques entre la baie de Seine et la baie de Somme[END_REF] measured a retreat of 0.02 m for a single event (a rapid thaw on 31 December 1995) along the same coastline. Fortunately, these debris falls were observed but were removed at high tide. Our repeated surveys by TLS and the resultant visualization of erosion in the centimeter scale better quantify these debris falls.

These surveys over 28 months also enable one of the modalities of cliff retreat to be identified. On the east side of the dry valley at Petit Ailly, the upward propagation of failure from a destabilizing notch at the cliff foot is observed. This recalls the usual scenario (sometimes considered simplistic) of a basal notch [START_REF] Sunamura | Beach morphologies and their change[END_REF][START_REF] Sunamura | Geomorphology of Rocky Coasts[END_REF][START_REF] Trenhaile | The geomorphology of rock coasts[END_REF][START_REF] Stephenson | Rock Coasts[END_REF][START_REF] Trenhaile | Rock coast erosional forms (notches and shore platforms) on the La Paz Peninsula, Southern Baja, Mexico[END_REF] leading to larger rock falls named overhanging movements [START_REF] Hantz | An historical, geomechanical and probabilistic approach to rock-fall hazard assessment[END_REF][START_REF] Andriani | Rocky coast geomorphology and erosional processes: A case study along the Murgia coastline South of Bari, Apulia -SE Italy[END_REF]. Our work reveals, like [START_REF] Rosser | Coastline retreat via progressive failure of rocky coastal cliffs[END_REF] along the cliffs of the North York Moors National Park (UK), that departure areas evolve over time around their periphery with a dominant upward direction (vertical and subvertical). Thus, the authors stated that the distribution of rock falls may not be random: "there is clear spatial clustering indicative of propagation when rock falls are considered as cumulative through time". These notches (created by debris falls or rock falls) are visible in many places along the Upper Normandy coast [START_REF] Costa | Dynamique littorale et risques naturels: L'impact des aménagements, des variations du niveau marin et des modifications climatiques entre la baie de Seine et la baie de Somme[END_REF], especially along Cap d'Ailly (Fig. 10). They may be a warning sign of more massive failure (the date is still difficult to predict) which can cover the whole cliff face [START_REF] Young | Comparison of short-term seacliff retreat measurement methods in Del Mar, California[END_REF]. As [START_REF] Terzaghi | Mechanism of landslides[END_REF] suggested, slow surface movements precede catastrophic landslides. He added, "if a landslide comes as a surprise to the eyewitnesses, it would be more accurate to say that the observers failed to detect the phenomena which preceded the slide…". Further investigations are needed to understand better the link between preparatory phenomena and rock falls.

The combination of knowledge about the location, the time of cliff retreat, and the type of movement (debris falls and rock falls) may provide hypotheses about the agents (marine or subaerial) and processes responsible for erosion. Debris falls affect both sites (Dieppe and Petit Ailly) and are present on the whole cliff faces. A large production of debris falls was observed at the foot of the Petit Ailly active cliff (green circles in electronic version of Fig. 8).

The location of erosion is specific: it occurs only at the first 10 m of the cliff face. This erosion is not found at the base of the abandoned cliffs in Dieppe. These features raise questions about the agents and processes responsible for erosion. This basal erosion of the active cliff may be induced by the water table, which saturates the chalk with water, prone to hydroclasty and cryoclasty. However, the abandoned cliffs where there is the water table and other subaerial agents should also have this basal erosion. Thus, marine actions may lead to basal erosion by debris falls. The first 10 m of erosion at the cliff foot are consistent with the height of the waves that can reach it locally. Erosion due to marine actions may be quantified by deduction. At the foot of the abandoned cliffs, the annual retreat rate related to debris falls, and exclusively due to subaerial agents, is 0.03 m y -1 . Along the active cliff, the retreat rate related to debris falls is 0.14 m y -1 (Fig. 9) but includes subaerial and marine agents.

Marine actions may be responsible for a retreat rate by debris falls of 0.11 m y -1 of the observed 0.14 m y -1 . Thus, at the active cliff foot, marine actions may generate a retreat by debris falls four times higher than subaerial actions. This simple (perhaps simplistic) deduction may provide the first elements of quantification of marine actions. Again, marine actions may be an efficient agent of erosion.

The marine actions may not be uniform at the active cliff foot (Fig. 8). The sides of the dry valley evolve differently. The west face has higher debris fall retreat at the cliff foot than the east face. This difference at fine scale may be due to the presence of a man-made structure, a groin, located in the axis of the dry valley. Indeed, this structure leads to an accumulation of gravels at the west face. As [START_REF] Robinson | Marine erosive processes at the cliff foot[END_REF] observed an increase in cliff erosion by a factor of 18 when beach sediments were present compared to when they were not, we suggest these gravels may be used as projectiles by the swell and may explain the high abrasion by debris falls at the cliff foot on the west face (Fig. 11). On the east face, waves breaking without projectiles may be less effective. These observations converge towards model results [START_REF] Sunamura | A wave tank experiment on the erosional mechanism at a cliff base[END_REF][START_REF] Sunamura | Geomorphology of Rocky Coasts[END_REF][START_REF] Limber | Beach and sea-cliff dynamics as a driver of long-term rocky coastline evolution and stability[END_REF][START_REF] Kline | The unsteady nature of sea cliff retreat due to mechanical abrasion, failure and comminution feedbacks[END_REF]. [START_REF] Sunamura | A wave tank experiment on the erosional mechanism at a cliff base[END_REF][START_REF] Sunamura | Geomorphology of Rocky Coasts[END_REF] showed in laboratory experiments that cliffs and beaches exhibit internal feedbacks. The amount and configuration of beach material can bring positive feedback with higher wave erosive efficacy by providing abrasive agents [START_REF] Sunamura | Geomorphology of Rocky Coasts[END_REF]. [START_REF] Kline | The unsteady nature of sea cliff retreat due to mechanical abrasion, failure and comminution feedbacks[END_REF] studied the role of mechanical abrasion by beach sediments in cliff/platform/beach evolution over a long timescale (up to 1,000 years). They suggest that "mechanical abrasion is a feasible mechanism of cliff and platform evolution". However, on the whole cliff face scale at Petit Ailly, the east face has a higher retreat rate than the west face (0.39 m y -1 against 0.12 m y -1 ). This is due to numerous rock falls that occur on the east face but rarely on the west face. [START_REF] Dewez | Probabilistic coastal cliff collapse hazard from repeated terrestrial laser surveys: case study from Mesnil Val (Normandy, northern France)[END_REF] also observed rock falls at the cliff foot at the downdrift side of the groin of Criel-sur-Mer (20 km north of Dieppe). They mentioned the caving effect of waves by hydraulic forces including water hammer and air compression, particularly effective without a beach (gravel transit is blocked by the 120 m-long groin). At the Petit Ailly, this effect is possible due to the lack of beach on the downdrift side of the groin. There is no protecting gravel beach. When a rock fall occurs, most fallen rocks are quickly removed. Therefore, water hammer and air compression may be more intense and may generate rock falls. This suggestion underlines the role of marine actions as an erosion agent and the dual role of a gravel beach, which can protect the cliff foot or attack it (Costa et al., 2006b). Future TLS surveys here will be valuable to provide complementary information over a longer timescale, leading to a better understanding of the roles of marine actions and gravel beaches. In this paper, erosion agents have been discussed -marine actions with mechanical abrasion, water hammer, air compression, and subaerial agents with runoff. These hypotheses open up research perspectives about the quantification of their action. Beyond increasing the temporal representativeness of monitoring, reducing the time interval between each survey and conducting surveys before/during/after specific weather and sea conditions including freeze/thaw cycles and storms, supplementary measurements will be carried out to 1) monitor the behavior of water tables that could affect the stability of the cliff; 2) obtain a fine acquisition of rainfall, thermal and swell data; and 3) quantify the role of marine actions in the destabilization of the chalk massif.

It is necessary to focus not only on the external agents of erosion but also on internal factors such as chalk fracturing, which alters material resistance and often predetermines the extent of rock falls. To deal with the problem of spatial representativeness and check if our results are replicable, other lithologies of cliff faces are currently under study.

Conclusions

In Upper Normandy, the repeated surveys over 28 months on two sites with similar lithostratigraphic characteristics but different exposures to marine actions, highlight that cliff retreat is highly variable in time, location, its modalities, and the agents/processes involved.

The active cliff of Petit Ailly (Varengeville-sur-Mer) has regressive dynamics 3-4 times greater than the abandoned cliffs of Dieppe (0.24 m y -1 against 0.06-0.08 m y -1 ). This difference highlights the importance of marine actions in erosion dynamics. Whereas the abandoned cliff recedes only with debris falls, the active cliff has a combination of debris falls (25% of the retreat) and rock falls (75%). On both sites, a spatial variation in retreat rates can be observed over this short timescale: the cliff top recedes faster than the cliff foot.

Moreover, due to the fine location of the retreat obtained by our methodology, one of the modalities of retreat is detected. Precursory movements creating a basal notch later generate massive rock falls on the whole cliff face. These results indicate that TLS can be very useful for the spatial prediction of rock falls and for contributing to the debate about the agents and processes responsible for erosion.

  beds and little or no flint. This stage outcrops from Cap d'Antifer to Etretat, from Fécamp to Eletot, and from Puys (east of Dieppe) to Le Tréport. Turonian chalk is covered with Coniacian chalk, outcropping between Cap d'Antifer and Saint-Valéry-en-Caux, and between Dieppe and Le Tréport. The overlying stage, Santonian chalk, appears in the central part of the study area between Saint-Valéry-en-Caux and Puys. Finally, Campanian chalk, the most recent one, is only found between Quiberville and Pourville-sur-Mer (Hautot-sur-Mer). In relation to geotechnical studies, Santonian and Campanian chalk seem more favorable to weathering than other stages of the Upper Cretaceous

  abandoned cliff only affected by subaerial agents; the other site is an active cliff, which is evolving under the influence of both subaerial and marine agents. The abandoned cliff face is located in Dieppe. This site was divided into two areas with different cliff face orientations: one corresponding to an exposure of 280°N (named Dieppe 1 W, 45 m long, 30 m high); and the other corresponding to an exposure of 010°N (named Dieppe 2 N, 80 m long, 30 m high). The site characterized by an active cliff face is along Cap d'Ailly. More precisely, it lies on either side of the Petit Ailly dry valley in Varengeville-sur-Mer (exposure of 010°N, 250 m linear, maximum height of 40 m) (Fig. 2).

Fig. 2 :

 2 Fig. 2: Location, lithostratigraphy and panorama of Petit Ailly and Dieppe (1 W and 2 N)

Fig. 3 :

 3 Fig. 3: Temporal distribution of point clouds between 10/07/2010 and 02/12/2013 (gray: point clouds affected by a high error margin; dotted line: unusable point cloud)

  . Retreat is calculated by dividing the volume of change on the cliff face by the monitored area. The volume of change does not include debris material after failure because this is generally quickly removed (in a few days or weeks) at Petit Ailly, and quickly covered by vegetation at Dieppe. The retreat is then divided by years to obtain the annual retreat rate. Of the 19 point clouds acquired, one was unusable (12/18/2011 at Dieppe 2 N) (Fig. 3, dotted line). Observation of the point cloud highlighted artifacts including the rain, which absorbed the laser pulse. Three other point clouds did not have good georeferencing (error from 0.04 to 0.08 m). Two point clouds (07/05/2011 at Dieppe 1 W and 02/12/2013 at Dieppe 2 N) were certainly disturbed during acquisition as a docking cross-Channel ferry created significant temporary vibrations. The other one (02/24/2011 at Petit Ailly) was probably disturbed by depression of the TLS during acquisition on a wet sandy foreshore. These three point clouds were not used to quantify the rate of retreat, but only to study the spatial distribution of material departures (Fig. 3, dates in gray). In February 2013, human activities (clearing work and setup of safety nets) disturbed measurements in Dieppe. All human impacts were removed in the calculations and tables to monitor the "natural" evolution of the chalk cliff in Dieppe.

Fig. 4 :

 4 Fig. 4: Successive retreat rates as a function of DoD (gray DEM: affected by a high error margin)

Fig. 5 :

 5 Fig. 5: Examples of debris falls (circles a and b) and rock falls (stars D and F) at Petit Ailly identified by TLS in Fig. 8 (ESTRAN organization, 2012)

Fig. 6 :

 6 Fig. 6: DoDs of the cliff face at Dieppe 1 W between 10/07/2010 and 02/12/2013 (gray title: DoD affected by a high error margin; F: fall, W: winter, SP: spring, SU: summer; *: with human actions)

Fig. 10 :

 10 Fig. 10: Sub-vertical cliff profiles and basal notches in Sainte-Marguerite-sur-Mer (Cap d'Ailly)

Fig. 11 :

 11 Fig. 11: Mid-tide (coefficient 106) at Petit Ailly and position of gravel beach

Acknowledgements

We thank the reviewers for their detailed reviews of the manuscript and their helpful comments.


Keywords: Hyperspectral, LiDAR, tropical forests, modeling

published or not. The documents may come

Mapping tropical forest diversity from multi-and hyper-spectral imagery

Mapping tropical forest diversity from multi-and hyperspectral imagery Presenter:

Colette BADOURDINE Email: firoza.badourdine@gmail.com Scientific Supervisors:

Raphaël PÉLISSIER, Grégoire VINCENT & Jean-Baptiste FÉRET

Tropical forests are receiving increasing attention given the rapid loss of biodiversity due to the combined action of global warming and increasing anthropogenic pressure. There is a need to go beyond monitoring deforestation and to set up monitoring systems capable of assessing tropical forest degradation in terms of biodiversity.

We use a botanical inventor y where each trunk is identified on the ground as well as a partial inventor y of the crowns segmented by LiDAR data on ver y high resolution images to explore the relationships between spectral and biological diversity (taxonomic and functional) in neotropical forests and its sensitivity to spectral and spatial resolution to help clarif y the relevance and scope of a future hyperspectral satellite mission heralding an obser vation system to monitor the evolution of forest biodiversity.

Hyperspectral data, because of their high dimensionality, are complex: methodological needs are mainly related to the quality of the estimators and their resistance to noise, due to spectral and spatial variability of the obser ved elements. Therefore, we need to find the right approach to be able to make the link with the diversity measured on the ground and to determine what can be measured via spectral diversity.

The choice of a diversity metric requires a preliminar y analysis in order to have a robust interpretation of the signal: knowing what is being measured when measuring pixel scale spectral diversity and what are the factors and components of spectral diversity. In a first analysis, we aim to estimate the intraspecific variability of species and delineated crowns and characterize the contribution of SWIR data on species inter/intra variability and separability.

Figure 1 .

 1 Figure 1. Time series of the spectral index «NDVI» (Sentinel-2 sensor) for two functional groups (red and blue)